ISSN 1023-0149 Yarmouk University Publications Deanship of Research and Graduate Studies ABHATH AL-YARMOUK Basic Sciences and Engineering Refereed Research Journal Vol. 16 No. 1 1428/2007 В© Copyright 2007 by Yarmouk University All rights reserved. No part of this publication may be reproduced without the prior written permission of the Editor-in-Chief. Opinions expressed in this Journal are those of the authors and do not necessarily reflect the opinions of the Editorial Board or the policy of Yarmouk University Proof Reading: Prof. Ibrahim Jibril, Chemistry Dept. Yarmouk Universty Typesetting and Layout Ahmad Abu Hammam and Majdi Al-Shannaq EDITORIAL BOARD Editor-in-Chief Professor Abdul Rahman S. Attiyat Members Professor Omar Rimawi Professor Mashhoor Al-Refai Professor Mohmmad Abu-Saleh Dr. Mohammad Sheboul Professor Hamed Zraiqat Dr. Mohammad Belal Al-Zoubi Editorial Secretary Ola Shaker Oqlah In the Name of God Most Gracious Most Merciful Abhath al-Yarmouk: is a refereed research journal Basic Sciences and Engineering Abbreviated: A.Y. (Basic Sci. & Eng.) NOTES TO CONTRIBUTORS Only original unpublished articles will be considered. LANGUAGE: Manuscripts may be written in Arabic or English. FORMAT: Manuscripts should be submitted in quadruplicate and typed double-spaced, on one side of the paper only, and with 2.5cm margins. 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SUBMISSION OF MANUSCRIPTS AND CORRESPONDENCE: Manuscripts and Correspondence should be sent to: The Editor-in-Chief Abhath al-Yarmouk (Basic Sciences and Engineering) Deanship of Research and Graduate Studies Yarmouk University, Irbid, Jordan SUBSCRIPTION INFORMATION: ABHATH AL-YARMOUK may be obtained through the Exchange Division of the Yarmouk University Library or through the Deanship of Research and Graduate Studies at JD 1.000 per single copy. Annual subscription rates for individuals and institutions: Jordan: JD2. 500; Arab World: JD 8.000 or US$ 12.00; countries outside the Arab World: US$ 18.00 or equivalent. TABLE OF CONTENTS Articles in English * Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Ibrahim M. Odeh, Waleed A. Saqqa and Denis Eberl 1 * Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan Khitam M Khasawinah and Khalid M. Abumurad 19 * Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using GammaRay Spectrometry Awad Ali Bin- Jaza and Abdulazize Omer Bazohair 27 * Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis Janti S. Qar and Mohammad A. Al-Adhami 39 * The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity Saad Al-Jassabi and Ahmad Khalil 49 * Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Ghunaim S. Nasher, Hakam A. Mustafa and Nabil Abderahman 59 * Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Talal Al-Momani 93 * Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Aymen Issa Zreikat 105 * A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Mohammad M. Hamdan 123 * Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Sameh H. Ghwanmeh 135 * New Techniques for Improving H.263 Videoconferencing Ammar M. Kamel and Moh'd Belal. Al-Zoubi 147 Articles in Arabic * Application of Unbounded Linear Operators in Hilbert Spaces Ahmad Ajour and Rainer Picard 1 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 1-17 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Ibrahim M. Odeh*, Waleed A. Saqqa** and Denis Eberl ***a Received on March 29, 2006 Accepted for publication on Nov. 5, 2006 Abstract The mean crystallite size (CSmean), mean thickness (Tmean) and crystallite thickness distributions (CTD) for illite (I) and kaolinite (K) have been determined for representative Jordanian mudrock samples of different ages. MudMaster analyses of the X-ray diffraction (XRD), based on the Bertaut-Warren-Averbach (BWA) method, have been employed in the calculations. The CSmean and Tmean for illite show a slight increase with a mean difference of +0.5nm and +1.4nm respectively with the increase of the present-day stratigraphic thicknesses (depths) of rock formations. An increase in the CSmean and Tmean of kaolinite proceeds only to certain depths (1.22km, 1.05km respectively). Beyond these depths, the two means flip with a mean difference of 0.7nm, -2.1nm, respectively, when the depth reaches 1.6km. The shapes of crystallite thickness distributions (CTD) for illite in all investigated mudrock samples are asymptotic. The asymptotic shape more likely mirrors the overlapping reflections of different generations of illite and mixed layer I-S phases. Shapes of CTD for kaolinite vary between asymptotic, multimodal and lognormal. This is more likely due to the presence of two generations of kaolinite growth coinciding with increasing depths of the rock formations. Keywords: X-ray diffraction, mudrock, kaolinite, illite, MudMaster, BWA-method, crystallite size, asymptotic, multimodal, lognormal. Introduction The use of X-ray diffraction (XRD) to study the crystalline structure of clay minerals, crystallite size - and shape of crystallite thickness distributions (CTDs) has attracted considerable attention over the past years. Crystallite size is a measurement of adjacent, repeating crystalline units. It is only equivalent to the grain size if the individual grains are perfect single crystals free of defects, grain boundaries or stacking faults. Crystallite size is determined by measuring the broadening of a particular XRD В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Physics, , Yarmouk University, Irbid, Jordan. ** Department of Earth & Environmental, Faculty of Sciences, Yarmouk University, Irbid, Jordan. *** U.S. Geological Survey, 3215 Marine St., Boulder, CO 80303-1066 USA. Odeh, Saqqa & Eberl peak associated with a particular planar reflection from within the crystal unit cell. It is inversely related to the FWHM (full width at half maximum) of the peak. The narrower is the peak, the larger the crystallite size. This is due to the periodicity of the individual crystallite domains, in phase, reinforcing the diffraction of the X-Ray beam, resulting in a tall narrow peak. If the crystal are defect free and periodically arranged, the X-Ray beam is diffracted to the same angle even through multiple layers of the specimen. If the crystallites are randomly arranged or have low degree of periodicity, the result is a broader peak. Crystallite thickness refers to the mode of stacking two or more crystals of a clay mineral. The Bertaut-Warren Averbach (BWA) method is adapted to study clay minerals having a periodic structure along the c-axis. The XRD-peak shapes for the 00l reflections are then analyzed to calculate the crystallite thickness distributions (CTDs). The shape of the CTDs is used to infer crystal growth mechanism undergone by clay minerals during diagenesis or alteration by applying a simulation technique. Dudek et al. [1] pointed to several mathematical approaches in order to obtain information about crystallite size from the XRD peak shapes. The Scherrer equation [2], variance method [3, 4], Voigt method [5] and Bertaut-Warren-Averbach (BWA) method [6, 7] are applied to determine crystallite size using the XRD spectra. The BWA-method is the most universal because it can be used to measure the crystallite size, strain and crystallite size distributions. The MudMaster, a computer program utilizing a version of the BWAmethod is applied to carry out such measurements [6, 7]. The evolution of illite as a function of burial diagenesis can be better explained by applying the BWA-method [6, 7, and 8]. The shapes of crystallite thickness distributions (CTD), asymptotic, lognormal and multimodal, may provide information regarding nucleation and crystal growth mechanisms of clay minerals [2, 6, 7, and 8]. The main task of the present study is to determine the mean crystallite size and thickness of illite and kaolinite from the XRD data and to interpret the shapes of size distributions from the 001 basal reflections in the XRD spectra. The MudMaster with the aid of the BWA-method has been extensively utilized for this purpose. Materials and Methods Representative mudrock samples were selected from different sites in Jordan as shown in Fig. (1). The samples represent the late Ordovician-early Silurian Batra Member kaolinitic claystone (Batn el-Ghol area), black shale of late Permian Umm Irna Formation (Dead Sea area), the gray-green kaolinitic claystone from the Lower Cretaceous Kurnub Group (Mahis area), the green claystone of the Turonian Shueib Formation (Tafila area), the red-brownish claystone of the Pleistocene and AlYamaniyya clay deposits (Al-Yamaniyya, Aqaba area). The abbreviations: SIL, UI, MAH, TAF, and YAM in the text are derived from the original names of the studied rock formations or their ages. They indicate the Silurian Batra Member claystone, Umm Irna black shale, Mahis, Tafila and Al-Yamaniyya clay deposits respectively. The samples were gently crushed using an agate mortar and pestle. They were then treated with 12% H2O2 to remove organic matter. After oxidation, samples were wet sieved using a test sieve of 45Вµm to separate coarser fractions. The clay fraction (<2 Вµm) obtained from the pass 45Вµm fraction by sedimentation, centrifugation and dialysis was 2 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan sedimented on a polished silicon substrate and left to dry at room temperature. After mounting on the substrates, air-dried samples were heat treated separately at 350В°C and 550В°C. Vaporization of ethylene glycol was used to saturate clay samples at 60В°C for 16 hours. PVP-10 intercalated air-dried clay samples were analyzed by XRD for the purpose of measuring the fundamental illite particle size and size distribution [9]. The ratios of PVP to clay intercalations were as follows: Sample Ratio PVP : CLAY YAM 4:1 TAF 3:1 MAH 2:1 UI 2:1 SIL 2:1 Clay fraction was suspended in distilled water (concentration 2.5mg clay/1ml H2O), mixed with an aqueous solution containing 5mg PVP/1ml H2O and fully dispersed by ultrasonic treatment. The proportion of clay to PVP used depended on the expandability of the clay sample. The larger the proportion of smectite layers the more PVP was added to obtain good intercalation [1]. The advantage of the PVP-10 intercalation was to remove the effect of peak broadening related to swelling interface of the exposed basal surfaces of illite. In this way, crystallite size can be accurately calculated by the BWAmethod. The use of silicon substrates improved the background of the XRD spectra [7, 9, and10]. The 001 reflection of PVP-illite and kaolinite were used to measure mean crystallite size (Csmean), mean crystallite thickness (Tmean) and crystallite thickness distributions [6, 8, and 11]. XRD diffraction spectra were carried out using a Phillips PW1710 Diffractometer equipped with copper tube, CuKО± radiation, and a theta compensatory slit assembly. The diffractometer was operated under the following experimental conditions: a voltage of 35 KV, beam current of 40mA , step size of 0.02 2Оё, counting time of 0.01sec/step, 1mm receiving slit and a scanning range of 2-65В° 2Оё. The BWA-method adapted in the MudMaster computer program is based on Fourier analysis of the interference function [2, 6]. Lithology of mudrocks Fig (2) illustrates the graphic logs for the different rock formations. The Batra Member of Late Ordovician-early Silurian (Batn el-Ghol, SE Jordan) consists of light gray-green kaolinitic clays with Graptolite remains along bedding planes. Reddish siltstone-fine sandstone beds intercalate the green clays with a total thickness of about 80m. The occurrence of Graptolite indicates marine origin [12]. The Umm Irna Formation of late Permian (Dead Sea area) consists principally of two quartz arenite sandstone facies (60 m. thick) with fining upward cycles. Each starts with pebbly sandstone at the base, changes upward into fine sandstone, siltstone and silty claystone. The uppermost two cycles are distinguished by the presence of reddish-brown and occasionally dark gray paleosol horizons separated from each other by dark gray-black 3 Odeh, Saqqa & Eberl shale beds with plant remains [13]. The Lower Cretaceous Kurnub Group (Mahis area) consists of a thick varicolored sandstone sequence (≈200m.) interbedded with kaolinitic clay beds. The Turonian Shueib Formation (Karak-Tafila area) consisting of green and red gypsiferous claystone beds interbedded with gypsum changes near the top to fossiliferous dolomitic limestone. The Al-Yamaniyya Pleistocene clay deposits consist of varicolored (gray, green, yellow, red-brown) claystone interbedded with pebblycoarse-fine sandstone beds. Al-Yamaniya clay deposits were more likely deposited in a nearshore environment [Note 1, 14, 15]. Experimental results a. XRD analysis The XRD diffraction patterns (Fig.3; Table 1) show that smectite (S) dominates other clay minerals in YAM claystone samples. The other clay minerals are kaolinite (K), illite (I), mixed layer illite-smectite (I-S), chlorite (Ch) and mixed layer illitechlorite (I-Ch). The 001 peak of S at 6.2В° 2Оё (14.25О‘В°) in air-dried samples expands to 5В° 2Оё (17.67О‘В°) after ethylene glycol saturation. The same peak collapsed upon heating at 550В°C to 9.04В° 2Оё (9.8О‘В°). Peaks of Ch and mixed layer I-Ch are apparent in heated samples as shown in Figure (3). In TAF clays, a broad peak appears in air-dried mounts at 8.02В° 2Оё (11.02О‘В°). This is more likely to be a mixture of вЂ�I’ and one-water layer S. After glycolation, the peak shifts to 5.4В° 2Оё (16.37О‘В°) and a new 001 peak of illite appears at 8.8В° 2Оё (10О‘В°). When heating at 550В°C, the broad peak at 11.02О‘В° collapsed to 10О‘В°. Kaolinite is also present in the TAF green claystone. In the UI black shale and MAH clay samples, asymmetric broad and low intensity mixed-layer I-S peaks appear at 7.7В° 2Оё (11.5О‘В°) and 7.2В° 2Оё (12.3О‘В°) together with I and K. The mixed layer I-S peaks collapsed upon heating (550В°C) to 8.8В° 2Оё (10О‘В°). Illite and kaolinite are dominant in the SIL clays. b. Crystallite size of illite and kaolinite versus depth Table (2) summarizes the results of mean crystallite size (CSmean), mean thickness (Tmean) and CTD shapes of illite and kaolinite. The CSmean (2.8nm-3.3nm) and Tmean (3.8nm-5.2nm) for illite show a slight increase (+0.5nm, +1.4nm respectively) with increasing depth of the rock formations (Fig.4.a). The CSmean and Tmean for kaolinite are somewhat different. The means of the two values range between 3nm-10.7nm and 7.5nm-16.8nm, respectively. A slight increase in the CSmean of K (+ 0.7 nm) occurs when the depth changes from shallow to 0.95km. This is followed by an abrupt increase from 3.7nm-9.0nm (+5.3nm) when depth is 1.05km. The CSmean increases by 1.7nm when the depth changes from 1.05km to1.22km. Beyond the 1.22km depth, the mean size flips (- 0.7 nm.) when the depth is 1.6km (Fig.4.b). The Tmean for kaolinite increases from 7.5nm to 11.3nm (+3.8nm) going from a shallow depth to 0.95km. The Tmean abruptly increases to 16.8nm (+5.5nm) at a depth of 1.05km and then eventually decreases to 14.7nm (-2.1nm) beyond this depth (Fig. 4.b). 4 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan c. Crystallite thickness distributions (CTD) for illite and kaolinite The crystallite thickness distributions (CTD) for air-dried PVP-illite and heated (350В°C) kaolinite samples were determined using MudMaster analysis based on the BWA- method ,area-weighted option [9]. Figures (5 and 6) illustrate the shapes of CTD for PVP-I and K respectively. The CTD shapes in PVP-I was asymptotic in all samples. This is more likely a result of overlapping reflections of different generations of illite and I-S phases in clay deposits [16]. Another view point relates the asymptotic shape to the great influence of simultaneous nucleation and crystal growth of illite [17, 18]. This is only very likely, if illite in the samples represents one generation devoted to one mechanism of formation [18]. However, the later explanation needs more investigation. The CTD shapes of kaolinite vary from asymptotic (YAM and TAF clays) to multimodal (MAH clays) and lognormal (UI and SIL clays). This variation reflects the occurrence of two generations for kaolinite growth in response to changes in depth from shallow to deep. Otherwise, the variation in the CTD can be explained on how the crystal growth mechanism of kaolinite alters from a constant rate nucleation accompanied with crystal growth (at shallow-moderate depths) to crystal growth without continuous nucleation (at greater depths) [17, 18]. Discussion Results of X-ray analyses give an initial impression on how the type and abundance of clay minerals in the investigated mudrock samples vary with the present-day stratigraphic thicknesses of rock formations (depths). Mineralogically, smectite predominates other clay minerals in Al-Yamaniyya Pleistocene superficial clay deposits, but deficient in the Tafila green claystone of the Turonian Shueib formation and the Lower Cretaceous Mahis clay deposits occurring at depths around one km. Smectite more likely changed to mixed layer I-S in the Tafila claystone. In the Lower Cretaceous Mahis clays, kaolinite predominates other clay minerals and illite is less dominant. Progressive illitization is possibly enhanced at depths over 1 km. Therefore, strong peaks of illite and kaolinte were typical in the late Permian Umm Irna black shale (depth of rock formation approximates 1.2km) and in the Upper Ordovician-Lower Silurian green claystone of Batra Member (depth around 1.6km). The distinct appearance of illite peaks in the Paleozoic mudrocks indicates diagenetic alterations of smectite and mixed layer SI precursors to illite. The degradation of smectite and its transformation to illite involve incorporation of potassium (K+) ions into smectite structure and loss of interlayer water [19, 20]. The compaction of mud through overburden pressure soon removes much of the water contained in clay mineral lattices and water adsorbed onto clay surface or the less common pore-filled water. At depths greater than one kilometer (temperature ≥45В°C), 70-90% of the original volume of water is reduced to about 30%. Further compaction through water loss requires temperature of about 100В°C (depths 2-4km) where dehydration of clays takes place causing some changes in clay mineral types [21, 22}. Final compaction, leading to mudrock formation with only small percent water needs much longer period of overburden pressure with elevated temperatures [22]. Despite the significant role of temperature and burial history in clay diagenesis, the role of tectonic uplift and sediment unroofing cannot be ignored. Another criterion which 5 Odeh, Saqqa & Eberl may complicate the origin of clay minerals is the possible occurrence of the same types of clay minerals in more than one particular environment (terrestrial-marine). This is despite differences in the physical and chemical conditions. In this work, we consider the issue of primary (detrital) origin of clay minerals of paramount importance. For instance, the coexistence of kaolinite and smectite in AlYamaniyya clay deposits can be explained on the basis of their primary origin after chemical weathering of source materials. The latter minerals are very likely weathering products of the very near Precambrian granites intruded by mafic dikes. Products of weathering were then transported by streams draining granite terrains and finally deposited in a lacustrine environment separated from sea by beach terraces [14, 15, and 23]. Leaching of iron and magnesium in source area leaves behind concentrations of silicon and aluminum. This is favorable for kaolinite formation. In the Tafila mudrocks, the presence of dolomite and gypsum beside the argillaceous sediments signifies a deposition in a coastal sabkha environment after an uplift at the beginning of the Turonian age. The tectonic event caused sea-level fall resulting in the development of the sabkha environment [24]. The Tafila mudrocks were more likely deposited during periodic influxes of fresh water which may facilitate illitization process [e.g. 25]. The green type of Tafila clays were possibly developed by leaching of nearby red clays and reduction of hematite under surface conditions. This idea can be supported by the absence of chlorite (not detected by X-ray analyses) from the green clays which can also impart green color for clay deposits in nature. We do believe that Tafila clays were subjected to illitization as a result of surface wet-dry cycles, evaporation, and fixation of K+ ions. The lack of sodium chloride (NaCl) in the depositional medium (absence of halite in the rock sequence) enhances K+ ions fixation in clays [26]. A burial depth of about one kilometer may help the transformation of smectite to mixed layer I-S. Many researchers [e.g. 27, 28, 29, 30] believe that illitization of smectite through I-S can take place under surface conditions when lake water becomes alkaline and saturated with K+ ions whereby wet-dry cycles and evaporation eventually lead to irreversible fixation of K+ ions and illite formation. Mahis kaolinitic clay deposits that are a part of fluvial system sediments [31], have two origins, detrital (primary) and authigenic. Khouri [23] mentioned neoformation of kaolinite flakes adhered to quartz grains surfaces in Mahis clay sediments. Intensive leaching of the detritus in acidic medium helps kaolinization aided by rainfall water. Field observations confirmed a presence of carbonized plant remains in Mahis clays. The breakdown of plant remains due to compaction releases CO2 and creates acidic pore water. This initiates neoformation of kaolinite at depths greater than 1km (T>50В°C). The minor content of I-S and the initial presence of illite in Mahis clays suggest advanced stages of illitization at such depths. Coalified plant remains are also found in the Late Permian Umm Irna black shale. This again prompts the creation of acidic medium in the pore-filling water as a result of organic matter decay and CO2 release possibly by thermal maturation at greater depths (>1200m). Accordingly, crystal growth of a primary kaolinite can take place. The strong appearance of illite and kaolinite peaks present in the XRD patterns supports the idea of precursor smectite illitization and the increase of kaolinite crystallinity with depth. The great compaction of green claystone and 6 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan sandstones of the Upper Ordovician-Lower Silurian Batra Member by overlying rocks (present-day depth>1.6km) undoubtedly produced a set of physical and chemical changes on these sediments. Hence, illitization process is continued and the crystallinity of K is well developed. Summary and conclusions The present work revealed that diagenetic changes of clay minerals in the investigated mudrock samples took place at various depths. The occurrence of smectite gradually diminished with depth and was replaced by illite through an intermediate stage of mixed-layer I-S. Transformations between clay minerals could be produced under different depositional settings regardless of the evolved physical and chemical conditions. For instance, the illitization of Tafila clays in a saline environment was enhanced by wet-dry cycles, evaporation, and K+-ions fixation at surface conditions. Burial depths and the increase of subaerial temperature were essential for illite crystallization and the increase of kaolinite crystallinity. The asymptotic CTD shape in illite indicates, at most, an overlap between different generations of illite and mixed layer I-S in clays. The variations in CTD shape of kaolinite (asymptotic, multimodal, and lognormal) explain the occurrence of two generations of kaolinite growth coincident with the continual increase of the present-day depths of the rock formations. Acknowledgments The authors would like to thank Dr. F. Ababneh from Physics Department, Yarmouk University for helping, partly, in operating the X-ray Diffractometer. We extend our appreciation to the anonymous referees for their comments and critique in advance. 7 ‫‪Odeh, Saqqa & Eberl‬‬ ‫اﺳпє�пєЁпєЄШ§Щ… ﻣﻄﻴﺎﻓﻴﺔ ﺣﻴﻮد Ш§п»·пє·п»Њпє” اﻟﺴﻴﻨﻴﺔ واﻟﱪﻧﺎﻣﺞ Ш§піЊпє¤п»®пєіпєђ )‪ (MudMaster‬ﻓﻲ‬ вЂ«ШҐп»іпє пєЋШЇ Ш§п»џпє¤пє п»ў Ш§п»џпє’п» п»®Ш±ЩЉ Щ€пє—п»®ШІп»іп»Љ Ш§п»·пєЈпє пєЋЩ… Ш§п»џпє’п» п»®Ш±п»іпє” п»џп»јп»іп»јп»іпє– واﻟﻜﺎوﻟﻴﻨﺎﻳﺖ п»‹п» п»° اﻋﻤﺎق‬ ‫ﻣﺨпє�п» п»”пє” п»џп» пє�ﻜﺎوﻳﻦ Ш§п»џпєјпєЁпє®п»іпє” п»“п»І اﻷردن‪.‬‬ ‫اﺑﺮاﻫﻴﻢ ﻣﺤﻤﺪ ﻋﻮدة‪ ،‬وﻟﻴﺪ п»‹пє’пєЄ Ш§п»џп»�пєЋШЇШ± Ш§п»џпєґп»�пєЋ Щ€ШЇп»іп»ЁпєІ د‪ .‬اﺑﺮﻳﻞ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻓп»�пєЄ пє—п»ў Ш§пєіпє�пєЁпєЄШ§Щ… ﻣﻄﻴﺎﻓﻴﺔ ﺣﻴﻮد Ш§п»·пє·п»Њпє” اﻟﺴﻴﻨﻴﺔ واﻟﺒﺮﻧﺎﻣﺞ اﻟﻤﺤﻮﺳﺐ "п»ЈпєЄ п»ЈпєЋпєіпє�пє®" п»џпє�пє¤пєЄп»іпєЄ п»Јпє�ﻮﺳﻂ‬ вЂ«Ш§п»џпє¤пє п»ў Ш§п»џпє’п» п»®Ш±ЩЉ Щ€п»Јпє�п»®пєіп»‚ اﻟﺴﻤﺎﻛﺔ Ш§п»џпє’п» п»®Ш±п»іпє”вЂЄ ،‬وأﻧﻤﺎط пє—п»®ШІп»іп»Љ اﻟﺴﻤﺎﻛﺎت Ш§п»џпє’п» п»®Ш±п»іпє” ﻟﺤﺒﻴﺒﺎت Ш§п»№п»іп» п» п»ґпє–вЂ¬ ‫واﻟﻜﺎؤﻟﻴﻨﻴﺖ п»“п»І ﻋﻴﻨﺎت ﺗﻤﺜﻞ пє»пєЁп»®Ш± ﻃﻴﻨﻴﺔ п»ЈпєЁпє�п» п»”пє” اﻷﻋﻤﺎر ﻣﻦ اﻷردن‪ .‬أﻇﻬﺮت Ш§п»џпєЄШ±Ш§пєіпє” ШІп»іпєЋШЇШ© ﻃﻔﻴﻔﺔ ﻓﻲ‬ ‫ﻣпє�п»®пєіп»‚ Ш§п»џпє¤пє п»ў Ш§п»џпє’п» п»®Ш±ЩЉ Щ€п»Јпє�п»®пєіп»‚ اﻟﺴﻤﺎﻛﺎت Ш§п»џпє’п» п»®Ш±п»іпє” ﻟﺤﺒﻴﺒﺎت Ш§п»№п»іп» п» п»ґпє– пє—пє�п»ЁпєЋпєіпєђ п»Јп»Љ пє—пє°Ш§п»іпєЄ أﻋﻤﺎق Ш§п»џпє�ﻜﺎوﻳﻦ‬ ‫اﻟﺼﺨﺮﻳﺔ اﻟﺤﺎﻟﻴﺔ‪ .‬أﻣﺎ пє‘пєЋп»џп»Ёпєґпє’пє” ﻟﺤﺒﻴﺒﺎت اﻟﻜﺎؤﻟﻴﻨﻴﺖ‪ ،‬ﻓпє�пєґпє�ﻤﺮ Ш§п»џпє°п»іпєЋШЇШ© п»“п»І п»Јпє�п»®пєіп»‚ Ш§п»џпє¤пє п»ў Ш§п»џпє’п» п»®Ш±ЩЉ Щ€п»Јпє�ﻮﺳﻂ‬ ‫اﻟﺴﻤﺎﻛﺎت Ш§п»џпє’п» п»®Ш±п»іпє” ШҐп»џп»° أﻋﻤﺎق пє—пєјп»ћ ШҐп»џп»° ‪1.22‬ﻛﻢ‪1.05 ،‬ﻛﻢ п»‹п» п»° Ш§п»џпє�ﻮاﻟﻲ‪ .‬ﻳпє�п»ЁпєЋп»—пєє п»›п»ћ ﻣﻦ п»Јпє�п»®пєіп»‚ Ш§п»џпє¤пє п»ўвЂ¬ ‫واﻟﺴﻤﺎﻛﺎت Ш§п»џпє’п» п»®Ш±п»іпє” п»‹п»ЁпєЄп»ЈпєЋ п»іпєјп»ћ اﻟﻌﻤﻖ ‪1.6‬ﻛﻢ‪ .‬ﻳﺄﺧﺬ п»Јп»Ёпє¤п»Ёп»° Ш§п»џпє�п»®ШІп»іп»Љ Ш§п»№пєЈпєјпєЋпє‹п»І ﻟﺴﻤﺎﻛﺔ пє‘п» п»®Ш±Ш§ШЄ Ш§п»№п»іп» п» п»ґпє– ﻗﻲ‬ ‫ﺟﻤﻴﻊ اﻟﻌﻴﻨﺎت اﻟﻨﻤﻂ اﻟﻤﺤﺎذي ﻣﻤﺎ ﻳﺸﻴﺮ ШҐп»џп»° пє—пєЄШ§пє§п»јШЄ п»ЈпєЁпє�п» п»”пє” ﻣﻦ أﺟﻴﺎل Ш§п»№п»іп» п» п»ґпє– Щ€п»ЈпєЁпє�п» п»‚ Ш§п»џп»„пє’п»”пєЋШЄ ШҐп»іп» п»ґпє–вЂЄ-‬‬ ‫ﺳﻤﻴﻜпє�ﻴﺖ‪ .‬أﻣﺎ пє‘пєЋп»џп»Ёпєґпє’пє” п»џпєёп»њп»ћ п»Јп»Ёпє¤п»Ёп»° пє—п»®ШІп»іп»Љ اﻟﺴﻤﺎﻛﺎت Ш§п»џпє’п» п»®Ш±п»іпє” ﻟﺤﺒﻴﺒﺎت اﻟﻜﺎؤﻟﻴﻨﻴﺖ‪ ،‬ﻳпє�п»”пєЋЩ€ШЄ ﺑﻴﻦ اﻟﻨﻤﻂ‬ ‫اﻟﻤﺤﺎذي‪ ،‬وﻣпє�п»ЊпєЄШЇ اﻟﻨﻤﺎذج‪ ШЊвЂ¬Щ€Ш§п»џп» п»®п»ЏпєЋШ±пє—п»¤п»І اﻟﻄﺒﻴﻌﻲ‪ ،‬اﻷﻣﺮ Ш§п»џпє¬ЩЉ п»іп»Њпє°Щ‰ ШҐп»џп»° пє—п»Ёп»®Ш№ ШЈп»ѓп»®Ш§Ш± ﻧﻤﻮ пє‘п» п»®Ш±Ш§ШЄвЂ¬ ‫اﻟﻜﺎوﻟﻴﻨﻴﺖ ﻣﻤﺎ п»іпє�п»®Ш§п»“п»– п»Јп»Љ ШІп»іпєЋШЇШ© أﻋﻤﺎق Ш§п»џпє�п»њп»®п»іп»ЁпєЋШЄ اﻟﺼﺨﺮﻳﺔ‪.‬‬ ‫‪References‬‬ ‫‪Dudek T., ЕљrodoЕ„ J., Eberl D.D., Elsass F. and Uhlik P., Thickness distribution of‬‬ ‫‪illite crystals in shales. 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Cryst. 11 (1978). 10-14.‬‬ ‫]‪[5‬‬ ‫‪8‬‬ Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan [6] Eberl D.D., Drits V.A., ЕљrodoЕ„ J. and NГјsch R., MudMaster: a program for calculating crystallite size distribuition and strain from the shapes of X-ray diffraction peaks. U.S. Geological Survey, Open-File Report, (1996) 96-171. [7] Drits V.A., Eberl D.D. and ЕљrodoЕ„ J., XRD measurement of mean thickness, thickness distribution and strain for illite and illite/smectite crystallites by the Bertaut-Warren-Averbach technique. Clays and Clay Minerals, 46 (1998) 38-50. [8] Brime C., Eberl D.D. and ЕљrodoЕ„ J., Growth mechanisms of low-grade illites based on the shapes of crystal thickness distributions. Schwarz. Mineral. Petrogr. Mitt., 82 (2002) 203-209. [9] Eberl D.D., NГјsch R. Е ucha, V. and Tsipursky S., Measurement of illite particle thicknesses by X-ray diffraction using PVP-10 intercalation. Clays and Clay Minerals, 46 (1998b) 89-97. [10] Bove D.J., Eberl D.D., McCarty D.K. and Meeker G.P., Characterization and modeling of illite crystal particles and growth mechanism in a zoned hydrothermal deposit, Lake City, Colorado. American Mineralogist, 87 (2002) 1546-1556. [11] Е ucha V., Kraus I., Е amajovГЎ E. and Puskelova L. Crystallite size distribution of kaolin minerals. Periodico di Mineralogia, 68 (1999) 81-92. [12] Abed A., Geology, Environment and water of Jordan (in Arabic). Jordanian Geological Association, Scientific Books Series 1, Amman, (2000) 571. [13] Makhlouf I., Turner B. and Abed A.M., Depositional facies and environments in the Permian Umm Irna Formation, Dead Sea area, Jordan. Sedimentary Geology, 73 (1991) 117-139. [14] Abu Halima K., Mineralogy, chemistry and industrial studies of Al-Yamaniyya clay deposits in Aqaba area. Unpublished M.Sc. thesis, University of Jordan, Amman (1993). [15] Saqqa W.A., Dwairi I.M. and Akhal H. M. Sedimentology, mineralogical evaluation and industrial applications of the Pleistocene Al-Yamaniyyah clay deposits, near вЂ�Aqaba, southern Jordan. Applied Clay Science 9, (1995) 443-458. [16] ЕљrodoЕ„ J., Precise identification of illite/smectite interstratifications by X-ray powder diffraction. Clays and Clay Minerals, 28 (1980) 401-411. [17] Eberl D.D., Drits V.A. and ЕљrodoЕ„ J. Deducing growth mechanisms for minerals from the shapes of crystal size distributions. American Journal of Science, 298(1998a) 499-533. [18] ЕљrodoЕ„ J., Eberl D.D. and Drits V.A. Evolution of fundamental-particle size during illitization of smectite and implications for reaction mechanism. Clays and Clay Minerals, 48 (2000) 446-458. 9 Odeh, Saqqa & Eberl [19] Dunoyer de Segonzac, G. The transformation of clay minerals during diagenesis and low grade metamorphism: a review. 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[26] Honty M., Uhlik P., Е ucha V., ДЊaploviДЌovГЎ M., FrancЕЇ J., Clauer N. and BiroЕ€ A., Smectite-to-illite alteration in salt-bearing bentonites (The east Slovak basin). Clays and Clay Minerals, 52(2004)533-551. [27] Stoffers P. and Singer A., Clay minerals in Lake Mobuto Seso Seko (Lake Albert) – their diagenetic changes as an indicator of the paleoclimate. Geologische Rundschau, 68(1979)1009-1024. [28] Eberl D.D., ЕљrodoЕ„ J. and Northrop H.R., Potassium fixation in smectite by wetting and drying. In: Geochemical Processes at Mineral Surfaces (J.A. Davis and K.F. Hayes, editors). ACS Symposium Series 323, American Chemical Society, (1986) 296-326. [29] Hay R.L. and Guldman S.G., Silicate diagenesis in sediments of Searles Lake, California. Clay Mineral Society Progress with Abstracts, Jackson, MS 15, (1986). [30] Turner C.E. and Fishman N.S., Jurassic Lake T’oo’dichi’: a large alkaline saline lake, Morrison Formation, eastern Colorado Plateau. Geological Society of America Bulletin, 103 (1991) 538-558. [31] Abed A., Depositional environments of the Early Cretaceous Kurnub (Hathira) Sandstones, North Jordan. Sedimentary Geology, 31, (1982) 267-271. Note 1: Ibrahim K. And Abdelhamid G., Al-Yamaniyya clay deposits. Unpublished Report, Natural Resources Authority, Amman, 1990. 10 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Table (1) :Summary for XRD data between 3В°-15 В° 2Оё. Name of Sample shifted to Ethyleneglycolated (2Оё) (dО‘В°) 5.0 17.67 collapsed toв†’ 9.04 9.8 n.d. в†’ n.d. n.d. в†’ 6.54 13.5 8.88 10 slightly increased to 8.68 10.10 slightly shifted to 9.04 9.8 n.d. n.d. в†’ 10.3 8.6 shifted to 9.04 9.8 12.42 7.13 в†’ 12.2 7.25 в†’ 12.62 7.02 12.48 7.09 в†’ 12.34 7.17 в†’ Air-dried (2Оё) (dО‘В°) 6.2 n.d. YAM TAF 14.25 8.02 11.02 12.32 7.18 6.92 12.7 MAH UI 8.8 0.0 12.38 7.7 8.94 12.4 7.15 11.5 9.89 7.13 8.92 9.91 SIL 12.44 7.12 (dО‘В°) (dО‘В°) Heated (550В°C) (2Оё) (dО‘В°) Clay mineral S I-Ch . I I-S Ch K destroyed Mixture of I and one layer S. S I K separated to two peaks: 1) 5.2 17.0 2) 8.8 10.0 1)collapsed to 2) unchanged unchanged 12.32 7.18 в†’ 1) 5.4 16.3 2) 7.2 12.3 1)collapsed to 2) в†’ 9.04 9.78 12.38 7.15 7.7 11.5 8.94 9.89 12.4 7.13 unchanged в†’ collapsed to unchanged в†’ 8.8 10 destroyed 8.8 10 8.94 9.89 destroyed I K I-S I K 9.02 9.8 unchanged 8.92 12.48 7.2 в†’ I K separated to two peaks: slightly shifted to unchanged unchanged unchanged unchanged v. little change unchanged 8.8 8.8 10.0 10.0 destroyed 8.8 I-S S I-S 10.0 в†’ 9.91 destroyed (n.d. = non detected, S = smectite, I = illite, I-S = mixed layer illite-smectite, Ch = chlorite, I-Ch= mixed layer illite-chlorite, K= kaolinite). Table (2): D-spacing of the 001 reflection, means of crystallite size (CSmean) and thickness (Tmean) and CTDs shapes of PVP-illite and kaolinite vs. depths. (A) PVP-illite (air-dried samples) Sample Depth(m) Mean size(nm) Thickness(nm) d-spacing(A пЂ© YAM TAF MAH UI SIL shallow 950 1050 1220 1600 (nm) 3.8 4 4 4.1 5.2 2.8 3 2.9 3 3.3 11 (A пЂ© 10.07 9.83 10.12 10.03 10.09 CTDs shape Asymptotic. Asymptotic Asymptotic Asymptotic. Asymptotic Odeh, Saqqa & Eberl (B) Kaolinite (heated samples at 350В°C ) Sample Depth (m) Mean size (nm) Thickness(nm) d-spacing(A пЂ© CTDs shape YAM TAF MAH UI SIL shallow 950 1050 1220 1600 3 3.7 8.9 10.7 10 7.5 11.3 16.8 14.7 14.7 12 7.13 7.17 7.17 7.13 7.16 Asymptotic Asymptotic Multimodal Lognormal Lognormal Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan 13 Odeh, Saqqa & Eberl Fig.3. XRD-patterns (air-dried, ethylene glycolated, heated at 550В°C) of study samples. S=smectite, I-S= mixed layer illite-smectite, I=illite, K=kaolinite, Ch =chlorite, I-Ch= mixed layer illite-chlorite, Si = silicon wafer 14 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Mean (nm) (a) Illite 6 Crystallite size 4 Crystallite thickness 2 0 0 500 1000 1500 2000 Depth (m) Mean (nm) (b) Kaolinite 20 15 Crystallite size 10 Crystallite thickness 5 0 0 500 1000 1500 2000 Depths (m) Fig.4. Means of crystallite size and thickness for illite (a) and kaolinite (b) vs. depths. 15 Odeh, Saqqa & Eberl (YAM) 0.6 F re q u en cy . F r eq u e n c y . 0.8 0.4 0.2 0 0 5 10 15 0.6 0.5 0.4 0.3 0.2 0.1 0 20 (TAF) 0 5 10 15 20 Thickness (nm) Thickness (nm) Frequency. 0.7 0.6 0.5 0.4 (U I ) 0.3 0.2 0.1 0 0 5 10 15 20 F requency. Thickness (nm) 0.6 0.5 0.4 0.3 0.2 0.1 0 (SIL) 0 5 10 15 20 Thickness (nm) Fig. 5. Shapes of PVP-Illite crystallite thickness distributions (CTDs) in the study samples using the BWA-method (MudMaster). 16 Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Frequency. 0.8 (YAM) 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 40 Thickness (nm) Frequency 0.6 0.5 0.4 0.3 0.2 0.1 0 (TAF) 0 5 10 15 20 25 30 35 40 Thickness (nm) Frequency 0.08 (MAH) 0.06 0.04 0.02 0 0 5 10 15 20 25 30 35 40 Frequency. Thickness (nm) 0.15 (UI) 0.1 0.05 0 0 5 10 15 20 25 30 35 40 Frequency. Thickness (nm) 0.08 (SIL) 0.06 0.04 0.02 0 0 5 10 15 20 25 30 35 40 Thickness (nm) Fig. 6. Shapes of kaolinite crystallite thickness distributions (CTDs) in the study samples using BWA-method (MudMaster). 17 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 19-26 Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan Khitam M. Khasawinah and Khalid M. Abumurad* 1 Received on April 24, 2006 Accepted for publication on Sept. 28, 2006 Abstract In this work, dwellings in Kharja village, north of Jordan were studied for background radiation doses due to radon using closed can techniques. The results obtained reveal that the indoor radon levels almost equal or less than the national average (45 Bqm-3). In addition, the consumed water (collected rain water or precipitation) characterized by moderate average radon concentration ~12.6 Bqв„“-1 which is less than the action level that was set by the Europeans Countries and the Alternative Maximum Contamination Level (AMCL) suggested by U.S.EPA for drinking water. Some locations of the studied area were relatively characterized by high radon levels in soil air (1.42 – 1.85 kBqm-3). The estimated dose equivalent for Kharja village inhabitants due to radon ranges from about 0.43 to 1.70 mSv, which is with in the acceptable range for background radiations. The increase in lung cancer risk due to these doses is estimated to be about 0.23 %. More studies should be carried out to look for other factors or reasons to explain the many cancer incidents among the dwellers of Kharja village. Keyword: Radon, Kharja Village, Jordan, Dose Equivalent. Introduction There is a strong epidemiologic evidence of the link between radon exposure and lung cancer in the studies of underground miners at exposure only one or two order of magnitude greater than typical lifetime exposure from indoor radon. Data from recent studies [1, 2] provides direct evidence of a statistically significant association of indoor radon exposure and lung cancer. Radon is an inert radioactive gas which is produced naturally in three isotopes, namely: actinon (219Rn), thoron (220Rn) and radon (222Rn).The mother radioactive series of these elements are Actinium, Thorium and Uranium, respectively. Environmentally speaking, 219Rn and 220Rn are immaterial.219Rn has half-life of about 4 seconds and 220Rn has half-life of about 55 seconds. These half-lives limit their spread and movement in the environment. 222Rn with half-life of about 3.82 days can move from its cradle to far away places by diffusion and/or convection mechanisms. В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Physics, Faculty of Science, Yarmouk University, Irbid 21163, Jordan. Khasawinah and Abumurad Soil and bedrocks beneath houses are considered to be the main source of radon in the environment. Thus, radon can seep into dwellings through foundation cracks, wall joints and openings for water and other services pipes. Radon progeny's of epidemiological concern are the ones with short half-lives i.e. polonium 218 and 214, these daughters can attached themselves to aerosol particles, which if they inhaled can stick to the inner walls of airways and the inner lining layers of the lung. Exposure for long times even for low radon levels may increase lung cancer risk. In a study of EPA in the United States, radon in homes causes more deaths than fires, drowning and airplanes accidents combined [3]. In this study, the area of Kharja, Governorate of Irbid, north of Jordan, was selected for radon concentration measurement in order to correlate between radon level and the many incidents of lung and other types of cancers; there are many reported cases of lung cancer in the area of study compared to other parts of the Governorate. So, this study aims to measure radon level in dwellings, soil air and water of Kharja region and hence to calculate dose equivalent and lung cancer risk increase. Experimental procedure Solid state nuclear track detectors CR-39 with zero background were used in this study. Those detectors were cut into 1.5cm x1.5cm pieces. For indoor study the techniques of long term integrated passive closed can dosimeters were used. This type of dosimeters was previously calibrated in the school of physics and space research at Birmingham University, UK. The detectors were distributed in the selected houses (group B) of Kharja where one or more cases of cancer were reported. Another group of houses (group A) in the same village was selected as a control group. No cancer incidents were reported among the inhabitants of this group. Two detectors for each house were used, one was located in the living areas and the other was placed in the bedrooms about 1m bellow the ceiling. Water samples were collected from underground reservoirs (50 – 80 m3 each) from 10 houses mentioned above. Small amounts (300 cm3) of these samples were placed in drinking water bottles of 1в„“ volume. The CR-39 pieces (detectors) were fixed in the inner bottoms of the bottle caps. The bottles were sealed tightly to prevent air exchange and evaporation from water samples. Similar empty bottles were calibrated separately. The detector height above the water sample was about 15cm. Soil samples were collected from the gardens of the above mentioned houses around 20cm beneath the ground surface. The samples were mixed thoroughly and extraneous materials were removed. About 200 gm of each sample was transferred to a bottle like those used for water and sealed with detectors inside. The detector was about 15cm above the surface of the soil sample. A total of 30 locations were selected for this stud After exposure time of about 90 days the dosimeters and detectors were separated from the sample cups and the sample bottles. There was no water droplets formed on the surface of the detectors in the soil or water samples. The detectors were removed and chemically etched using a 30% solution of KOH at a temperature of 70 oC for eight hours. An optical microscope with a proper magnification was used to count the number 20 Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan of alpha tracks per unit area. The standard deviation of the data was taken as the uncertainty in the reported results. Calibration of dosimeters for water and soil studies Twelve dosimeters were prepared for calibration process and three for the background. The prepared dosimeters were placed in a chamber with standard radon concentration (170 kBqm-3). Two detectors were removed from the chamber after 0.5, 1, 2, 4, 8, 16 hours. These irradiated detectors were chemically etched using 30% KOH at 70 oC for 8 hours. The track density, ПЃo, (tracks.cm-2) was measured and plotted against the exposure time to as shown in Fig 1. 12000 Track Density (#/cm2) 10000 8000 6000 4000 2000 0 0 2 4 6 8 10 12 14 16 18 Exposure Time (hrs) Fig. 1: Calibration curve for dosimeters used in water and soil samples. Theoretical Background Indoor study To calculate radon concentration, the radon activity density in the can air was determined by measuring the tracks density on the detector according to the following relation: C= co t o ПЃ ПЃ o t .................................................................................................. (1) Where co, to ,ПЃo are radon level in the calibration chamber (90kBqm-3), exposure time(48 h) and the surface density of tracks on the calibrated detector (3.032x104), respectively. ПЃ and t are the measured surface density of tracks on exposed detectors and the exposure time (2160 h), respectively. 21 Khasawinah and Abumurad Water study To calculate radon concentration, the radon activity density ca in the bottle air above water sample was determined by measuring the tracks density on the detector according to the following relation: ca = ПЃ 1 t Вµ .................................................................................................... (2) Where ПЃ is the average number of tracks on the detector, t is the exposure time (2160h) of our sample and Вµ is the sensitivity of the detectors which equals to (3.688x103 (tracks.cm-2.h-1)/(Bqm-3)). However, Вµ was calculated by dividing the slope of Fig. 2 on the radon concentration in the calibration chamber. The radon activity density in water samples, cw, was calculated by using a model proposed by Somogyi et al. [4]. The concentration of radon atoms exhaled can be calculated according to the following relation cw = О»c a ht l .......................................................................................... (3) Where О» is the decay constant of 222Rn =7.56 *10-3h-1, h is the distance from the surface of water in the bottle to the detector, t is the exposure time and в„“ is the thickness of the sample. Soil study To measure radon concentration and the exhalation rates, sealed bottle technique was used. The radon concentration A (l) Bq/m3 in the bottle air above the sample is related to the aerial exhalation rate E(Bq/m2.h ) as k в€’1 A(l ) = Ao k ........................................................................................... (4) Where Ao is the radon concentration for very large relative thickness of the sample, k is the geometrical correction factor for the sealed bottle k = 1+ pd l tanh hв€’l d ................................................................................... (5) 1 2 Where p is the porosity of the sample, d is the diffusion length (= ( D / О» ) ≈ 1) [4] and the aerial exhalation rate is given by 22 Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan E (l ) = О».(h в€’ l ). A(l ) ................................................................................ (6) Where О» is the decay constant and Ds (= 2 в€— 10 coefficient of radon. в€’6 m 2 s в€’1 ) is the diffusion One can calculate also the mass exhalation rate M (l ) at the surface of the sample from the following equation: M (l ) = О» Where Оґ hв€’l A(l ) hОґ .................................................................................... (7) is the mass density of the sample in crushed form? The concentration A is given in terms of track density on the CR-39 detector by equ. (2). 1Пѓ Вµ t ........................................................................................................ (8) A Where Вµ was defined above, t is the exposure time (2160h) and Пѓ is the density of = tracks on the exposed detectors. Results and Discussion Indoor radon concentrations in the bed rooms in Kharja village were found in the range of 16 - 90.0 Bqm-3 with an average of 32.9 Bqm-3 for group A and in the range of 14-186 Bqm-3 with an average of 66.1В±11 Bqm-3 for group B as shown in Table (1). The highest concentration was found in a newly built house and the lowest level was found in a house which was built on a rock foundation and has good ventilation. The average radon level in group B more than twice of its average in group A. However, the average radon level in Kharja village was about 43.3 В± 8.6Bqm-3. Assuming the indoor average occupancy and the equilibrium factor are 0.8 and 0.45 respectively, one can calculate the effective doses by using the dose conversion factor of 1.0 mSv per 40 Bqm-3 [5]. The results of the average dose estimation for residents in group A and B from inhalation of radon progeny show that the annual effective doses are 0.88 and 1.76 mSv, respectively. From the data shown in Table (1), no positive associations of lung cancer cell type with radon were observed. For example, in a house with lung cancer patient, radon levels in the bedroom and in the living room were 78.3 and 24.9 Bqm-3, respectively; the bedroom is almost always closed. But no lung cancer cases were reported among the dwellers of other houses characterized by high radon level (186 Bqm-3) in spite of the inhabitants of these two houses have almost the same living conditions, ages and family numbers. However, there is no significant excess risk of lung cancer to more heavily exposed residents. Further studies in other population groups are needed to clarify the carcinogenic potential of indoor radon. Following Darby and his colleagues [2], the lung cancer risk increase due to these doses was estimated to be about 0.28 %. 23 Khasawinah and Abumurad Group A B Group A B Table 1: Indoor radon levels in different rooms of the studied houses. Rooms Max (Bqm-3) Min (Bqm-3) Avg (Bqm-3) Dose (mSv) Bed 90 16 32.9В±6.4 0.84 Living 20 13 17.0В±3.1 0.43 All Rooms 90 13 27.0В±5.2 0.69 Bed 186 14 66.1В±11.0 1.70 Living 91 9 32.2В±5.8 0.83 All Rooms 186 9 50.5В±9.8 1.29 Table 2: Radon levels in drinking water (rain collected water). Max (Bql-1) Min (Bql-1) Avg (Bql-1) Contribution to indoor radon 7 21.3 4.9 6 6В±0.8 12.6В±2.6 0.6 Bqm-3 1.3 Bqm-3 Table (2) shows the results of radon concentrations in water consumed in the study area. Most of the inhabitants use collected rain water from the roofs of their houses during winter season. The radon levels range from 6 to 21 Bqв„“-1 with an average of about 12.6 Bqв„“-1 for group B; while for group A the levels are almost the same. The over all average of radon in water is about 10 Bqв„“-1, which is about the international accepted level. EPA has set a maximum contamination level (MCL) of 11 Bqв„“-1 and an Alternative Maximum Contamination Level (AMCL) of 150 Bqв„“-1 in the drinking water at the United States [6], and European Countries has set reference levels range from about 20 to 1000 Bqв„“-1. The upper limit considered in many European Countries as an action level for radon in drinking water [7]. In spite of the fact that water contributes only about 0.01% to the indoor air radon, these levels should be seriously considered when cancers of gastrointestinal tract reasons are studied. Since stomach cancer represents only about 7% while liver cancer represents more than 25% of all reported cancer cases in the studied groups. Further studies are needed to illustrate the factors (if any) affecting liver cancer. Table 3 reflects the levels of radon in soil air; the aerial and mass exhalation rates for soil samples from different houses in group B. Locations 1, 2, 3, and 4 almost have the same moderate levels. But locations 5, 7, and 9 characterized relatively by high levels, while location 6 has the lowest radon level. At least one or more inhabitants of these locations have one kind of cancer incident. Table3: Radon concentration, A, aerial, E, and mass, M, exhalation rates for soil samples from gardens of different houses in group B. M(Bqkg-1h-1) Porosity Location A(kBqm-3) E(Bqm-2h-1) 1 1.44 293 1.18 0.511 2 1.25 273 1.14 0.444 3 1.20 265 1.13 0.533 4 1.27 269 1.09 0.488 5 1.46 319 1.35 0.488 6 0.66 0.511 .560 138 7 1.85 377 1.46 0.444 8 1.42 331 1.56 0.533 24 Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan Conclusion The geometric and arithmetic mean of radon activity in indoor of Kharja dwellings were 36 and 50.5 Bqm-3, respectively. Opposite to what was expected, these values are equal to or less than the mean values assessed in other Jordanian cities and villages [811]. In spite of the calculated cancer risk increase, this study did not find positive associations between lung cancer and radon concentration in the studied samples. This leads to examine other factors such as smoking and chemical air pollutants especially air refreshers and insects' killers. Most consumed water (public and collected rain water) in Kharja demonstrate low radon levels, since these waters were subject to aeration and other processes which allow removal of dissolved radon and other gases. The average radon level in drinking water in the study region is equal to the assumed world average which is about 10 Bqв„“-1 [12-13] 1996). The soil air demonstrates, relatively, low radon level compared to other locations in Jordan. Acknowledgement The authors acknowledge the financial support by grant number 2003/3 from the Deanship of Scientific Research and Higher Education at Yarmouk University. ‫دراﺳﺔ Ш§п»џпє пє®п»‹пє” اﻹﺷﻌﺎﻋﻴﺔ Ш§п»џп»ЁпєЋпє—пє пє” ﻋﻦ п»ЏпєЋШІ اﻟﺮادون‬ ‫ﻓﻲ п»—пє®п»іпє” пє§пє®пєџпєЋ – ﻣﺤﺎﻓﻈﺔ Ш§Ш±пє‘пєЄ – اﻷردن‬ ‫ﺧпє�пєЋЩ… ﺧﺼﺎوﻧﺔ Щ€пє§пєЋп»џпєЄ ШЈпє‘п»® ﻣﺮاد‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻟп»�пєЄ пє—п»ў п»“п»І п»«пє¬Щ‡ Ш§п»џпєЄШ±Ш§пєіпє” ﺗﻌﻴﻴﻦ Ш§п»џпє пє®п»‹пє” اﻻﺷﻌﺎﻋﻴﺔ اﻟﻤﻨﺒﻌﺜﺔ ﻣﻦ п»ЏпєЋШІ Ш§п»џпє®Ш§ШЇЩ€Щ† Ш§п»џпє�п»І п»іпє�п»Њпє®Ш¶ ﻟﻬﺎ ﺳﻜﺎن‬ ‫ ШЇп»џпє– Ш§п»џп»Ёпє�пєЋпє‹пєћ ШЈЩ† п»Јпєґпє�ﻮﻳﺎت‬.‫ﻗﺮﻳﺔ пє§пє®пєџпєЋ п»“п»І ﺷﻤﺎل Ш§п»џп»¤п»¤п» п»њпє” اﻷردﻧﻴﺔ اﻟﻬﺎﺷﻤﻴﺔ пє‘пєЋпєіпє�пєЁпєЄШ§Щ… п»ѓпє®п»іп»�пє” Ш§п»џп»®п»‹пєЋШЎ Ш§п»џп»¤п»ђп» п»–вЂ¬ ‫ ШЈп»ЈпєЋ ﻣﻴﺎه Ш§п»џпєёпє®ШЁ )Ш§п»џп»¤пє п»¤п»®п»‹пє” ﻣﻦ‬.(45 Bqm-3) ‫اﻟﺮادون اﻟﻤﻨﺰﻟﻲ п»іпєґпєЋЩ€ЩЉ пє—п»�пє®п»іпє’пєЋЩ‹ ШЈЩ€ ШЈп»—п»ћ ﻣﻦ اﻟﻤﺴпє�п»®Щ‰ اﻟﻮﻃﻨﻲ‬ ‫ Щ€п»«п»® ШЈп»—п»ћ ﺑﻜﺜﻴﺮ‬.‫ пє—п»�ﺮﻳﺒﺎ‬12.6 Bqв„“-1 ‫ﻣﺎء اﻟﻤﻄﺮ п»“п»І Шўпє‘пєЋШ±( п»“п»�пєЄ ﺗﻤﻴﺰت пє‘пє�ﺮﻛﻴﺰ п»Јп»Њпє�пєЄЩ„ п»џп» пє®Ш§ШЇЩ€Щ† ﺑﻤﺎ п»Јпє�ﻮﺳﻄﺔ‬ ‫ ШЈп»ЈпєЋ п»“п»І п»«п»®Ш§ШЎ Ш§п»џпє�пє®пє‘пє” п»“п»�пєЄ اﺗﺴﻤﺖ пє‘п»Њпєѕ اﻟﻤﻮاﻗﻊ‬.‫ﻣﻦ Ш§п»џпє¤пєЄ Ш§п»·п»‹п» п»° اﻟﻤп»�пє’п»®Щ„ ﻋﺎﻟﻤﻴﺎً ﻓﻴﻤﺎ п»іпєЁпєє ﻣﻴﺎه اﻟﺸﺮب‬ ‫ ﺑﻴﻨﺖ Ш§п»џпєЄШ±Ш§пєіпє” ШЈЩ† Ш§п»џпє пє®п»‹пє” اﻟﻤﻜﺎﻓﺌﺔ п»џп» пє�ﺮاﻛﻴﺰ اﻟﻤп»�ﺎﺳﺔ‬.(1.42 – 1.85kBqm-3) ً‫ﺑﻤﺴпє�п»®п»іпєЋШЄ Ш±Ш§ШЇЩ€Щ† ﻋﺎﻟﻴﺔ ﻧﺴﺒﻴﺎ‬ ‫( Щ€п»«пє¬Ш§ п»іп»Њпє�пє’пє® ﺿﻤﻦ اﻟﻤﺪى‬0.43 to 1.70mSv) ‫ﻣﻦ Ш§п»џпє®Ш§ШЇЩ€Щ† п»“п»І اﻟﻤﻨﻄп»�пє” ﻗﻴﺪ Ш§п»џпє’пє¤пєљ пє—пє�пє®Ш§Щ€Ш пє‘п»ґп»¦ اﻟﺤﺪﻳﻦ‬ ШЊ0.23% ‫ п»іпє°ШЇШ§ШЇ пє§п»„пє® Ш§п»»пє»пєЋпє‘пє” пє‘пєґпє®п»ѓпєЋЩ† Ш§п»џпє®пє‹пє” ﻟﻤﺜﻞ п»«пє¬Щ‡ اﻟﻤﺴпє�п»®п»іпєЋШЄ ﻣﻦ Ш§п»»пє·п»ЊпєЋШ№ ﺑﺤﻮاﻟﻲ‬.вЂ«Ш§п»џп»¤пєґп»¤п»®Ш п»џп»јпє·п»ЊпєЋШ№вЂ¬ ‫ﻣﻤﺎ п»іпє п»Њп»ћ п»«п»ЁпєЋЩѓ пєЈпєЋпєџпє” ﻟﻤﺰﻳﺪ ﻣﻦ Ш§п»џпєЄШ±Ш§пєіпєЋШЄ п»џп» пє’пє¤пєљ ﻋﻦ ШЈпєіпє’пєЋШЁ ШЈпє§пє®Щ‰ п»џпє�ﻔﺴﻴﺮ пєЈпєЋп»»ШЄ Ш§п»џпєґпє®п»ѓпєЋЩ† Ш§п»џп»ЊпєЄп»іпєЄШ© ﺑﻴﻦ‬ .‫ﺳﻜﺎن Ш§п»џп»�ﺮﻳﺔ‬ 25 Khasawinah and Abumurad References [1] Krewski D., Lubin J. H., Zeilinski J. M. Alavanja M., Catalan V. S. and Field R. W., Residential radon and risk of lung cancer: A combined analysis of 7 North American casecontrol studies. Epidemiology, 16 (2), (2005)137-145. [2] Darby S., Hill D., Auvinen A., Barros-Dios J. M., Baysson H. and Bochicchio F., Radon in homes and risk of lung cancer: Collaborative analysis of individual data from 13 European case-control studies. Brit. Med. J., 330 (7485): (2005) 223. [3] EPA's Assessment of risks from radon in homes (EPA Doc. No. 402-R-03-003), Washington, D.C. 20460. (2003). [4] Somogyi G., Hafez A., Hunyadi I. and Toth-Szilagyi M., Measurement of exhalation and diffusion parameters of radon in solids by plastic track detectors. Nucl. Tracks Radiat. Meas., 12(1-6) (1986) 701-704. [5] UNSCEAR, Sources and effects of ionizing radiation. Report to the General Assembly, United Nations, New York. (1997). [6] EPA, A citizen guide to radon (EPA Doc. No. 402-K-02-006), Washington, D.C. 20460. (1994). [7] EC, Commission recommendation of 20 December 2001 on the protection of members of the public to exposure of radon in drinking water supplies. 2001/928/euratom. Official Journal of the European Commission, L344, (2001) 85-88. [8] Abumurad K. M., Kullab M. K., Al-Bataina B. A., Ismail A. M. and Lehlooh A., Estimation of Radon Concenrations Inside Houses in some Jordanian Regions. Mu`tah J. for Research & Studies, 9(5) (1994). [9] Abumurad K. M., Al-Bataina B., Ismail A., Kullab M. and Al-Eloosy A., A Survey of Radon Levels in Jordanian Dwellings during an Autumn Season. Radiation Protection Dosimetry, 69(3)(1997) 221-226. [10] Abumurad K. M., Chances of Lung Cancer due to radon exposure in Al-Mazar Al-Shamali, Jordan. Radiat. Meas. 34 (2001) 537-540. [11] Kullab M., Al-Bataina B., Ismail A., Abumurad K. M. and Ghaith A., 1997. A Study of Radon-222 Concentration. Levels inside Kindergartens in Amman. Radiation Measurements, 28(1-6)(1997) 699-702. [12] WHO, Indoor quality: a risk-based approach to health criteria for radon indoors. Report on a WHO Working Group, Eilat, Israel, 28 march - 4 April 1993; EUR/ICP/CEH 108 (A). WHO Regional Office for Europe. Denmark. (1996). 26 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 27-37 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry Awad Ali Bin- Jaza* and Abdulazize Omer Bazohair* a Received on Sept. 14, 2005 Accepted for publication on Aug. 2, 2006 Abstract In this research five surface soil samples were taken from some of Hadhramout’s valleys in Yemen (Khrid , Arf , Huwayrah , Buwaish , Khirbah ) in the years from (1999) to (2002) and analyzed using gamma-ray spectrometry. The spectra of samples were measured using a multichannel analyzer (MCA) connected with measurement system for this purpose. A high purity germanium(HpGe) detector with resolution of (2.11keV) at gamma-line(1332keV) of radioactive source(Co-60) was used for detecting (U238, Th232 , K40 , Cs137 ) in the samples. The results showed that the average specific activities of radioactive nuclides in the samples for uranium ranged from(37.56 Bq/Kg) to(46.58 Bq/Kg), and for thorium ranged from(37.93 Bq/Kg) to(47.28 Bq/Kg), and for potassium ranged from(347.57 Bq/Kg) to(850.10 Bq/Kg), and for cesium ranged from(13.01 Bq/Kg) to(15.86 Bq/Kg), and the measured precision of samples ranged from(4.71%) to (9.23%). Keywords: specific activity, surface soil, gamma-ray spectrometry Introduction: The soil surface is contaminated by the nuclear fallout caused by nuclear weapons tests, which are still being carried out by some countries, nuclear accidents such as that of Chernobyl nuclear reactor in 26 April 1986 that released a high radioactivity to the atmosphere[6] and finally by cosmic rays . The background natural radioactivity essentially consists of primary radiation emanating from the uranium series ( U238, half-life = 4.5x109yr.), thorium series ( Th232, half-life = 1.4x1010yr.), potassium ( K40, half-life = 1.3x109yr.), and the artificial fission product is (Cs137, half-life = 30yr.). All these radiations are assimilated into plants and body tissues of organisms and human beings. В© 2007 by Yarmouk University, Irbid, Jordan. * Physics Department, Faculty of Education- Mukalla.University of Hadhramout of science & Technology , Yemen. Bin-Jaza and Bazohair The environmental contamination is mainly caused by the spread of radioactive materials on the soil surface samples .This contamination is of two kinds ; natural contamination as in the case of uranium, thorium and potassium nuclides and artificial or external contamination as in the case of cesium nuclide . Most of people live in the regions of study use soil for agriculture and building, so they afraid from the accumulations of its radiations. Consequently this study will provide the concerned authorities in the Yemeni government with good information about the natural and artificial radioactivity distribution in the Yemeni surface soils or its contamination level. Many studies were made to estimate the concentration of radio nuclides of U238, Th , K40 and Cs137 in surface soils in different countries of the world[2,3,7 -17 ] . 232 Experimental Procedures: Five soil surface samples were taken from some of Hadhramout’s valleys in Yemen ( Khrid , Arf , Huwayrah , Buwaish and Khirbah ) and illustrated in the map in fig(1) , in the years from (1999) to (2002) , from an area of about 100cm2 and 5cm depth . These samples were cleaned from stones and any other impurities and dried at 80ВєC for one day, and grounded in the same mach. The samples were put in Marrinelli beaker, sealed and then stored for a period of time without measurement so as to reach the natural radio nuclides in an equilibrium state between the parent nuclei ( U238, Th232 ) and their daughters of radon R222 and thoron R220 respectively . The gamma spectrometry consists of horizontal high purity germanium (HpGe) detector with sealed preamplifier, a bias high voltage supply, a linear amplifier, a detector's shield made of (5cm) thick lead lined with aluminum, iron and copper plates for x-ray degradation, and a multichannel analyzer (MCA) of Ortec model 6240B with (1024) channel . The (HpGe) detector is a Canberra model (7229N) with a crystal diameter of (7cm) and a length of (7.5cm). It has a resolution of (2.11keV) at gamma-line (1332keV) for (Co60 ) radioactive source . 28 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry AL-Huwarah’s valley Khrid’s valley Arf’s valley Buwash’s valley AL-Dees AL-Shihir Khrbah’s Shohair Arabia Sea Mukalla Fowah 0 20km Fig (1) The location of valleys on the map Results and Discussion: Energy was calibrated by the least square fit method through the use of standard radioactive sources with well- known energies and relative intensities to identify the photo peaks present in the spectrum on the screen of (MCA)and recording the number of channels corresponding to every gamma line (photo peak). Efficiency calibration is necessary for activity measurements, so we used a sealed ( Eu152 ) radioactive source contained in Marrinelli beaker(*) [4],and has a long half-life of (13.50yr.) and produces multilined spectra that include the major photo peaks usually encountered in natural radioactivity measurements. The efficiency of any photo peak included in the sample was calculated by the following formula : Efficiency (Оµ ) = Cps Г— 100(%) ................................................................(1) A Г— IОі Where : Cps – is the count rate or count per second . A- is the activity of reference radio nuclide in (Bq) at measurement . IОі- is the intensity per decay (%) of photo emission at energy (E) . (*) Marrinelli beaker is a plastic beaker whose geometrical shape was designated for making the contents of the sample near the effective region of the detector so as to allow high efficiency counting the gammarays which are emitted from the radio nuclides present in the sample. 29 0 0 350 700 1050 Bi214 (2204KeV) (210Tl Pair Peak) (1919KeV) 0.01 (Tl210 +Ac228) (1650KeV) K40 (1460KeV) (Tl210+Bi212) (1080KeV) Cs137(662KeV) (Tl210+Ac228) (911KeV) 1.00 Tl208214 (583KeV) Bi (609KeV) Count x 1000 100.00 (U235+Th228+Ac227) (167KeV) Bin-Jaza and Bazohair 1400 Channel No. Fig (2) The typical Оі-ray spectrum of one of the studied soil sample From the analysis of photo peaks of the studied soil samples shown in fig (2), we see that there are many spectral lines. For this reason we choose the energy line (609keV) for radio nuclide (Bi214) to indicate the presence of ( U238 ) in the soil samples , also we choose another energy line (583keV) for radio nuclide ( Tl208 ) to indicate the presence of ( Th232 ) in the soil samples and we calculated its specific activities in the soil samples according to the following causes : (1) There is no interference of the chosen energy lines with the other energies of radionuclides. (2) They have high relative intensities. (3) The statistical errors of their radioactivities are very low. To measure the specific activities of radio nuclides in the soil surface samples , five soil samples in Marrinelli beaker were measured by the detector (HpGe) for (40000)sec. Because of the low radioactivity level. The specific activities of radio nuclides U238, Th232 , K40 and Cs137 in (Bq/kg) of the soil samples were calculated as following[13] : 30 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry S . A.( Bq / kg ) = 1000 Г— (C / t c ) ............................................................................(2) ОµI Оі m Where : C- is the net count of the photo peak in (Bq) . tc- is the time count of measurement (sec.) . Оµ- is the counting efficiency at the specific energy (%) . IОі- is the intensity per decay (%) of photon emission at the energy (E) . m- is the mass of the sample (gm) . Table(1) shows the specific activities of radio nuclides in different Yemeni soil samples . The detection limit (D.L.) of our method is calculated by Currie equation [5] as following: D.L. = 2.77 В± 3.29 B.G. Concentration(C )( Bq / kg ) .................................(3) A Where : D.L.- is the detection limit . B.G.- is the background (cps.) . C.-is the concentration of radio nuclide of the sample (Bq/kg) . A- is the net peak area (cps.) . Table(2) shows the detection limit of our method in the studied surface soil samples. Table(3) shows the specific activities of ( U238, Th232 , K40 ,Cs137 ) in some countries of the world and comparing with Yemeni surface samples . The precision of the different radio nuclides in the samples was calculated by the following equation : R.S .D.(%) = Пѓ x Г— 100 .......................................................................................(4) Where : R.S.D.- is the relative standard deviation (precision) . x - is the average concentration. Пѓ – is the standard deviation . Table(4) shows the precision analysis of radio nuclides (U238, Th232 , K40 ,Cs137 ) in different studied samples . 31 Bin-Jaza and Bazohair Table(1) The specific activities of radio nuclides in Yemeni surface soil samples No. of sample Name of valley 12345No. of sample Khrid Arf Huwayrah Buwaish Khirbah Name of valley 2000 2001 Uranium-238 concentration ( Bq/kg ) 43.63В±3.42 40.1.3В±298 48.91В±4.22 38.79В±4.11 35.47В±3.14 42.64В±3.86 41.35В±3.18 38.91В±2.75 45.82В±3.99 36.34В±2.84 35.62В±2.40 40.69В±3.07 45.09В±4.33 43.84В±3.58 51.07В±4.81 Thorium-232 concentration ( Bq/kg ) 12345No. of sample Khrid Arf Huwayrah Buwaish Khirbah Name of valley 38.62В±2.84 34.71В±3.09 43.41В±3.01 47.49В±1.41 42.97В±4.01 53.23В±4.62 45.80В±0.72 40.66В±3.72 48.62В±4.77 41.61В±2.03 39.92В±3.08 45.29В±3.64 37.95В±3.01 34.64В±2.71 40.68В±3.55 Potassium-40 concentration ( Bq/kg ) 40.23В±3.34 45.41В±2.95 43.79В±4.19 42.63В±3.71 38.46В±3.09 12345No. of sample Khrid Arf Huwayrah Buwaish Khirbah Name of valley 428.81В±17.99 409.84В±16.31 470.61В±15.83 375.26В±11.62 356.17В±10.92 382.34В±12.01 346.38В±15.23 320.94В±7.62 365.43В±14.52 618.74В±24.51 584.52В±18.30 662.34В±21.56 874.38В±29.35 761.65В±22.50 892.73В±25.62 Cesium-137 concentration ( Bq/kg ) 440.23В±16.20 360.64В±13.40 357.53В±14.01 596.71В±20.70 871.62В±22.03 12345- Khrid Arf Huwayrah Buwaish Khirbah 14.71В±0.32 13.68В±0.53 13.31В±0.52 16.23В±074 12.46В±0.27 15.23В±0.21 15.74В±0.13 14.49В±0.09 16.35В±0.14 13.38В±0.08 1999 14.23В±01.25 13.45В±0.21 13.18В±0.19 16.03В±0.62 12.29В±0.26 32 13.64В±0.38 12.93В±0.29 12.79В±0.12 14.84В±0.54 13.91В±0.37 2002 45.64В±3.04 40.82В±2.78 41.74В±3.62 37.57В±2.84 46.31В±4.05 Average concentration В± S.D. 44.58В±3.68 39.43В±3.0 7 41.96В±2.8 6 37.56В±2.2 4 46.58В±3.1 6 Average concentration В± S.D. 39.24В±3.62 47.28В±4.38 44.72В±3.35 42.36В±2.25 37.93В±2.49 Average concentration В± S.D. 437.37В±25.46 368.60В±12.26 347.57В±19.40 615.58В±34.24 850.10В±59.70 Average concentration В± S.D. 14.45В±0.68 13.95В±1.23 13.44В±0.73 15.86В±0.69 13.01В±0.77 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry Table(2) The detection limit of some surface soil sample No. of sample Radio nuclide Energy of radio nuclide ( keV ) Concentration of radio nuclide (Bq/kg) Detection Limit (D.L.) (Bq/kg) 1- Bi-214 609 44.58В±3.68 4.52 Tl-208 583 39.24В±3.62 3.68 K-40 1460 437.37В±25.46 24.18 Cs-137 662 14.45В±0.68 1.62 Bi-214 609 41.96В±2.86 4.01 Tl-208 583 44.72В±3.35 3.45 K-40 1460 347.57В±19.40 16.74 Cs-137 662 13.44В±0.73 0.71 Bi-214 609 46.58В±3.16 3.95 Tl-208 583 37.93В±2.49 2.67 K-40 1460 850.10В±59.70 33.49 Cs-137 662 13.01В±0.77 0.84 3- 5- Table(3) The specific activities of radio nuclides in some countries of the world and compared with Yemeni surface soil samples Serial No. Country 1- The specific activities of radio nuclides (Bq/kg) No. of reference U-238 Th-232 K-40 Cs-137 West Malaysia 51.80В±10.36 70.30В±36.63 - 87.88В±15.83 [7],[8] 2- U.S.A. 38.85В±17.76 36.26В±17.02 472 82.51В±38.11 [12],[15] 3- Bangladesh 88.10В±4.80 68.20В±5.28 256.40В±16.30 7.50В±1.62 [10],[11] 4- Finland 37 43 1043 147.35В±74.65 [14] 5- Iraq 34.89В±17.66 8.78В±1.10 579.50В±156 3.23В±1.51 [9],[16] 6- Tunis 17.10В±2.54 19.54В±3.47 284.20В±55.45 8.72В±7.57 [13] 7- Taiwan 30 44 462 <D.L. [17] 8- Hong Kong 73 73 482 <D.L. [3] 9- Australia 24.79В±24.61 32.56В±19.98 172.79В±156 <D.L. [2] 10- Yemen 42.02В±3.67 42.31В±3.84 523.84В±210.66 14.14В±1.10 This work 33 Bin-Jaza and Bazohair Table(4) The precision analysis of radio nuclides in some studied samples x В±Пѓ No. of sample Radio nuclide Energy ( keV ) 1- Bi-214 609 44.58В±3.68 8.25 Tl-208 583 39.24В±3.62 9.23 K-40 1460 437.37В±25.46 5.82 Cs-137 662 14.45В±0.68 4.71 Bi-214 609 46.58В±3.16 6.78 Tl-208 583 37.93В±2.49 6.56 K-40 1460 850.10В±59.70 7.02 Cs-137 662 13.01В±0.77 5.92 5- (Bq/kg) R.S.D. (%) The results showed [ table (1) ] that the average specific activities of radio nuclides in the various valleys Yemeni surface soil samples for uranium ranged from ( 37.56 Bq/kg) to (46.58 Bq/kg), for thorium ranged from ( 37.93 Bq/kg) to ( 47.28 Bq/kg), for potassium ranged from ( 347.57 Bq/kg) to ( 850.10 Bq/kg) and for cesium ranged from ( 13.01 Bq/kg) to ( 15.86 Bq/kg). But the final specific activities averages of these radio nuclides in the Yemeni samples were ( 42.02В±3.67 ) Bq/kg for uranium , ( 42.31В±3.84) Bq/kg for thorium, ( 523.84В±210.66 ) Bq/kg for potassium and ( 14.14В±1.10) Bq/kg for cesium as shown in table (3) . Table (3) shows that the specific activities of these radio nuclides in the Yemeni samples is more than their specific activities in some countries and in some cases it is less than that in some other countries, however the specific activities of these radio nuclides in the Yemeni samples is small and within the possible range[6]. Also from table(3) we see that the specific activities of potassium in the Yemeni soil samples is high except when it is compared with that in Iraq and Finland . This indicates that the floods or torrents in Hadhramout’s valleys come from the near by mountains which are very rich in potassium[1]. The presence of cesium-137 in Yemeni environment results from the seasonal winds which come to Yemen from the southern oceans ( the Indian and the southern Atlantic oceans ) as a result of the different atmospheric pressures in the area . From table(1) we see that the specific activities of 238U, 232Th and 40K are more than in 137Cs because the presence of U,Th,K in soil surfaces are terrestrial, whereas the presence of Cs is aerial. In year 2001 fall heavily rains on Hadhramout more than the years 1999,2000,2002 , so the precipitation of radio nuclides U,Th,K and Cs in its valleys are larger. From table(3) the average specific activity of cesium-137 in Yemeni soil samples is small in comparison with some countries, but it is very small in comparison with some countries of the world near the nuclear accident regions which reached more than ( 300Bq/kg ) according to IAEA report[6]. All these radio nuclides are transferred to the soil surface by the factor of erosion and rains. 34 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry The detection limits of radio nuclides in the studied samples were good as shown in table(2). The results for measuring radionuclides in soil samples were obtained according to the best or optimum practical procedures by using: (1) Large geometry for the detector crystal in detecting more number of falling radionuclides on it by the samples. (2) Long measuring time ( 40000sec.) . (3) Large weight of the studied samples . Conclusions From this research, we deduce the following: (1) The presence of radionuclides in soil samples of the valleys of Hadhramout which resulted from the volcanic mountains chain surrounding the valleys. (2) The average specific activities of radio nuclides in the studied soil samples is less than the international concentration level. (3) The specific activities of radio nuclides in Yemeni soil samples is within the permissible range, so there is no dangerous level as pollution in soils taking into consideration that most of the houses in Hadhramout were built and they are still being built with these sands. There is also no danger in the use of these sands in agriculture. (4) The analytical precision for radio nuclides analysis in Yemeni soil samples is statistically good because its value is less than ( 10%) . (5) The detection limits of radio nuclides in the studied samples are good . (6) The radio nuclides in the studied samples were measured according to optimum practical procedures such as: (a) the large geometry of detecting samples (b) long measuring time (c) large weight of samples . (7) The high concentration of potassium in the Yemeni soil samples can be economically exploited. (8) There should be coordination with the concerned authorities in the Yemeni government to provide them with information about the natural and artificial radio activities distribution in the Yemeni soil as well as its contamination level . 35 Bin-Jaza and Bazohair ‫ﺗﺤﺪﻳﺪ Ш§п»џп»ЁпєёпєЋШ· Ш§п»№пє·п»ЊпєЋп»‹п»І Ш§п»џп»Ёп»®п»‹п»І п»џп» п»Ёп»®Щ‰ Ш§піЊпєёп»Њпє” п»џп» п±°ШЁ اﻟﺴﻄﺤﻴﺔ п»џпє’п»Њпєѕ أودﻳﺔ‬ ‫ﺣﻀﺮﻣﻮت п»“п»І اﻟﻴﻤﻦ пє‘пєЋпєіпє�пєЁпєЄШ§Щ… Ш§п»џпє�пє¤п» п»ґп»ћ اﻟﻄﻴﻔﻲ п»·пє·п»Њпє” ﻛﺎﻣﺎ‬ ‫ﻋﻮض п»‹п» п»І ﺑﻦ пєџпєЋШІШ№ Щ€ п»‹пє’пєЄ Ш§п»џп»Њпє°п»іпє° ﻋﻤﺮ ﺑﺎزﻫﻴﺮ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻓﻲ п»«пє¬Ш§ Ш§п»џпє’пє¤пєљ пє—п»ў пє—пє¤п» п»ґп»ћ ﺧﻤﺲ ﻋﻴﻨﺎت ﻣﻦ Ш§п»џпє�пє®пє‘пє” اﻟﺴﻄﺤﻴﺔ ШЈпє§пє¬ШЄ ﻣﻦ пє‘п»Њпєѕ ШЈЩ€ШЇп»іпє” пєЈп»Ђпє®п»Јп»®ШЄ ﻓﻲ‬ ‫ Щ… пє‘пєЋпєіпє�пєЁпєЄШ§Щ… пє—п»�ﻨﻴﺔ‬2002 ‫ و‬1999 ‫ пє§пє®пє‘пє” ( п»“п»І Ш§п»џп»”пє�пє®Ш© ﺑﻴﻦ‬، ‫ ﺑﻮﻳﺶ‬، ‫ ﺣﻮﻳﺮة‬، ‫ ﻋﺮف‬، ‫اﻟﻴﻤﻦ Щ€п»«п»І ) ﺧﺮد‬ (MCA) ‫ ﻗﻴﺴﺖ اﻷﻃﻴﺎف اﻹﺷﻌﺎﻋﻴﺔ п»џп» п»Њп»ґп»ЁпєЋШЄ пє‘п»®пєіпєЋп»ѓпє” п»Јпє¤п» п»ћ п»Јпє�п»ЊпєЄШЇ Ш§п»џп»�ﻨﻮات‬. ‫اﻟпє�пє¤п» п»ґп»ћ اﻟﻄﻴﻔﻲ п»·пє·п»Њпє” ﻛﺎﻣﺎ‬ ‫( Ш°Щ€ ﻗﺪرة‬HpGe) ‫ Ш§пєіпє�пєЁпєЄЩ… п»›пєЋпє·п»’ Ш§п»џпє пє®п»ЈпєЋп»§п»ґп»®Щ… п»‹пєЋп»џп»І Ш§п»џп»Ёп»�ﺎوة‬. ‫اﻟﻤﺮﺗﺒﻂ ﺑﻤﻨﻈﻮﻣﺔ ﻗﻴﺎس п»Јпє�п»њпєЋп»Јп» пє” ﻟﻬﺬا اﻟﻐﺮض‬ ‫( п»џп» п»њпєёп»’ ﻋﻦ‬Co60 )‫( Ш§п»џп»ЁпєЋпє—пєћ ﻣﻦ اﻧﺤﻼل اﻟﻤﺼﺪر اﻟﻤﺸﻊ‬1332keV) ‫( п»‹п»ЁпєЄ Ш§п»џпєЁп»‚ اﻟﻜﺎﻣﻲ‬2.11keV) вЂ«пє—пє¤п» п»ґп» п»ґпє”вЂ¬ ‫ أﻇﻬﺮت Ш§п»џп»Ёпє�пєЋпє‹пєћ ШЈЩ† п»Јп»ЊпєЄЩ„ Ш§п»џп»ЁпєёпєЋШ· اﻹﺷﻌﺎﻋﻲ‬. ‫ ( п»“п»І اﻟﻌﻴﻨﺎت‬Cs137, K40 , Th232 ,U238 ) ‫اﻟﻨﻮي اﻟﻤﺸﻌﺔ‬ (37.56Bq/Kg) ‫ ﺑﻴﻦ‬U238 ‫اﻟﻨﻮﻋﻲ ﻟﻬﺬه Ш§п»џп»Ёп»®Щ‰ اﻟﻤﺸﻌﺔ п»“п»І اﻟﻌﻴﻨﺎت пє—пє®Ш§Щ€пєЈпє– п»‹п» п»° Ш§п»џпє�ﺮﺗﻴﺐ ﻟﻨﻈﻴﺮ اﻟﻴﻮراﻧﻴﻮم‬ ‫( وﻟﻨﻈﻴﺮ اﻟﺒﻮﺗﺎﺳﻴﻮم‬47.28Bq/Kg)‫( و‬37.93Bq/Kg) ‫ ﺑﻴﻦ‬Th232 ‫(وﻟﻨﻈﻴﺮ اﻟﺜﻮرﻳﻮم‬46.58Bq/Kg)‫و‬ (13.01Bq/Kg) ‫ ﺑﻴﻦ‬Cs137 ‫( وﻟﻨﻈﻴﺮ اﻟﺴﻴﺰﻳﻮم‬850.10Bq/Kg)‫( و‬347.57Bq/Kg) ‫ ﺑﻴﻦ‬K40 . (9.23%) ‫( و‬4.71%) ‫ Щ€п»—пєЄ пє—пє®Ш§Щ€пєЈпє– ШЇп»—пє” Ш§п»џп»�ﻴﺎس п»џп» п»Њп»ґп»ЁпєЋШЄ ﺑﻴﻦ‬، (15.86Bq/Kg)‫و‬ References: [1] AL-Khirbash S. and AL-Anbawi M., The geology of Yemen, First Edition (1996) . [2] Beretka J. and Mathew P.J., Natural radioactivity of Australian building materials, industrial wastes and by products, Health physics , 48 (1) (1985) 87 – 95 . [3] Chung-Keung Man , Shun-Yin Lau, Shui-Chun Au and Wai-Kwok Ng , Radio nuclide contents in building materials used in Hong Kong, Health physics , 57(3) (1989) 397 – 401 . [4] Costrell L., Sanderson C., Persyk D.E., Walford G. and Walter F.J., Germanium semiconductor detector efficiency determination using a standard Marinelli (Reentrant) beaker geometry, Health physics, 38(2) (1980) 229 - 232 . [5] Currie L.A., Limits for qualitative detection and quantitative determination (Application to radiochemistry), Anal. Chem., 40(3) (1968) 586 – 596 . [6] EG and G ORTC, Food monitoring Note, Nuclear spectroscopy systems (1987)18 36 Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using Gamma-Ray Spectrometry [7] Lowe B.G., Levels of 137Cs in soils and vegetation of west Malaysia, Health physics, 34 (1978) 439-444 . [8] Mahat R.H. and Amin Y.M., Concentration of radon precursors in some Malaysian building materials, J . Radioanal . Nucl . Chem., letters, 144(5) (1990) 375- 378. [9] Marouf B.A., AL-Haddad I.K., Tomma N.A., J.A. and Tawfiq N.F., Monitoring of environmental radioactivity around the Tuwaitha site, Environmental management and Health, 3(3) (1991) 14-17 . [10] Mollah A.S., Ahmed G.U., Hessian S.R. and Rahman M.M., The natural radioactivity of some building materials used in Bangladesh, Health physics , 50(6) (1986 ) 849-851 [11] Mollah A.S., Rahman M.M. and Hussain S.R.,Distribution of Оі-emitting radio nuclides in soils at the atomic energy research establishment , Savar ,Bangladesh, Health physic, 50(6) (1986 ) 835-838 . [12] Myrick T.E., berven B.A. and Haywood F.F., Determination of concentrations of selected radio nuclides in surface soil in the U.S., Health physics,45(3) (1983) 631- 642. [13] Nafaa R. and Hedi B., Monitoring and measurements of radioactivity in Sidi Thabet: Future site of the National Center for Nuclear sciences and Technologies Fourth Arab Conference the peaceful uses of Atomic energy , Tunis , 14 - 18 /11/1998 AAHA . [14] Pallai K.C., Assessment of natural radioactivity levels in building materials and evaluation of indoor radiation exposure, Environmental technology letters , 5 (1984)81-88 . [15] Romney E.M., Lindberg R.G., Kinnear J.E. and Wood R. A., Strontium-90 and Cs-137 in soil and biota of fallout areas in southern Nevada and Utah, Healthphysics,45(3) (1983) 643-650 . [16] Shatha A.M., M.Sc., Finding the concentrations of radioactive materials in soil by using the natural gamma-ray spectrometry, thesis, college of Education Ibn AlHaitham, university of Baghdad. March (1996). [17] Yu-Ming Lin, Pei-Huo Lin , Ching-Jiang Chen and Ching- Chung, Measurements of terrestrial Оі-radiation in Taiwan, Republic of China, Health physics, 52(6) (1987) 805 - 811 . 37 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 39-48 Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis Janti S. Qar and Mohammad A. Al-Adhami *a Received on May 4, 2006 Accepted for publication on Sept. 12, 2006 Abstract The origin and migration of primordial germ cells (PGCs) were studied in six embryonic stages of mosquitofish, Gambusia affinis (Cyprinidontiformes, Teleostei). In the earliest stage studied here (having 1pair of somites), the PGCs are observed in splanchnic layer of the lateral plate mesoderm. Depending on their morphology alone, this may be one of the earliest stages at which PGCs could be observed. No worth mentioning change was observed at six pairs of somites. PGCs aggregate in the proximal part of the lateral plate in embryos having 9 and 12 pairs of somites and are found in the splanchnic mesoderm coating the gut in embryos with 14-16 pairs of somites. In embryos having white-grey eyes, PGCs are found on either side of the dorsal mesentery and start gathering underneath the pronephric duct. Finally, the PGCs reach the germinal ridge and reside there in embryos with black eyes and reduced yolk sac. The present study clearly indicates that PGCs in G. affinis are of mesodermal origin. It also indicates that their migration from the lateral plate to the germinal ridges is composed of at least three steps; two of which are active and one is passive. The results are in general agreement with those observed for other teleosts, particularly zebrafish. Keywords: primordial germ cells, teleosts, mosquitofish. Introduction It is well established that the primordial germ cells (PGCs) are the only source of sex cells in vertebrates [1]. Reports on the origin of PGCs are, however, conflicting even in related species [2, 3]. In nearly all species studied so far, these cells are first recorded in places other than the germinal ridge. Later on, they migrate to reside in the gonadal tissue [4, 5]. Among vertebrates, the origin, migration and characterization of PGCs are best studied in amphibians [6, 7]. PGCs are of mesodermal origin in anuran amphibians [8] and of endodermal origin in urodelian amphibians [3]. В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Biologiccal Sciences, Faculty of Sciences, Yarmouk University, Irbid, Jordan. Qar and Al-Adhami The origin of PGCs in teleosts is almost neglected, apart from a few early publications [9, 10]. Later studies are confined to the description and differentiation of PGCs at late embryonic stages, i.e. those having already migrated to the gonads [11, 12, 13]. Recently, the origin, characterization and migration of PGCs in zebrafish has been the focus of intensive work [4, 14, 15, 16, 17]. This study is an attempt to throw light on the morphological description, site of origin and route and mode of migration of PGCs in the mosquitofish, Gambusia affinis, and comparing the results with similar observations on other teleost species. Materials and Methods Embryonic stages of the ovoviviparous, G. affinis (Cyprinidontidae, Teleostei) were used in this study. To obtain different embryonic stages, pregnant females kept in aquaria at 20-22oC were sacrificed by an overdose of MS222 and dissected at various intervals. The embryos were liberated from the ovarian follicles and placed in physiological saline using watchmaker forceps. They were then characterized according to Kunz [18] before fixation in alcoholic Bouin's fluid. To avoid yolk brittleness and obtain thin, serial sections (4 Вµm thick), Steedman's ester wax technique [19] was used for embedding. Dehydration and fixation were carried in changes of cellosolve (2-ethoxyethanol) as follows: 70%: 8h; 90%: overnight; three changes of pure cellosolve: 3h each; cellosolveester wax 50:50 overnight. The sections were stained with hematoxylin and eosin. Infiltration was made in three changes (one hour each) of pure wax. Stains used were Weigert's hematoxylin counterstained with van Gieson. This stain gives better differentiation of PGCs than the routine stains. Results A few isolated, PGCs are observed in embryos having a single pair of somites. They are sporadically found in the proximal part of the presumptive lateral plate mesoderm at the level of, and posterior to, the differentiated somites (Fig. 1). A PGC can be easily distinguished from the neighboring mesodermal cells by its remarkably bigger size (Table 1) and weaker staining affinities. Its nucleus is large, round , vesicular, and often deeply notched. Many chromatin granules underlie the nuclear envelope. One or two nucleoli are also observed. In embryos with six pairs of somites, the PGCs are still confined to the proximal part of the lateral plate or its forerunner at the level of the differentiated somites and the undifferentiated mesoderm posterior to them. They are totally lacking in regions anterior to the first pair of somites. PGCs are still isolated and a cross section rarely shows more than one cell on either side (Fig. 2). 40 Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis Table 1. Numbers and dimensions of PGCs at different developmental stages of G. affinis (Average of Seven Samples Each). Stage Number of PGCs Diameter of PGCs (in Вµm) (Number of somites) Left side Right side Total 1 18 35 53 14.06 6 24 27 51 14.10 9 34 40 74 14.89 12 38 32 70 14.68 14-16 47 40 87 14.73 white-grey eyes 190 180 370 14.54 Embryos with 9 pairs of somites and eye lens placodes show a clear increase in numbers of PGCs (Table 1). Cross sections through the levels of posterior somites show up to seven PGCs on at least one side of the embryo. These are either linearly arranged or clustered into bunches (Figs. 3, 4). The increase of cells per section is not only due to the overall increment of their total number, but also due to their migration along the longitudinal axis towards the mid trunk region. The PGCs are found in the proximal splanchnic mesoderm of the lateral plate. This location, however, is almost confined to the posterior somites. PGCs at this stage seem to be absent at the level of the anterior few somites. In rare observations, few PGCs may be seen in the core of a somite. No significant change in embryos with 12 pairs of somites is observed (Fig. 5). In embryos with 14-16 pairs of somites and a single pair of aortic arches, some PGCs are observed in the splanchnic mesoderm enclosing the gut at the levels where lateral body folds have formed (Fig. 6). Posterior to the body folds, the PGCs are still seen in the proximal ends of the splanchnic mesoderm (Figs. 7, 8). At the stage when three aortic arches and white-grey eyes are developed, PGCs are found on either side of the dorsal mesentery of the gut or at the future site of the germinal ridge underneath the pronephric duct (Figs. 7, 8). This stage witnesses a sharp increase in the number of PGCs. At the stage with black eyes and reduced yolk sac, well defined early gonads are observed. PGCs are seen within these gonads. They are sheathed by flattened cells in some individuals (Figs. 9, 10). It is concluded that these gonads are ovaries. Discussion The findings of the present work on the origin and migration of the PGCs in mosquitofish are in general accordance with results obtained in other teleosts, particularly in zebrafish [5, 6]. Yet, these findings raise a few, interesting points. These points are dealt with separately. 41 Qar and Al-Adhami Origin: The results of this study are in favor of the widely accepted proposal that PGCs in chordates originate somewhere away from the gonads [1, 3, 20]. In G. affinis, PGCs are first seen in embryos with a single pair of somites. This is one of the earliest stages involved in similar studies [9, 10, 14, 15]. The earliest stage of zebrafish at which Braat et al. [14] were able to identify PGCs depending on their morphology alone (light and electron microscopy) was the five somite stage. The site of origin of PGCs in G. affinis recorded in this study is the proximal part of the lateral plate mesoderm. This observation is in accordance with early observations on the teleosts Fundulus heteroclitus [21],Cottus bairdii [22], Platypoecilus maculatus [9] and Micropterus sal [10]. Nieuwkoop and Sutasurya [3], however, suggest that PGCs in teleosts originate in the extraembryonic endoderm of the yolk sac. Accordingly, they suggest a close phylogenetic relationship of teleosts with urodele amphibians in which the same site of PGCs origin as teleosts has been recorded. Recently, Braat et al. [14] proposed that PGCs formation might require a close contact with the mesoderm and/or endoderm. This proposal might explain the contradictory observations on the origin of PGCs in teleosts. Migration: The present work indicates a stepwise migration of PGCs from their site of origin to the germinal ridges. The process seems to involve a passive and an active modes of migration. PGCs migrate from their site of origin in the lateral plate along almost the entire embryo to aggregate in the mid-posterior trunk region at the level of the pronephroi. This step is most likely an active one [23]. From their new location, they passively migrate to the splanchnic mesoderm that coats the endodermal gut and to the dorsal mesentery of the gut. This seems to take place via the enfolding of the splanchnic mesoderm (formation of lateral body folds). Such a mechanism and route of PGCs migration has early been suggested by Wolf [9]. Most workers [6, 13, 24] overlook early developmental stages and begin their investigation with stages having PGCs in the dorsal mesenteries or in the primordial gonads. It is suggested here that the PGCs actively migrate from the dorsal mesenteries to the gonads. Stepwise migration of PGCs in zebrafish has been well studied and documented [4, 17]. During the active migration, PGCs possess filipodia and pseudopodia, but these were not observed during the present study because these structures are of very brief duration and persist for a minute or even shorter than that. Morphology and count: The morphological description (shape, staining affinities and measurements) given here for PGCs is in general accordance with that supplied by other workers [11, 13, 14]. At early stages of G. affinis studied here, the number of PGCs range from 30 to74 per individual embryo. The distribution of PGCs on either side of the embryo is likewise variable. This variation is also observed in other teleost species [9, 13] and in amphibians [25]. PGCs counts in the different embryonic stages studied here show a slow, but a continuous proliferation during migration. Finally, it is suggested here that the study of the origin and migration of PGCs in vertebrates can be very valuable in a number of aspects including the mechanism of differentiation of these cells and other types of cells, cellular migration and phylogenetic relationships between the different vertebrate taxa. 42 ‫‪Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis‬‬ ‫ﻣﻨﺸﺄ Щ€п»«пє пє®Ш© Ш§п»џпєЁп»јп»іпєЋ Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ п»“п»І ﺳﻤﻜﺔ Ш§п»џпє’п»Њп»®Ш¶ ‪Gambusia affinis‬‬ ‫ﺟﺎﻧпє�п»І пє»п»јШ Ш§п»џпєЄп»іп»¦ п»—пєЋШ± وﻣﺤﻤﺪ أﻣﻴﻦ اﻷﻋﻈﻤﻲ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫درس ﻧﺸﻮء Щ€п»«пє пє®Ш© Ш§п»џпєЁп»јп»іпєЋ Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻻوﻟﻴﺔ п»“п»І пєіпє– п»Јпє®Ш§пєЈп»ћ ﺟﻨﻴﻨﻴﺔ ﻟﺴﻤﻜﺔ Ш§п»џпє’п»Њп»®Ш¶ ‪Gambusia‬‬ ‫)‪ .affinis (Gyprinidontiforme, Teleostei‬ﻟﻮﺣﻈﺖ Ш§п»џпєЁп»јп»іпєЋ Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ п»“п»І Ш§п»џп»„пє’п»�пє” اﻟﺤﺸﻮﻳﺔ‬ ‫ﻟﺼﻔﻴﺤﺔ اﻟﻤﻴﺰودرم Ш§п»џпє пєЋп»§пє’п»ґпє” п»“п»І ﺟﻨﻴﻦ Ш°ЩЉ ШІЩ€Ш¬ Щ€Ш§пєЈпєЄ ﻣﻦ Ш§п»џпє’пєЄп»іп»ЁпєЋШЄ )‪ (somites‬وﻫﻮ ШЈпє»п»ђпє® п»Јпє®пєЈп» пє” درﺳﺖ‬ ‫ﺧﻼل п»«пє¬Ш§ اﻟﺒﺤﺚ‪ .‬واﻋпє�ﻤﺎدا п»‹п» п»° Ш§п»џпєјп»”пєЋШЄ اﻟﻤﻈﻬﺮﻳﺔ п»“п»�ﻂ‪ ،‬ﻓп»�пєЄ пє—п»њп»®Щ† п»«пє¬Щ‡ ШЈпє»п»ђпє® п»Јпє®пєЈп» пє” пєіпє п» пє– ﻓﻴﻬﺎ اﻟﺨﻼﻳﺎ‬ вЂ«Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ ﺑﻴﻦ اﻷﺳﻤﺎك اﻟﻌﻈﻤﻴﺔ‪ .‬وﻟﻢ ﻳﺸﻬﺪ Ш§п»џпє п»Ёп»ґп»¦ Ш°Щ€ пєіпє– ШЈШІЩ€Ш§Ш¬ ﻣﻦ Ш§п»џпє’пєЄп»іп»ЁпєЋШЄ ШЈЩЉ ﺗﻐﻴﺮ ﻳﺬﻛﺮ‪.‬‬ ‫وﻓﻲ Ш§п»·пєџп»Ёпє” Ш°Щ€Ш§ШЄ ‪ 9‬أو ‪ 12‬زوﺟﺎ ﻣﻦ اﻟﺒﺪﻳﻨﺎت‪ ШЊвЂ¬пє—пє п»¤п»Њпє– Ш§п»џпєЁп»јп»іпєЋ п»Јп»®пєїп»®Ш№ Ш§п»џпєЄШ±Ш§пєіпє” п»“п»І اﻟﻨﻬﺎﻳﺔ اﻟﺪاﻧﻴﺔ‬ вЂ«п»џп» п»¤п»ґпє°Щ€ШЇШ±Щ… Ш§п»џпє¤пєёп»®ЩЉ п»џп» пєјп»”п»ґпє¤пє” Ш§п»џпє пєЋп»§пє’п»ґпє”вЂЄ ،‬ﺑﻴﻨﻤﺎ ﻟﻮﺣﻈﺖ п»«пє¬Щ‡ Ш§п»џпєЁп»јп»іпєЋ п»“п»І اﻟﻤﻴﺰودرم Ш§п»џпє¤пєёп»®ЩЉ اﻟﺬي‬ вЂ«п»іп»ђп» п»’ Ш§п»џп»�п»ЁпєЋШ© اﻟﻬﻀﻤﻴﺔ п»‹п»ЁпєЄ п»Јпєґпє�п»®Щ‰ Ш§п»џп»�ﻨﺎﺗﻴﻦ Ш§п»џп»Њп» п»®п»іпє�ﻴﻦ اﻷﻣﺎﻣﻴпє�ﻴﻦ п»“п»І Ш§п»·пєџп»Ёпє” Ш°Щ€Ш§ШЄ ‪ 16-14‬زوﺟﺎ ﻣﻦ‬ ‫اﻟﺒﺪﻳﻨﺎت‪ .‬إﻣﺎ п»“п»І Ш§п»џпє п»Ёп»ґп»¦ Ш°ЩЉ اﻟﻌﻴﻨﻴﻦ اﻟﺒﻴﻀﺎوﻳﻴﻦ Ш§п»џпє®п»ЈпєЋШЇп»іпє�ﻴﻦ‪ ،‬ﻓп»�пєЄ пє·п»®п»«пєЄШЄ Ш§п»џпєЁп»јп»іпєЋ Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ‬ вЂ«п»‹п» п»° ﺟﺎﻧﺒﻲ اﻟﻤﺴﺮاق اﻟﻈﻬﺮي п»џп» п»�п»ЁпєЋШ© اﻟﻬﻀﻤﻴﺔ‪ .‬وأﺧﻴﺮا‪ ШЊвЂ¬пєіпє п» пє– Ш§п»џпєЁп»јп»іпєЋ Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ п»“п»І اﻟﻐﺪد‬ ‫اﻟпє�п»ЁпєЋпєіп» п»ґпє” اﻟﻤﺒﻜﺮة п»“п»І ШЈпєџп»Ёпє” Ш°Щ€Ш§ШЄ ﻋﻴﻨﻴﻦ ﺳﻮداوﻳﻦ وﻛﻴﺲ п»Јпєў п»ЈпєЁпє�ﺰل‪ .‬ﺗﺒﻴﻦ Ш§п»џпєЄШ±Ш§пєіпє” اﻟﺤﺎﻟﻴﺔ ШҐЩ† اﻟﺨﻼﻳﺎ‬ вЂ«Ш§п»џпє пє®пє›п»®п»Јп»ґпє” اﻷوﻟﻴﺔ п»“п»І ﺳﻤﻜﺔ Ш§п»џпє’п»Њп»®Ш¶ пє—п»Ёпєёпє„ п»“п»І ﻣﻴﺰودرم اﻟﺼﻔﻴﺤﺔ Ш§п»џпє пєЋп»§пє’п»ґпє”вЂЄ ،‬وأﻧﻬﺎ ﺗﻬﺎﺟﺮ ﻣﻦ п»«п»ЁпєЋЩѓ إﻟﻰ‬ ‫اﻟﻐﺪد Ш§п»џпє�п»ЁпєЋпєіп» п»ґпє” اﻷوﻟﻴﺔ пє‘пєњп»јШ« ﺧﻄﻮات‪ ،‬اﺛﻨпє�пєЋЩ† ﻣﻨﻬﻤﺎ п»“п»ЊпєЋп»џпє�пєЋЩ† )п»«пє пє®Ш© п»“п»ЊпєЋп»џпє”( Щ€Щ€Ш§пєЈпєЄШ© пєіп» пє’п»ґпє”вЂЄ .‬وﺗпє�п»”п»– ﻫﺬه‬ ‫اﻟﻨпє�пєЋпє‹пєћ пє‘пєјп»®Ш±Ш© إﺟﻤﺎﻟﻴﺔ п»Јп»Љ Ш§п»џпєЄШ±Ш§пєіпєЋШЄ Ш§п»џпєґпєЋпє‘п»�пє” п»“п»І اﻷﺳﻤﺎك اﻟﻌﻈﻤﻴﺔ اﻷﺧﺮى‪ ،‬وﺑﺨﺎﺻﺔ اﻟﺴﻤﻜﺔ اﻟﻤﺨﻄﻄﺔ‬ ‫)‪.(Danio rerio‬‬ ‫‪43‬‬ Qar and Al-Adhami References [1] Timmermans L. P. M., Origin and differentiation of primordial germ cells in vertebrates especially fishes. Netherlands J. Zool. 46 (1996) 147-162. [2] Humphrey R. R., The primordial germ cells of Hemidactylium and other Amphibia. J. Morph. Physiol. 41 (1925) 1-43. [3] Nieuwkoop P. D. and Sutasurya L. A., Embryological evidence for a possible polyphyletic origin of the recent amphibians. J. Embryol. exp. Morphol. 35(1) (1976) 159-167. [4] Weidinger G., Wolke U., KoprГјnner M., Klinger M. and Raz E., Identification of tissue and patterning events required for distinct steps in early migration of zebrafish primordial germ cell. Devel. 126 (1999) 5295-5307. [5] Dumstrei K., Mennecke R. and Raz E., Signaling pathways controlling primordial germ cell migration in zebrafish. J. Cell Sci. 177 (2004) 4787-4795. [6] Al-Mukhtar K. A. K. and Webb A. C., An ultrastructural study of primordial germ cells, oogonia and early oocytes in Xenopus laevis. J. Embryol. exp. Morph. 26(2) (1971) 195-216. [7] Heasman J., Mohun T. and Wylie C. C., Studies on the locomotion of primordial germ cells from Xenopus laevis in vitro. J. Embryol. exp. Morph. 42 (1977) 149161. [8] Ljri K. and Egami N., Mitotic activity of germ cells during normal development of Xenopus laevis tadpoles. J. Embryol. exp Morph. 34(1975) 687-694. [9] Wolf L. E., The history of the germ cells in the viviparous teleost Platypoecilus maculates. J. Morph. Physiol. 52(1)(1931) 115-153. [10] Johnston P. M., The embryonic history of the germ cells of the large mouth black bass, Micropterus salmoides. J. Morph. 88(1951) 471-542. [11] Satoh N., An ultrastructural study of sex differentiation in the teleost Oryzias latipes. J. Embryol. exp. Morphol. 32(1)(1974) 195-215. [12] Hamaguchi S. A., Light microscopic and electron microscopic study on the migration of primordial germ cells in the teleost Oryzias latipes. Cell Tissue Res. 227(1982) 139-151. [13] Parmentier H. K. and Timmermans L. P. M., The differentiation of germ cells and gonads during development of carp (Cyprinus carpio L.). A study with anti-carp sperm monoclonal antibodies. J. Embryol. exp Morph. 90(1985) 13-32. [14] Braat A. K., Speksnijder J. E. and Zivkovic D., Germ line development in fishes. Int. J. Dev. Biol. 43(1999) 745-760. 44 Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis [15] Weidinger G., Wolke U., KoprГјnner M., Thisse C., Thisse B. and Raz E., Regulation of zebrafish primordial germ cell migration by attraction towards an intermediate target. Devel. 129(2002) 25-36.. [16] Raz E., Primordial germ-cell development: the zebrafish prospective. Nat. Rev. Genet. 4(2003) 690-700. [17] Blaser H., Eisenbeiss S., Neumann M., Reichman-Freid M. Thisse B., Thisse C. and Raz E., Transition from non-motile behavior to direct migration during early PGC development in zebrafish. J. cell Sci. 118(2005) 4027-4038. [18] Kunz Y. W., Histological study of greatly enlarged pericardial sac in the embryo of the viviparous teleost Lebistes reticulates. Rev. Suisse. Zool. 78(1)(1971) 187207. [19] Steedman H. F. Section Cutting in Microscopy. Oxford Co. London.(1960). [20] Otani S., Maegawa S. Inoue K. Arai K. and Yamaha E., The germ cell lineage identified by vas-nRNA during the embryogenesis in goldfish. Zool. Sci. 19: (2005) 519-526. [21] Richards A. and Thompson J., The migration of the primary sex cells of Fundulus heteroclitus. Biol. Bull. 40(1921) 325-348. [22] Hann H. W., The history of germ cells of Cottus bairdii, Girard. J. Morph. Physiol. 43(1935) 427-449. [23] Doitsidu M., Reichman-Fred M., Stebler J., Koprunner M., Dorries J., Meyer D., Esguerra C. V., Leung T. and Raz, E., Guidance of primordial germ cell migration by the chemokine SDF-1. Cell 111(2002) 647-659. [24] Shibata N. and Hamaguchi S., Electron microscopic study of the blood-testis barrier in the teleost Oryzias latipes. Zool. Sci. 3(1986) 331-338. [25] Kita Y. and Wakahara M., Cytological analyses of factors which determine the number of primordial germ cells (PGCs) in Xenopus laevis. J. Embryol. exp. Morph. 90(1985) 251-265. 45 Qar and Al-Adhami Legends of Figures Figures 1 and 2. Cross section through the first somite level of embryos with one pair and six pairs of somites, respectively. A single PGC (arrow) is seen in the proximal part of the lateral plate (thick arrow). The endoderm (open arrow) is still stretched as a flattened layer. Abbreviations: N: neural tube; Nc: notochord; S: somite; E:ectoderm; Y:yolk. (X: 200) Figure 3. Embryo with 9 pairs of somites. A cross section through the level of the third somite (S). A cluster of primordial germ cells (arrows) are seen in the proximal part of the lateral mesoderm. Thick arrow: roling up endoderm. (X: 250) Figures 4 and 5. Embryo with 9 pairs of somites. Cross sections through the level of the posterior somites showing clusters of PGCs (arrows) in the proximal parts of the lateral plate. Thick arrows: endoderm; S: somite; other abbreviations as in figure 3. (X: 150) Figure 6. Embryo with 14-16 pairs of somites. A cross section through the level of the pronephroi. A PGC (arrow) is seen in the splanchnic mesoderm of the intestine (I). The notochord (Nc) and dorsal aorta (DA) are indicated. (X: 250). Figures 7 and 8. Embryo with white to grey eyes. A cross section through the level of the pronephroi. PGCs (arrows) can be seen on either side of the dorsal mesentery or extending underneath the pronephric duct (asterisks). (X: 250). Figures 9 and 10. Embryo with black eyes reduced yolk sac. A cross section through the level of the early gonads (G). Abbreviations: BV: blood vessel; I: intestine; OC: ossifying cartilage; P: pancreas. (X: 250). 46 Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis 47 Qar and Al-Adhami 48 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 49-57 The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity Saad Al-Jassabi and Ahmad Khalil* 1 Received on March 29, 2006 Accepted for publication on Aug. 10, 2006 Abstract The aim of this study was to investigate the potential benefits of dietery supplementation of selenium and or lycopene as antioxidants on microcystin toxicity in mouse liver. Microcyitin-LRS (MC-LR) was isolated from Microcystis aeruginosa blooms in King Talal Reservoir (Jordan). The LD50 for MC-LR, measured intraperitoneally in Balb/c mouse was found to be 56 Вµg/kg body weight. Mice were pretreated for two weeks either with sodium selenite (1.5 Вµg / mouse/ day), or with lycopene (10 mg / mouse / day) before an intraperitoneal injection (i.p.) of 75 Вµg/kg of MC–LR. Selenium supplementation was found to provide some protection to the action of the toxin, while lycopene supplementation showed an excellent protection (about four times as much as that observed for selenium). In both cases , and compared to the toxincontrol group, the liver damage caused by toxin was reduced as reflected in the reduction of serum alanine transaminase(ALT) and lipid peroxidation level as well as prevention of glycogen loss compared to non-supplemented toxin- treated mice. The increased level of liver glutathione peroxidase (GPX) activity following selenium or lycopene supplementation may indicate the possible route of selenium or lycopene protection in the mice. Keywords: microcystin; lycopene; selenium; King Talal Reservoir Introductions The contamination of aquatic ecosystems as a consequence of human activities is a well established fact. In direct pollution processes like eutrification favors cyanobacterial blooms, some of which are toxin producers [1-3]. These toxins are believed to be products of the secondary metabolism of cyanobacteria, and it has been hypothesized that they constitute a chemical defence against herbivores [4]. Microcystin–LR (MC–LR), one of the toxins produced by these cyanobacteria, is a potent hepatotoxin [5, 6]. This toxin is produced principally by Microcystis aeruginosa and it is a potent hepatotoxin [7]. It is transported specifically into the liver by multi specific bile acid transporters [8,9], thereby inducing severe intrahepatic hemorrhaging necrosis and apoptosis [10,11]. MC- LR specifically inhibits serine/threonine protein В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Biological Sciences, Yarmouk University, Irbid – Jordan. Al-Jassabi and Khalil phosphates (PP1 and PP2A), which results in the disruption of many important cellular processes [12-15]. Recently, M.aeruginosa was collected from King Talal Reservoir in Jordan for the first time [16]. In this study, the bioactivity of the isolated MC-LR was provided by phosphates inhibition and the HPLC analysis confirmed the identity of the toxin. MC-LR causes oxidative stress and increased reactive oxidative species ( ROS ), as well as lipid peroxidation concomitant with an increase in lactate dehydrogenase(LDH ) release from primary rat hepatocytes [9,17]. Later work indicated a biphasic response in cellular glutathione levels in primary rat hepatocytes exposed to MC–LR [17]. Sky Herman et al [19] showed that hydrophobic antioxidants provide some protection against lethal dose of MC–LR. Lycopene was defined as a nonvitamine active carotenoid that has high oxygen radical scavenging and quenching capacity [20]. It is very beneficial in the tissue to reduce the risk of adverse oxidative reactions that produce hydroxy radicals and peroxides [14, 21]. Selenium is another antioxidant that appears to have a protective effect against oxidative stress when provided prior to exposure to pro-oxidant [9, 22]. Selenium supplementation has been shown to increase the activity of the selenoenzymes, glutathione peroxidase (GPX) and thioredoxin reductase [23], both are important in the reduction of lipid peroxides hydro. The aim of this study is to investigate the role of each of selenium and lycopene pretreatment on MC–LR induction of liver injury in mice. Materials and Methods Chemicals All chemicals used in this study were purchased from Sigma Co., otherwise indicated. All the chemicals were of analytical grade. Animals Five to seven weeks old male albino Balb/c mice (average weight 30 g.) were used in this study. All animals were maintained under controlled conditions and on diet ad labium and water in the animal house unit at Yarmouk University. Microcystis cells Microcystis aeruginosa cells were collected from selected sites of King Talal Reservoir during June, July, August and September of 2003 (twice a month). Isolated cells were cultivated in a culture medium as recommended by Lehtimaki [24]. Toxin extraction The toxin was extracted from the freez-dried cells using the method of Gehringer et al [9]. 50 The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity LD50 determination The LD50 of the toxin extract was determined according to the up – down method of Farwell et al [25], which reduces the number of mice used and the quantity of toxin required. Toxicological studies Thirty mice were divided into six groups (five mice each). Group 1 was the control group with mice receiving neither toxin nor selenium or lycopene supplementation; group 2 received selenium supplementation (1.5 Вµg of sodium selenite / mouse /day) for two weeks prior to sacrification; group 3 received lycopene supplementation (10 mg/ mouse/day) for two weeks prior to sacrification; group 4 received a single i.p. dose of toxin (75 Вµg/kg); group 5 received toxin (same amount) after two weeks of selenium supplementation (same amount given to group 2) and group 6 received the same amount of toxin after two weeks of lycopene supplementation (same amount given to group 3). All toxin –treated mice were sacrificed 24 h. after injection of the toxin. The blood was collected and the serum stored at – 70Co for alanine transaminase (ALT) determination, while the liver was perfused with Hanks buffered saline to remove excess blood. Liver tissues were homogenized using (Ultra Turrax homogenizer ) in buffer ( 0.01 M Tris – HCl pH7.8, 0.2 mM Dithiothreitol (DTT) and protease inhibitors : (7.5 mM PMSF , 2.5 mM EDTA, 3.25 ВµM bestatin, 2.5 ВµM eupeptic and 0.75 ВµM apoprotinin). The homogenate was centrifuged and the supernatant stored at -70oC for the glutathione-Stransferase (GST) and glutathione peroxidase (GPX) assays. ALT and lipid peroxide determination ALT was determined in the serum sample and lipid peroxide in the liver sample were performed according to Gehringer method [9]. Glycogen assay A 0.5 g section of liver was homogenized in 1 ml of distilled water [26]. The homogenate was diluted and added to 0.2% anthrone reagent, boiled for 10 min and read at 620 nm as previously reported [27]. GST and GPX determination GST assay and GPX determination were carried out according to the method recommended by Gehringer et al [9]. Protein phosphates (PP1) activity Protein phosphates (PP1) activity was determined by measuring the rate of colour production from the dephosphorylation of para-nitro-phenolphosphate (ПЃ NPP) substrate as a function of time using the micro titer plate reader according to Ane and Carmichael method [28]. 51 Al-Jassabi and Khalil Results The results showed that the liver weight (as % of body weight) increased significantly (6.68) in toxin-treated mice ( without any supplementation) ( group 4 ) when compared with non-toxin treated control groups ( group 1, 2 and 3 ).The weight decreased significantly in groups that were toxin-treated with selenium or lycopene supplemented ( groups 5 and 6 ) as shown in Table (1). In this study we found that the approximate intraperitoneal LD50 of the microcystin (from M. aeruginosa of King Talal Reservoir) extract for the Balb/c mice was 56 Вµg toxin/ kg mouse. Therefore, as recommended by earlier workers [10], the toxin dose 75Вµg/kg body weight, which is expected to kill all experimental mice, was chosen for further experiments. The average serum ALT levels per ml were calculated as shown in Table (1). The average ALT value for the experimental group 4 which received toxin without any supplementation showed a significant increase (p≤ 0.05). The ALT values decreased in those groups received supplementation especially in case of group 6 which received lycopene. All livers of control groups (1, 2 and 3) contained normal levels of glycogen, while toxin-treated group (group 4) showed a decrease in liver glycogen level. Group 5 and 6 (selenium and lycopene supplemented mice receiving toxin) showed a smaller decrease in the amount of glycogen in the liver (18.80 mg/g liver and 20.22 mg/g liver, respectively) than mice in group 4 not receiving supplementation (7.66 mg/g liver) as shown in Table (1). The average of thiobarbituric acid (TBA) values were calculated and plotted as shown in Table (1). The average TBA value for experimental group (group 4) treated with toxin showed a significant increase (p ≤ 0.05) in lipid peroxidation levels when compared with control groups (group 1, 2 and 3). In contrast, toxin-treated groups ( group 5 and 6 ) receiving supplementation at 1.5 Вµg selenium / mouse/ day , or 10 mg / mouse/day lycopene showed significantly lower values( p≤ 0.05) than the toxin-treated group receiving no supplementation (Table 1). The average GST levels per ml of liver homogenate are as shown in table (1). The levels were significantly lower in toxin-treated mice (group 4) than the control ones, and significantly increased in toxin-treated mice with the supplementation of either selsnium (group 5) or lycopene (group 6). In comparison with the other groups, the levels of the GPX activity were increased after supplementation of either selenium (group 2) or lycopene (group 3). Discussion In the present study we have confirmed the identity and bioactivity of the isolated toxin that have been reported before [16]. To avoid differences that may result from sex, only male mice were used. The i.p. LD50 for this toxin when given to Balb/c mice was found to be within the range reported in the literature [10]. The signs of toxin – induced 52 The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity injury such as hemorrhage, cell death, and apoptosis were observed [3, 9, 11, and 25]. The expected biochemical changes in serum ALT, liver glycogen content, TBA values, GPX and GST activities were also observed in our study. In our results, less severe liver damage was observed in groups 5 and 6 (supplemented with selenium and lycopene, respectively) than that occured in group 4 (toxin control). In the latter group, the wt. of the liver inceased as shown in table (1) which confirms the occurrence of liver damage, and thus led to the accumulation of fluids [11]. Further support for the ability of selenium or lycopene to protect the liver from toxin injury was observed in the favorable changes in the biochemical markers serum ALT, liver glycogen content, TBA values, GPX and GST activities with selenium or lycopene treatment prior to toxin administration. It was shown before [14] that MC-LR was a strong Reactive Oxygen Species (ROS) inducer in hepatocytes of rat because of cytoskeleton disruption and mitochondrial alterations. It has been well documented that ROS can affect the microtubules, intermediate filaments and microfilaments organization due to their ability to oxidize the cytoskeleton proteins or disturb the intracellular thiol balance [14, 29]. Ding et al [18] showed that the disruption of the cytoskeleton led to the ALT leakage, suggesting that the disruption of the cytoskeleton could have played a crucial role in microcystin- induced hepatotoxicity. Our results showed a significant decrease in glycogen in the liver of toxin control mice (group 4) when compared with other groups (Table 1). MC-LR is known to cause the depletion of glycogen in the liver, possibly via the direct inhibition of glycogen synthase an indirect activation of glycogen phosphorylase [9, 30]. In this study, it was shown that the levels of lipid peroxidation were increased in toxin-treated mice (group 4) as reflected in increased TBA values because of the severe liver damage, necrotic change, hemorrhaging, and apoptosis [17, 31, 32]. These levels were decreased in group 5 and 6 (supplemented with selenium and lycopene respectively), presumably via the ability of selenium and lycopene to quench free radicals. A significant decrease in liver GPX activity was observed in toxin-treated mice (group 4), while the activity of GPX in selenium control (group 2) and lycopene control (group 3 ) were significantly high comparing with other groups as shown in Table 1. Our results showed increased level of GST activity in toxin-treated mice (group 4) which confirms the work of Pietsch et al [33]. GST is a phase II detoxification enzyme known to be involved in the detoxification of MC-LR [34]. It was found by [9, 35] that the inhibition of GST occurs by increased level of lipid peroxidation (Table 1). Stahl and Sies [36] indicated that lycopene is an a cyclic carotenoid containing a conjugated double bonds arranged in the all-trans form, thus, it acts as antioxidant through physical and chemical quenching of singlet oxygen and traps peroxyl radicals. Therefore, it can be concluded that selenium and lycopene taken as a dietary supplement could confer some protection against MC-LR in contaminated water sources. Finally, the relation 53 ‫‪Al-Jassabi and Khalil‬‬ ‫‪between the enzyme glutathione peroxidase, glutathione reductase and catalase needs‬‬ ‫‪further experimentation.‬‬ ‫دور Ш§п»џпєґп»ґп» п»ґп»Ёп»ґп»®Щ… Щ€Ш§п»џп» п»ґп»њп»®пє‘пІ” п»“п»І ﺣﻤﺎﻳﺔ Ш§п»џп»”пєЊпє®Ш§Щ† ﻣﻦ Ш§п»џпє�ﺴﻤﻢ пє‘пєЋпіЊпєЋп»іп»њпє®Щ€пєіпєґпє�ﲔ‬ ‫ﺳﻌﺪ Ш§п»џпє пєґпєЋпє‘п»І وأﺣﻤﺪ пє§п» п»ґп»ћвЂ¬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻫﺪﻓﺖ п»«пє¬Щ‡ Ш§п»џпєЄШ±Ш§пєіпє” ШҐп»џп»° Ш§пєіпє�п»�пєјпєЋШЎ Ш§п»µпє›пєЋШ± اﻟﻤﻔﻴﺪة п»№пєїпєЋп»“пє” Ш§п»џпєґп»ґп» п»ґп»Ёп»ґп»®Щ… Щ€Ш§п»џп» п»ґп»њп»®пє‘п»ґп»¦ ﻛﻤﻮاد ﻣﺎﻧﻌﺔ п»џп» пє�ﺄﻛـﺴﺪ‬ ‫إﻟـــﻰ п»ЏЩЂЩЂЩЂпє¬Ш§ШЎ Ш§п»џп»”пєЊЩЂЩЂЩЂЩЂпє®Ш§Щ† п»“ЩЂЩЂЩЂп»І Ш§п»џпє�п»�п» п»ґЩЂЩЂЩЂЩЂп»ћ ﻣـــﻦ ﺳــــﻤﻴﺔ اﻟﻤﺎﻳﻜﺮوﺳـــﺴпє�ﻴﻦ п»“ЩЂЩЂЩЂп»І اﻟﻜﺒــــﺪ‪ .‬وﻟп»�ЩЂЩЂЩЂпєЄ пє—ЩЂЩЂЩЂЩЂп»ў Ш§пєіЩЂЩЂЩЂпє�пєЁп»јШµ ﺳــــﻤﻮم‬ ‫اﻟﻤﺎﻳﻜﺮورﺳпє�ﻴﻦ ﻣﻦ Ш§п»џпє’п»њпє�пє®п»іпєЋ Ш§п»џпєЁп»Ђпє®Ш§ШЎ – اﻟﻤﺰرﻗﺔ ﻣﻦ ﻧﻮع اﻟﻤﺎﻳﻜﺮوﺳﺴпє�пєІ Ш§Ш±п»іпє п»Ёп»®ШІШ§ اﻟﻤﻮﺟﻮدة п»“ЩЂп»І ﻣﻴـﺎه ﺳـﺪ‬ вЂ«Ш§п»џп»¤п» ЩЂЩЂп»љ ﻃــﻼل‪ .‬ﻓп»�пє’ЩЂЩЂп»ћ пєЈп»�ــﻦ п»“пєЊЩЂЩЂпє®Ш§Щ† Ш§п»џпє�пє ЩЂЩЂпєЋШ±ШЁ пє‘пє пє®п»‹ЩЂЩЂпєЋШЄ ﻣــﻦ اﻟﻤﺎﻳﻜﺮوﺳــﺴпє�ﻴﻦ‪ ،‬ﺗــﻢ ШҐп»‹п»„ЩЂЩЂпєЋШЎ Ш§п»џп»¤пє п»¤п»®п»‹ЩЂЩЂпє” Ш§п»·Щ€п»џЩЂЩЂп»° ﻣــﻦ‬ ‫اﻟﻔﺌﺮان пєџпє®п»‹пє” ﻣﻦ ﺳﺎﻻﻧﺎﻳﺖ Ш§п»џпєјп»®ШЇп»іп»®Щ… )‪ 1.5‬ﻣﻴﻜﻮﻏﺮام п»џп»њп»ћ п»“пєЋШ± ﻳﻮﻣﻴﺎ(‪ .‬أﻣـﺎ Ш§п»џп»¤пє п»¤п»®п»‹ЩЂпє” اﻟﺜﺎﻧﻴـﺔ‪ ،‬ﻓп»�ЩЂпєЄ أﻋﻄﻴـﺖ‬ ‫ﻻﻳﻜﻮﺑﻴﻦ Щ€п»џп» п»”пє�пє®Ш© ﻧﻔﺴﻬﺎ Щ€пє‘пє�ﺮﻛﻴﺰ ‪ 10вЂ¬п»Јп»ґп» п» п»ґп»ђпє®Ш§Щ… п»џп»њп»ћ п»“ЩЂпєЋШ± ﻳﻮﻣﻴـﺎ‪ .‬وﻟп»�ЩЂпєЄ ﺑﻴﻨـﺖ Ш§п»џп»Ёпє�ЩЂпєЋпє‹пєћ Ш§п»џпє�ЩЂп»І пє—ЩЂп»ў Ш§п»џпє¤ЩЂпєјп»®Щ„ п»‹п» п»ґп»¬ЩЂпєЋвЂ¬ ‫أن пє—пє°Щ€п»іЩЂЩЂпєЄ п»ЏЩЂЩЂпє¬Ш§ШЎ Ш§п»џп»”пєЊЩЂЩЂпє®Ш§Щ† ﺑﻬــﺬا اﻟﻤп»�ЩЂЩЂпєЄШ§Ш± ﻣــﻦ Ш§п»џЩЂЩЂпєґп» п»ґп»Ёп»ґп»®Щ… п»—ЩЂЩЂпєЄ ﻣﻨﺤﻬــﺎ пє‘п»ЊЩЂЩЂпєѕ Ш§п»џп»®п»—пєЋп»іЩЂЩЂпє” ﻣــﻦ ﺗــﺄﺛﻴﺮ п»«ЩЂЩЂпє¬Ш§ Ш§п»џп»ЁЩЂЩЂп»®Ш№ ﻣــﻦ‬ ‫اﻟﺴﻤﻮم ‪.‬‬ ‫وﺑﺎﻟﻤп»�пєЋпє‘ЩЂЩЂп»ћ ‪ ،‬أﻇﻬــﺮت п»ЈЩЂЩЂпєЋШЇШ© اﻟﻼﻳﻜــﻮﺑﻴﻦ ﺗــﺄﺛﻴﺮات п»ЈЩЂЩЂп»ЂпєЋШЇШ© ﻟــﺴﻤﻴﺔ п»ЈЩЂЩЂпєЋШЇШ© اﻟﻤﺎﻳﻜﺮوﺳــﺴпє�ﻴﻦ пє—пє’п» ЩЂЩЂп»Ћ ШЈШ±пє‘ЩЂЩЂп»Љ ﻣــﺮات‬ ‫ﺑп»�ЩЂЩЂпєЄШ± ﺗــﺄﺛﻴﺮ Ш§п»џЩЂЩЂпєґп»ґп» п»ґп»Ёп»ґп»®Щ…вЂЄ .‬وﺑﻤп»�ﺎرﻧــﺔ Ш§п»џп»Ёпє�ЩЂЩЂпєЋпє‹пєћ Ш§п»џпє�ЩЂЩЂп»І пєЈЩЂЩЂпєјп» п»ЁпєЋ п»‹п» п»ґп»¬ЩЂЩЂпєЋ ﻣــﻦ Ш§п»џп»”пєЊЩЂЩЂпє®Ш§Щ† Ш§п»џпє�ЩЂЩЂп»І пєЈп»�п»ЁЩЂЩЂпє– пє‘пєЋп»џЩЂЩЂпєґп»ў пє‘ЩЂЩЂпєЄЩ€Щ† ШЈЩ† п»іЩЂЩЂпє�ﻢ‬ ‫إﻋﻄﺎﺋﻬﺎ Ш§Щ‰ п»Јп»ЂпєЋШЇШ§ШЄ أﻛﺴﺪة‪ ،‬ﻟﻮﺣﻆ Щ€пє‘пєёп»њп»ћ Щ€Ш§пєїЩЂпєў ﺗـﺄﺛﻴﺮ п»›ЩЂп»ћ ﻣـﻦ Ш§п»џЩЂпєґп»ґп» п»ґп»Ёп»ґп»®Щ… واﻟﻼﻳﻜـﻮﺑﻴﻦ п»‹п» ЩЂп»° Ш§п»џпє�п»�п» п»ґЩЂп»ћ ﻣـﻦ‬ ‫ﺗــﺄﺛﻴﺮ اﻟﻤﺎﻳﻜﺮوﺳـﺴпє�ﻴﻦ اﻟﻤпє�п» ЩЂЩЂп»’ п»·п»§ЩЂЩЂпєґпє пє” Ш§п»џп»њпє’ЩЂЩЂпєЄ Щ€Ш°п»џЩЂЩЂп»љ ﺑﺎﻧﺨﻔــﺎض п»ЈЩЂЩЂпєґпє�п»®п»іпєЋШЄ أﻧــﺰﻳﻢ اﻻﻻﻧــﻴﻦ ﺗــﺮاﻧﺲ اﻣﻴﻨﻴــﺰ ﻓــﻲ‬ ‫ﻣﺼﻞ اﻟﺪم‪ ،‬وﻛﺬﻟﻚ п»Јпєґпє�п»®Щ‰ ШЈп»›пєґпєЄШ© Ш§п»џп» п»ґпє’п»ґЩЂпєЄШ§ШЄ ШҐпєїЩЂпєЋп»“пє” ШҐп»џЩЂп»° п»Јп»ЁЩЂп»Љ пє—пє¤ЩЂпє®Ш± اﻟﻜﻼﻳﻜـﻮﺟﻴﻦ ﻣـﻦ Ш§п»џп»њпє’ЩЂпєЄ Щ€Ш§п»џЩЂпє¬ЩЉ ﻳﺤـﺼﻞ‬ ‫ﻋﺎدة пє‘пєґпє’пєђ пє—п» п»’ اﻟﻜﺒﺪ‪ .‬ﻛﻤﺎ ШҐЩ† ШІп»іпєЋШЇШ© п»Јпєґпє�п»®Щ‰ ﻧﺸﺎط أﻧﺰﻳﻢ Ш§п»џп»њп» п»®пє—пєЋпє›пєЋп»іп»®Щ† ﺑﻴﺮوﻛﺴﻴﺪﻳﺰ п»“ЩЂп»І Ш§п»џп»њпє’ЩЂпєЄ п»‹п»�ЩЂпєђ пєЈп»�ـﻦ‬ ‫اﻟﺴﻢ п»“п»І пєЈпєЋп»џпє” Ш§п»џп»”пєЊпє®Ш§Щ† Ш§п»џпє�п»І пє—п»ў ШҐпєїЩЂпєЋп»“пє” п»›ЩЂп»ћ ﻣـﻦ Ш§п»џЩЂпєґп»ґп» п»ґп»Ёп»ґп»®Щ… ШЈЩ€ اﻟﻼﻳﻜـﻮﺑﻴﻦ ШҐп»џЩЂп»° п»ЏЩЂпє¬Ш§ШЎ п»›ЩЂп»ћ ﻣﻨﻬـﺎ п»—ЩЂпєЄ ﻳـﺸﻴﺮ إﻟـﻰ‬ ‫اﻵﻟﻴﺔ اﻟﻤﺤпє�п»¤п» пє” п»џпє�ﺄﺛﻴﺮ п»›п»ћ ﻣﻨﻬﻤﺎ п»“п»І ﺣﻤﺎﻳﺔ Ш§п»џп»”пєЊпє®Ш§Щ† ﻣﻦ п»«пє¬Щ‡ اﻟﺴﻤﻮم ‪.‬‬ ‫‪References‬‬ ‫‪Carmichael W.W., The toxins of cyanobacteria. 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Clin.Nutr. 62 (1996) 1366 – 1378. 56 The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity Table 1: Summary of the biochemical effects of selenium and lycopene supplementation in Balb/c mice receiving single lethal dose of microcystin. Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 ( saline ) (selenium (lycopene (toxin (selenium (lycopene (1) control) control) control) + toxin) + toxin) Liver( % 4.22В±0.117 4.39В±0.105 4.52В±0.077 6.68В±0.022 4.40В±0.064 4.32В±0.066 Body wt.) (2) ALT 0.68В±0.004 0.44В±0.002 0.39В±0.006 3.16В±0.015 0.53В±0.006 0.42В±0.006 20.40В±0.198 22.50В±0.188 23.30В±0.108 7.66В±0.099 18.81В±0.117 20.22В±0.109 0.020В±0.001 0.023В±0.006 0.022В±0.002 0.052В±0.004 0.027В±0.001 0.024В±0.001 1.84В±0.008 6.22В±0.079 7.88В±0.062 1.27В±0.008 2.28В±0.035 2.08В±0.022 20.05В±0.166 37.8В±0.011 38.08В±0.198 46.66В±0.208 32.22В±0.221 36.89В±0.217 (U/ml) Glycogen ( mg/g) TBA Values (3) GPX Activity ( U/ml ) GST Activity (U/ml) (1) Each group consists of 5 mice. (2) Values represent the meansВ± standard errors of the mean of two experiments. (3) Values read spectrophotometrically according to Gehringer et al.[9]. 57 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 59-91 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan. Ghunaim S. Nasher, Hakam A. Mustafa and Nabil Abderahman*a Received on Nov. 22, 2005 Accepted for publication on Sept. 12, 2006 Abstract Geoelectrical and hydrochemical investigations were carried out in the Hallabat area, north of Jordan, to study the groundwater salinization, and to assess the quality of groundwater for its suitability for domestic and irrigation purposes. The area falls under a semi-arid climate and water extraction is from basalt and limestone. Interpretations of electrical survey data show that a low resistivity layer is present at depths ranging from 55 – 130 m, with lowest resistivity values (less than 20Ω.m) and highest depth found at the central part of the study area. The data also show the continuity of this layer to the surface which reflects the role of irrigation return flow for salinity build up. Chemical analyses of the groundwater samples show that, the mean concentration of the cations is in the order Na+ > CaВІ+ > MgВІ+ > K+ while for anions is in the order Cl ВЇ > HCO3ВЇ > SO4ВІВЇ >NO3ВЇ. Three major water types occur in the study area namely alkaline earth waters with increased portion of alkalies with prevailing chloride which is characterized by high concentration of chloride and represents 61.9%, alkaline waters with prevailing chloride which represent 33.3%, and alkaline earth waters with prevailing chloride which represent 4.8%. High TDS levels accompanied with high nitrate levels were observed in water from private wells in the cultivated land. The pollution with respect to NO3ВЇ, Cl ВЇ, which are the main sources for salinity build up, is mainly attributed to the extensive use of fertilizers, and excessive pumping from private wells. Most of the sampled water is not suitable for drinking purposes due to the high NO3ВЇ content. It can be used for irrigation purposes as the sodium hazard is low but it needs treatment to reduce salinity that ranges from medium to very high hazard. Keywords: geoelectrical, hydrochemical, pollution, Hallabat, Jordan, Amman Formation, Wadi Es – Sir Formation, Basalt. В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Earth and Environmental Sciences, Faculty of Science, Yarmouk University, Irbid, Jordan. 59 Nasher, Mustafa and Abderahman Introduction The study area forms a part of the Hallabat catchment area which is, hydrogeologically, considered as a part of the Zarqa Basin. The investigation of this area is important due to: Its large population, the wide distribution of its cultivated land which is considered as one of the major irrigated areas in Jordan, its high rates of groundwater recharge, the industrial activities, and the importance of shallow aquifers consisting of Upper Cretaceous cherty and calcareous rocks, and Upper Tertiary and Quaternary basaltic rocks. Groundwater abstraction from both private and government wells in the study area began early 1960s. Agricultural activity is the major groundwater user in this area. Continual withdrawl has resulted in problems such as regional decline of groundwater levels and degradation of water quality. With passage of time salt concentration in the water increased and became a real problem facing the domestic uses and irrigation in this area. The study area (Fig. 1), is located in the northern part of Jordan, some 45 km to the northeast of the capital city Amman, it forms a part of the Hallabat catchment area. It is defined by the coordinates E 277 – E 285 and N 1165 – N 1172 (Palestine Grid, PLG). Many geological, hydrogeological, hydrochemical, environmental, and geophysical studies were carried out on the study area for different purposes since the sixties of the last century: Fig.1: Location map of the study area. 60 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Mac Donald et al, [1-3] and Abu Obeid [4,5] studied the water resources in the northeastern part of Jordan including the study area. They found that the water is of good quality and can be used for irrigation and the lowering of water table in this area to overpumping. Al – Zabet [6] conducted a study of two – dimensional finite element model for groundwater flow of Dhuleil – Hallabat region. This model was run using the water level of 1992 as a base level and with a pumping rate of 30 MCM/a to predict the fluctuation of the water levels in 2012. He found that the drawdown will be 8 meters in 1992 and will reach up 13.25 meters by 2012. Salameh [7] investigated the water quality degradation in different areas in Jordan including the study area and Bajjali [8] studied the building up of salinity in groundwater over time in Dhuleil, Hallabat and Samra areas to the west of the study area. they found that changes in the groundwater quality in Dhuleil area are attributed mainly to irrigation return flows and to salinization of aquifers as a result of overpumping and also the infiltration of the semi-treated waste water of Khirbet Es-Samra into the aquifer. Al-Bis [9] applied aeromagnetic, gravity, electrical resistivity (VESs), electromagnetic (VLF) methods on the upper aquifer system to the west of the study area to study the subsurface structures to determine the relationship between structures and groundwater movements. The present study aims at determining the depth and chemical characteristics of the groundwater, the areal water – quality distribution and the factors that affect the water quality in the study area. Methodology The present study involves geoelectrical measurements and hydrochemical investigations. The geoelecrical resistivity survey in Hallabat area was carried out in Septemper 2003. All measurements were taken using an ABEM- Terrameter SAS- 300B of the Department of Geology, University of Jordan. The survey is of Vertical Electrical Sounding (VES) type. This configuration is widely used to measure vertical changes in the resistivity of the subsurface rocks below given points on the earth’s surface. A sum of 12 VES profiles was conducted with half spacing between current electrodes ranging between 400m to 800m (Fig.2). The maximum separation of current electrodes was affected by the accessibility situation. 61 Nasher, Mustafa and Abderahman Fig. 2: Distribution of all vertical electrical sounding ( VES) in the study area. For hydrochemical investigation twenty one water samples from twenty one production wells were collected in October, 2003. These samples were taken after operating the wells of about 2 – 4 hours. The samples were stored in clean polyethylene bottles, that have been washed by diluted HCl and by distilled water in the laboratory. In the field, the bottles are well washed by sampled water, adequately labeled and preserved in the refrigerator until they were taken to the laboratory for chemical analysis. pH and electrical conductivity (EC) values were measured in the field using pHmeter and EC-meter respectively. The coordinates of the wells (Fig. 3) were measured in the field by using Maggellan Global Positioning System (GPS). The laboratory analyses of the collected groundwater samples were performed in the laboratories of the Yarmouk University. The determination of chloride (ClВЇ) and Alkalinity which is related to bicarbonate (HCO3ВЇ) was determined by titration. Sulfate (SO4ВІВЇ) and Nitrate (NO3ВЇ) determination were done by spectrophotometery . 62 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Determination of the major cations CaВІ+, MgВІ+, K+, and Na+ were done by using atomic absorption spectrophotometer (ASS). Fig. 3: Distribution of studied wells in the study area. stratigraphy The area east of Mafraq-Azraq-Wadi Sirhan referred to as the northeastern desert of Jordan comprises two morphological units, the first is the NE Basalt Plateau and the NE Limestone plateau (Fig.4). The Northeastern Limestone Plateau extends from the eastern margin of the basalt plateau with elevations of about 625 m (a.s.l) in the WNW to more than 800 m (a.s.l) in the ENE. The rocks exposed in the area consist mainly of limestone, marl, chalk, and alluvium, and volcanics ranging in age from Late Cretaceous to Recent, and belong to Ajlun, Belqa and Plateau Groups [2,10]. Ajlun Group Only the Shueib and Wadi Es-Sir Formations are exposed in the study area. The Shueib formation is exposed in the southern part of the study area. It consists of yellow, brown, blue – grey and black marl, containing 63 Nasher, Mustafa and Abderahman Fig.4: Geology of the study area (as coated from Bajjali, [8]). Sometimes pyrite, with marly limestones and occasional thin crystalline and shelly limestone. its thickness reaches more than 50 meters [11]. The Wadi Es-Sir is Turonian age. It consists of grey, white and pinkish crystalline limestone overlying porcellanceous, marly and chalky limestone. The massive limestone forming the top 20 meters of the formation shows open jointed and strongly developed karstic weathering in outcrop [11]. There is transition into the underlying Shueib Formation. Its thickness ranges between 70 and 110 meters. Belqa Group The lower lying Umm Ghudran Formation (B1) consists mainly of white and pink chalk, marl and occasional marly limestone with a total thickness between 15 and 35 meters [2,4]. The younger Amman Formation (B2) consists of chalk, marl, massive chert, with relatively thin, white crystalline and shelly limestone. Only the lower part of this formation is exposed. However, its whole thickness is estimated to be 47 meters [12]. Plateau Group Plateau Group of Early Eocene to Late Pleistocene age, comprises the Older Alluvial Formation, the basalt, and the Younger-Recent Alluvium[2]. The Older Alluvial formation underlies the oldest basalt flow and is intercalated with the different younger basalt flows. It consists mainly of silts and clays in addition to gravels. 64 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan The basalt appears in massive, vesicular, and amygdaloidal texture, and with occasional scoriaceous zones. A petrological study of the basalt indicates that the basaltic flows in Jordan are in general similar, differences in mineralogical composition have been found. The rocks consist essentially of ( 42 to 68%) plagioclase , 25% olivine, 9 to 23% pyroxene, and 2 to 9% magnetite, with calcite as a very common secondary mineral [13]. The basalt flows separated by paleosoil and alluvial deposits consist of grey, brown, silty clays, with limestone and chert fragments and also beds of volcanic ash. There are six lava flows in north Jordan [13]. The characteristics of each flow differ texturally from one to other. The thickness of the basalt ranges between less than 50 meters in the western part of the study area to more than 100 meters in the east (Fig. 5). Fig. 5: Isopach map of the basalt in the study area ( after BGR-WAJ, [14]) The Younger – Recent Alluvium Formation occurs widely over the basalt. It consists mainly of coarse well-cemented outwash gravels, sands, river gravels, scree, hill wash, and soil with limited thickness of 0 – 14 m. These deposits are hydraulically connected to the upper surface of water bodies and with underlying permeable beds of Upper Cretaceous or younger basaltic rocks. Structure Most of the structures within the sedimentary rocks are trending NE – SW. To the north of the study area, the structures are hidden completely beneath the basalt flows. Generally, the NW – SE trending tensional fractures saved as feeding dykes for the flood basalt which had filled the major synclinal structures plunging ESE. Drilling of exploration wells in the vicinity of the study area suggests the presence of a major fault, which is probably an easterly extension of this flexure. Drilling activities have stopped in most of the wells before penetrating the whole sequence of basalt so the whole structures are not known. However, low dips and gentle folding the most marked structural features are the abrupt flexures and associated faults. 65 Nasher, Mustafa and Abderahman From the linear characteristics and extensions, the major trend of the lineaments in the study area is NE – SW (Fig.6). Two fold systems occurred in and around the study area trending NE – SW, and NW – SE [2]. The first fold system belongs to the Amman – Hallabat structure system, pronounced gentle anticline, striking NE – SW, plunge at Qaser Hallabat toward east to northeast under the plateau basalt [15,16] The second fold system occupies the southern part of the study area and strike NW – SE, with dip of the axial planes towards the NW. Fig. 6: Rose diagram showing the trend of the linear features delineated from landsat TM images for Dhuleil – Hallabat area ( After Al-Bis,[9]). climate The study area experiences a semiarid climate which is defined by hot – dry weather in summer and cold – humid in the winter with an average annual rainfall varying from 120 mm to 170 mm. The monthly average temperatures vary from 8 ВєC in January to over 26 ВєC in July, and the maximum recorded temperature was 45ВєC [1,17]. Rainfall occurs between October and May, the highest rainfall occurs between December and March, while the average annual evaporation exceeds 89 % [17]. The residual water 66 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan forms a runoff in the valley from December to March ( e.g Wadi Dhuleil, Wadi ErRukban). Hydrogeology The hydrogeology of the study area is controlled by the geological set up, which also controls the piezometry, occurrence and movement of the groundwater, and the distribution of productive areas in the aquifers. Three aquifer systems are recognized in the study area: Wadi As-Sir Aquifer It is an excellent aquifer especially when it is structurally deformed parts because the resulting fissures and joints have been enlarged by solution. The potentiality of this formation depends whether the formation lies below or above the zone of saturation. The yield is poor to moderate ranging from 5 mВі/hr to 54 mВі/hr. Transmissibilities determined at several locations indicate generally that this formation shows poor ability for transmitting water. The base of this formation is about 400 meters above mean sea level (asl) or less (Fig. 7). There is no individual base map for A7 and B2, because there is a hydraulic connection between them [18]. Fig. 7: Structural contour map of the base of A7/B2 aquifer [14]. Amman Aquifer This formation underlies the basalt, and can be considered as a good aquifer, it can yield water readily to the wells. The Amman formation (B2) is encountered only in few wells. Because of the deep erosion in pre – basalt times, therefore the aquifer has probably limited lateral extension [11]. 67 Nasher, Mustafa and Abderahman The Older Alluvial and Basalt Aquifer It represents the main aquifer in the study area. The old alluvial formation lies below or within the basaltic sequences as interflows marker, it ranges in thickness from 0 to 32 m. This formation can be considered as good conductor for groundwater or a good reservoir depending on lithology. The basalt is scoriaceous and jointed. A zone of scoriaceous basalt reaching a thickness of 45 meters is considered to be the primary aquifer. The transmissivity and the specific yield values are considered to be very high indicating that the scoriaceous zone is highly developed and uniformly jointed. High transmissivity and yield wells sometimes characterize the scoriaceous zone by partial or complete loss of circulation during drilling. The basalt aquifer is made up of a series of semi – independent channels or pipes, lying side by side, and it is possible to pump from one such pipe without affecting the other. Groundwater Movement Generally, groundwater movement depends on the hydraulic conductivity and hydraulic gradient. It moves from high pressure (head) to low pressure (head) to reach the stable condition. In figure (8) the detailed water levels map in the study area is illustrated, before heavy pumping started. The depth to water table varied from 20 meters in the far west to 106 meters in the northeast [19]. The flow net configuration of the groundwater in the Dhuleil and the surrounding areas is highly influenced by the pumping history. The groundwater flows show a general trend to the south and west direction . Fig. 8:Groundwater flow pattern of the study area (Raikes and Partners 1972) Geoelectrical Survey The direct current (DC) resistivity method relies on the application of Ohm’s Law V=I*R (where V is potential difference, I gives current, and R denotes resistance) to constrain the composition, structure, and/or hydrology of the subsurface. R is related to apparent resistivity ПЃa through both the path length L and the cross-sectional area A 68 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan through which the current flows. DC resistivity surveys are usually conducted by electrifying two electrodes and measuring the potential across another pair of electrodes. Various electrode configurations which can be used in resistivity surveying. The apparent resistivity ПЃa which is measured by the array depends on the geometry of the electrodes. Fig. 9: Electrode Configurations. A) Wenner array , B) Schlumberger array.C1, C2 are current electrodes, and P1, P2 are potential electrodes. Data Processing The first step in the resistvity data analysis is to calculate the apparent resistivity ПЃa corresponding to each measured resistance ( ∆V/ I ) for each profile. The apparent resistivities ПЃa are calculated using the following formula which depends on the electrodes arrangements: ПЃa = K * R Where ПЃa : apparent resistivity in ( Ω.m ). R : Resistance in ( Ω ). K : The geometrical factor which depends on the arbitarily chosen distances between electrode locations. The calculated apparent resistivities are plotted against half electrode distance (AB/2) on log – log papers. The utilized field layout includes changing potential electrodes separation (MN), so that, the field data are obtained in the form of overlapping segments, each segment is being for a fixed MN dipole due to inhomogeneities near electrodes M and N. These overlapping segments are processed to obtain a single continuous field curve. 69 Nasher, Mustafa and Abderahman Interpretation Both qualitative and quantitative methods were used to interpret the resistivity measurements. Qualitative Interpretation Iso- Resistivity contour maps The surface iso- resistivity contour map is constructed by contouring the values of apparent resistivities at AB/2 = 20m (Fig.10). Through the investigation of the surface distribution of the surface rocks and variation in the apparent resistivity of the surface layer, it can be noticed that, the northern part of the study area is characterized by high resistivity values due to presence of Quaternary basalt. To the south of the study area there is a sharp decrease in the resistivity values. The occurrence of inland saline surface waters and salt accumulations which are common phenomena in arid and semiarid regions as occur in the study area, is the main cause of the sharp decrease in resistivity values. Also three iso – resistivity contour maps were constructed for AB/2 values of 100, 200, and 400 m (Figs. 11, 12 and 13), respectively. They show lateral variations values that suggest the presence of water bearing sediments. The spatial distribution of low resistivity zone shown on the maps indicates the observed contamination area clearly at the spacing AB/2, increases from 200 m to 400 m. It also shows a general decrease in resistivity values toward the central part of the study area. The comparison between these maps and hydrochemical data indicates that the variation in resistivity values is most probably due to the salinization of groundwater. Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.10: Iso-resistivity contour map (in Ω.m)for AB/2=20m 70 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.11: Iso-resistivity contour map (in Ω.m) for AB/2= 100m Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.12: Iso-resistivity contour map (in Ω.m) for AB/2=200m 71 Nasher, Mustafa and Abderahman Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.13:Iso-resistivity contour map (in Ω.m) for AB/2=400m. Quantitative Interpretation The quantitative interpretation is concerned with calculations of the true resistivity and the thickness of the layers. This process depends on applying ПЃa and the half electrode spacing (AB/2). The final resistivity structures of sounding data were determined applying the automatic interpretation method [ 20]. Figure. (14) shows an example of sounding curve and its interpretation in the northern part of the study area utilizing previously method. a) b) Fig. 14: An example of sounding curve (a), and its interpretation (b) in the northern part of the study area. 72 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Representations of the Quantitative Interpretation This is achieved by drawing a contour map between the sounding stations which are distributed along two profiles at different directions. There are some geologic informations that were obtained from drilled boreholes but most of the boreholes are quite distant from the sounding point and the circumference of the study area. Therefore, these informations were considered as background geological information, incorporated in interpretation of sounding data. Following is a description of the geoelectric sections: Geoelectric section (A – AВЇ ) Seven ( VES’s) were measured along this section ( Fig. 2), nearly in N – S direction. The length of this profile is about 6.5 km starting at sounding VES-1 ( about 200m north to the well AL 2597) and ending almost east of Hallabat ( 100m west of well AL 1093). Interpretation of geoelectrical section (Fig.15) indicates that the first layer has resistivity values of about 5 – 519 Ω.m and extends to about 1 m – 19 m depth from the surface; it is interpreted as top soil. The resistivity values tend to decrease with depth beneath all VESs of this section except VES-1. This may be attributed partly to the dry nature of the surface and partly because of the presence of fresh water that is just added to the cultivated land. The high resistivity values were found in the northern part of the study area beneath VES-1 which can be attributed to the presence of Quaternary basalt. The second layer stretching between VES-1 and VES-3 has resistivity values between 34 – 248 Ω.m with thickness of 14 m – 78 m; it can be related to basalt intercalated with clay beds. The third layer reveals a low resistivity value that decreases with depth to 16 Ω.m and a thickness of about 40 – 70 m. This zone correlates with fractured limestone saturated with saline water. The conductive layer overlies the moderate resistive layer which has resistivity values that increase with depth in the range 50 - 180 Ω.m. This layer seems to correlate probably with hard crystalline limestone. The low resistivity zone which corresponds to the salinization is especially thick in the central portion of the survey lines, as it is shown clearly beneath VES-4 and VES-5. 73 Nasher, Mustafa and Abderahman Fig.15: Geoelectrical cross – section A – AВЇ . Geoelectric section (B – BВЇ ) Five geoelectric soundings were measured along this profile ( Fig.2) in the N – S direction. The length of this section is about 4.5 km. The profile starts at VES-8 about 200m east of well AL 1111 and ends at VES-12. 74 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan The resistivity and thickness of the layers are illustrated in ( Fig.16). The interpreted layers differ from the northern part towards the southern part of the study area. The analysis of this section reveals that the first layer has resistivity values in the range 3 – 95 Ω.m, it extends to about 4.1–14m depth from the surface, and can be related to top soil. The resistivity values of this layer decrease with depth; this can be attributed to the dry nature at the surface. Near the surface the soil contains fresh water without dissolved salts which increase during the movement of return flow downward. Because wells in this area are found in cultivated land, top soil contains a large quantity of water. Therefore, a correlation between top soil and sounding data and boreholes data is difficult. In the northern part of this section, the second layer between VES-9 and VES-10 has resistivity values of about 25 – 135 Ω.m with thickness of 20 – 81 m, it is considered as basalt interbedded with clay. The resistivity of the third layer ranges from 13 – 40 Ω.m. This value seems to be low compared to the ordinary rock types in the study area. This seems to result from the presence of saline water. The evidence of salinization of water is clearly shown in the interpretation of VES-9. In this interpretation, the layer of low resistivity extends to depth exceeding 130 m. In the fourth layer there is a continous increase in resistivity values, which exceed 160 Ω.m, it can be correlated with water unsaturated basalt water in the northern part and massive limestone toward the southern part. Comparing the two geoelectrical sections, the overall resistivity structures are somewhat similar and reveal clearly the continuity to the surface which leads to the increase of water salinity due to the irrigation return flow especially in the central portion of the study area. The extent and magnitude of groundwater salinization occurs at variable depths and also has variable resistivity values. The depth of this layer varies from 40 m to more than 130 m with resistivity values in the range 13 Ω.m to 72 Ω.m ( Figs. 17 and 18 ), respectively. 75 Nasher, Mustafa and Abderahman .m .m .m Fig. 16: Geoelectrical cross – section B - BВЇ The low resistivity layer (Fig.18) extends in two main zones with different depths. The first zone covers extensive parts of the area specially the central part and extends to the southeast with depth ranging between 90 – 130 m; it is characterized by the lowest 76 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan resistivity values 19 – 30 Ω.m (Fig. 17). The second zone is located in the southwestern and northeastern parts with depth ranging between 30 – 70 m. Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.17:Depth to low resistivity layer (in m). Long. 279 280 281 282 283 284 171 170 Lat. 169 168 167 166 165 Fig.18:Isoresistivity contour map (in Ω.m )for the low resistivity layer. 77 Nasher, Mustafa and Abderahman Hydrochemistry The conditions of population growth, industrial, irrigation and other human activities (addition of fertilizers, biocides …etc) lead to increase of water demand as well as deterioration of water quality. An example is the chemical fertilizers that dissolve in the irrigation water and may end up in the aquifer. accordingly, the quality of groundwater would be affected. This results in a major increase in cations and anions contents in water. The determination of the quality of groundwater is essential for assessing the suitability of water for the various drinking, domestic, industrial and agricultural purposes. Some of these constituents are present in large quantities, others are secondary or minor. These constituents include the cations ( Na+, K+, CaВІ+, MgВІ+ ) and anions ( ClВЇ, HCO3ВЇ, SO4ВІВЇ, NO3ВЇ ). These ions are considered the most important parameters for determining the water quality. Results and Interpretations of Hydrochemical data The results of the analyses of groundwater samples are summerized in (Table 1). The ionic concentrations are presented in milligram per liter (mg/l). The mean concentration of the cations is in the order Na+ > CaВІ+ > MgВІ+ > K+ while for anions it is in the order ClВЇ > HCO3ВЇ > SO4ВІВЇ > NO3ВЇ. The statistical analyses were performed on the different analyzed and calculated parameters using MINITAB(1998). The Total Dissolved Solids (TDS) of water samples were found to correlate directly in different degrees with ions (Fig. 23). The relationships between TDS and Cl and Mg are nearly perfect, with a correlation coefficient being very high at 0.984 and 0.965 respectively. There are also strong correlation between TDS and NO3 ,Ca and Na with the correlation coefficients ( r ) 0.837, 0.749, and 0.883 respectively. In addition to the overall salinity dependence on Cl ВЇ concentration, the dominance of the Cl ВЇ was also illustrated by performing linear regression analysis of the concentration of Na+, CaВІ+, and MgВІ+ against the ClВЇ concentration, which indicates Cl ВЇ, Na+, CaВІ+, and MgВІ+ are the main chemical constituents and also NO3ВЇ that increase TDS of groundwater and the previous cations were present in a chloridic form (Fig.19). 78 Parameters Well Name AL 1093 AL 1095 AL 1097 AL 1109 AL 1111 AL 1113 AL 1762 AL 1763 AL 2353 AL 2567 AL 2571 AL 2574 AL 2587 AL 2594 AL 3285 AL 3286 AL 3305 AL 3306 AL 3445 AL**** AL 2597 EC Вµs/cm 930 659 1027 2050 1280 2450 1119 699 2010 727 1710 752 2260 2970 1235 1295 711 730 859 3000 2110 pH value 8.24 8.24 7.27 7.83 7.7 7.98 7.97 8.21 7.89 8.13 8.04 8.2 7.7 7.51 7.93 7.96 8.1 8.05 8.18 7.8 7.34 TDS mg/l 595.2 421.76 657.28 1312 819.2 1568 716.16 447.36 1286.4 465.28 1094.4 481.28 1446.4 1900.8 790.4 828.8 455.04 467.2 549.76 1920 1350.4 385.045 141.027 271.348 610.541 644.591 819.005 293.723 189.378 662.04 160.361 747.281 260.056 1171.09 993.126 259.347 276.378 155.122 167.367 183.94 1504.9 1036.87 TH mg/l 100.8 25.3 51.5 105.21 142.2 140.15 46.1 36.67 119.84 32.23 181.8 63.99 284.1 80.96 55.08 56.71 28.15 30.26 38.48 361.7 220.9 CaВІ+ 32.45 18.97 34.78 84.76 70.51 114.3 43.53 23.83 88.4 19.46 71.41 24.41 112.4 192.86 29.67 32.83 20.67 22.37 21.4 146.5 118.2 MgВІ+ Table 1: Chemical analyses of groundwater samples (ions in mg/l). 79 96.18 68.77 78.43 158.7 91.17 161 102.35 56.58 132.25 80.73 161.1 68.84 145.2 211.6 142.14 146.74 74.29 77.51 95.45 151.8 146.3 NaВ№+ 0.81 6.65 7.82 13.29 4.927 14.08 8.99 7.04 12.9 5.47 4.671 0.669 10.24 17.6 6.26 7.43 5.87 6.65 7.82 10.9 9.706 KВ№+ 144 90.89 105.72 86.62 120 86.26 100.04 100.56 89.06 134.2 140 150 130 76.25 142.13 148.84 106.75 98.82 134.2 120 130 HCO3В№+ 188 131.35 298.21 474.28 334 629.66 233.24 112.89 501.61 119.28 440 191 680 784.55 255.96 268.74 129.58 144.84 159.75 910 590 ClВ№ВЇ 3 19.86 29.76 172.32 21.9 162.72 83 60.48 130.56 43.68 4.7 3 13.5 248.64 79.68 87.84 33.6 36.96 55.68 6.1 5.5 SO4ВІ+ Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan 40.35 18.7 24.25 73.49 85.1 106.69 28.79 21.39 53.6 12.21 61.65 31.8 122.9 75.92 12.62 10.83 14.97 17 7.94 127.1 126.33 NO3В№ВЇ 1.87 2.67 2.19 2.92 1.5 2.57 2.73 1.92 2.36 2.88 2.24 1.87 1.77 3.06 3.94 3.95 2.71 2.74 3.21 1.82 1.85761 SAR% 34.32 52.82 39.93 37.20 23.50 30.99 44.32 41.06 31.45 53.22 30.20 36.66 20.52 32.66 54.99 54.30 52.13 51.38 54.17 19.47 23.11 Na% Nasher, Mustafa and Abderahman Fig. 19: The relation between. a) Cl and TDS, b) NO3ВЇ and TDS, c) MgВІ+ and ClВЇ, d) Na and ClВЇ, e) CaВІ+ and ClВЇ (all concentrations in mg/l). Water Types The major ion compositions of twenty-one representative water analyses were plotted on trilinear diagram of Piper [21]. According to these plots (Fig. 20), and based on Langguth's [22] classification of water types, the groundwater in the study area can be classified into three types: Вѓ Alkaline earth waters with increasing portion of alkalis and prevailing chloride. This type is characterized by a high concentration of chloride and represents 61.9% from the collected water samples. Вѓ Alkaline waters with prevailing chloride. This type of waters represents 33.3% from the collected water samples. Вѓ Alkaline earth with prevailing chloride, which represents only 4.8% of the waters. These high concentrations of Cl ВЇ in groundwater in the area suggest a long history of evaporation. 80 Na CO 3 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan M g K HC O3 + + Fig. 20: Trilinear diagram showing the chemical composition of water, shows the different water types with prevailing chloride ion. Physical Parameters The measured pH – values of the water in the present study range from 7.27 to 8.24, thus classified as alkaline. Electrical conductivity (EC) is the ability of substances to conduct electrical current. The lowest measured EC value was found to be about 650 Вµs/ cm in well AL 1095, while the highest was about 3000 Вµs/ cm in well Al ****. The (TDS) in the study area vary in the range of 421.8 mg/l (in the well Al 1095) to 1920 mg/l (in the well Al ****). The groundwater in the study area falls within fresh ( TDS<1,000 mg/l) to brakish ( TDS> 1,000 mg/l) type of water [23]. The salinity of all wells exhibits with Cl ВЇ and NO3ВЇ concentrations significant and positive relationships, where there is a highly positive correlation between TDS – ClВЇ ( r = 0.984) and TDS – NO3ВЇ ( r = 0.925) (Fig. 19) and can be perfectly quantified. 81 Ghunaim S. Nasher; Hakam A. Mustafa; Nabil Abderahman The TDS in the study area (Fig.21) increases toward the central eastern of this area. This is compatible with the presence of farmland in this part, so that this increase may be, as also postulated by Schiffler [24], due to the excessive pumping, and it is believed that continued re-irrigation of the soil from the groundwater aquifer is causing a build up in salinity. Various techniques are used for irrigation including sprinkler and open channel. The latter makes the water subject to intensive evaporation. Irrigation water evaporating from the soil and the roots of plants precipitates salts above and below the soil surface. Constant irrigation from the groundwater of the same area continues to dissolve the accumulated salts from the soil. The salt is flushed and washed out repeatedly from the soil causing infiltration of the solute into the subsurface thereby increasing the salinity of groundwater. This practice has continued for more than three decades near the productive wells in the area. Fig. 21: The concentration map of TDS in the study area showing the highest concentration in an area extending NW – SE of the upper half of the study area. Chemical Parameters Calcium is the most abundant dissolved cationic constituent of groundwater, and is responsible for water temporal hardness. Ca concentration ranges from 25.3 mg/l (in the 82 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan well Al 1095) to 361 mg/l (in the well Al ****). The correlation coefficient of CaВІ+ versus HCO3ВЇ, Na+, and MgВІ+ is 0.148, 0.51, and 0.7, respectively. Therefore, the concentration of CaВІ+ is mainly attributed to association with carbonates and to plagioclase and mafic minerals found in basalt [25]. CaВІ+ has also high positive correlation coefficient with NO3ВЇ ( 0.892); it can be attributed to association of CaВІ+ in fertilizers. Ca comes also from plagioclase. The minimum value of Magnesium is about 18.97 mg/l in well Al 1095 and the maximum about 192.86 mg/l in well Al 2594. The major source of increasing magnesium in the groundwater is the ion exchange of minerals in rocks and soils by water. In volcanic rocks groundwater derives MgВІ+ from the minerals like olivine and pyroxene. The concentration of sodium ranges from 68.77 mg/l (in well Al 1095) to 211.6 mg/l (in well Al 2594). The increase of Na+ probably comes from the decomposition of plagioclase. An increase of sodium is also assumed to result from cation exchange of calcium and magnesium ions by water-rock interaction. For this reason, there is a positive correlation between these cations. K+ is considered as the minor trace cation in the groundwater; it is less than Na+, CaВІ , MgВІ+. Potassium in the groundwater is derived salty rocks used in industry. It is also used as an agricultural fertilizer, this can lead to significantly higher potassium concentrations in groundwater below cultivated areas [26]. + Generally, potassium content decreases in the groundwater because it can be easily adsorbed by clays. The potassium analysis shows concentration of potassium ranges from 0.669 mg/l (in well Al 2574) to 17.6 mg/l (in well Al 2594). The concentration of chloride in the study area is high; it is increased many times in comparison with other major cations and anions. The high concentration values of chloride in groundwater is the result of dissolution of chloride minerals accumulated either in the soil due to high evaporation rate in this area, or deposited in the subsurface formations. It ranges from 131.35 mg/l (in well Al 1095) to 910 mg/l (in the well Al ****). Chloride causes in concentrations above 250 mg/l corrosion, while above 400 mg/l it causes a salty taste in water [27]. The high chloride concentrations suggest that the chemical character of the water is influenced by recharge from meteoric water, weathering and subsequent release of ions from soil Alkalinity measurements are routinely conducted as part of standard water – quality determintations. Typically, these values are taken to be an indication of the concentration of bicarbonate ( HCO3ВЇ) or carbonate (CO3ВІВЇ) in the sample [28-31]. The concentration of carbonate ranges from 86.26 mg/l (in well Al 1095) to 148.84 mg/l (in the well Al 3286). The concentration values are high near limestone and low around volcanic rocks. This increase is attributed to the lithology changes. Sulfate is abundant in most groundwater. It enters to the groundwater through the weathering of sedimentary rocks which contain sulfate minerals or by dissolution of 83 Ghunaim S. Nasher; Hakam A. Mustafa; Nabil Abderahman evaporite deposits. Further additions of sulfate to groundwater arise from the leacheable sulfate from fertilizers. It may cause detectable tastes at concentrations of 300 – 400 ml/l [27]. The highest concentration of sulfate was found in the well Al 2595 with about 248.64 mg/l, while the lowest concentration was 3 mg/ l in the wells Al 2574 and Al 1093. High nitrate concentrations in water supplies are potenial hazards to infant health, as recommended by the WHO [32]. The susceptibility of infants to nitrate has been attributed to their high intake relative to body weight, to the presence of nitrate-reducing bacteria in the upper gastrointestinal tract, and to the greater ease of oxidation of fetal hemoglobin [32]. The nitrate concentrations in the study area range from 10.83 mg/l (in the well Al 3286) to 127.1 mg/l (in the well Al ****). The average groundwater nitrate concentration for the study area was 51.125 mg/l, and in ten samples out of the twentyone water samples ( 47.6%) exceeded the maximum permissible level making groundwater unsuitable for drinking purposes. The increased usage of fertilizers can be considered as the main source of nitrate in the study area which greatly increases the concentration of nitrate especially below the cultivated lands. Water Quality The purpose of this section is to characterize the waters for both domestic as well as for irrigation purposes. Domestic purposes: Two parameters Total Hardness ( TH ) and WHO [33] and Jordanian standards [36] were used to determine whether water is suitable for domestic purposes; The Total Hardness (TH) is the sum of calcium and magnesium concentration. These ions react with soap to form precipitates. Hard water are unsatisfactory for household cleaning purposes, so that, water softening processes are needed for removal of hardness [34]. All wells except well Al 1095 are characterized by hard to very hard water according to Sawyer and McCarty [35]. The high increase in TH in the study area can be attributed to the dissolution of carbonate rocks and washing of soils during the movement of groundwater. Water with TH greater than 80 mg/l can not be used for domestic purposes, because it coagulates soap water. All wells have TH values greater than the permissible value for domestic purposes; therefore, this water need softening to eliminate the effect of TH. The results of chemical analyses are compared with the international guide lines limits of drinking water of the World Health Organization [33] and the Jordanian drinking water standard. Most well waters are unsuitable for domestic purposes due to the high NO3ВЇ and ClВЇ content, in addition to the high TDS as well. 84 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Irrigation Water Criteria Numerous parameters are used to define irrigation water quality. Two criteria were used in this study for evaluating irrigation water quality; total soluble salt content (salinity hazard) and the relative proportion of sodium cations (Na+) to other cations (sodium hazard). The main problem with high sodium concentration is its effect on soil permeability and water infiltration. Sodium also contributes directly to the total salinity of the water and may be toxic to sensitive crops such as fruit trees. The sodium hazard of irrigation water is estimated by the sodium absorption ratio (SAR). This is the proportion of sodium to calcium plus magnesium in the water. The Sodium Adsorption Ratio (SAR) is calculated as: SAR = Na * 100 _________ в€љ(Ca + Mg )/2 ( Todd, 1980). All ionic concentrations are expressed in milliequivalent per liter. High values for SAR imply a hazard of sodium replacing adsorbed calcium and magnesium, and this replacement is damaging to the soil structure. The SAR was plotted on the USA salinity laboratory diagram in which the SAR appears as an index for sodium hazard (S) and EC as an index of salinity hazard (C) (Fig.22). The water classes according to SAR method are shown in (Table 1). The waters were found mostly confined in three classes of water types: C2-S1, C3-S1 and C4-S1 which means medium to very high salinity hazards and low sodium alkalinity hazards. Medium – salinity – low – sodium waters are useful for irrigation purposes, whereas most of wells water in the study area has high to very high – salinity – low – sodium hazard and needs adequate drainage to overcome salinity problems for irrigation purposes. The sodium concentration is important in classifying the water quality, where the sodium content is usually expresed in terms of percent sodium which is defined according to Todd (1980) by the equation: Na% = Na + K * 100 Ca + Mg + Na + K All ionic concentrations are expressed in milliequivalent per liter. 85 Ghunaim S. Nasher; Hakam A. Mustafa; Nabil Abderahman Fig. 22: Diagram for classification of irrigation waters (Richards, 1954). The irrigation water containing high proportion of sodium will increase the exchange of sodium content of the soil, affecting the soil permeability, and texture; it makes the soil hard to plough and unsuitable for seedling emergence. If the percentage of sodium is above 50% in irrigation water, calcium and magnesium exchange with sodium, thus causing deflocculation and impairment of tilth and permeability of soils [37]. A sodium percentage of more than 60% is considered unsafe for irrigation. The sodium content in the groundwater, is regarded as low and the water can be used for most crops and for irrigation on almost all soils according to the classification of Wilcox [38]. Discussion According to the geoelectrical sections (Figures 15 and 16), the high resistivity values in the northern part of the study area can be attributed to the presence of Quaternary basalt. Comparing the two geoelectrical sections, the overall resistivity structures are somewhat similar, the low resistivity zone which corresponds to the zone of interest to us ( salinization zone) is especially thick in the central part of the study area ( VESs 4, 5 and 9) (Figures 19 and 20), and reveals clearly the continuity to the surface which leads to the increase of water salinity due to the irrigation return flow especially in the central portion of the study area. 86 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan The low resistivity layer in the study area which reflects the extent and magnitude of groundwater salinization occurs at variable depths and also has variable resistivity values ( Figures. 17 and 18), respectively. The greater depth in the central part of the study area is most probably due to fractures ( faults) . The depth of this layer varies from 40 m to more than 130 m with resistivity values in the range 13 Ω.m to 72 Ω.m. The hydrochemical investigation indicates that the water type falls within fresh to brakish type of water. The areal distribution of many of the dissolved chemical species, TDS and EC in the groundwater shows systematic variations in the centeral portion towards the northwest due to the fracturing possibility in this direction. The very high Cl ВЇ contents in groundwaters in the study area suggest a long history of evaporation, and the pollution with respect to NO3ВЇ is mainly attributed to the extensive use of fertilizers due to irrigation return flow. These are the two main sources for the salinity build up of the groundwaters in the study area. The hydrochemical results relatively conform with the geoelectrical results and reveal clearly the pattern of salinity distribution of groundwater in the study area. Conclusions The combination of interpretted electrical resistivity data and hydrochemical data successfully established the nature and configuration of salinization of groundwater in the Hallabat area. The study shows the following results: • The resistivity values are high in the northern and southrn parts of the study area and decrease gradually toward the central part. The high resistivity values in the northern part reflect the presence of basaltic rocks. • The low resistivity values (16 – 70 Ω.m) of the third geoelectric layer represent approximately the water bearing sediments and show clearly the conducting with the land surface. This reflects the role of the irrigation return flow which caused the salinity build up. • As the depth increases the true resistivity values decrease, and the geoelectrical layer of the low resistivity is detected at depth ranging from 55 – 130 m. The depth to low resistivity layer increases toward the central part of the study area. • The groundwater in the study area falls under fresh ( TDS<1,000 mg/l) to brakish ( TDS> 1,000 mg/l) type of water. • Most of the waters are unfit for drinking because of the high NO3ВЇ, and ClВЇ contents, TH and TDS contents are as well high. • Since SAR is low and salinity hazard is variable (from medium to very high) most of well waters need suitable drainage to overcome salinity problems for irrigation purposes. • The increase in salinity is attributed to the increasing of NO3ВЇ, and ClВЇ salts of Na+, CaВІ+, and MgВІ+, which is indicated by linear correlation between the cations Na+, CaВІ+, and MgВІ+ and the anion Cl ВЇ. 87 Ghunaim S. Nasher; Hakam A. Mustafa; Nabil Abderahman • The increasing of salinity of groundwater came close to private wells. • Hydrochemically, these groundwaters are classified into three types; • - Alkaline earth waters with increasing portion of alkalis and prevailing chloride. This type is characterized by a high concentration of chloride and represents 61.9% from the collected water samples. - Alkaline waters with prevailing chloride . this type of waters represents 33.3% from the collected water samples. - Alkaline earth with prevailing chloride, which represents only 4.8% of the waters. The present groundwater problems of overdraft and salinity increase are largely caused by inaccurate early estimates of the resource potentiality and inadequate management practices. Recommendations • As the quality of groundwater is a general problem, the government authorities strongly advised to protect water supply over the long term. • The groundwater quality management should be attempted in the study area. • Decrease the use of fertilizers and use the modern method in irrigation. • Closing of wells yielding brakish water. ‫ ﺷﻤـــﺎل اﻷردن‬,‫اﺳпє�п»�пєјпєЋШЎ ﺟﻴﻮﻛﻬﺮﺑﺎﺋﻲ Щ€ ﻫﻴﺪروﻛﻴﻤﻴﺎﺋﻲ п»“п»І п»Јп»Ёп»„п»�пє” اﻟﺤــﻼﺑﺎت‬ ‫ ﻧﺒﻴــــﻞ ﻋﺒﺪاﻟﺮﺣﻤﻦ‬،‫ пєЈп»њЩЂЩЂЩЂЩЂЩЂЩЂЩЂп»ў ﻣﺼﻄﻔــــــــﻰ‬،‫ﻏﻨﻴﻢ ﻧﺎﺷﺮ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ ﻟﺪراﺳﺔ‬،‫ ﺷﻤﺎل п»Џпє®ШЁ اﻷردن‬،‫ﺗﻢ ШҐпєџпє®Ш§ШЎ Ш§пєіпє�п»�пєјпєЋШЎ ﺟﻴﻮﻛﻬﺮﺑﺎﺋﻲ وﻫﻴﺪروﻛﻴﻤﻴﺎﺋﻲ п»“п»І п»Јп»Ёп»„п»�пє” اﻟﺤﻼﺑﺎت‬ ‫ اﻟﻤﻨﻄп»�пє” Щ€Ш§п»—п»Њпє” пє—пє¤пє– п»Јп»ЁпєЋШ® ﺷﺒﻪ‬.‫ Щ€пє—пє¤пєЄп»іпєЄ п»—пєЋпє‘п» п»ґпє” пє—п» п»љ اﻟﻤﻴﺎه п»№п»Џпє®Ш§Ш¶ Ш§п»џпєёпє®ШЁ Щ€Ш§п»џпє°Ш±Ш§п»‹пє”вЂ¬ШЊвЂ«пє—п»¤п» пєў اﻟﻤﻴﺎه Ш§п»џпє п»®п»“п»ґпє”вЂ¬ ‫ ﻳﻈﻬﺮ ﺗﻔﺴﻴﺮ ﻣﻌﻄﻴﺎت اﻟﻤﺴﺢ اﻟﻜﻬﺮﺑﺎﺋﻲ‬.‫و п»іпє�п»ў Ш§пєіпє�пєЁпє®Ш§Ш¬ اﻟﻤﻴﺎه ШҐп»ЈпєЋ ﻣﻦ пє—п»њп»®п»іп»ЁпєЋШЄ Ш§п»џпє’пєЋШІп»џпє– ШЈЩ€ اﻟﻜﺮﺑﻮﻧﺎت‬,‫ﺟﺎف‬ ‫ ﺣﻴﺚ Ш§пє§п»”пєѕ ﻗﻴﻢ‬،(‫ م‬130 – 55) ‫أن Ш§п»џп»„пє’п»�пє” Ш°Ш§ШЄ اﻟﻤп»�ﺎوﻣﻴﺔ اﻟﻤﻨﺨﻔﻀﺔ пєЈпєЄШЇШЄ п»‹п» п»° أﻋﻤﺎق пє—пє�пє®Ш§Щ€Ш пє‘п»ґп»¦вЂ¬ ‫ Щ€ ﻳﻈﻬﺮ ШЈп»іп»ЂпєЋЩ‹ Ш§п»»пє—пєјпєЋЩ„ ﺑﻴﻦ‬.‫ Щ€ п»«п»І ШЈп»›пє’пє® ﻋﻤп»�пєЋ Щ‹ п»“п»І Щ€пєіп»‚ п»Јп»Ёп»„п»�пє” اﻟﺪراﺳﺔ‬.(‫ م‬.‫ اوم‬20 ‫اﻟﻤп»�ﺎوﻣﻴﺔ )ШЈп»—п»ћ ﻣﻦ‬ ‫اﻟﻤﻴﺎه Ш§п»џпє п»®п»“п»ґпє” п»Јп»Љ Ш§п»џпєґп»„пєў Щ€Ш§п»џпє�п»І пє—п»Њп»њпєІ ШЇЩ€Ш± اﻟﻤﻴﺎه Ш§п»џпє®Ш§пєџп»Њпє” ﻣﻦ Ш§п»»пєіпє�пєЁпєЄШ§Щ… п»“п»І Ш§п»џпє°Ш±Ш§п»‹пє” п»“п»І ШІп»іпєЋШЇШ© п»Јп» п»®пєЈпє” اﻟﻤﻴﺎه‬ ‫ ﺗﺒﻴﻦ Ш§п»џпє�ﺤﺎﻟﻴﻞ اﻟﻜﻴﻤﻴﺎﺋﻴﺔ ﻟﻌﻴﻨﺎت اﻟﻤﻴﺎه ШЈЩ† п»Јпє�п»®пєіп»‚ ﺗﺮﻛﻴﺰ Ш§п»џпєёп»®Ш§Ш±ШЇ )اﻷﻳﻮﻧﺎت( اﻟﻤﻮﺟﺒﺔ пє—п»њп»®Щ† п»‹п» п»°вЂ¬.вЂ«Ш§п»џпє п»®п»“п»ґпє”вЂ¬ ‫ ﺑﻴﻨﻤﺎ пє—п»њп»®Щ† п»џп» пєёп»®Ш§Ш±ШЇ )اﻷﻳﻮﻧﺎت( Ш§п»џпєґпєЋп»џпє’пє” п»‹п» п»°вЂ¬,‫اﻟпє�ﺮﺗﻴﺐ Ш§п»џпєјп»®ШЇп»іп»®Щ… < اﻟﻜﺎﻟﺴﻴﻮم < اﻟﻤﻐﻨﺰﻳﻮم < اﻟﺒﻮﺗﺎﺳﻴﻮم‬ ‫ пє—п»®пєџпєЄ пє›п»јпє›пє” أﻧﻮاع رﺋﻴﺴﻴﺔ п»џп» п»¤п»ґпєЋЩ‡ п»“п»І п»Јп»Ёп»„п»�пє” اﻟﺪراﺳﺔ‬.‫اﻟпє�ﺮﺗﻴﺐ Ш§п»џп»њп» п»®Ш± < اﻟﺒﻴﻜﺮﺑﻮﻧﺎت < Ш§п»џпєґп» п»”пєЋШЄ < Ш§п»џп»Ёпє�ﺮات‬ 88 Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan ‫ وﻣﻴﺎه п»—п» п»®п»іпє”вЂ¬ШЊ%61.9 ‫ ﻣﻴﺎه п»—п» п»®п»іпє” أرﺿﻴﺔ п»Јп»Љ ШІп»іпєЋШЇШ© п»“п»І ﺗﺮﻛﻴﺰ Ш§п»џп»њп» п»®Ш±п»іпєЄ ﺣﻴﺚ пє·п»њп» пє– п»ЈпєЋ ﻧﺴﺒпє�ﻪ‬،‫وﻫﻲ п»›пєЋп»џпє�ﺎﻟﻲ‬ ‫ Щ€Ш§п»џп»Ёп»®Ш№ اﻷﺧﻴﺮ Щ€п»«п»® ﻣﻴﺎه п»—п» п»®п»іпє” أرﺿﻴﺔ п»Јп»Љ ШІп»іпєЋШЇШ© ﺗﺮﻛﻴﺰ‬،%33.3 ‫ﻣﻊ ШІп»іпєЋШЇШ© ﺗﺮﻛﻴﺰ Ш§п»џп»њп» п»®Ш±п»іпєЄ Щ€пє·п»њп» пє– п»ЈпєЋ ﻧﺴﺒпє�ﻪ‬ ‫ Щ€пєџпєЄ ШЈЩ† Ш§п»џпє�ﺮاﻛﻴﺰ Ш§п»џп»Њп» п»ґпєЋ п»џп» п»¤п» п»®пєЈпє” пє—пє�пє®Ш§п»“п»– п»Јп»Љ Ш§п»џпє�ﺮاﻛﻴﺰ Ш§п»џп»Њп» п»ґпєЋ п»џп» п»Ёпє�пє®Ш§ШЄ ﻓﻲ‬.%4.8 вЂ«Ш§п»џп»њп» п»®Ш±п»іпєЄ Щ€пє·п»њп» пє– п»ЈпєЋ ﻧﺴﺒпє�ﻪ‬ ‫ Щ€Ш§п»џпє�п»І пє—п»Њпє�пє’пє® اﻟﻤﺼﺎدر اﻟﺮﺋﻴﺴﻴﺔ‬،‫ п»іпє®пєџп»Љ пє—п» п»®Ш« اﻟﻤﻴﺎه Ш§п»џпє п»®п»“п»ґпє” пє‘пєЋп»џп»Ёпє�пє®Ш§ШЄ Щ€Ш§п»џп»њп» п»®Ш±вЂ¬.‫اﻵﺑﺎر Ш§п»џпєЁпєЋпє»пє” п»“п»І اﻟﻤﺰارع‬ ‫ اﻟﻤﻴﺎه ﻏﻴﺮ ﻣﻨﺎﺳﺒﺔ‬.‫ ШҐп»џп»° Ш§п»»пєіпє�пєЁпєЄШ§Щ… اﻟﻤﻔﺮط ﻟﻸﺳﻤﺪة Щ€Ш§п»џп»Ђпє¦ Ш§п»џпє пєЋпє‹пє® ﻣﻦ Ш§п»µпє‘пєЋШ± اﻟﺨﺎﺻﺔ‬،‫ﻻزدﻳﺎد Ш§п»џп»¤п» п»®пєЈпє”вЂ¬ ‫ ШЈп»ЈпєЋ п»џп»ёп»Џпє®Ш§Ш¶ اﻟﺰراﻋﻴﺔ ﻓﻴﻤﻜﻦ ШҐпєіпє�ﺨﺪاﻣﻬﺎ ﻧпє�п»ґпє пє”вЂ¬ШЊвЂ«п»·п»Џпє®Ш§Ш¶ Ш§п»џпєёпє®ШЁ пє‘пєґпє’пєђ Ш§п»џп»�ﻴﻤﺔ اﻟﻤﺮﺗﻔﻌﺔ ﻧﺴﺒﻴﺎً п»џп» п»Ёпє�ﺮات‬ ‫ وﻟﻜﻦ пє—пє¤пє�пєЋШ¬ اﻟﻤﻴﺎه ШҐп»џп»° п»‹п»¤п» п»ґпєЋШЄ п»Јп»ЊпєЋп»џпє пє” п»№Ш±пєџпєЋШ№ ﺗﺄﺛﻴﺮ Ш§п»џп»¤п» п»®пєЈпє” Щ€Ш§п»џпє�п»ІвЂ¬ШЊвЂ«п»џп» п»�ﻴﻤﺔ اﻟﻤﻨﺨﻔﻀﺔ п»·пє›пє® اﻟﺼﻮدﻳﻮم‬ .ً‫ﺗпє�пє®Ш§Щ€Ш п»Јп»¦ ﺗﺄﺛﻴﺮ п»Јпє�п»®пєіп»‚ ШҐп»џп»° п»‹пєЋЩ„ ﺟﺪا‬ References [1] MacDonald S. M. and Partners in Cooperation with technical Service LTD. Wadi Dhuleil investigation (stage-I). WAJ, Amman, Jordan, 1964. [2] MacDonald S.M.and Partners in Cooperation with technical Service LTD., Wadi Dhuleil investigation (stage-II). WAJ, Amman, Jordan, (1965). [3] MacDonald,S.M.and Partners in Cooperation with Hunting Technical Services LTD. Wadi Dhuleil irrigation project, hydrology. WAJ, Amman, Jordan, (1966). [4] Abu Obeid H., Hydrology of Dhuleil area. NRA, Amman, Jordan, (1967). [5] Abu Obeid H., Salinization of groundwater in Dhuleil – Hallabat area. National Resources Authority (NRA), Amman, Jordan, (1972). [6] Al-Zabet T. G., Two dimentional finite element model for groundwater flow of Dhuleil – Hallabat system. Department of Geology University of Jordan, Jordan, (1993). [7] Salameh E., Water Quality Degradation in Jordan. (impacts on environment, economy, and future generations resource base). Royal Society for Conservation of Nature, Amman, Jordan, (1996). [8] Bajjali W., Using Arc View GIS to determine the origin of groundwater salinity in Dhuleil, Hallabat and, Samra Area of Jordan. ESRI user conference , San Diego, CA, USA, (1997). [9] Al-Bis A. A., Hydrogeological and geophysical investigation on the upper aquifer system in Dhuliel- Hallabat Area (Jordan). Department of Geology University of Jordan, Jordan, (2000). [10] Bender F., Geologie von Jordonien. Gebrueder Borntraeger, Berlin, Stuttgart, (1968). [11] Piper H., Hydrogeology study of the Wadi Dhuleil area. Msc. Thesis, London, (1966). 89 Ghunaim S. Nasher; Hakam A. Mustafa; Nabil Abderahman [12] Parker D. H., Investigation of the sandstone aquifers of east Jordan: The hydrogeology of the Mesozoic-Cainozoic aquifers of the western highlands and plateau of east Jordan. FAO/UNDP.Rome, (1970). [13] Boom Den V. and Suwwan O., Report on the geological and petrological studies of the plateu basalts, Arch. Bundesanst, F. Bodenforsch Hannover. (1966). [14] BGR, WAJ. 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[34] Todd D., Groundwater Hydrology. 2nd edition. John Wiley and Sons, Canada, (1980). [35] Sawyer C. and Mc Carty P., Chemistry of Salinity Engineers. Mc Graw-Hill, New York, (1967). [36] Jordan Standards, Jordanian Standards for drinking water, Ministry of Industry, (1990) 6. [37] Karanth K. R., Groundwater Assessment, Development and Management. Tata McGraw Hill, New Delhi, (1987). [38] Wilcox L. V., Classification and use of irrigation waters. U.S Dept. of Agr, (1955). 91 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 93-103 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan. Talal Al-Momani* 1 Received on April 24, 2006 Accepted for publication on Dec. 10, 2006 Abstract The results indicated that minimum negative environmental impact of exploration, prospecting, testing, processing and treatment stages for the Hiswa clay deposit expected in the present time if mining and processing take place in the Hiswa area, South Jordan. This study indicated that the mining area is suitable to extract kaolinite as a major product, taking into consideration the availability of the raw material, energy supply, water supply, transportation facilities, and the absence of any rare or protected flora and fauna. Keywords: Environmental Impact Assessment (EIA); Clay Deposits; Hiswa; Jordan. Introduction: Clays have always played a major role in human life. Kaolin is one of the most common examples of clay minerals and important natural industrial substances. This is largely because of their wide-ranging properties, high resistance to atmospheric conditions, and easy access to their deposits near the earth’s surface and low price (Konta, 1995)[1]. Kaolin is a commercial term to describe white clay composed essentially of the clay mineral kaolinite. The term is typically used to refer to both the raw clay and the refined commercial product. Kaolin is a naturally occurring white mineral. It is relatively inert when mixed with other materials and has unique flow characteristics when incorporated or mixed with liquids or placed in fluid systems such as paints and paper industry. In addition, raw kaolin has few practical uses. Industrial beneficiation is necessary in order to separate non-clay minerals from the kaolin. Clay industry in common with open cast mining has some basic environmental effects on the surrounding area. There are visual and other impacts of both clay extraction and processing. The whole process may interrupt the existing land uses and may pose difficult restoration problems if permanent change in land use is to be avoided. In general, the exploration phase involves little or no permanent environmental damage. The impact of mineral exploitation on the environment depends upon factors such as mining procedure, local hydrologic conditions, climate, rock types encountered, size В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Earth and Environmental Sciences, Faculty of Science, Yarmouk University, Irbid, Jordan. Al-Momani of operation, topography, and many more interrelated factors. Furthermore, the impact varies with the stage of development of the resources. According to Ward (1992)[2]; John et. al. (1994)[3]; Peter and Riki (1995)[4]; and Larry (1996)[5], environmental impact assessment (EIA) constitutes one of the prime instruments for development planning and resource management. This paper sets the groundwork for the environmental impact assessment (EIA) of mining activities of the Hiswa area, South Jordan. The main benefits of introducing environmental impact assessment (EIA) are as follows: - Achieving a balance between environmental protection and economic development; - Better environmental resources management and minimization of wasted time, money and raw materials; - Prevention of pollution and improvement in health and safety standards; and - Improved environment for future generations. Location and Geological Setting of the Study Area The study area lies in Aqaba Region, and it is situated in southern Jordan. The area is located 20 km to the southeast of Ad-Disa Village at a distance of about 100 km east of Aqaba (Figure 1). The principal geological sequences cropping out in the study area are of Paleozoic age. Three formations are cropping out in the study area, with a general dip towards the southeast. These are from bottom to top (Khalil, 1994) [6]: 1- Umm Sahm Sandstone (Bedded brownish weathered sandstone) Formation. 2- Hiswa Sandstone (Graptolite sandstone) Formation. 3- Dubaydib Sandstone (Sabellarifex sandstone) Formation. The Hiswa Sandstone (Graptolite Sandstone Formation) of Khreim Group is subdivided into the Shale Member and the Sandstone-Siltstone Member. The Shale Member consists of kaolinite of various colors, which range from light gray, dark gray, violet, brown-red, and red. Environmental Impact Assessment (EIA) Guidelines The environmental impact assessments (EIA) of mining activities were investigated by many authors in different areas around the world. This study is based on the available data related the environmental impact assessment (EIA) guidelines issued by Patnaik (1990)[7]; Trivedy and Sinha (1990)[8]; Johnson and Sides (1991)[9]; Environmental Protection Agency (EPA) (1995)[10]; Sadar, (1996)[11]; and the General Corporation for the Environmental Protection (1999)[12]. 94 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Results and Discussion Table (1) summarized the environmental impact assessment (EIA) of mining activities of the Hiswa area. Exploration and Prospecting The environmental impact of exploration, prospecting and testing stages for the Hiswa clay deposit are usually non significant, but in some cases the mentioned stages may involve, for instance, drilling operations with significant noise and vibration. Selection of the Mine Site and Site Preparation The determination of the most suitable location of the mine site is critical. The clay deposits in Hiswa Formation - South Jordan were first investigated by Jordanian Company for Mining and Processing of Kaolin and Feldspar in 1995. The preliminary investigations have recommended an exploration program for kaolin deposits in the area. According to the economic viability and environmental impacts of clay deposits from Hiswa area, this area is suitable to extract kaolinite as a major product; this is based on the availability of raw materials; energy supply; water supply; appropriate transportation facilities. In addition, the absence of any rare or protected flora and fauna and the absence of negative impact on human settlements. On the other hand, the company has started mining the area since 1997 on a small mining scale for the production of commercial kaolin. In addition, the company carried out the following activities: Land acquisition and transformation; construction excavation of access secondary roads; construction of transmission lines and pipelines; construction of offices, housing and other services for the labor forces; construction of material storage; construction of electrical energy supply; and construction of water supply. Mining Operations and Transportation Impact The Jordanian Company for Mining and Processing of Kaolin and Feldspar has constructed a suitable plant for mining and simple processing operations (breaking, crushing, screening, and loading). Most of the study area is readily accessible and is crossed by the Aqaba-Ma’anAmman Highway in the northwest, by the Aqaba - Batn El Ghul - Hisa railway from the northwest to northeast, and by the El Rashdiah - Qa’Disi - Ram asphaltic road. Currently, transportation services mainly associated with the Port of Aqaba, the road transport link to Amman, airport of Aqaba and the railway services (Figure 1). The present road situation is quite satisfactory with the exception of necessary improvements to the Hiswa-Ma’an road and some secondary roads. See Table (1). 95 Al-Momani Figure (1): Location map of the study area. 96 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Table (1): Environmental impact assessment of Hiswa clay deposits (Based on Sadar (1996)[11]). Impacting Actions Environmental Parameters Air quality Water resources Water quality Noise and vibration Land use Vegetation Human settlement Health Infrastructure and support services Employment Places of tourist or archaeological importance KEY: + sign shows beneficial impact - sign shows adverse impact • sign shows impact must be monitored and mitigated Ої sign shows no impact * Pre-mining Phase A – Land acquisition and transformation B – Civil works construction C – Erection of mechanical and mining equipment Pre-mining Phase* A B C Ої Ої Ої Ої Ої Ої Ої Ої Ої Ої + + + Ої Ої Ої + + + Ої Ої Ої + + + + + + D • Ої • + Ої + • + + E Ої Ої • Ої Ої Ої Ої • Ої Ої F • Ої • Ої Ої Ої Ої • Ої Ої G Ої Ої Ої + + Ої + + + + H Ої + + Ої + + + + + + I • Ої Ої + Ої • • + + J Ої Ої Ої Ої Ої Ої + + + + K + + + Ої + + + + + + Ої Ої Ої Ої Ої Ої Ої Ої Ої Ої Ої Operational Phase** ** Operational Phase D - Mining operations E - Disposal of liquid effluent F- Disposal of solid wastes on land for reclamation G - Housing provision H - Provision of water, sewage, electricity and other civic amenities I - Transportation J - Medical facilities K - Land reclamation Water Supply Impact Ground water resources are available in the region. According to Salameh (1996)[13], Jafr groundwater basin is subdivided into Jafr and Disi-Mudawwara aquifer systems. The study area lies within the Disi aquifer system. The Disi aquifer consists of medium- to - fine grained sandstones with a total thickness of about 1000 meters. The average precipitation over the area is around 80 mm/year, with an average potential evaporation of 4000 mm/year. The groundwater in the Disi area is unconfined and lies at a depth of around 80 meters below the surface. At present, it is generally accepted that the groundwater in Disi area does not receive major replenishment. This means that the groundwater in the aquifer is fossil and that its extraction is at the expense of storage. 97 Al-Momani In order to meet the needs of commercial kaolinites, low-grade kaolinite is fed to beneficiation plants to produce high-grade kaolinite. The intensive use of water for wet processing and production of clay deposits cause a significant water shortage. Accordingly, water must be recycled in the beneficiation plants, but when it becomes rich in impurities, the water must be treated for reuse. Pollution control and recycling of water, which emphasizes the need for delineation, water protection areas in order to safeguard groundwater resources. Air Quality and Dust Impact The main air pollution problem in the surface mining is dust. The dust pollution may have significant impacts on vegetation, soil, equipment, and most importantly, on human health. There are various methods available to prevent or minimize dust emission. These include the use of cyclones, filters, and other pollution control technologies, water sprays, and paving roads. These methods are considerable choices, which will be helpful to eliminate the dust impact and to conserve the environmental medium in Hiswa area almost clean. Noise and Vibration Impact Drilling and heavy machinery are used regularly at mining sites, resulting in potentially harmful amounts of noise pollution. Miners subject to high noise levels for extended periods of times may become permanently deaf. The European Community has set limits for daily exposure at 85 decibels with no peak sounds above 140 decibels (Environmental Protection Agency, 1995)[10]. Noise levels can be monitored and steps should be taken to reduce volumes where appropriate. Ear plugs or other noise-dampening devices may be appropriate for employees in some cases. Ecology (Wildlife), Agriculture and Land Use The Royal Society for Conservation of Nature have indicated that there are no species of wildlife or plant life in the study area that have any protected national or international status. Accordingly, no unique habitat or species will be lost. On the other hand, agricultural activities are negligible at present in the study area. Tourism, Archaeology and Heritage Tourism plays an important role in the national economy. The most important tourist sites in South Jordan with national and international significance are Aqaba’s beaches and marine life, the ancient Nabatean city of Petra and the unique desert landscape of Wadi Rum. These sites will not be affected by mining activities of Hiswa area. There is no archaeological site in the study area. The major archaeological site in the region is Wadi Rum (approximately 30 km) from the study area. The Hiswa mining and processing activities will not affect the site. 98 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Drainage and Topography Impacts Most of the study area has an altitude of 860 to 940m. The eastern part has a lower relief compared to the western part. The topography of the area shows decrease in the eastern direction. Accordingly, land reclamation is highly important after the life-time of mining stage. Socio-economics Impacts (e.g. population, employment): The Hiswa clay deposit area is deserted. Mining activity in the area will attract workers and would contribute to reducing unemployment. In addition, the increase of income is expected for some people from the surrounding areas. See Table (1). Safety A serious problem associated with mineral resources development is the possible release of trace elements in hazardous concentrations into the environment. Trace elements such as cadmium, cobalt, copper, lead, molybdenum, and others when leached from mining wastes and become concentrated in water, soil, or plants, may be toxic or may cause diseases to people and other animals who drink the water, eat the plants, or use the soil (Keller, 1985[14] Patnaik, 1990[7]; Montogomery, 1995[15]; Murck et al., 1996[16]). Table (2): Minimum, maximum, and average values for the different trace elements of the whole rock samples of Hiswa clay deposits compared with the standard shales and the deep-see clays. Trace elements (ppm) Ba Hiswa clay deposits Maximum Average (ppm) (ppm) 421 264 Standard Deep-sea shales* clays* (ppm) (ppm) 580 2300 0.3 0.43 Cd 5 18 13 3.98 0-11** 0.1-1** Co 8 52 26 8.96 19 74 17.80 90 90 Cr 50 115 75 30-590** 90** 45 250 Cu 55 154 104 28.67 18-120** 250** Ni 63 225 123 35.61 68 225 20 80 Pb 45 220 139 41.67 16-50** 80** Rb 43 117 95 15.03 140 -Sr 47 161 86 22.50 300 180 V n.d n.d n.d --130 120 95 165 Zn 30 195 109 44.64 18-180** 165** * (Forster and Wittmann, 1983[17] ; Bowie and Thornton, 1985[18] ; and Montogemry, 1995[15]). ** (Keller, 1985[14] ). Minimum (ppm) 150 Standard deviation 58.06 Table (2) shows the trace elements (Ba, Co, Cr, Cu, Ni, Rb, Sr, V, and Zn) in the studied whole rock samples are low when compared with the standard shales and the deep-see clays. In addition, lead and cadmium (Pb and Cd) occur relatively in high 99 Al-Momani amounts. It is important to relate trace elements to human use (Tables 3 and 4). Accordingly, geochemical studies are vital to determine the prevalence of such elements, so that proper human adjustments can be made. In addition, monitoring the presence of high concentration of trace elements in water results from mine wastes and smelters is highly important. Table (3): Comparison between the different trace elements (ppm) of the Hiswa clay deposit and different commercial clays. Trace elements (ppm) Ba Clays* Natural Average Clay* Average (Hiswa Clay) Standard shales** Commercial Pharmaceutical 248 147 75 580 264 Cd 0.18 0.02 1.3 0.3 13 Co 13.3 5 28 19 26 Cr 81.6 5.4 96.8 90 75 Cu 16.7 4.71 154 45 104 Ni 40 5 324 68 123 Pb 11.9 8.01 27 20 139 Rb 83 11 32 140 95 Sr 695 100 42 300 86 300 V 109 24 749 130 127 Zn 61 9 58 95 109 130 95 18-180*** 580 0.3 0-11*** 19 90 30-590*** 45 18-120*** 68 20 16-50*** 140 * (Mascola et al., 1999) [19]. ** (Forster and Wittmann, 1983; Bowie and Thornton, 1985; and Montogemry, 1995). *** (Keller, 1985). Table (4): Trace elements guidelines for soil quality; water quality and average body concentration. Trace elements Ba Cd Co Cr Cu Ni Pb Rb Sr V Zn *Guidelines for soil quality Levels for agricultural use (Вµg/gram) 750 3 40 750 150 150 375 --200 600 Levels for industrial use (Вµg/gram) 2,000 20 300 800 500 500 1,000 ---1500 * (Dublanc, 1998) [20] ** (Montogomery, 1995). [15] 100 *Guidelines for water quality Levels for irrigation use (Вµg/litre) **Average body concentration (ppm) 10 50 100 200 200 200 --100 2,000 -0.7 0.02 0.03 1.0 0.1 ----33 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Conclusion Mining and processing of mineral resources may have a considerable impact on the land, water and, air. What must be done is to develop resources with a minimum of adverse impact. Minimum environmental impact of exploration, prospecting, testing, processing and treatment stages for the Hiswa clay deposit expected in the present time if mining and processing take place in the Hiswa area. The mining area is suitable to extract kaolinite as a major product, taking into consideration the availability of the raw material, energy supply, water supply, transportation facilities, and the absence of any rare or protected flora and fauna. Many problems and adverse effects can be mitigated by integrating environmental consideration into the overall planning and by the development of balanced, well-worded and enforceable planning conditions. The pollution control essentially involves good environmental management in mining activities combined with adequate training and education of the workers as well as other people in society. In addition, monitoring the presence of high concentration of trace elements in water results from mine wastes and smelters is highly important. Jordan is rich in its industrial rocks and minerals. The problem is that most of the natural commodities are not evaluated for their industrial use and environmental impacts. The exploration and evaluation of Jordanian raw materials for industrial use is an important step for encouraging new industries. At the same time, the environmental impact assessment, environmental planning and environmental legislation and enforcement of future mining, beneficiation, and industrial use must be carried out for these commodities. On the other hand, the demand for clay mineral resources in Jordan is going to increase. Accordingly, planning, management, training, and education must be given a top priority. In addition, one of the most important strategies of kaolin production concerning the future generations is the environmental impact of mining and processing. Environmental protection and land reclamation must take a special attention. 101 Al-Momani .‫ пєџп»Ёп»®ШЁ اﻷردن‬،‫ﺗп»�ﻴﻴﻢ Ш§п»·пє›пє® اﻟﺒﻴﺌﻲ п»џпє�п»®пєїп»ЊпєЋШЄ пєЈпєјп»®Ш© اﻟﻄﻴﻨﻴﺔ‬ ‫ﻃﻼل ﻣﺤﻤﺪ اﻟﻤﻮﻣﻨﻲ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫أﺷﺎرت Ш§п»џп»Ёпє�пєЋпє‹пєћ пє‘пє„Щ† Ш§п»·пє›пє® اﻟﺒﻴﺌﻲ Ш§п»џпєґп» пє’п»І Ш§п»џп»ЁпєЋпє—пєћ ﻋﻦ п»‹п»¤п» п»ґпєЋШЄ Ш§п»»пєіпє�п»њпєёпєЋЩЃ Щ€Ш§п»џпє�п»Ёп»�ﻴﺐ Щ€п»Јпє®Ш§пєЈп»ћ п»Јп»ЊпєЋп»џпє пє”вЂ¬ ‫وﺗﺮﻛﻴﺰ пє—п»®пєїп»ЊпєЋШЄ пєЈпєјп»®Ш© اﻟﻄﻴﻨﻴﺔ ﺳﻴﻜﻮن п»Јпє¤пєЄЩ€ШЇ ШҐШ°Ш§ ﺗﻤﺖ п»«пє¬Щ‡ Ш§п»џп»Њп»¤п» п»ґпєЋШЄ п»“п»І Ш§п»џп»®п»—пє– Ш§п»џпє¤пєЋпєїпє® п»“п»І п»Јп»Ёп»„п»�ﺔ‬ .‫ﺣﺼﻮة – пєџп»Ёп»®ШЁ اﻷردن‬ ‫ﻛﻤﺎ ШЈпє·пєЋШ±ШЄ Ш§п»џпєЄШ±Ш§пєіпє” ШҐп»џп»° ШЈЩ† п»Јп»Ёп»„п»�пє” Ш§п»џпє�ﻌﺪﻳﻦ п»Јп»ЁпєЋпєіпє’пє” п»»пєіпє�пєЁпє®Ш§Ш¬ اﻟﻜﺎوﻟﻴﻨﺎﻳﺖ Щ€Ш°п»џп»љ п»џпє�п»®п»“пє® اﻟﻤﻮاد اﻟﺨﺎم‬ ‫وﻣﺼﺪر Ш§п»џп»„пєЋп»—пє” Щ€пє—п»®п»“пє® اﻟﻤﻴﺎه Щ€Щ€пєіпєЋпє‹п»ћ Ш§п»џп»Ёп»�п»ћ ШҐпєїпєЋп»“пє” ШҐп»џп»° пє§п» п»® اﻟﻤﻨﻄп»�пє” ﻣﻦ Ш§п»џп»њпєЋпє‹п»ЁпєЋШЄ اﻟﺤﻴﺔ اﻟﺤﻴﻮاﻧﻴﺔ واﻟﻨﺒﺎﺗﻴﺔ‬ .‫اﻟﻤﺤﻤﻴﺔ ШЈЩ€ اﻟﻨﺎدرة‬ References [1] Konta J., Clay and Man: Clay Raw Materials in the Service of Man. Applied Clay Science, 10(1995)275-335. [2] Ward M. H., Mining and the Environment. Mineral Industry International, (1992) 33-41. [3] John G., Riki T. and Andrew C., Introduction to Environmental Impact Assessment : Principle and Procedure, Process, Practice and Prospects. UCL, London, (1994). [4] Peter M. and Riki T., Methods of Environmental Impact Assessment. UCL, London, (1995). [5] Larry W. C., Environmental Impact Assessment. McGraw-Hill, New York, (1996). [6] Khalil B., The Geology of Ad-Disa Area (Qannassiya), Map Sheet No 3149 III. Bulletin 26. Geology Directorate, Geological Mapping Division, Natural Resources Authority (NRA), Amman, Jordan, (1994). [7] Patnaik L. N., Environmental Impact of Industrial and Mining Activities. Ashish Publishing House, New Delhi, (1990). [8] Trivedy R. K. and Sinha M. P., Impact of Mining on Environment. Ashish Publishing House, New Delhi, (1990). 102 Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan [9] Johnson M. S. and Sides A., Environmental Assessment of New Mining Projects – Code of Practice for Appointment and Manegement of Environmental Consultants. Mining Industry International, (1991) 13-17. [10] Environmental Protection Agency., Profile of the Non-fuel, Non-metal, Mining Industry. EPA 310-R95-011, USA, (1995) [11] Sadar M. H., Environmental Impact Assessment. Carleton University Press, Canada, (1996). [12] General Corporation for the Environment Protection., Environmental Impact Assessment. GCEP, Amman, (1999). [13] Salameh, E., Water Quality Degradation in Jordan (Impact on Environment, Economy and Future Generations Resources Base). The Higher Council of Science and Technology, Amman, (1996). [14] Keller E. A., Environmental Geology. Charles, E. Merrill Publishing Company, USA, (1985). [15] Montogomery C. W., Environmental Geology. Wm. C. Brown Publisher, USA, (1995). [16] Murck B. W., Skinner B. J. and Porter S. C., Environmental Geology. John Wiley and Sons, UK, (1996). [17] Forstner U. and Wittmann G. T. W., Metal Pollution in the Aquatic Environment, 2nd. Edition. Springer-Verlag. Berlin, (1983). [18] Bowie S. H. U. and Thornton I. (editors), Environmental Geochemistry and Health. 1st. edition. D. Reidel Publishing Company, Holland, (1985). [19] Mascolo N., Summa V. and Tateo F., Characterization of Toxic Elements in Clay for Human Healing Use. Applied Clay Science, 15 (1999) 491-500. [20] Dublanc E., Argentina’s Mining and Environmental Legislation. Industrial Minerals, (1998) 98-104. 103 Directives for ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 105-122 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Aymen Issa Zreikat* 1 Received on April 22, 2006 Accepted for publication on Oct. 1, 2006 Abstract In this paper, performance evaluation of one UMTS cell is presented. The UMTS stands for Universal Mobile Telecommunication Systems, the third generation of mobile networks. The queuing model of one UMTS cell is suggested and solved for the first time using MOSEL-2 language, which is the new version of MOSEL, developed by the group of MOSEL in the University of Erlangen, Germany. The pre-processor rule of MOSEL-2 is used in this paper, which is useful to solve the model using both exponential and non-exponential distributions. The effect of important parameters on UMTS performance is studied in this analysis, such as the variability of service time, the availability of the codes and the effect of the arrival rate, О». It is shown that the mentioned parameters have a major effect on UMTS performance and should be taken into consideration by the network designers. Based on the above, critical performance measures such as blocking probability and utilization are found and discussed. Keywords: MOSEL-2 language, Performance Modelling, Performance Measures, Queuing Model, UMTS systems. Introduction European Telecommunications Standard Institute (ETSI), found in 1998, is working in Europe to develop technical standards for UMTS. The Third Generation Partnership Project (3GPP) is a co-operation between international standard bodies and third generation mobile telephony technical specifications [1-3]. The UMTS is one of the Third Generation (3G) cellular systems being developed within the framework defined by the ITU (International Telecommunications Union) and known as IMT-2000 (International Mobile Telephony, 3rd generation networks are referred to as IMT-2000 within ITU). It is a realization of a new generation of broadband multi-media mobile telecommunications technology. The UMTS technology demands a very high amount of system simulation and modelling, not only because of the involved novelty inherent to the interaction between the traditional IP systems and the new W-CDMA technology used in the air interface, but also because of the complexity of the UMTS radio interface. The new technology В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Information Technology, Mu’tah University, Al-Karak, Jordan. Zreikat offers improvements from a radio resource allocation perspective. Extensive efforts are necessary to optimize the main algorithms and to efficiently plan the network to be deployed. The interaction between typical IP and wireless worlds requires simulation of the complete end-to-end system modelling, to determine the network performance and the quality of service available to UMTS customers at the application level. In previous works [4-10], the performance of the UMTS cell is studied either by simulation [4][5], or by finding the analytical solution [6-10], without presenting the queuing model. Significantly, in this paper, the queuing model of a single UMTS cell is presented and the numerical solution of different zones is found. The shared buffer queuing system with different virtual zones is solved numerically using the Modelling Specification and Evaluation Language (i.e. MOSEL-2). The rest of the paper is organized as follows. In Section 2, the queuing model is presented. The set of modelling assumptions are listed in Section 3. MOSEL-2 environment is given in Section 4. In Section 5, the rule pre-processor of MOSEL-2 is presented. The description of the model by MOSEL-2 language is presented in Section 6. The numerical results and discussion are in Section 7, followed by the conclusions and the suggestions for the future work in Section 8. Queuing Model The multiple queuing system of the UMTS cell is given in Figure 1. This model is a SRXR (GE/GE/1)/N system which consists of R virtual zones. The SRXR (GE/GE/1)/N system is such a system that the overall inter-arrival times and service times at a RГ—R switch queue, are heterogeneous and GE (General Exponentially) distributed where each output port has a single server and the total capacity of the system is given. Each virtual equal zone is separated by a single channel and each zone includes a queue and a service. These queues are dependent on each other since the total number of connections in all zones cannot exceed nmax. Namely, in a permissible system state: R ∑ i =1 n i ≤ n m a x , where ni denotes the number of active connections in zone i. 106 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 R The condition: ∑ i =1 n i ≤ n m ax Figure 1: The shared buffer queuing model SRXR(GE/GE/c)/nmax of a UMTS system with R virtual single-channel zones. Modelling Assumptions The following assumptions are considered in the analysis: • Only one cell is considered. • Ideal free space propagation of the radio signal. • The interference factor to be equal for all code combinations. • Users within the considered cell are all using the same radio service. • No movement is considered. • The power gains of node B antenna and mobile equipment antenna to be 1. • The call arrival process is a Poisson process. • An exponentially distributed and general exponentially distributed burst size within each active connection is assumed for both the arrival and the service times. • The overall traffic intensity over the cell area is О». 107 Zreikat The cell area is virtually divided into R concentric zones of equal areas. Only four zones are considered in this analysis. When the number of zones increases, the state space increases dramatically, which leads to the state space explosion problem. Notations О» is the mean arrival rate of calls in the system . О»i is the mean arrival rate of calls going to Zone i, О»i = О» Г— Pi (i = 1, 2,..., R ). Pi is the probability that the call going to Zone i, Pi = 1/ R (i = 1, 2, ..., R ). C2a is the SCV(Squared Coefficient of Variation) of the inter-arrival time distribution of those calls entering to the system . C2ai is SCV of the inter-arrival time distribution of those calls entering to Zone i (i = 1,2,…,R). C2si is the SCV of the transmission time distribution of Zone i, C 2 si = C 2 s (i = 1, 2,..., R). Вµi is the mean departure rate of Zone i, Вµi = Вµ (i = 1,2,…,R). Mosel-2 Environment The Modelling Specification and Evaluation Language version 2 (i.e. MOSEL-2) is similar to the predecessor MOSEL, which is developed at the university of Erlangen, Germany [11]. The main objectives behind MOSEL-2 language are to: • Provide system oriented language. • Have easy to understand and learn the language. • Be universally applicable, but with independent evaluation method. • Have a language which comprises translators for several (already existing), welltested and good performance evaluation tools. -The following 6 steps are to describe the work-flow of the performance evaluation procedure using MOSEL-2: 1. Inspecting the real system where the modeler builds a high-level, textual system description using the MOSEL2 specification language and specifies the desired performance and reliability measures. 2. The MOSEL2 environment checks the input file for syntactical and semantical errors. If no error occurs, the MOSEL2 model gets translated to the system description of the evaluation tool selected by the user. 108 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 3. The chosen tool is started by MOSEL2 environment. 4. The tool evaluates the model by using numerical analysis methods or discrete-event simulation. 5. The evaluation tool saves its results in one or more tool-specific output files. 6. The MOSEL2 environment provides the results in a single textual and graphical file. Figure 2 shows the above 6 steps explained graphically. Introducing General Distributions: the rule pre-processor In the old version of MOSEL, only Markovian models are allowed. Usually nonMarkovian models have to be evaluated using discrete-event simulation, which is a very time-consuming task. It is now possible to enable an approximate numerical analysis for a subclass of general distributions where their two first moments are: the mean and the variance. These are called subclass empirical distributions (EMP), because mean and variance can be obtained quite easily from measurements [12]. Figure 2: Modeling and analysis process in MOSEL2 environment [12]. It is possible to use an empirical distribution directly in MOSEL-2 by applying: EMP (mean, var), where mean is the mean and var is the variance of the firing time’s distribution. The rule can then be substituted by one or several sub-rules depending on the square coefficient of variation (SCV or c2) shown in Eq. (1): 109 Zreikat 2 c = var ( mean) 2 ............................................................................................... (1) If c2 equals one, the empirical distribution is equivalent to an exponential distribution. If it is greater than one, the distribution can be approximated by a general exponential distribution. If c2 is smaller than one, the distribution can be approximated by a hypo-exponential distribution. The following MOSEL-2 rule can be represented by the Petri Net shown in Figure3. FROM p1 TO p2 EMP (mean, var); The pre-processor rule has been applied in MOSEL-2 program (Figure 4, lines 21, 24-25). EMP (mean, var) Figure 3: Example for transition with empirical distribution firing times. MOSEL-2 Description The queuing model of Figure 1 can be follows. (See Figure 4). solved numerically by MOSEL-2 as The Mosel-2 description can be divided into 7 parts: 1. Constant and Parameter part (lines 2-15). 2. Node part (line 16). 3. Function part (unused in this example). 4. Condition (Assertion) part (line 17). 5. Rule part (lines 18-25). 6. Result part (lines 26-29). 7. Picture part (lines 30-40). 110 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 /*------------- UMTS.mos -------------------------*/ 1 /*------------- Contants and parameter part---------*/ 2 CONST R:= 4; 3 PARAMETER N:= 16,32,64; 4 @<1..R>{CONST p#:=1.0/R;} 5 @<1..R>{CONST N#:=p#*N;} 6 PARAMETER u:= 1,2,3,4,5,6,7,8,9,10; 7 PARAMETER lambda:=1,5,10; 8 @<1..R>{CONST mue#:= lambda/u;} 9 CONST Ca:=1; // SCV of inter-arrival time 10 PARAMETER Cs:=5,10,50; // SCV of service time 11 @<1..R>{CONST lambda#:=p#*lambda;} 12 @<1..R>{CONST mean_lambda#:=1.0/lambda#;} 13 @<1..R>{CONST mean_mue#:=1.0/mue#;} 14 @<1..R>{CONST var1# := Ca * (mean_lambda#*mean_lambda#);} 15 @<1..R>{CONST var2# := Cs * (mean_mue#*mean_mue#);} /*---------------NODES------------------------------- */ 16 @<1..R>{NODE S#[N#];} /*--------------------Assertion-----------*/ 17 ASSERT NOT (@<1..R>"+"{S#}) > N; /*-----Transition Rates (Rules Part) -------------------*/ 18 IF (@<1..R>"+"{S#}) < N 19 THEN 20 { 21 @<1..R>{FROM EXTERN TO S# EMP(mean_lambda#, var1#);} 22 } 23 @<1..R>{IF S#>0 24 FROM S# TO EXTERN 25 EMP(mean_mue#, var2#);} /*--------- Results ------------------------------*/ 26 @<1..R>{PRINT MEAN_S# := MEAN(S#);} 27 PRINT MEAN_T := @<1..R>"+"{MEAN_S#}; 28 PRINT blk_T := PROB((@<1..R>"+"{S#}) >= N); 29 PRINT util := (MEAN_T/N); 30 //----PICTURES------------------31 PICTURE "BLOCKING" 32 PARAMETER u 33 XLABEL "Traffic load, u [Erlang]" 34 YLABEL "Blocking" 35 CURVE blk_T 36 PICTURE "UTILIZATION" 37 PARAMETER u 38 XLABEL "Traffic load, u [Erlang]" 39 YLABEL "Utilization" 40 CURVE util Figure 4: MOSEL-2 Description 111 Zreikat The numerical solution in Figure 4 is explained by the following steps: • The assumed number of zones, R = 4 (line 2). • The assumed number of codes, N = SF x 2 = 16, 32 or 64 (line 3). In MOSEL-2, if we have more than one constant, the word “PARAMETER” is used instead of the word “CONST”. • Line 4 defines the probabilities (p1…p4) given in Figure 1. p1=p2=p3=p4 = Вј. • The maximum size of each node is defined in line 5 as follows: N1 = p1x N , N2 = p2 x N, N3 = p3 x N, N4 = p4 x N. • The traffic load is defined in line 6 as follows: u = 1,2,3,4,5,6,7,8,9,10. • “Lambda” in line 7 can take different values in turn: 1, 5 or 10. • Accordingly, the service rate for each server is computed in line 8. • Lines 9 and 10 assume different values to the square coefficient of variation for both the arrival (i.e. Ca) and service times (i.e. Cs). • Lines 11-13, the mean inter-arrival and mean service-time is computed. They are used in lines 14 and 15 to compute the variance (i.e. var) in Eq. (1). • Line 16 defines the nodes. As we have assumed that R = 4 zones, then 4 nodes should be defined with their maximum capacities. But the total capacity of all nodes should not exceed the total number of codes, N. This condition is tested in line 17 using the “ASSERTION” concept of MOSEL-2. • The transition rates of the queuing model of Figure 1 is written in MOSEL-2 in lines 18-25. This part defines the call admission control of the system. Line 18 checks whether there are available codes in the system. The transition triggers only if there are available codes in the system, otherwise the call is blocked. If the condition in line 18 is true, then the transition starts at line 21. As the “loop” concept is used here, the transition happens to each zone in turn. For example: Line 21 can be translated as: FROM EXTERN TO S1 EMP (mean_lambda1, var11); FROM EXTERN TO S2 EMP (mean_lambda2, var12); FROM EXTERN TO S3 EMP (mean_lambda3, var13); FROM EXTERN TO S4 EMP (mean_lambda4, var14); “FROM EXTERN” means that the call moves from the external population (outside) to the given zone (zone 1,…,zone 4) with rates defined by the pre-processor rule defined in Section 5 (i.e. EMP (mean, var)). In such a case, the rate can be 112 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 exponential or non-exponential, depends on the square coefficient of variation for both the arrival and service time (Ca and Cs, respectively). • In Lines 23-25, if there is a call in a given node and this call ends its service, then the call moves from the given node to the outside world with the transition rate which is given by the pre-processor rule defined above. Certainly, this applies to all nodes in the system. • The “result part" is given in lines 26-29. It uses the word “PRINT” to compute the mean of each server at line 26. In line 27, the total mean is computed. In line 28, the blocking probability is computed and in line 29, the total utilization of the system is computed. • The last part of the numerical solution is the “picture part”. In this part, the IGL program defined above is used to generate the required figures. In lines 30-35, the figure for the “blocking probability” is generated, while, lines 36-40 generate the “utilization” figure. In each figure, the same parameters are defined. “PARAMETER” gives the x-axis values of the given parameter (u is given here). “XLABEL” names the x-label, followed by the label name between double quotes. “YLABLE” names the y-label and “CURVE” defines the curve values of its followed name. A more detailed description of MOSEL-2 can be found in [15]. In order to avoid repetition, the “loop” concept is used in the above MOSEL-2 program. For example, line 4 in the above program: 4 @<1..R>{CONST p#:=1.0/R;} following 4 statements: CONST p1 := 1.0/R; CONST p2 := 1.0/R; CONST p3 := 1.0/R; CONST p4 := 1.0/R; could also be written in MOSEL-2 by the But repeating these four statements without using the "loop" concept is intractable and time-consuming. MOSEL-2 program can be written in any text editor, but the program has to be saved as “filename.mos” similar to the name which is written on top of the above MOSEL-2 program (i.e. UMTS.mos). MOSEL-2 program can then be compiled with the following DOS command: > mosel2 –options filename.mos The option ”-option” tells MOSEL-2 to translate the model to a specified evaluation tool: 113 Zreikat (i.e. “-cs” for SPNP [12][13], “-ms” for MOSES [14] or “-Ts” for TimeNET [15][16]. If the program is compiled successfully without any error, then MOSEL-2 will automatically generate two output files (i.e. result file “filename.res” and IGL file “filename.igl”). This is accomplished by the second option “-s” which orders MOSEL-2 to generate the suitable outputs. One can then browse the result file to see the results of different performance measures. Additionally, to visualize the results by IGL file, the following command line is used: > igl filename.igl Additionally, the comments in MOSEL-2 can be written between “/* */” or after “//”. For example, lines 1 and 9 of Figure 4 are examples of using different comments in MOSEL-2 language. Numerical Results and Discussion The numerical results are divided into four groups with two figures in each group. One figure is for the blocking probability and the other is for the utilization. The effect of the three main parameters are discussed in this analysis. The assumed parameters are given in Table 1. The effect of the variability of service time Four figures are considered in this group (Figures 5-8). In the first two figures (Figures 5 and 6), two values for the square coefficient of variation of the service time (i.e. Cs = 1, 5) are considered, while the other parameters are left as they are mentioned in Table 1. It can be seen from Figures 5 and 6 that for higher Cs (Cs = 5), we gain better blocking probability but worse utilization. It is worth mentioning here that when Cs = 1, this means that the service time is exponentially distributed, while when Cs is greater than one, then the service time is a general exponential distribution. This factor should be taken into consideration when the UMTS performance is studied. It can be seen from Figures 5 and 6 that at traffic load 4 the blocking probability is 0.10 and the utilization is about 0.94 when Cs = 5. While it is about 0.24 blocking and about 0.88 utilization when Cs = 1, which means that the exponential distribution service time gives us worse blocking probability but better utilization. This means that the change in the service time has a dramatic effect on the performance especially on the blocking probability, even for higher traffic load, as it has been explained above. On the other hand, the effect on the utilization is positive at lower traffic load values (i.e. up to 3 Erlang), as shown in Figure 6. It starts to get worse for higher load values because as the traffic load increases, the variability of the service time neglects the effect of the utilization when the variability of the arrival time is equal to one (i.e. Ca = 1). 114 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Table 1: Assumed Default Parameters. Parameters Spreading factor, SF (N = SF * 2) Number of Zones, R Square Coefficient of Variation of inter-Arrival time, Ca Square Coefficient of Variation of inter-Arrival time, Cs Traffic load, u [Erlang] = О»/Вµ Values 8, 16, 32 4 1 1, 5, 10, 50 1, 2,…,10 5, 10 Arrival rate to the whole cell, О» Figures 7 and 8 show the blocking probability and the utilization for different values of Cs (Cs = 5, 10, 50). It can be seen from these figures that the variability of the service time, Cs, has a clear effect on the performance of both the blocking probability and the utilization. The higher Cs, the better the performance. According to this, the network designers are facing a very important issue when planning the network, because choosing the suitable value of Cs is an optimization issue. However, this is out of the scope of this paper. The effect of the availability of the codes Figures 9 and 10 show interesting results. Figure 9 shows the blocking probability, while Figure 10 shows the utilization for different number of available codes (i.e. N = 16, 32, 64). Very interesting results can be seen in Figure 9 where it explains clearly that when the traffic is low (i.e. up to 4 Erlang), there is no effect of the number of codes on the performance since the effect of the interference between users is much higher than the effect of the number of codes. It can be seen that at traffic load 4 Erlang, the graph behaviour starts to change as we become close to the base station and hence, the density of the traffic increases, which means that the effect of the number of codes starts at this point. Additionally, the increase in the number of codes has a positive effect on both the blocking probability and the utilization of the UMTS. This behaviour can be seen clearly in both Figures 9 and 10. The effect of the arrival rate to the whole cell О» In Figures 11 and 12, two different values of О» are considered (i.e. О» = 5, 10). It can be noticed from these two figures that when О» is increasing, both the blocking probability and the utilization are also increasing. The two figures show clearly that the whole arrival rate has an effect on the performance of UMTS network and designers. This should be taken into account as an important planning issue. Conclusions and Future Work This paper presents a numerical solution of one UMTS cell using the MOdeling Specification and Evaluation Language (MOSEL-2). It is shown in this paper that it is possible to find the numerical solution by MOSEL-2 for any system represented either by queuing model or Petri Net with different square coefficient of variations. Thus, it is possible with the new version of MOSEL (i.e. MOSEL-2) to solve any queuing model with exponential and non-exponential distributions by applying the pre-processor rule 115 Zreikat mentioned above. The effect of different parameters on the performance of the UMTS such as: the variability of the service time, the variability of the arrival rate and the availability of the codes, were shown and discussed. It is shown that all of these parameters affect the performance of the UMTS network and should be considered by the network operators and designers. Only 4 zones are considered in the work of this paper, because when the number of zones is increasing, the state space is also increasing. This leads to the state space explosion problem and therefore, in order to consider higher number of zones, we need to run MOSEL-2 program on machines with very high specifications. It would be possible to do this in the future. Therefore, in the future work of this paper, higher number of zones will be considered. Additionally, in order to cope with the requirements of the new technology of multimedia services (i.e. IP based services) in the UMTS, it is possible with MOSEL-2 to have firing rates of different distributions (i.e. Pareto distribution). It would be interesting to have Pareto arrival and service time distributions to the above type of queuing system. ‫ Щ€Ш§пєЈпєЄШ© пє‘п»®Ш§пєіп»„пє” п»џп»ђпє” اﻟﻨﻤﺬﺟﺔ واﻟﻮﺻﻒ‬UMTS ‫ﺗп»�ﻴﻴﻢ Ш§п»·ШЇШ§ШЎ п»џпєЁп» п»ґпє”вЂ¬ (MOSEL-2) ‫واﻟпє�п»�ﻴﻴﻢ‬ ‫أﻳﻤﻦ ﻋﻴﺴﻰ ШІШ±п»іп»�ﺎت‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ п»«п»® ШҐпє§пє�пєјпєЋШ± ﻷﻧﻈﻤﺔ اﻹﺗﺼﺎﻻت‬UMTS .UMTS ‫ﻓﻲ п»«пє¬Щ‡ Ш§п»џп»®Ш±п»—п»Є اﻟﺒﺤﺜﻴﺔ пє—п»ў пє—п»�ﻴﻴﻢ Ш§п»·ШЇШ§ШЎ п»џпєЁп» п»ґпє”вЂ¬ (Queuing ‫ п»џп»�пєЄ пє—п»ў ШҐп»—пє�пє®Ш§Ш Щ€пєЈп»ћ اﻟﻨﻤﻮذج اﻟﺼﻔﻲ‬.‫ Ш§п»џпє п»ґп»ћ Ш§п»џпєњпєЋп»џпєљ ﻣﻦ Ш§п»џпєёпє’п»њпєЋШЄ Ш§п»џпєЁп» п»®п»іпє”вЂ¬,вЂ«Ш§п»џпєЁп» п»®п»іпє” اﻟﻌﺎﻟﻤﻴﺔ‬ ‫( Ш§п»џпє�п»І пє—п»Њпє�пє’пє® ﻧﺴﺨﺔ пєџпєЄп»іпєЄШ© ﻣﻦ ﻟﻐﺔ‬MOSEL-2) ‫ п»·Щ€Щ„ п»Јпє®Щ‡ пє‘пєЋпєіпє�пєЁпєЄШ§Щ… ﻟﻐﺔ‬UMTS ‫ п»џпєЁп» п»ґпє”вЂ¬Model) (pre- ‫ ШҐпєіпє�пєЁпєЄЩ… ﻣﺒﺪأ‬.‫ п»“п»І اﻟﻤﺎﻧﻴﺎ‬Erlangen ‫( Ш§п»џпє�п»І пє—п»ў пє—п»„п»®п»іпє®п»«пєЋ пє‘п»®Ш§пєіп»„пє” п»“пє®п»іп»– ﻣﻦ ﺟﺎﻣﻌﺔ‬MOSEL) ‫( Щ€Ш§п»џпє¬ЩЉ п»іпєґпєЋп»‹пєЄ п»“п»І пєЈп»ћ اﻟﻨﻤﻮذج пє‘пєЋпєіпє�пєЁпєЄШ§Щ… п»›п»ћ ﻣﻦ Ш§п»џпє�ﻮزﻳﻊ‬MOSEL-2) ‫ اﻟﻤпє�п»®п»“пє® п»“п»І ﻟﻐﺔ‬processor) ‫ п»џп»�пєЄ пє—п»ў ШЇШ±Ш§пєіпє” ﺗﺄﺛﻴﺮ п»Јпє п»¤п»®п»‹пє”вЂ¬. (Exponential and non-exponential distribution) ‫اﻷﺳﻲ وﻏﻴﺮ اﻷﺳﻲ‬ ‫ п»ЈпєЄЩ‰ ﺗﻮﻓﺮ‬,(service time) ‫ Ш§п»џпє�ﻐﻴﺮ п»“п»І زﻣﻦ اﻟﺨﺪﻣﺔ‬:‫ ﻣﺜﻞ‬UMTS ‫ﻣﻦ اﻟﻤпє�ﻐﻴﺮات اﻟﻤﻬﻤﺔ п»‹п» п»° ШЈШЇШ§ШЎ пє§п» п»ґпє”вЂ¬ ‫ Щ€п»џп»�пєЄ ﺗﺒﻴﻦ ШЈЩ† ﻟﻬﺬه اﻟﻤпє�ﻐﻴﺮات ﺗﺄﺛﻴﺮ пєџпє¬Ш±ЩЉ п»‹п» п»° أداء‬.О» (arrival rate) ‫ وﺗﺄﺛﻴﺮ п»Јп»ЊпєЄЩ„ اﻟﻮﺻﻮل‬, codes ,‫ пє‘п»ЁпєЋШЎШЈ п»‹п» п»° п»ЈпєЋ Ш°п»›пє® пєіпєЋпє‘п»�ﺂ‬.UMTS ‫ Щ€п»іпє пєђ ШЈЩ† п»іпє†пє§пє¬ ﺑﻌﻴﻦ Ш§п»№п»‹пє�пє’пєЋШ± ﻣﻦ п»—пє’п»ћ ﻣﺼﻤﻤﻲ ﺷﺒﻜﺔ‬UMTS вЂ«пє§п» п»ґпє”вЂ¬ (blocking ‫ ШҐпєЈпє�ﻤﺎﻟﻴﺔ ШҐпєЈпє’пєЋШ· اﻟﻤﻜﺎﻟﻤﺔ‬:‫ﺗﻢ ШҐп»іпє пєЋШЇ Щ€п»Јп»ЁпєЋп»—пєёпє” пє‘п»Њпєѕ اﻟﻤпє�ﻐﻴﺮات Ш§п»џпє¤пє®пєџп»Є п»џп» п»Ёп»€пєЋЩ… ﻣﺜﻞ‬ .‫( п»џп» п»Ёп»€пєЋЩ…вЂ¬utilization) ‫ Щ€ ШЇШ±пєџпє” Ш§п»№пєіпє�пєЁпєЄШ§Щ… اﻷﻓﻀﻞ‬probability) 116 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 References [1] Aghvami B. H., Multiple Access Protocols for Mobile Communications, GPRS, UMTS and beyond, John Wiley and Sons , (2002). [2] Muratore F. : UMTS : Mobile Communications for the Future, John Wiley and Sons, (2001). [3] Holma H. and Toskala A., WCDMA for UMTS: Radio Access for Third Generation Mobile Communication, John Wiley and Sons, (2001). [4] Zreikat A. and Al-Begain K., Simulation of 3G Networks in Realistic Propagation Environments, International Journal on Simulation: Systems, Science, and Technology, 4 (3-4) (2003) 21-30. [5] Jaroslav H. and Pavel P., Simulation of UMTS Capacity and Quality of Coverage in Urban Macro- and Microcellular Environment, RadioEngineering, 14 (4) (2005) 21-26. [6] Schueller J., Begain K., Ermel M., Mueller T. and Schweigel M., Performance Analysis of a Single UMTS Cell, European Wireless, VDE Verlag, Berlin, (2000) 281-286. [7] Ishikawa Y. and Umeda N.: Capacity Design and Performance of CAC in Cellular CDMA Systems, IEEE Journal on Selected Area in Communications, 15, (1997) 1627-1635. 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Available: http://pdv.cs.tuberlin.de/~timenet/TimeNET-UserManual30.ps.gz.(Date-ofAccess: 2005 ). 118 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Figure 5: Blocking against traffic load for (Cs = 1, 5, Ca = 1) Figure 6:Utilization against traffic load for (Cs =1, 5 Ca = 1) 119 Zreikat Figure 7: Blocking against traffic load for different Cs values Figure 8: Utilization against traffic load for different Cs value 120 Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Figure 9: Blocking against traffic load for different N values Figure 10: Utilization against traffic load for different N values 121 Zreikat Figure 11: Blocking against traffic load for different values of О» Figure 12: Utilization against traffic load for different values of О» 122 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 123-134 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Mohammad M. Hamdan* 1 Received on July 12, 2005 Accepted for publication on Feb. 28, 2006 Abstract The standard map higher order function is commonly used by the parallel functional programming community to apply a function to the elements of a list data structure in parallel. In this work, a generic parallel map was developed. The design and implementation of the generic parallel map was based on the integration of a sequential generic functional programming language, a data distribution algorithm, a parallel master slave template and generic sends. The new generic parallel map can take a function and apply it on any data type. Results are shown for parallelizing a ray tracer using the generic parallel map. Speedup results are good. Keywords: functional programming, parallel processing, generic programming, data distribution, templates, ray tracing, genetic algorithms. Introduction There is a big need within the scientific computing community for programming methodologies that facilitate the development of computer application that can run sequentially and possibly in parallel. These methodologies are required as programmers need to focus on the problem being solved rather than looking at how to speed their program. Therefore, the idea of skeletons or templates or even patterns [1,2] was welcomed by the scientific computing community because of their implicit parallelism. However, the work on templates has primarily focused on parallelizing lists. Most of the problems had to be converted from their original data structure representation into a list. For example, a vector can be represented using a list and a tree can be represented using a list of lists. This conversion process is expensive as it requires the programmer to think of the problem in a different format and the algorithm had to be modified to work on the new data structure. Previous work on generic functions provided either sequential functions such as PolyP [3] and Generic Haskell [4] that can work on any data type or parallel functions В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Computer Science, Faculty of IT, Yarmulke University, Jordan. Hamdan using an explicit approach such Janus [5] and extending C++ standard template library [6]. These approaches are compared to the work in this paper in Section 4. Using the power of generic programming [7,8] which is available in Fish [9] and the basic ideas in parallel algorithmic skeletons enabled us to implement a generic parallel map (called gpmap). The gpmap can be used with complex data structures and its underlying parallel implementation will do the work in parallel. The rest of the paper is organized as follows. Section 2 describes how the generic parallel map was engineered. The results are shown in Section 3. In Section 4, comparison to related work is outlined and finally Section 5 concludes and outlines future work. Engineering a Generic Parallel Map The generic parallel map was a result of the integration of a host language (Fish), a generic sequential map, a static data distribution algorithm, a static master slave template and generic sends. The following subsections will explain each part in detail. The Host Language A generic function is a function which is able to handle any data structure containing any kind of numerical data such as integers, floats, Boolean, lists … etc. It is polymorphic in the choice of the structure used to hold the data. To explain the idea of generic programming [3, 5], take a look at the following example: equal 1 2 equal 3.4 6.7 equal true false equal [1,2,3] [1,2,3] As we can see, arguments for the function equal can be of different types. There is one implementation for the function and it can take many different data types as arguments. This is similar to the idea of overloading functions and templates in C++ [10]. However, we are interested in a functional language rather than an imperative or an object-oriented language due to the advantages of using functional languages such as the declarative style which matches our goal of implicit parallelism. The host language for this work is a well known functional programming language called Fish [9]. Fish stands for Functional = Imperative + Shape and it is designed to be an array programming language. Its main features are the expressive power of functional languages and the efficient execution of imperative languages. The power in Fish comes from static shape analysis [11], which is done at compile-time in order to reduce functional programs to simple imperative forms. Moreover, it supports generic programming using the idea of constructor calculus [12] which is based on generic pattern matching. 124 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Fish was chosen for the gpmap due to the availability of the source code for the compiler and its support for generic programming. The Fish code shown below, illustrates how to define a binary tree with two data types: real for leaf nodes and integer for root and intermediate nodes. Its graphical visualization is shown in Fig. 1. datatype btree (a,b) = leaf a | node b : btree(a,b) : btree (a,b) let Tree = node 4 (node 6 (leaf 3.2) (node 10 (leaf 4.8) (leaf 1.3)) The tree can hold mixed data types such as integers and reals by using the constructor calculus [12]. The constructor calculus allows generic pattern matching to branch on any constructor of any type. 4 10 6 5 3.2 2.5 4.8 1.3 3.7 Fig.1: The tree data structure with mixed data types A Generic Sequential Map In FISh there is a built in generic sequential map that can apply a function or more to a data structure that contains more than one data type. To illustrate how the generic map works, an example is shown below. In the code we define two functions: the first function fun1 takes an integer and returns an integer while the second function fun2 takes a real and returns a real. The generic map can take a tuple of these two functions and apply them to the values stored in the tree. The resulting tree is shown in Fig. 2. let fun1 x = x + 3 let fun2 y = y +. 4.5 map (fun1,fun2) Tree Tree = node 7 (node 9 (leaf 7.7) (node 8 (leaf 7.0) (leaf 8.2))) (node 13 (leaf 9.3) (leaf 5.8)) 125 Hamdan 7 9 13 7.77 8 9.3 7.0 5.8 8.2 Fig 2: Applying a tuple of two functions to the mixed data type tree using the sequential generic map. Data Distribution The basic idea of data distribution [13] is to take a data structure and distribute it across a given number of processors. In case of an array or a list this is an easy task where we divide the number of elements over the number of processors. Each processor will get its piece of the array accordingly. The advantages of data distribution are load balancing and improve data locality. Nonetheless, few processors might get less or more data than the others and this might cause load imbalance. However, the problem with data distribution is how to distribute complex data structures such as trees. There are two approaches: the first one is to flatten the data structure to bytes which is quite expensive and looses locality of data and might have extra overhead due to load imbalance and the second one is generic which is not expensive and preserves locality of data but difficult to implement. A compile-time algorithm was developed that distributes a tree across a given number of processors. We illustrate in Fig. 3 a distribution for the tree data structure that was defined in section 3.1 and a flow chart for the algorithm is shown in Fig. 4. 4 Processor 2 Processor 1 10 6 3.2 4.8 5 2.5 1.3 3.7 Fig. 3: Distributing the tree data structure across two processors. 126 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Start Find size of Tree Take a sub-tree If size of subtree is small enough according to work to be assigned to every processor ? No Yes Assign the sub-tree to the processor with the least amount of work so far Put the sub-tree on the root processor Yes More sub-trees ? No End Fig 4. Flow chart for the distribution algorithm. The result of the algorithm is a list of lists of pieces as shown in Fig. 5. Each sublist will be assigned to a processor and hopefully amount of work is balanced across all processors. 127 Hamdan 6 4 4.8 5 3.2 10 2.5 1.3 3.7 Fig. 5: Generating a list of lists of unprocessed pieces. The result of applying the gpmap on the tree that was defined in Section 2.1 would be as shown in Fig. 6. The final step is to reconstruct the tree from the processed list of lists of processed pieces. 9 7 9.3 8 7.7 13 7.0 5.8 8.2 Fig. 6: The processed list of lists of piece The Static Master Slave Template Template-oriented parallel programming is a well methodology for parallel programming. It has two components: a high-level interface for templates that the programmer can use in his program in order to parallelize it and a low-level implementation that will be used to parallelize the high-level interface. The user is not responsible for any coordination, messages, load balancing or any other parallel programming issues. All these are taken care of using the pre-implemented template. The programmer is only responsible for choosing the suitable template and instantiate it with the needed function and data. The choice can be from a variety of templates such as the master slave, pipeline, divide and conquer and geometric parallelism. These templates correspond to the common algorithms that are normally used in developing parallel applications. To illustrate the methodology lets take the map Higher-Order Function (HOF) as an example. The user may in his program apply a function to the elements of a list. This can be easily done using the map HOF as follows: fun square x = x * x; map square [1, 2, 3, 4, 5] => [square 1, square 2, square 3, square 4, square 5] => [1, 4, 9, 16, 25] 128 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures We may note that the square function can be applied to each element in the list simultaneously as each element is independent from the other one. This type of implicit parallelism can be easily exploited by the compiler using a master slave template. The parallelizing compiler will replace the map function with the master slave template in the generated object code. Once the program is executed the square function will be applied to the elements of the list in parallel. We have implemented modified version of the static master salve template for the generic parallel map. The master sends a list of pieces to each worker. Each slave will receive its list of pieces, process it and send the result back to the farmer. Note that the farmer after the send process will do work as well. Once the master finishes its computation then it is ready to receive the result from the workers. The pseudo-code for the master and slave template are shown below: The Master Alg. 1) Send the nth list of pieces to the nth worker 2) Process the 1st list of pieces 3) Receive the kth list of pieces from the kth worker 4) Build a list of lists of processed pieces The Worker Alg. 1) Receive the nth list of pieces from Master 2) Process the nth list of pieces 3) Send the list of processed pieces to Maste Generic Sends The gpmap requires generic sends. Therefore, it was required to add functions to be used by the master slave template that can send and receive complex data structures. Since any Fish data structure can be translated using the shape information into one or up to four basic arrays (int, float, char, Boolean). Simply, to send arbitrary data structures: either send the four arrays using separate messages or combine the four arrays into one array and transmit the data structure using one send message. The receive process is similar. It important to note that there is no need to flatten or unflatten a data structure at run-time. Using the message passing interface library (MPI) [14] it was possible to combine the four arrays and send them as one big message. This was achieved by defining a new data structure composed from the four arrays using MPI’s built-in datatypes. The new data structure is then send using a standard send routine. Results To test the generic parallel map, we have implemented a ray tracer in Fish. The ray tracer is a well known example that has been used by the parallel functional 129 Hamdan programming community as an application to test their methodologies and techniques. Therefore, the program was converted from ML [15] to Fish. The original program was taken from Impala suite [16] for parallel benchmark programs. The basic idea of the program is to generate a 2D image from a 3D scene which consists of spheres. In the resulting 2D image each pixel in the grid will be colored according to traced ray for that pixel. During the tracing of a ray, all intersections of this ray with the given objects are computed. The ray is reflected once an intersection is found and the color of the intersection point is computed based on the strength of the ray. The program was tested at Heriot-Watt University's Beowulf cluster which is based on Intel Celeron 533MHz, 128KB cache, 128 of DRAM and 5.7GB of IDE disk. The workstations are connected through a 100 Mb/s fast Ethernet switch. Fig 7 shows the execution time and speedup for the ray tracing of an image (512 x 512) consisting of 9 Spheres and 2 light sources. Speedup are results are good and better than those presented in [17] up to 6 processors. However, there is drop in performance when 8 processors where used. This might be caused by the increase in size of the resulting object code and possibly less utilization of the cache. It is important to note that this is caused by the FISh compiler as it generated bigger code size as we increase the number of processors. It is possible to solve this issue by adding run-time shape analysis and not relying completely on compile time analysis. The resulting ray traced spheres are shown in Fig. 8. Ray Tracer Execution Time Ray Tracer Speedup 140 6 5 100 Speedup Time (seconds) 120 80 60 40 4 3 2 1 20 0 0 1 2 3 4 6 1 8 2 3 4 6 Processors Processors Fig. 7: The execution time and speedup for the ray tracer program. 130 8 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Fig. 8: The result of applying the ray tracer on a scene Consisting of 9 spheres and 2 light sources. Comparison with other Models Table 1 presents a comparison between gpmap and other models. It is important to note that gpmap differs from most of these models as it is based on a functional language and it has the advantage of the implicit parallelism that is available in HOFs. The other implementations are semi-explicit and rely on the programmer to parallelize the sequential application. Therefore, it is expected that gpmap will be preferred by programmers as it encapsulates implicit parallelism and the user does not have to worry about communication, coordination and any parallel processing issues. Table 1: Comparison between gpmap and other models. Models gpmap Janus PolyP Generic Haskell PMLS [18] GpH [19] Eden [20] Functional or Imperative Functional Imperative Imperative List Data Structure Yes Yes Yes Generic Data Structures Yes No No Supports Parallelism Yes No No Parallelism Type Implicit N/A N/A Run-time Support Skeleton-library N/A N/A Functional Yes Yes No N/A N/A Functional Yes No Yes Implicit Skeleton-library Functional Yes No Yes Semi-Implicit Graph-Reduction Functional Yes No Yes Semi-Implicit Graph-Reduction 131 Hamdan 5 Conclusions and Future Work It was possible to design and implement a generic parallel map that can apply a function to arbitrary data structures. It was engineered from different components: a host language, a generic programming, master slave template, data distribution and generic sends. It was used on a decent example (the ray tracing of spheres) which consisted of a slightly complex data structure due to the lack of description of applications using generic programming languages [21]. It is planned to use the generic parallel map for further examples. Also it is possible to think of adding cost models with real hardware parameters to the generic distribution. It is important to note that a good application for the gpmap would be in the parallelization of genetic algorithms Gas [22]. To explain, in a GA there are different types of representations such as binary, float, arithmetic, trees … etc according to the encoded problem. The GA operators such as the crossover operator is nearly the same operation regardless of the representation method. Therefore, a generic crossover could be implemented that works on different datatypes (representations) and used a function argument for gpmap to applied in parallel on the population strings. Acknowledgment The author would like to thank Dr. C. B. Jay and Dr. Q. T. Nquyen from University of Technology, Sydney, Australia for access to the Fish compiler and the useful discussions during the development of this work. Also, the author would like to thank Dr. Greg Michaelson from Heriot-Watt University for giving the author access to HeriotWatt's Beowulf cluster. :‫اﻗﱰان ﺗﻄﺒﻴп»�п»І п»Јпє�п»®Ш§ШІЩЉ ﻋﺎم‬ ‫ﺗﻄﻮﻳﺮ Ш§п»—п±°Ш§Щ† Ш§п»џп»�ﺎﺋﻤﺔ ﻟﻴﺸﻤﻞ ﻫﻴﺎﻛﻞ اﻟﺒﻴﺎﻧﺎت اﻟﻌﺎﻣﺔ‬ ‫ﻣﺤﻤﺪ ﺣﻤﺪان‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫إن Ш§п»—пє�пє®Ш§Щ† Ш§п»џп»�ﺎﺋﻤﺔ Ш§п»џп»ЊпєЋШЇЩЉ п»«п»® Ш§п»—пє�пє®Ш§Щ† ШЇШ±пєџпє” ﺛﺎﻧﻴﺔ пє·пєЋпє‹п»Љ Ш§пєіпє�пєЁпєЄШ§п»Јп»Є ﻣﻦ п»—пє’п»ћ п»Јпє’пє®п»Јпє п»І Ш§п»џпє’пє®п»Јпє пє” Ш§п»»п»—пє�ﺮاﻧﻴﺔ‬ ‫ ﻓﻲ‬.‫ п»«пє¬Ш§ Ш§п»»п»—пє�пє®Ш§Щ† ﺑﺎﻟﻤﻜﺎﻧﺔ ШЈЩ† п»іпє„пє§пє¬ Ш§п»—пє�пє®Ш§Щ† Шўпє§пє® وﺗﻄﺒﻴп»�п»Є п»‹п» п»° п»‹п»ЁпєЋпє»пє® Ш§п»џп»�ﺎﺋﻤﺔ п»“п»�п»‚ пє‘пєёп»њп»ћ п»Јпє�ﻮازي‬.‫اﻟﻤпє�ﻮازﻳﺔ‬ ‫ пє—п»ў ﺗﺼﻤﻴﻢ Щ€пє—п»„п»®п»іпє® п»«пє¬Ш§ Ш§п»»п»—пє�пє®Ш§Щ† ﻣﻦ пє§п»јЩ„ ШЇп»Јпєћ Ш§п»—пє�ﺮان‬.‫ﻫﺬا Ш§п»џпє’пє¤пєљ пє—п»ў пє—п»„п»®п»іпє® Ш§п»—пє�пє®Ш§Щ† ﺗﻄﺒﻴп»�п»І п»Јпє�п»®Ш§ШІЩЉ ﻋﺎم‬ ‫ ШҐЩ† Ш§п»»п»—пє�ﺮان‬.‫ Щ€ ﻫﻴﻜﻞ пє§пєЋШЇЩ… وﻋﻤﻴﻞ Щ€п»Јпє®Ш§пєіп»јШЄ ﻋﺎﻣﺔ‬،‫ Щ€ ﺧﻮارزﻣﻴﺔ пє—п»®ШІп»іп»Љ ﺑﻴﺎﻧﺎت‬،‫ﺗﻄﺒﻴп»�п»І п»‹пєЋЩ… пє—пє�ﺎﺑﻌﻲ‬ ‫اﻟпє�ﻄﺒﻴп»�п»І اﻟﻤпє�п»®Ш§ШІЩЉ Ш§п»џп»ЊпєЋЩ… Ш§п»џпє пєЄп»іпєЄ ﺑﺎﻟﻤﻜﺎﻧﺔ ШЈпє§пє¬ Ш§п»—пє�пє®Ш§Щ† Шўпє§пє® وﺗﻄﺒﻴп»�п»Є п»‹п» п»° п»‹п»ЁпєЋпє»пє® ﻣﻦ ﻧﻮع Щ€Ш§пєЈпєЄ ШЈЩ€ أﻛﺜﺮ‬ ‫ п»“п»І п»«пє¬Ш§ Ш§п»џпє’пє¤пєљ пє—п»ў Ш§пєіпє�пєЁпєЄШ§Щ… Ш§п»»п»—пє�пє®Ш§Щ† Ш§п»џпє пєЄп»іпєЄ п»џпє’пє®п»Јпє пє” ﺑﺮﻧﺎﻣﺞ пє—пє�пє’п»Љ اﻷﺷﻌﺔ‬.‫ﻟﻬﻴﺎﻛﻞ اﻟﺒﻴﺎﻧﺎت пє‘пєёп»њп»ћ п»Јпє�ﻮازي‬ .‫ ﻧпє�пєЋпє‹пєћ Ш§п»џпє�пєґпєЋШ±Ш№ اﻟﻤﻌﺮوﺿﺔ ﺟﻴﺪة‬.‫ﺑﺸﻜﻞ п»Јпє�ﻮازي‬ 132 A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures References [1] Cole M. 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Journal of Functional Programming, 8(1) (2000)23-60. [20] Breitinger S. et al., Eden: Language Definition and Operational Semantics. Technial Report Bericht 96-10, Reihe Informatik, Fachbereich Mathematik und Informatik, Philipps-Universitat Marburg, Germany. Revised version, (1998). [21] Cunha A., Automatic Visualization of Recursion Trees: a Case Study on Generic Programming, Electronic Notes in Theoretical Computer Science, 86 (2003) 3. [22] Hamdan M., Collective Communication, Multiple Mutation Operators and the Global Parallelization of Genetic Algorithms. In Proceedings of the 5th International Conference on Recent Advances in Soft Computing (RASC2004), Nottingham, UK, (2004) 300-305. 134 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 135-145 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Sameh H. Ghwanmeh*1 Received on Oct. 23, 2005 Accepted for publication on July 30, 2006 Abstract The effect of moving the access point on the performance of the wireless network has been presented using an advanced network simulator. The Network Performance has been shown via a series of simulation tests with different access points locations. The simulation results are presented showing satisfactory network performance when the access point is chosen to include maximum possible number of users over the RF coverage area, geographical nature of the considered area and the number of access points. Keywords: access points, wireless networks, remote access, performance. Introduction Wireless local area networks (WLAN) enables people to communicate with anyone, anywhere, at anytime, using a range of multimedia services. The exponential growth of cellular telephone and mobile systems coupled with the spreading of laptop computers indicate a bright future for such networks.[1] The next stage of its development will be in complementing or replacing the network infrastructure that was traditionally wired as well as enabling network infrastructures. However as the communications field become a key factor in many other fields such as medical, teaching, business, information technology and other, the need for the communication to be anywhere without the problem of cables and the position of the user was increased and applying the wireless network become more important and essential in this fields, thus this help to spread these technology as fast as possible. WLAN technologies employ infrared, laser, spread spectrum, microwave, and satellite for supporting voice, video, and data transmission in local area and wider area environments [2,3]. The wireless networks gives the user to use any applications regardless to its source or vendors and the type of the application which can be data, video, real-time applications or others. However, the WLAN performance and quality of transmission are key factors in spreading and usage of such technologies [4,5]. This paper deals with the WLAN performance techniques based on advanced network simulator, OPNET modeler. В© 2007 by Yarmouk University, Irbid, Jordan. * Director, Computer and Information Centre. Computer Engineering Department, Yarmouk University 211-63, Irbid, Jordan. E-mail: [email protected] Ghwanmeh The effect of moving the access point on the performance of the wireless network has been presented. The Network Performance has been shown via a series of simulation tests with different access points locations. WLAN Configurations Wireless LAN configurations range from extremely simple to very complex. The simplest WLAN is an independent, peer-to-peer configuration where two or more devices with wireless adapters connect to each other, as depicted in Fig. 1. Peer-to-peer configurations are often called ad hoc networks since they do not require any administration or pre-configuration [1]. They also do not require the use of an access point, as each adapter communicates directly to another adapter without going through a central location. Figure 1 Peer-to-peer WLAN configuration. Peer-to-peer networks are very useful when a group of users need to communicate with one another in an unstructured way. A wireless network can also use an access point (AP). The access point acts like a hub, providing connectivity for the wireless computers (Fig. 2). It can connect the wireless LAN to a wired LAN, allowing wireless computer access to LAN resources, such as file servers or existing Internet Connectivity. Figure 2 WLAN configuration with access point. 136 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler In a corporate environment, many access points can work together to provide wireless coverage for an entire building or campus. The coverage area from each access point is called a cell. 2.2 Setting up a WLAN Access Point Overlapping AP Configuration When adjacent access points are located close enough to each other, parts of the coverage area of access points may overlap with each other. Figure 3 shows that when two adjacent access points, A and B, are located close enough to each other, a part of the coverage area of access point A overlaps that of access point B. Figure 3 Overlapping Access Points. The overlapping area has two very important attributes: any workstation situated in the overlapping area can associate and communicate with either AP A or AP B and any workstation can move continuously through the overlapping coverage areas without losing its network connection [2]. Non-Overlapping AP Configuration Wireless LANs congested with many network users and heavy traffic load may require non-overlapping, multi-AP configuration. In a non-overlapping, multi-AP configuration, several APs are installed in the same location (Fig. 4). Figure 4 Non-overlapping AP configuration. In non-overlapping configuration, each AP has the same coverage area, creating a common coverage area that increases aggregate throughput. Any workstation in the overlapping area can associate and communicate with any AP covering that area. 137 Ghwanmeh Description of the Simulation Tool The OPNET (Optimized Network Engineering Tool) can be best described as a set of decision support tools, providing a comprehensive development environment for the specification, simulation and performance analysis of communication networks, computer systems and applications, and distributed systems. Discrete event simulations are used as the means of analyzing system performance and their behaviour. This sophisticated package comes complete with a range of tools which allows us to specify models in great detail, identify the elements of the model of interest, execute the simulation and analyze the generated output data. The OPNET simulator has many features such as object orientation and hierarchical modelling [6,7]. OPNET provides four editors that are used to develop a representation of a system being modeled. These editors, the Network, Node, Process and Parameter Editors, are organized in a hierarchical fashion as shown in Fig. 5. This hierarchical organization supports the concept of model reuse. Models developed at one layer can be used by another model at a higher layer. The Network Domain deals with the specification of the physical topology of a communications network. The basic building block is a node. An underlying model, developed using the node editor, defines the specific capabilities of each node. Each node instance has a set of parameters or characteristics that can be set to customize the node's behavior. The number of node models that can be used in a network model is unrestricted. The Node Domain deals with the specifications of the communication devices created and interconnected at the network level. These nodes correspond to communicating devices such as personal computers, workstations, file servers, printers, bridges, routers or switches. Process Domain created using the process editor, which are used to describe the behavior of processor and queue modules within the node domain. These models are used to simulate software subsystems, such as a communication protocol, and also to model hardware subsystems, such as the memory of a switching device. Each process that executes in a queue or processor module is an instance of a particular process model. Process models are expressed in a language called Proto-C. OPNET's Proto-C consists of state transition diagrams (STDs), a library of kernel procedures, and the standard C programming language. The high level of flexibility offered by the Proto-C language enables almost any type of task, collection of specific data and definition of any protocol is performed [8]. 138 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Figure 5. Simulation tool: the four OPNET editors. Move-Test Description The move-test solution can be considered as a basic step in building wireless network and optimizing it. Wireless service providers need to optimize their networks, as new access points installed, new buildings constructed or other condition changed. An overview of the optimization process is shown in Fig. 6. Move-testing is the first step in the process, with the goal of collecting measurement data as it relates to a user's location. Once the data have been collected over the desired RF coverage area, the data is outputted to a post-processing software tool. Engineers can use the postprocessing and collection tools to identify the causes of potential RF coverage or interference problems can be solved. Once the problems, causes, and solutions are identified, steps are performed to solve the problem [9]. 139 Ghwanmeh Figure 6 Optimization Process. The key characteristic of building wireless network is the WLAN Coverage. The WLAN will lose its reliability if it cannot respond to the user requests [10]. The wireless service providers will not give chance to this disadvantage to occur using Move- test solution. Before installing the access point we have to perform site evaluation to determine an appropriate location for the new access point by transmitting a continues signal from the undertest location and measure it using mobile receiver which moves over the coverage area to determine the locations of poor RF coverage. Move-Test Simulation Results The WLAN testing framework consists of a network contains workstations with wireless NICs, and a single access point to enable the workstations to access the connected wired network which provides several services such as FTP, HTTP and Email. We note that the workstations are distributed in different locations, the workstations in the left side are group_1 and the others are group_2. First, the access point is set in location 1 as shown in Fig. 7. Figure 7 Access point location 1. 140 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Figure 8 Simulation results of AP location 1. Because all workstations are in group_2 are out of the transmitting and receiving RF rang of the access point, which shown as green cycle with radius of 1160.5m (Fig. 7). The data dropped at this location mainly caused by the workstations of group_2 because they are out of the coverage. The buffer size Specifies the maximum size of the higher layer data buffer in bits. Once the buffer becomes full, the data packets arrived from higher layer will be discarded until free space is available, the buffer size of the OPNET wireless nodes is 256000 bit. It can be noted that the wireless LAN delay is approximately constant since the location of each workstation is fixed respect to the Access point. We can also note that the values of the throughput and load are equal at any given execution time since the number of bits that are stored in the higher layer queue in transmitter nodes (which reflect the load) is equal to the number of bits that received in the receiver node (Fig. 8). Figure 9 Access point location 2. 141 Ghwanmeh Figure 10 Simulation results of AP location 2. In the second test the access point is set at location 2 (Fig. 9) which is closer to group_2. From Fig. 10 it can be noted that the number of data dropped in the WLAN increases due to increasing the number of workstations that are out of the RF coverage range. Other statistics are mainly collected from group_2 workstations. In the third test the Access point is moved to a newly location (Fig. 11). At this location, the access point is distant from both groups and few workstations are included in the RF coverage range of the access point. Hence, the data dropped reaches the maximum value. It can be seen that the media access delay increases by increasing the load of the wireless network (Fig. 12). In the fourth test, the AP is set at location 4 (Fig. 13). As it can be seen from Fig. 14, this test demonstrates no data dropped from both groups, which improves the reliability of the wireless network. Further the throughput reaches its maximum value compared with previous test locations. Figure 11 Access point location 3. 142 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Figure 12 Simulation results of AP location 3. Figure 13 Access point location 4. Figure 14 Simulation results of AP location 4. 143 Ghwanmeh Conclusions The OPNET advanced simulator has been used to study the effect of access-point moving on the WLAN performance. Simulation results indicate that we can greatly improve the WLAN performance. The location of the access point plays a very important role in enhancing the performance of the WLAN and choosing unsuitable location will prevent some users from accessing the network. The simulation results presented showing satisfactory WLAN performance when the access point is chosen to include maximum possible number of users over the RF coverage area, geographical nature of the considered area and the number of access points. ‫ﺗﺄﺛﲑ пє—п»ђпІ‘ п»Јп»њпєЋЩ† ﻧп»�п»„п»Є Ш§п»»пє—пєјпєЋЩ„ п»‹п» п»° п»›п»”пєЋШЎЩ‡ ﺷﺒﻜﻪ‬ ‫اﻻﺗﺼﺎﻻت Ш§п»џп»јпєіп» п»њп»ґп»Є пє‘пєЋпєіпє�пєЁпєЄШ§Щ… اوﺑﻨﺖ‬ ‫ﺳﺎﻣﺢ ﻏﻮاﻧﻤﺔ‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻓــﻲ п»«ЩЂЩЂпє¬Ш§ Ш§п»џпє’пє¤ЩЂЩЂпєљ пє—ЩЂЩЂп»ў ШЇШ±Ш§пєіЩЂЩЂпє” ﺗــﺄﺛﻴﺮ ﺗﻐﻴــﺮ п»Јп»њЩЂЩЂпєЋЩ† ﻧп»�п»„ЩЂЩЂп»Є Ш§п»»пє—ЩЂЩЂпєјпєЋЩ„ п»‹п» ЩЂЩЂп»° п»›п»”ЩЂЩЂпєЋШЎШ© пє·ЩЂЩЂпє’п»њп»Є Ш§п»»пє—ЩЂЩЂпєјпєЋп»»ШЄ Ш§п»џп»јпєіЩЂЩЂп» п»њп»ґп»ЄвЂ¬ ‫ пє—п»ў ﺗﻨﻔﻴﺬ пєіп» ЩЂпєґп» п»Є ﻣـﻦ пє—пє ЩЂпєЋШ±ШЁ اﻟﻤﺤﺎﻛـﺎة п»џп»ЊЩЂпєЄШ© п»Јп»®Ш§п»—ЩЂп»Љ п»џп»Ёп»�ЩЂпєЋШ· Ш§п»»пє—ЩЂпєјпєЋЩ„ п»‹п» ЩЂп»°вЂ¬ШЊ ‫ﺑﺎﺳпє�пєЁпєЄШ§Щ… ﺑﺮﻧﺎﻣﺞ اﻟﻤﺤﺎﻛﺎة اوﺑﻨﺖ‬ ‫ ﺑﻴﻨﺖ Ш§п»џп»Ёпє�пєЋпє‹пєћ п»›п»”пєЋШЎШ© ﻋﺎﻟﻴﻪ п»џп» пєёпє’п»њп»Є п»‹п»ЁпєЄп»ЈпєЋ п»іпє�п»ў Щ€пєїп»Љ ﻧп»�п»„п»Є Ш§п»»пє—пєјпєЋЩ„ ﺑﺤﻴـﺚ пє—п»ђп»„ЩЂп»І Ш§п»›пє’ЩЂпє® п»‹ЩЂпєЄШЇ ﻣﻤﻜـﻦ ﻣـﻦ‬. ‫اﻟﺸﺒﻜﻪ‬ .‫اﻟﻤﺴпє�ﺨﺪﻣﻴﻦ ﺿﻤﻦ п»ЈпєЄЩ‰ Ш§п»џпє�ﻐﻄﻴﺔ п»Јп»Љ п»Јпє®Ш§п»‹пєЋШ© п»‹пєЄШЇ ﻧп»�пєЋШ· Ш§п»»пє—пєјпєЋЩ„ وﻃﺒﻴﻌﺔ اﻟﻤﻨﻄп»�пє” Ш§п»џпє п»ђпє®Ш§п»“п»ґпє”вЂ¬ References [1] Rappaport T., “Wireless Communications: Past Events and a Future Perspective”, IEEE Commun. Mag, (40)(2) (2002)148-161. [2] Katzela I., Modeling and Simulating Communication Networks: A Hands-on Approach Using OPNET, Upper Saddle River, NJ, Prentice Hall, (1999). [3] Ellison, High-performance wireless ISP solution, Computing Canada, (2002). [4] Papavassiliou Xu S., and Narayanan S., “Layer-2 multi-hop IEEE 802.11 architecture: design and performance analysis”, IEE ProceedingsCommunications, 151(1) (2004) 460-466. [5] Andrews G. J. and Meng H., “Performance of Multicarrier CDMA With Successive Interference Cancellation in a Multipath Fading Channel”, IEEE Transactions on Communications, 5 (2004), 811-822. [6] Opnet Tutorial Manual, MIL 3, Inc. Configuring Application and Profiles, (2002). [7] OPNET Contributed Model Depot: http://www.opnet.com/services. March, 2005. 144 Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler [8] Nazy M., “Simulation of Packet Data Networks Using Opnet”, http://citeseer.ist.psu.edu/336278.html. (2005). [9] Edoardo B., Cooper E. and Sansom R., “Designing a Practical ATM LAN”, IEEE Network, (1993). [10] Henderson R, “Host Mobility for IP Networks: A Comparison”, IEEE Network, 6 (2003) 8-26. 145 ABHATH AL-YARMOUK: "Basic Sci. & Eng." Vol. 16, No.1, 2007, pp. 147-161 New Techniques for Improving H.263 Videoconferencing Ammar M. Kamel and Moh'd Belal Al-Zoubi* 1 Received on Aug. 2, 2006 Accepted for publication on Feb. 18, 2007 Abstract Two-way real time videoconferencing techniques have become the big challenge of the Internet revolution. The ITU-T H.263 is designed for very low-bit rate coding, which is concerned with real-time two-way communication. Motion estimation\compensation is the core of H.263 video coding. Different motion estimation techniques were developed to enhance the ability and efficiency of H.263 technique for video compression. In this paper, two new techniques have been developed; Thresholding Half-pixel and OddEven motion search techniques. The first technique increases the image quality of video frames. The second one minimizes the encoding delay time through eliminating the searching points in each searching window of the video frame. The extracted results proved the effectiveness of the proposed techniques in comparison with the well-known motion search techniques in terms of delay time, image accuracy and compression ration. Keywords: Videoconferencing, Motion estimation, H.263, Image/video compression... Introduction Digital video communications technology has impressed the lives of people everywhere in the world. Digital video has an inherently high bandwidth (i.e., a digitized video signal requires a very high data rate for transmission). In order to store and transmit this information effectively, it is necessary to develop techniques for video data compression; otherwise, raw video may require large storage space and bandwidth [6, 11, 12]. Special techniques, for example (MPEG1, MPEG2, MPEG4, H.261 and H.263), which take the characteristics of the video into account, can compress the video with a high compression ratio [8]. H.263 is mostly used for dialogue mode applications in network environments. for example, video telephony and video conferencing[5, 7, 8]. The resulting continuous bit rate is eminently suitable for today’s wide area networks operating with ISDN, leased lines, and some other connections. The H.263 ITU coding standard for low bit rate В© 2007 by Yarmouk University, Irbid, Jordan. * Department of Computer Information Systems, University of Jordan, Amman, Jordan. Kamel and Al-Zoubi videoconferencing is based on a hybrid motion estimation/compensation video coding method [6, 13, 14]. Hybrid video compression exploits temporal redundancy by motion compensation and spatial redundancy by DCT transformation. Motion estimation is a major part in such video compression systems. Many block matching search techniques (such as Three-Step search, 2D-Logarithm search, Conjugate search, and Full search) have been developed to reduce the complexity of the motion estimation that is associated with exhaustive searches [1, 2, 3, 4, 9, 10, 12]. These techniques reduce the video frame total searching points, which greatly affect the encoding delay time. The encoding delay time and image accuracy are major problems that limit the H.263 efficiency. The encoding delay time significantly contributes to the video conferencing interactivity achievement through decreasing the elapsed time in the video compression. On the other hand, increasing the image accuracy directly affects the video compression ratio. In this paper, two new techniques are developed; Thresholding Half-pixel and OddEven motion Search (OES) to enhance the efficiency of the H.263 videoconferencing technique. The first technique increases the image quality of video frames. The second one decreases the total elapsed time of video compression (encoding the delay time). H.263-Motion Estimation-compensation: Proposed Improvements In this section, two considerably improved techniques are developed to enhance the efficiency of the H.263 technique. This is done through enhancing the data rate and reducing the transmission delay limitations. The techniques also improve the video sequence quality. The first technique (called Thresholding Half-pixel technique) greatly intensifies the performance of the traditional half-pixel technique by adding a threshold value which controls the clarity and smoothness of each of the pixel groups included from which video frames are composed. The second technique (called OddEven search technique) employs a new search strategy to match similar blocks from video successive frames and exclude the similar blocks. This technique achieves an efficient compression process. These techniques are explained below.. Thresholding Half-Pixel Accuracy Improvement H.263 uses a sub-pixel accuracy for motion compensation instead of using a loop filter to smooth the anchor (reference) frame as in H.261. The half-pixel technique achieves the image smoothing by considering a pixel and its neighbors, eliminating any extreme values (high frequency-noise) in this group. The values of half-pixel are found using bilinear interpolation [6]. Half-pixel technique does not take into account the color distance relationship among pixels directly, but rather produces values representing half the distance among these pixels. 148 New Techniques for Improving H.263 Videoconferencing In the current study, we improved the technique by adding an equilibrium factor to achieve a high level of smoothness among anchor frame pixels through computing threshold value. The threshold value stands for the average difference between two pairs of pixels, which reduces the noisy pixel’s values (not correlated pixels) resulted from the half-pixel technique. This makes the pixel values of each group closer and enhances the video anchor frames. The improvement of the half-pixel accuracy is explained in Fig. (1) and equation (2.1) [8]: where A, B, C, and D are grouped pixels and There is an additional value used to reduce the extreme half-pixel values. According to equation (2.1), the threshold value will decrease the color distance for group (a, b, c, and d) and produce a new group of pixels with a suitable color approximation. OddEven Search Technique (OES) The main idea of the proposed OddEven Search (OES) algorithm is to compute the cost function (typically, the MAD function is used [12]) for the odd blocks of y-axis and for the even blocks of x-axis finding the best match. Where F (i,j) represents an (m x n) macroblock from the current frame, G (i,j) represents the same macroblock from a reference frame (past or future), (Dx, Dy) a vector representing the search location. The matching candidate block contains the minimum value of the computed cost function values in the search windows of the previous frame. This block represents the most similar block for the selected block in the current frame of the video sequence. The matching process starts by calculating the cost function of the odd locations of the y-axis and even locations of the x-axis in the search window. The location that produces the smallest cost function becomes the center location for the next step, and the search range is reduced by half. 149 Kamel and Al-Zoubi The matching process of the OES algorithm will continue until the minimum computed cost function value is equal to or less than the threshold value previously determined to achieve the matching process. The threshold value is determined depending on the requirements of the applications that use the proposed algorithm. The threshold value controls the speed and efficiency of the block matching process. This effectively affects the H.263 bit rate and the encoding delay time. Fig. (2a) shows the block matching process on the y-axis. Fig. (2b) shows the block matching process on the x-axis. OddEven Control Parameters This technique uses two control values to produce the best and fastest block matching process. These control values are: Information Density Control Value: A value is determined representing the number of bits from which the maximum color value of the matched block is composed. This value represents the amount of color information distributed on the matched block. The following formula is used to compute this value: MADThreshold = пЈ®Log 2 ( Max( SBlk ))пЈ№ where SBlk represents the current frame candidate block for the matching process. The computed value of the MADThreshold is compared to the minimum MAD computed values. If the selected MAD minimum value is less than or equal to the MADThreshold value, the matching process will be terminated. The block of the minimum MAD value is the approximate match of the SBlk. Loop Step Size Control Value: Three values are used (0.5, 0.7, or 0.9) to reduce the matching process comparison on the searching window blocks to find the best match. The 0.5 value divides the loop iteration by 2; this makes the OddEven technique compare half of the searching window blocks. When the value is 0.7, the OddEven technique compares one third of the searching window blocks. However, when the value is 0.9, the OddEven technique compares all of the searching window blocks. Experimental Results In this section, four well-known techniques are evaluated and compared with the proposed OddEven Search (OES) technique: Full Search (FS), Conjugate search, 2-D logarithmic search, and Three-Step Search (3SS). Several results are constructed and analyzed according to the total delay time, the average of PSNR, and the total of the compression ratio. In addition, another proposed Thresholding Half-pixel technique is compared with the classical Half-pixel technique. The proposed and the four well-known techniques are reviewed in this study. The obtained results have been developed using MATLAB 6.5 and a computer system with a PIII processor and 128 MB memory. 150 New Techniques for Improving H.263 Videoconferencing Image Accuracy Evaluation The proposed Thresholding Half-pixel technique was simulated and compared with the traditional Half-pixel technique. PSNR and eRMS are used as two measures utilized to evaluate the image quality. Results illustrated in Table (1) indicate that the proposed technique has achieved a clear increase in the PSNR compared with the PSNR of the traditional Half-pixel technique. Increasing the PSNR means that the enhanced decompressed image maintains color properties close to those of the original image. Fig. (3a) represents an image after compression and decompression using JPEG technique, while Fig. (3b) represents the histogram of the decompressed image. Fig. (4a) denotes the decompressed image after applying the traditional Half-pixel technique. Fig. (4b) represents the histogram of the decompressed image. Fig. (5a) represents the decompressed image after applying the proposed Thresholding Half-pixel technique. Fig. (5b) shows that the color distribution of the image is better than that of Fig. (4b). The Evaluation of Block Matching Search Techniques The proposed OddEven Search (OES) algorithm is simulated using the luminance component of the first 10 QCIF frames of (Foreman, Miss America, Employer) video sequence. These sequences consist of a large amount of information and different scenes movement. The Mean Absolute Difference (MAD) is used as the cost function to calculate the similarity between the matched blocks. The maximum displacement in the search area is (В±7) pixels in both horizontal and vertical directions for a block size, of 16 Г—16. The proposed OES technique uses one of three different threshold values that control and affect the search process. These values are (0.5, 0.7, and 0.9). The performance comparison between OES, FS, Conjugate search, 2-D logarithmic, and 3SS in terms of the total delay time are shown in Tables (2), (5) and (8). Table (8) shows that the proposed OES algorithm that uses three different threshold values (0.5, 0.7, and 0.9) achieved good results. This was obtained through decreasing the elapsed time for the matching process in comparison with the well-known techniques, particularly, the 3SS algorithm, which had the second less delay time. Tables (2) and (5) show that the proposed OES algorithm that uses two different threshold values (0.5, 0.7) achieved the best results in comparison with the 3SS algorithm. Tables (3), (6) and (9) give some PSNR statistical comparisons between the proposed technique and each of the four well-known techniques. Tables (6) and (9) illustrate that the proposed OES algorithm that uses the three different threshold values (0.5, 0.7, and 0.9) resulted in the highest PSNR in comparison with the FS. Tables (4), (7) and (10) show another comparison according to the Compression ratio (Cr). Tables (4), (7) and (10) show that the proposed OES algorithm that uses the three threshold values (0.5, 0.7, and 0.9), has come near to the value of 3SS. 151 Kamel and Al-Zoubi Discussion In this study several improvements on the parameters that hinder the H.263 CODEC efficiency are performed in order to improve the image accuracy and transmission delay time. These improvements are done by Thresholding and traditional Half-pixel techniques in order to enhance the video frame accuracy. This considerably improves the performance of H.263 motion estimation/compensation. The improvement results indicate the following: 1. When computing the PSNR of the decompressed image applying both the proposed Thresholding Half-pixel technique and the traditional Half-pixel technique, it appeared to be 39.025 for the proposed technique and 38.976 for the traditional one. The higher PSNR of the proposed technique indicates remarkable image accuracy and clarity. 2. When testing a decompressed image and applying the proposed technique, eRMS appeared to be 0.0223 compared with 0.0255 for the traditional Half-pixel technique. The nearer the eRMS value is to zero, the closer the decompressed image is to the original one. The other improvement deals with the block matching search time. Using the proposed OES of one of the threshold values (0.5, 0.7, or 0.9) gave higher results in comparison with the well-known four search methods. The elapsed time for the block matching search and determining the Motion Vectors (MV) have been decreased considerably, which in turn would decrease the encoding delay time and increase the efficiency of H.263 CODEC. The results of testing the four well-known techniques (FS, Conjugate, 2-D logarithmic, and 3SS) and the proposed (OES) indicate a reverse relationship between the PSNR and the Compression ratio (Cr). Maintaining equilibrium between the PSNR and the Cr and increasing both of them would result in a great improvement in H.263. It can be noticed that: 1. Using both the proposed OES and the Thresholding Half-pixel resulted in a noticeable increase in the PSNR compared with the PSNR of the traditional FS technique, which is characterized with a high PSNR value. 2. Increasing the PSNR using the two proposed techniques (Thresholding Half-pixel and OES), a fair Compression ratio (Cr) was maintained in comparison with the 3SS technique. Conclusion In this study, two algorithms have been developed: Thresholding half-pixel technique and OddEven technique. These algorithms have enhanced video compression. The idea of the first algorithm is to increase the image clarity and accuracy, while the second one is concerned with decreasing the elapsed time of video compression and increasing the compression ratio. Testing these two techniques gave good results, improving the performance of the H.263 technique significantly. Applying the proposed technique (Thresholding Half152 New Techniques for Improving H.263 Videoconferencing pixel) resulted in high accuracy and clarity in the decompressed images compared with the traditional Half-pixel technique. The proposed OES technique has remarkably decreased the elapsed time of video compression in comparison with the four wellknown techniques (FS, Conjugate, 2-D logarithmic and 3SS). Using three different threshold values by OES resulted in a fast block matching process; decreasing the encoding delay time clearly. Choosing simple scenes with few moving objects (called Head and Shoulder) increases Cr and decreases the video compression delay time. Each motionless object is considered similar to an object in the same location in the next frame. These blocks can be substituted without computing the Motion Vector (MV) for each block. ‫ п»џп» п»¤пє†пє—п»¤пє®Ш§ШЄ اﻟﻔﻴﺪﻳﻮﻳﺔ‬H.236 ‫ﺗп»�ﻨﻴﺔ пєџпєЄп»іпєЄШ© п»џпє�пє¤пєґпІ” ﺧﻮارزﻣﻴﺔ‬ ‫ﻋﻤﺎر п»›пєЋп»Јп»ћ Щ€ ﻣﺤﻤﺪ пє‘п»јЩ„ اﻟﺰﻋﺒﻲ‬ вЂ«п»Јп» пєЁЩЂЩЂпєєвЂ¬ .‫( пє—пє¤пєЄп»іпєЋЩ‹ ﻛﺒﻴﺮاً п»“п»І п»‹пєЋп»џп»ў اﻹﻧпє�ﺮﻧﺖ‬H.236 Videoconferency) ‫ﺗﻤﺜﻞ пє—п»�ﻨﻴﺔ اﻟﻤﺆﺗﻤﺮات اﻟﻔﻴﺪﻳﻮﻳﺔ‬ ‫ Ш§п»џпє�п»�ﻨﻴﺔ‬.‫وﻗﺪ пє—п»ў пє—п»„п»®п»іпє® пє—п»�ﻨﻴпє�ﻴﻦ ﺟﺪﻳﺪﺗﻴﻦ п»џп»Ђп»ђп»‚ п»«пє¬Ш§ Ш§п»џп»Ёп»®Ш№ ﻣﻦ اﻟﺒﻴﺎﻧﺎت п»“п»І п»«пє¬Ш§ اﻟﺒﺤﺚ‬ ‫( Щ€Ш§п»џпє�п»І ﻣﻦ ﺷﺄﻧﻬﺎ ﺗﺤﺴﻴﻦ ﻧﻮﻋﻴﺔ пє»п»®Ш± اﻟﻔﻴﺪﻳﻮ ШЈпє›п»ЁпєЋШЎ п»‹п»¤п» п»ґпєЋШЄ اﻟﻀﻐﻂ‬Thresholding Half-pixel) ‫اﻷوﻟﻰ‬ ‫( п»џпє�п»�п» п»ґп»ћ Ш§п»џп»®п»—пє– Ш§п»џп»јШІЩ… п»џп» пє�ﺸﻔﻴﺮ Щ€Ш§п»џп»Ђп»ђп»‚ ﻋﻦ ﻃﺮﻳﻖ‬OddEven motion search techniques) ‫واﻟﺜﺎﻧﻴﺔ‬ ،‫ Щ€п»—пєЄ ШЈпє›пє’пє�пє– ﻧпє�пєЋпє‹пєћ Ш§п»џпє’пє¤пєљ п»“пєЋп»‹п» п»ґпє” Ш§п»џп»„пє®п»іп»�пє�ﻴﻦ Ш§п»џпє пєЄп»іпєЄпє—п»ґп»¦вЂ¬.‫ﺣﺬف пє‘п»Њпєѕ اﻟﺒﻴﺎﻧﺎت اﻟﻬﺎﻣﺸﻴﺔ ШЈпє›п»ЁпєЋШЎ п»‹п»¤п» п»ґпєЋШЄ اﻟﺒﺤﺚ‬ .‫ﻋﻦ п»ѓпє®п»іп»– п»Јп»�ﺎرﻧﺔ Ш§п»џп»Ёпє�пєЋпє‹пєћ п»Јп»Љ пє—п»�ﻨﻴﺎت ﻋﺎﻟﻤﻴﺔ п»Јп»Њпє®Щ€п»“пє” п»“п»І п»«пє¬Ш§ Ш§п»џп»¤пє пєЋЩ„вЂ¬ References [1] ALexis M., Guobin S., Ming L., Oscar C. and Ishfaq A., “A New Predictive Diamond Search Algorithm for Block Based Motion Estimation”. Proceeding of Visual Communication and Image Processing (VCIP-2000). Perth. Australia, (2000). [2] Bagni D., de Haan G. and Riva V., “Motion Compensated Post-Processing for Low-bit Rate Videoconferencing on ISDN Lines,” in Proc. of the ICCE'97, (1997) 28-29. [3] Cheung C. and Po L., “A Hierarchical Block Matching Algorithm Using Partial Distortion Measure,” in Proc. of IEEE International Conference of Image Processing. 3, Santa Barbara. CA. USA, (1997) 606-609. [4] Gharavi H. and Mills M., “Block Matching Motion Estimation Algorithm – New Results,” IEEE Transactions on Circuits System, 37 (1990) 649-651. 153 Kamel and Al-Zoubi [5] Halsall F., Computer networking and the internet, 5th ed., Addison-Wesley, (2005). [6] ITU-T Draft Recommendation H.263, “Video Coding for Low Bit Rate Communication”, (1996). [7] Konrad J., “Visual Communications of Tomorrow: Natural, Efficient and Flexible”, IEEE Communications Magazine, 39(1) ( 2001) 126–133. [8] Li Z. and Drew M., “Fundamentals of Multimedia”, Prentice Hall, (2004). [9] Po L. and Ma W., “A Novel Four-Step Search Algorithm for Fast Block Motion Estimation,” IEEE Trans., on Circuits and Systems for Video Technology 3, 6 (1996) 313-317. [10] Poynton C., “Digital Video and HDTV Algorithms and Interface”, Morgan Kaufmann, (2003). [11] Srinivasan R. and Rao K., “Predictive Coding Based on Efficient Motion Estimation,” IEEE Transaction and Communication, 33 (1985) 888-896. [12] Tartagni M., Leone A. and Guerrieri R., A Low-Power Block-Matching Cell for Video Compression, 27 (3) (2001) 259-271. [13] Wang Y., Ostermann J. and Zhang Y., “Video Processing and Communications”, Prentice Hall, (2002). [14] Yun Q. and Huifang S., Image and Video Compression for Multimedia Engineering, 1st Ed. CRC Press: USA, (2000). 154 New Techniques for Improving H.263 Videoconferencing List of Tables Table (1): PSNR and eRMS comparison criteria between the proposed Thresholding Half-pixel technique and the well-known Half-pixel technique Image Technique Proposed Thresholding Half-pixel Half-pixel PSNR 39.025 38.976 eRMS 0.0223 0.0255 Table (2): Elapsed delay time comparison between the four well-known techniques and the proposed OddEven technique for Forman video sequence Frame 1 I 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 P Total Delay Time Full search FS 11.257 ms 31.826 ms 30.404 ms 30.363 ms 30.493 ms 30.364 ms 30.304 ms 30.714 ms 30.494 ms 31.335 ms 287.554 ms Conjugate search 2-D logarithmic search 11.257 ms 11.257 ms 6.469 ms 7.251 ms 6.470 ms 7.250 ms 6.479 ms 7.261 ms 6.469 ms 7.210 ms 6.440 ms 7.190 ms 6.479 ms 7.201 ms 6.480 ms 7.200 ms 6.459 ms 7.210 ms 6.479 ms 7.231 ms 69.481 ms 76.261 ms ThreeStep Search (3SS) 11.257 ms 6.489 ms 6.449 ms 6.429 ms 6.419 ms 6.419 ms 6.439 ms 6.439 ms 6.500 ms 6.429 ms 69.369 ms Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 11.257 ms 11.257 ms 11.257 ms 6.158 ms 6.329 ms 6.499 ms 6.149 ms 6.249 ms 6.479 ms 6.169 ms 6.229 ms 6.489 ms 6.159 ms 6.259 ms 6.499 ms 6.149 ms 6.239 ms 6.500 ms 6.139 ms 6.229 ms 6.469 ms 6.168 ms 6.239 ms 6.500 ms 6.149 ms 6.229 ms 6.490 ms 6.178 ms 6.239 ms 6.479 ms 66.675 ms 67.498 ms 69.661 ms Table (3): PSNR comparison between the four well-known techniques and the proposed OddEven technique for Forman video sequence Frame Average of PSNR Full search FS Conjugate search 2-D logarithmic search ThreeStep Search (3SS) Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 39.778 38.222 39.298 38.499 39.433 39.603 39.484 155 Kamel and Al-Zoubi Table (4): Compression ratio (Cr) comparison between the four well-known techniques and the proposed OddEven technique for Forman video sequence Frame Compression ratio (Cr) Full search FS Conjugate search 2-D logarithmic search ThreeStep Search (3SS) Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 Total Cr 45.527 49.822 59.693 64.520 62.114 64.388 62.865 Table (5): Elapsed delay time comparison between the four well-known techniques and the proposed OddEven technique for Miss America video sequence Frame 1 Full search FS I 10.756 ms 2 P 3 P 4 P 5 P 6 P 7 P 8 P 9 P 10 P Total Delay Time 28.691 ms 29.323 ms 29.022 ms 28.571 ms 29.242 ms 29.443 ms 29.242 ms 29.032 ms 29.101 ms Conjugate search 10.756 ms 6.459 ms 6.309 ms 6.309 ms 6.309 ms 6.319 ms 6.319 ms 6.329 ms 6.329 ms 6.299 ms 67.737 ms 272.423 ms Three-Step Proposed 2-D Proposed logarithmic search (OddEven) (OddEven) search 3SS search search threshold = threshold = 0.5 0.7 10.756 10.756 10.756 10.756 ms ms ms ms 7.211 ms 6.549 ms 6.099 ms 6.309 ms 7.831 ms 6.890 ms 6.349 ms 6.249 ms 7.110 ms 6.309 ms 6.209 ms 6.269 ms 7.110 ms 6.339 ms 6.109 ms 6.259 ms 7.131 ms 6.339 ms 6.098 ms 6.249 ms 7.110 ms 6.349 ms 6.098 ms 6.279 ms 7.131 ms 7.040 ms 6.088 ms 6.259 ms 8.051 ms 6.339 ms 6.119 ms 6.239 ms 7.121 ms 6.339 ms 6.129 ms 6.229 ms 76.562 ms 69.249 ms 66.054 ms Proposed (OddEven) search threshold = 0.9 67.097 ms 10.756 ms 6.599 ms 6.610 ms 6.600 ms 6.610 ms 6.589 ms 6.600 ms 6.609 ms 6.609 ms 6.630 ms 70.212 ms Table (6): PSNR comparison between the four well-known techniques and the proposed OddEven technique for Miss America video sequence Frame Full search FS Conjugate search 2-D logarithmic search ThreeStep search 3SS Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 Average of PSNR 41.289 40.157 41.143 40.907 41.518 41.370 41.311 Table (7): Compression ratio (Cr) comparison between the four well-known techniques and the proposed OddEven technique for Miss America video sequence Frame Compression ratio (Cr) Full search FS Conjugate search 2-D logarithmic search ThreeStep Search (3SS) Total Cr 34.364 34.609 43.686 45.453 156 Proposed (OddEven) search threshold = 0.5 44.190 Proposed (OddEven) search threshold = 0.7 45.335 Proposed (OddEven) search threshold = 0.9 45.26 New Techniques for Improving H.263 Videoconferencing Table (8): Elapsed delay time comparison between the four well-known techniques and the proposed OddEven technique for Employer video sequence Frame Full search FS 1. I 2. P 3. P 4. P 5. P 6. P 7. P 8. P 9. P 10. P Conjugate search 11.076 ms 31.315 ms 31.225 ms 31.546 ms 31.736 ms 31.455 ms 31.625 ms 31.465 ms 31.034 ms 31.796 ms Total Delay Time 294.273 ms 2-D logarithmic search 11.076 ms 11.076 ms 6.719 ms 7.621 ms 6.559 ms 7.451 ms 6.549 ms 7.470 ms 6.559 ms 7.451 ms 6.559 ms 7.441 ms 6.559 ms 7.430 ms 6.520 ms 7.441 ms 6.550 ms 8.332 ms 6.550 ms 7.430 ms 70.200 ms 79. 143 ms ThreeStep Search (3SS) 11.076 ms 6.609 ms 6.530 ms 7.421 ms 6.509 ms 6.560 ms 7.380 ms 6.579 ms 6.559 ms 7.401 ms 72.624 ms Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 11.076 ms 11.076 ms 11.076 ms 6.179 ms 6.269 ms 6.559 ms 6.179 ms 6.279 ms 6.519 ms 6.189 ms 6.299 ms 6.509 ms 6.148 ms 6.309 ms 6.549 ms 6.168 ms 6.299 ms 6.540 ms 6.159 ms 6.289 ms 6.559 ms 6.159 ms 6.289 ms 6.569 ms 6.169 ms 6.289 ms 6.559 ms 6.139 ms 6.309 ms 6.539 ms 66.565 ms 67.707 ms 69.978 ms Table (9): PSNR comparison between the four well-known techniques and the proposed OddEven technique for Employer video sequence Frame Average of PSNR Full search FS Conjugate search 2-D logarithmic search ThreeStep search 3SS Proposed (OddEven) search threshold = 0.5 Proposed (OddEven) search threshold = 0.7 Proposed (OddEven) search threshold = 0.9 39.951 38.715 39.899 39.613 40.001 40.042 40.062 Table (10): Compression ratio (Cr) comparison between the four well-known techniques and the proposed OddEven technique for Employer video sequence Frame Compression ratio (Cr) Full search FS Conjugate search 2-D logarithmic search ThreeStep Search (3SS) Total Cr 57.760 43.11 64.588 67.45 157 Proposed (OddEven) search threshold = 0.5 67.41 Proposed (OddEven) search threshold = 0.7 65.556 Proposed (OddEven) search threshold = 0.9 66.164 Kamel and Al-Zoubi The Figures Fig. (1): The Thresholding Half-pixel technique Fig. (2a): The OddEven search procedure. Points at (0,-3), (-2,-3), and (-2,-2) are found to give the minimum dissimilarity in steps 1,2, and 3 respectively. 158 New Techniques for Improving H.263 Videoconferencing Fig. (2b): The OddEven search procedure. . Points at (-2, 0), (-2, 2), and (-3, 2) are found to give the minimum dissimilarity in steps 1, 2, and 3 respectively. 159 Kamel and Al-Zoubi Fig. (3): (a) Applying the JPEG technique on the decompressed image. (b) Image histogram. Fig. (4): (a) Applying the traditional Half-Pixel technique on a decompressed Image. (b) Image histogram Fig. (5): (a) Applying the proposed Thresholding Half-Pixel technique on a decompressed Image. (b) Image histogram. 160 New Techniques for Improving H.263 Videoconferencing Fig. (6): Samples of Foreman video frames. (a) Current frame. (b) Previous frame. (c) The difference blocks between the current and previous frames using the proposed OddEven Search (OES) technique. Fig. (7): Samples of Miss America video frames. (a) Current frame. (b) Previous frame. (c) The difference blocks between the current and previous frames using the Three-Step Search (3SS) technique. Fig. (8): Samples of Employer video frames. (a) Current frame. (b) Previous frame. (c) The difference blocks between the current and previous frames using the 2-D logarithmic technique. 161 вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ 2 ( ) elements of a basis of H H . Finally, we find the relation between the residual spectrum of that operator and its norm and we present some example too. Reference [1] Conway J., Acourse in Functional Analysis, printed in the United States of America Springer-Verlag New York ,inc, 1990. [2] Julian M., WsД™p do Analizy Funconalney, Panstwowe Wydawnictwo Naukowe.Warszwa, 1976. [3] Pedersen M., Functional Analysis in Applied Mathematics and Engineering, Chapman Hall crc by Crcpressllc, 2000. [4] Picard R., Evolution Equstions as Operator Equations in Lattices of Hilbert Spaces, Glasnik Matematicki,Vol.35 (55) (2000),III-136 [5] Walter R., Real And Complex Analysis, New Y0rk: McGraw-Hill: 1966. [6] Wawrzynczyk-Antonl "Group Rrpresesentions and Special Functions" D.Reidel Publishing Company Dordrecht-Luncaster Company Copyright by Pwn-Polish Scientific Publishers Warszawa,1984. [7] Yosida K., Functional Analysis, 2dprint Springer-Verlag Berlin. Holmberg. New York, 1966. 24 ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ {Ei }iв€ћ=1 вЉ‚ H 2 (H ) .....................................................................‫ﻗﺎﻋﺪة‬ {ei}iв€€Z ....................................................................‫ﻗﺎﻋﺪة п»“п»І п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄвЂ¬ K ..............................................................‫ﺣп»�п»ћ пє—пєЋЩ… п»‹пєЄШЇЩЉ п»Јпє®п»›пєђ ШЈЩ€ пєЈп»�ﻴп»�ﻲ‬ H ..................................................................................‫ﻓﻀﺎء п»«п» пє’пє®ШЄвЂ¬ H 2 (H) H S ................................................................ ‫ﻓﻀﺎء п»«п» пє’пє®ШЄ ﺷﻤﺖ‬ вЂ«п»Јпє п»¤п»®п»‹пє” п»Јпє†пє›пє®Ш§ШЄ ﺧﻄﻴﺔ п»Јп»ђп» п»�пє” п»Јп»Њпє®ЩЃ п»›п»ћ ﻣﻬﺎ Щ€ п»Јпє®Ш§п»“п»�п»Є п»‹п» п»° п»Јпє п»¤п»®п»‹пє” ﻛﺜﻴﻔﺔ ﻓﻲ‬ H ( ) H H Hr (H ) ШЊ p ШЊ H! (H) ................................................. (11) ‫اﻧﻈﺮ اﻟﺼﻔﺤﺔ‬ I .............................................................вЂ«п»Јпє п»¤п»®п»‹пє” ШЈШЇп»џпє” ЩЊп»—пєЋпє‘п» пє” п»џп» п»ЊпєЄ п»‹п» п»° اﻷﻛﺜﺮ‬ A, B r A, B в€ћ Ae i i =1 ri = C r2 ∑ p , Be i ri , A, B в€ћ пЈ« 1 пЈ¶ = C ∑ пЈ¬ 2 p пЈ· Aei , Bei пЈё i =1 пЈ i 2 p # H = C 2 ∑ fi iв€€I A, B ! = C 2 ! H 2 , Aei , Bej в€ћ ∑ i =1 Aei Bei , i! i! H H Application of Unbounded Linear Operators in Hilbert Spaces Ahmad Ajour and Rainer Picard Abstract H (H ) to be the class of all closed unbounded linear operators A * such that the domains of A and its adjoint operator A contain a basis of the Hilbert space H 2 and they are also dense in H. We show that H (H ) is a Hilbert space with a norm related to a basis of H and we show that, this norm is independent of the chosen basis. We study the 2 2 orthogonality of the subspace of H (H ) and we write any linear operator of H (H ) as the In this paper, we define 2 sum of two orthogonal operators. Moreover, we rewrite that operator as an infinity sum of 23 вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫‪.‬‬ ‫‪=0‬‬ ‫‪jxdx‬‬ ‫‪⋅ 2π‬‬ ‫‪2‬‬ ‫‪π‬‬ ‫)!‪∑ ∫ ( j‬‬ ‫‪jв€€Z −π‬‬ ‫‪=C‬‬ ‫‪2‬‬ ‫!‬ ‫‪H‬‬ ‫‪π2‬‬ ‫‪3‬‬ ‫‪Mej ∂e j‬‬ ‫‪,‬‬ ‫!‪j‬‬ ‫!‪j‬‬ ‫و ﻳﻤﻜﻦ ШЈЩ† ﻧﻜпє�пєђ ШЈп»іп»ЂпєЋ ‪ ∂ В± О»I , M ! = 0 :‬ﻟﻜﻞ ‪ λ‬ﻣﻦ Ш§п»џпє¤п»�п»ћ ‪K‬‬ ‫=‬ ‫‪π2‬‬ ‫)!‪∑3в‹… ( j‬‬ ‫‪2‬‬ ‫∑‬ ‫‪jв€€Z‬‬ ‫‪jв€€Z‬‬ ‫‪=C‬‬ ‫‪2‬‬ ‫!‬ ‫‪M, ∂ ! = C‬‬ ‫‪2‬‬ ‫!‬ ‫اﻟﻤп»�пє�пє®Щ† ШЁ )] ‪([в€’ ПЂ ,π‬‬ ‫‪2‬‬ ‫‪.L‬‬ ‫ﻧпє�пєЋпє‹пєћ Ш§п»џпє’пє¤пєљ Щ€ أﻫﺪاﻓﻪ‪ .‬ﻟп»�пєЄ ﺑﻴﻨﺎ п»“п»І п»«пє¬Ш§ Ш§п»џпє’пє¤пєљ إﻣﻜﺎﻧﻴﺔ Щ€ пєџп»®ШЇ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ ﻣﻦ اﻟﻤﺆﺛﺮات اﻟﺨﻄﻴﺔ ﻏﻴﺮ‬ ‫اﻟﻤﺤﺪودة пє‘пєёп»њп»ћ п»‹пєЋЩ… Щ€ إﻣﻜﺎﻧﻴﺔ пєЈпєґпєЋШЁ ﻧﻈﻴﻢ п»«пє¬Ш§ اﻟﻤﺆﺛﺮ п»Јп»Љ п»›пє�пєЋпє‘пє” اﻟﻤﺆﺛﺮ ﻣﻦ пє»п»’ اﻟﻤﺆﺛﺮات اﻟﻤﻌﺮف п»‹п» п»°вЂ¬ ‫ﺷﻜﻞ п»Јпє п»¤п»®Ш№ пє§п»„п»І ﻟﻤﺆﺛﺮﻳﻦ إﺣﺪاﻫﻤﺎ п»Јпє¤пєЄЩ€ШЇ п»‹п» п»° п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ اﻟﻤﺆﺛﺮ Ш§п»·пє»п» п»ІвЂЄ .‬ﺑﻴﻨﺎ Щ€пєџп»®ШЇ п»—пєЋп»‹пєЄШ© ﻣﻦ‬ ‫اﻟﻤﺆﺛﺮات اﻟﺨﻄﻴﺔ اﻟﻤпє�п»ЊпєЋп»ЈпєЄШ© п»“п»І п»«пє¬Ш§ اﻟﻔﻀﺎء‪ ،‬ﻛﻤﺎ ﺑﻴﻨﺎ Щ€пєџп»®ШЇ п»‹п»јп»—пє” ﺑﻴﻦ ﻧﻈﻴﻢ п»«пє¬Ш§ اﻟﻤﺆﺛﺮ Щ€ ﺑﻴﻦ اﻟﻄﻴﻒ‬ ‫اﻟﻤﻨﻔﺼﻞ ﻟﻬﺬا اﻟﻤﺆﺛﺮ‪.‬ﺣﺎوﻟﻨﺎ Ш§п»џпєЄпє§п»®Щ„ ШҐп»џп»° ﻧﻈﺮﻳﺔ اﻟﻄﻴﻒ‪.‬‬ ‫اﻋпє�п»�пєЄ ШЈЩ† п»џп» пє’пє¤пєљ أﻫﻤﻴﺔ п»“п»І Ш§п»»п»џп»њпє�ﺮوﻧﻴﺎت Щ€ п»“п»І ﻧﻈﺮﻳﺔ اﻟﻜﻢ‪.‬‬ вЂ«Ш§п»џп»њп» п»¤пєЋШЄ Ш°Щ€Ш§ШЄ Ш§п»џпєЄп»»п»џпє” )‪(Keywords‬‬ ‫ﻣﺆﺛﺮ пє§п»„п»І ‪A,B..................................................................................‬‬ ‫ﻏﻼﻗﺔ п»Јпє†пє›пє® ﺧﻄﻲ‬ ‫‪A‬‬ ‫‪:‬و п»«п»® ШЈпє»п»ђпє® пє§п»„п»І п»Јп»ђп» п»– ﻳﺤﻮي‬ ‫‪A‬‬ ‫‪A .....................................‬‬ ‫ﻣﺆﺛﺮ пє§п»„п»І Щ€ п»Јпє¤пєЄЩ€ШЇ п»іп»Њпє�пє’пє® Ш§п»џпє пє°ШЎ Ш§п»·Щ€Щ„ ﻣﻦ ⊥‪AD .................................. A = AB + A‬‬ ‫⊥‪A‬‬ ‫ﻣﺆﺛﺮ пє§п»„п»І ﻏﻴﺮ п»Јпє¤пєЄЩ€ШЇ ШҐЩ† п»џп»ў ﻳﻜﻦ п»Јп»ЊпєЄЩ€п»ЈпєЋЩ‹ п»«п»® Ш§п»џпє пє°ШЎ اﻟﺜﺎﻧﻲ ﻣﻦ ⊥‪A = AB + A‬‬ ‫اﻟﻤﺆﺛﺮ اﻟﻤﺮاﻓﻖ п»џп» п»¤пє†пє›пє® ‪A* ....................................... ......... ................ A‬‬ ‫‪− 1‬‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪−‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪2‬‬ ‫‪i‬‬ ‫‪f‬‬ ‫∑‬ ‫‪iв€€ I‬‬ ‫‪ n‬‬ ‫‪2‬‬ ‫‪cn = пЈ¬ ∑ f i ‬‬ вЂ«вЂЄпЈ i =1‬‬ ‫‪‬‬ ‫‪,‬‬ ‫‪‬‬ ‫‪C := ‬‬ ‫‪пЈвЂ¬вЂ¬ ‫‪,‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪−‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪−‬‬ ‫‪ в€ћ 1 ‬‬ ‫‪Cr = пЈ¬ ∑ 2 ‬‬ вЂ«вЂЄпЈ i =1 r ‬‬ ‫‪,‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪ в€ћ 1 ‬‬ ‫‪ 1‬‬ ‫‪‬‬ ‫∑ ‪, Cp = пЈ¬ ∑ 2 p пЈ· C ! = ‬‬ ‫‪2 ‬‬ ‫(‬ ‫)‬ ‫‪i‬‬ ‫!‬ вЂ«вЂЄпЈ i =1‬‬ ‫‪‬‬ вЂ«вЂЄпЈ i =1 i ‬‬ ‫‪−‬‬ ‫∞‬ вЂ«п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ اﻟﻤﺆﺛﺮ ‪D( A) ................................................................. A‬‬ ‫ﻣﺆﺛﺮ пє—п»”пєЋпєїп» п»І ‪∂ ................................................................................‬‬ ‫‪22‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ A в€€ H 2 (H ) :‫ﻧﻜпє�ﺐ‬ 2 A в€’ О»I 2 = Оµ Ih 2 ОµI = H ( A в€’ О» )h = H 2 h # 2 2 h H 2 Оµ = H 2 = Оµ H 2 h # h в€€ D( A) ‫( ﻟﻜﻞ‬2 ‫و‬ H 2 Оµ > 2 h h 4 2 H ПЂ пЈ± пЈј 2 [ ] H = L пЈ®в€’ ПЂ ,ПЂ пЈ№ = пЈІ f : в€’ ПЂ ,ПЂ в†’ C, measurable, ∫ f ( x) dx < в€ћпЈЅ ‫ ﻟﻴﻜﻦ‬.4‫ﻣﺜﺎل‬ в€’ПЂ пЈі пЈѕ 2 ∂ f (x ) = :‫ﺑﺎﻋпє�ﺒﺎر‬ df ( x ) :‫ ∂ пє‘пєЋп»‹пє�ﺒﺎر‬: D(∂ ) вЉ‚ L2 ([в€’ ПЂ , ПЂ ]) в†’ L2 ([в€’ ПЂ , ПЂ ]) : ‫ﻧﻌﺮف اﻟﻤﺆﺛﺮ‬ dx M : L2 ([в€’ ПЂ , ПЂ ]) в†’ L2 ([в€’ ПЂ , ПЂ ]) : ً‫أﻳﻀﺎ‬ ‫ ﻛﺜﻴﻔﺔ‬D(∂) = C1([в€’ ПЂ ,ПЂ ]) ‫ و‬L 2 2 A! =C 2 ! 2 H 2 ! C ([в€’ ПЂ , ПЂ ]) ∑ iв€€Z Aei i! 2 ∑ jв€€Z пЈ« в€ћ Ae = C ∑ i пЈ¬ i =1 i! пЈ 2 2 i! H пЈ« eijx пЈ¬пЈ¬ d ПЂ 2ПЂ = ∫ пЈ dx в€’ПЂ ∂ej eijx , j в€€ Z = {0,В±1,В±2,...} 2ПЂ 2 :‫ ﻧﺴпє�ﻌﻤﻞ اﻟﻨﻈﻴﻢ اﻟﻤﻌﻄﻰ ﻓﻲ‬. L ([в€’ ПЂ , ПЂ ]) ‫ﻓﻲ‬ H ! (H ) ‫( п»“п»І اﻟﻔﻀﺎء‬22 ) H в€ћ +∑ i =1 Aei i! пЈ¶ 2 1 пЈ·, Ci! = в€ћ пЈ· 1 HпЈё 2∑ 2 i =1 (i!) 2 2 пЈ¶ пЈ·пЈ· пЈё dx 2 2 :‫ = ! ∂ п»џпє¬Ш§ ﻧﻜпє�ﺐ‬C ПЂ 2 ! ∑ ∂e j j! jв€€Z M ! =C ∑ jв€€Z 2 :‫و п»Јп»Ёп»Є п»§пє пєЄвЂ¬ H 2 ij dx j2 j2 2 = C ∑ ∫ 2 = C ∑ 2 = 2C! ∑ 2 < в€ћ. j! H jв€€Z в€’ПЂ ( j!) ПЂ jв€€Z ( j!) jв€€Z ( j!) 2 ! 2 ! 2 2 ! ‫و‬ ‫ п»—пєЋп»‹пєЄШ© ﻓﻲ‬e j (x) = 2 . M , ∂ ! = ? ‫ пє›п»ў ﻧﺤﺴﺐ‬M 2 ‫ﻧﻌﺮف‬ {ei}iв€€Z ‫ إﻧﻪ ﻣﻌﺮوف‬. x в€€ [в€’ ПЂ ,ПЂ ] ‫( ﻣﻦ ШЈпєџп»ћ ﻛﻞ‬Mf )(x ) = xf (x ) :‫ﺑﺎﻋпє�ﺒﺎر‬ ∂e j ‫اﻟﻤﺆﺛﺮ‬ Me j j! 2 ПЂ =C 2 ! H xeijx dx ∑ ∫ ( j!) ПЂ 2 j в€€Z в€’ ПЂ 21 C = C2 ! ! ПЂ = ? ‫ﻧﺤﺴﺐ اﻵن‬ x 2 dx ∑ 2 ∫ jв€€Z в€’ ПЂ 2ПЂ ( j!) вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫‪2‬‬ ‫ﻧﺒﺮﻫﻦ اﻵن‪= 1,в€Ђi, j в€€ N :‬‬ ‫)в€— в€— в€—(‬ ‫‪ Eiej‬ﻓﻲ‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫ﺑﺎﻻﺳпє�п»”пєЋШЇШ© ﻣﻦ‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪ 1 = E i e1вЂ¬п»§пє пєЄвЂЄ:‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪+ f2‬‬ ‫‪H‬‬ ‫ﻟﺒﺮﻫﺎن ‪= 1, в€Ђi, n в€€ N‬‬ ‫(‬ ‫‪2‬‬ ‫و ﻛﺬﻟﻚ‬ ‫ﻣﻦ‬ ‫‪#‬‬ ‫‪#‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪Ei e1‬‬ ‫‪2‬‬ ‫‪= f1‬‬ ‫‪fi‬‬ ‫‪2‬‬ ‫∑‬ ‫‪i =1‬‬ ‫و пє‘пєЋп»»пєіпє�п»”пєЋШЇШ© ﻣﻦ اﻟﻤﺴﺎواة )в€— в€— в€—( п»§пє пєЄвЂ¬ ‫‪n‬‬ ‫‪2‬‬ ‫‪ Ei en‬ﻟﺪﻳﻨﺎ ‪1 = Ei Hn = cn2 ∑ f j Ejej :‬‬ ‫‪H‬‬ ‫‪#‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪ij=11‬‬ ‫‪n в€’1‬‬ ‫‪j =1‬‬ ‫اﻟﻤﺴﺎوﻳпє�ﻴﻦ‬ ‫(‬ ‫‪2‬‬ ‫و Ш°п»џп»љ ﻣﻬﻤﺎ ﻳﻜﻦ ‪. i, j в€€ N‬‬ ‫‪= cn2в€’1 ∑ f j Ei e j‬‬ ‫‪2‬‬ ‫‪Ei e1, Eje1‬‬ ‫‪.‬‬ ‫‪ 1 = Ei e2‬و п»›пє¬п»џп»љ ﻧﻜпє�пєђ п»“п»І ) ‪H 2 (H2‬‬ ‫‪0 =c22 f1 Eie1,Eje1 + f2 Eie2,Eje2‬‬ ‫‪0 = Ei e2 , E j e2‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪ 1 = c2 f1 Eie1 H + f2 Eie2‬ﻟﺬا ﻧﻜпє�ﺐ‪:‬‬ ‫‪E i e2‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪ . H‬ﻧﺮى أن‬ ‫‪= 0, в€Ђi, j в€€ N &i в‰ j & k = 1‬‬ ‫و п»›пє¬п»џп»љ п»“п»І ) ‪ H (H‬ﻟﺪﻳﻨﺎ ‪) :‬‬ ‫)‬ ‫) ‪(H 1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪E ie1‬‬ ‫= ‪ 1‬و‬ ‫ﻧﺤﺼﻞ‬ ‫اﻟﺴﺎﺑп»�пє�ﻴﻦ‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪1 = Ei H n в€’1‬‬ ‫‪= 1, в€Ђ i , n в€€ N‬‬ вЂ«п»‹п» п»°вЂ¬ ‫‪2‬‬ ‫‪H‬‬ ‫‪. E i en‬‬ ‫‪ 0 = Eien , Ejen‬ﻣﻬﻤﺎ ﻳﻜﻦ ‪ n в€€ N :‬و ‪ . в€Ђ i, j в€€ N & i в‰ j‬ﻧﻜﺮر Ш§п»џп»њпє�ﺎﺑﺔ‪:‬‬ ‫‪Eiek , Ejek‬‬ ‫‪n‬‬ ‫‪2‬‬ ‫‪k‬‬ ‫‪∑f‬‬ ‫‪k =1‬‬ ‫‪ 0 = cn‬و‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪E i ek , E j ek‬‬ ‫‪n в€’1‬‬ ‫‪0 = c n2 в€’1 ∑ f k‬‬ ‫‪2‬‬ ‫‪k =1‬‬ ‫ﻣﻦ اﻟﻤﺴﺎوﻳпє�ﻴﻦ ﻧﺤﺼﻞ п»‹п» п»° Ш§п»џп»¤п»„п» п»®ШЁвЂЄ.‬‬ ‫‪2‬‬ ‫ﻧﻈﺮﻳﺔ اﻟﻄﻴﻒ‪ .‬ﻧﻔﺮض ‪ {ei }i =1‬ﻗﺎﻋﺪة п»“п»І п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ ‪. Aв€€H (H) ШЊ H‬‬ ‫∞‬ ‫‪ (1‬إذا п»›пєЋЩ† ‪ Aei = О»ei , i = 1,2,... :‬ﻓﺈن ‪A # = λ‬‬ ‫‪ (2‬إذا п»›пєЋЩ† )‪h в€€ D( A‬‬ ‫‪H‬‬ ‫‪h‬‬ ‫‪ Ah = (О» + Оµ )h ,‬و ‪ Оµ > 0‬ﻓﺈن‪:‬‬ ‫‪ε‬‬ ‫‪2‬‬ ‫>‬ ‫‪H‬‬ ‫‪− О» )h‬‬ ‫‪(A‬‬ ‫=‬ ‫‪H‬‬ ‫‪h‬‬ ‫‪#‬‬ ‫‪A в€’ О»I‬‬ ‫اﻟﺒﺮﻫﺎن‪ (1 .‬إذا п»›пєЋЩ† ‪ Aei = О»ei , i = 1,2,... :‬ﻓﺈن ‪= О» , i = 1,2,...‬‬ ‫‪2‬‬ ‫‪fi‬‬ ‫∞‬ ‫∑‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪= λ‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪Ae i‬‬ ‫‪2‬‬ ‫‪fi‬‬ ‫∞‬ ‫∑‬ ‫‪2‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪i =1‬‬ ‫‪20‬‬ ‫‪= λ‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪. A‬‬ ‫‪H‬‬ ‫‪Aei‬‬ ‫ﻧﺒﺮﻫﻦ‬ ‫اﻵن‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ = B в€— o A, I B A, B =C # 2 в€ћ ∑ 2 fi i =1 в€ћ . # = C 2 ∑ fi 2 i =1 Ae i , Be i I Aei , Aв€— o Bei = I A , Aв€— o B в€ћ Ei , E j = C2 ∑ fk # ШЊ H 2 (H ) ‫ﻗﺎﻋﺪة ﻓﻲ‬ ‫و‬nв€€ N : # 2 ik =1 = E в€—j o Ei , I j # H . E в€—j o Ei ek , I j ek H . .‫( ﺗﺒﺮﻫﻦ пє‘п»Ёп»”пєІ Ш§п»џп»„пє®п»іп»�ﺔ‬27 ) ‫( و‬26 ) ‫إن اﻟﻤﺴﺎواة‬ {Ei }iв€ћ=1 вЉ‚ H 2 (H ) ‫ﻣﻬﻤﺎ ﻳﻜﻦ‬ H {ei }iв€ћ=1 ‫ و‬H ‫ﻗﺎﻋﺪة п»“п»І п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄвЂ¬ 0 = Ei en , E j en Eie j ‫و‬ # H .5‫ﻧﻈﺮﻳﺔ‬ = 1, в€Ђi, j в€€ N :‫ﻋﻨﺪﺋﺬ‬ . в€Ђ i, j в€€ N & i в‰ j { } :ً‫ Щ€ ﻧﻌﺮف Ш§п»џп»”п»ЂпєЋШЎ أﺑﻀﺎ‬Hn := hn = ( x1, x2 ,...xn ,0,0...) : h = {xi }i =1 ‫ ﻧﻌﺮف‬.‫اﻟﺒﺮﻫﺎن‬ в€ћ пЈ± H 2 (Hn ) = пЈІAH n : A в€€ H 2 (H ) : AH n пЈі пЈ« n 2пЈ¶ cn2 = пЈ¬ ∑ f i пЈ· пЈ i =1 пЈё H 2 (H 1 ) вЉ‚ H (H 2 ) вЉ‚ # n 2 2 пЈј = cn2 ∑ fi Aei H пЈЅ i =1 пЈѕ 1 2 H1 вЉ‚ H2 вЉ‚ ... вЉ‚ Hn вЉ‚ ...H ‫و‬ 2 в€’ 2 ... H 2 (H n ) вЉ‚ ... H 2 (H ) :‫ﻧﺮى أن‬ :‫و ﻧﻼﺣﻆ‬ 2 n пЈ«в€ћ 2 2 2 пЈ¶ lim∑ fi Aei в€’ ∑ fi Aei H пЈ· = 0 : ‫ ﻷن‬lim AHn пЈ· nв†’в€ћпЈ¬ nв†’в€ћ i =1 H пЈё пЈ i=1 2 . lim cn f i n в†’в€ћ 19 2 AHn 2 H 2 # = A# = A # :‫و п»«пє¬Ш§ п»іпє†ШЇЩЉ إﻟﻰ‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ 1 ‫ в€€ ∂ ﻷﻧﻪ п»Јп»ђп» п»– Щ€ ﻧﻈﻴﻤﻪ п»Јпє¤пєЄЩ€ШЇ ﻣﻦ أﺟﻞ‬H p (H ) ‫ﻋﻨﺪﺋﺬ‬ 2 . H ‫ﻓﻲ‬ 1 :‫ п»‹п»ЁпєЄпє‹пє¬ п»§пє пєЄ أن‬fn ( x) = sinnx, x в€€ [в€’ ПЂ ,ПЂ ], n = 1,2,... ‫ﻟﻴﻜﻦ‬ n ‫ Щ€ п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»”п»Є ﻛﺜﻴﻒ‬p в€’ 1 > f n в€€ D(∂), n в€€ N . fn 2 ПЂ ПЂ 1 = ∫ sin x dx = 2 ‫ﻣﻮﺿﺤﻴﻦ أن‬ n n в€’ПЂ 2 L2 :‫و ﻧﺮى ﺑﺴﻬﻮﻟﺔ‬ fn в€’ 0 L2 = fn ПЂ = L2 n в†’в€ћ пЈ§ nпЈ§ пЈ§в†’ 0 :‫و ﻟﻜﻦ‬ ПЂ 2 ∂f n L 2 ∫π = в€’ 2 d 1 sin nx dx = dx n ПЂ ∫π cos nx 2 dx = ПЂ в‰ 0 в€’ : ‫و п»Јп»Ёп»Є п»іп»Ёпє�ﺞ‬ . ∂ ‫ Щ€ п»«пє¬Ш§ п»іп»Њп»Ёп»І п»‹пєЄЩ… Ш§пє—пєјпєЋЩ„ اﻟﻤﺆﺛﺮ‬. ‫ﻗﺎﻋﺪة ﻓﻲ‬ {Ei }iв€ћ=1 вЉ‚ H 2 (H ) A, B в†’в€ћ ∂fn в€’0 L2 пЈ§nпЈ§в†’ пЈ§ ПЂ в‰ 0 ‫ Щ€ ﻟﻜﻦ‬f n пЈ§пЈ§H в†’ 0 , n в†’ в€ћ ШЊ H ‫ﻗﺎﻋﺪة п»“п»І п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄвЂ¬ ‫ ﻧﻔﺮض‬.‫ﻧﻈﺮﻳﺔ ﺗﻤﻬﻴﺪﻳﺔ‬ : ‫ ﻋﻨﺪﺋﺬ‬A, B в€€ H 2 (H ) ‫ و‬H 2 (H ) = B в€— o A, I B # {ei }iв€ћ=1 # = I A , A* o B (25) # I A : D ( A) в†’ H , I A h = h 0 = Ei , E j # 1 = Ei , , E i = E в€—j o Ei , I j $ # = I i , Eiв€— o E j , i в‰ j # = I i , Eiв€— o Ei # = Eiв€— o Ei , I i # Ii : D(Ii ) в†’ H, Iih = h, I j : D(I j ) в†’ H, I jh = h,i, j = 1,2,... :‫ﺑﺎﻋпє�ﺒﺎر‬ (26) (27 ) ‫ﺑﺎﻋпє�ﺒﺎر‬ : (8) ‫( ﻧﺴпє�ﻌﻤﻞ Ш§п»џпє�ﻌﺮﻳﻒ‬25) ‫ ﻟﺒﺮﻫﺎن‬.‫اﻟﺒﺮﻫﺎن‬ A, B в€ћ # = C 2 ∑ fi 2 i =1 в€ћ = C 2 ∑ fi i =1 Aei , Bei 2 H B в€— o Aei , I B ei H 18 ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫ﻧﻈﺮﻳﺔ‪ .4‬ﻧﻔﺮض ‪ {ei }i =1‬ﻗﺎﻋﺪة п»“п»І п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄвЂ¬ ‫∞‬ ‫‪A в€€ H 2 (H ) ШЊ H‬‬ ‫و п»«пє¬Ш§ ﻳﻌﻄﻲ‪ :‬ﻳﻮﺟﺪ‬ ‫‪ . в€Ђh в€€ D ( A) ШЊ Ah H в†’ 0, h в†’ 0,в‡’ A # < M ШЊ M > 0‬و ﻟﻜﻦ Ш§п»»п»—пє�п»ЂпєЋШЎ Ш§п»џп»Њп»њпєґп»І ﻏﻴﺮ‬ ‫ﻣﺤп»�ﻖ‪.‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻟﻴﻜﻦ ) ‪ A в€€ H (H‬و )‪ h в€€ D( A‬ﺑﺎﻋпє�ﺒﺎر‪→ 0 , for , h в†’ 0 :‬‬ ‫‪H‬‬ ‫‪ Ah‬ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪< δ‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪ ШЊ в€€> 0‬ﻳﻮﺟﺪ ‪ Оґ (в€€) > 0‬ﺑﺎﻋпє�ﺒﺎر‪<в€€ :‬‬ ‫أن ﻧﻜпє�ﺐ‪≤ M f i :‬‬ ‫‪H‬‬ ‫‪. h‬ﻟﺬا ﻳﻤﻜﻦ‬ ‫‪ f i Aei‬و п»Јп»Ёп»Є ﻧﻜпє�ﺐ‪:‬‬ ‫‪2‬‬ ‫و пєЈпєґпєђ пє—п»Њпє®п»іп»’ اﻟﻨﻈﻴﻢ‪:‬‬ ‫‪H‬‬ ‫‪Ah‬‬ ‫و ﻫﻜﺬا‬ ‫‪2‬‬ ‫‪fi‬‬ ‫‪≤ M‬‬ ‫∞‬ ‫∑‬ ‫‪2‬‬ ‫‪≤M‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪f i Ae i‬‬ ‫∞‬ ‫∑‬ ‫‪i =1‬‬ ‫‪. A‬‬ ‫ﻟﻜﻦ Ш§п»џп»Њп»њпєІ ﻏﻴﺮ ﺻﺤﻴﺢ ﻟﻬﺬا п»іп»њп»”п»І пє—п»�пєЄп»іп»ў اﻟﻤﺜﺎل Ш§п»џпє�ﺎﻟﻲ‪:‬‬ ‫‪π‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪2‬‬ ‫ﻣﺜﺎل‪ .3‬ﻟﻴﻜﻦ‪, ∫ f (t ) dt < в€ћпЈЅ :‬‬ ‫‪ H =: L = пЈІ f : [в€’ ПЂ ,ПЂ ] в†’ R, measurable‬و‬ ‫‪−π‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪2‬‬ ‫)‪df (x‬‬ ‫)] ‪ D( A) = C1 ([в€’ ПЂ , π‬ﺑﺎﻋпє�пє’пєЋШ± ‪:‬‬ ‫‪dx‬‬ ‫∞‬ ‫إﻧﻪ п»Јп»Њпє®Щ€ЩЃ ШЈЩ† ) ∂( ‪ DвЂ¬п»Јпє п»¤п»®п»‹пє” ﻛﺜﻴﻔﺔ п»“п»І ‪ L2‬و ‪: {ei }i =1‬‬ ‫‪1‬‬ ‫‪sin x‬‬ ‫‪cos x‬‬ ‫‪sin 2x‬‬ ‫‪cos2x‬‬ ‫= )‪e0 ( x‬‬ ‫)‪, e1, ( x‬‬ ‫= )‪, e2 ( x‬‬ ‫)‪, e3 ( x‬‬ ‫= )‪, e4 (x‬‬ ‫‪,...‬‬ ‫‪π‬‬ ‫‪π‬‬ ‫‪π‬‬ ‫‪π‬‬ ‫‪2π‬‬ ‫ﻛﺜﻴﻔﺔ п»“п»І ‪، L2‬اﻧﻈﺮ п»“п»І ]‪ [2‬و ﻫﻜﺬا‪:‬‬ ‫‪∂ : C1([в€’ ПЂ ,ПЂ ]) вЉ‚ L2 в†’ L2 & A = ∂ :‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫∞‬ ‫‪d (sin nx ) dx‬‬ ‫‪d (cos nx ) dx‬‬ ‫∫ ∑ ‪2p +‬‬ ‫‪n‬‬ ‫‪n2 p‬‬ ‫‪dx в‹… π‬‬ ‫‪n =1 в€’ ПЂ dx в‹… π‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪π‬‬ ‫‪π‬‬ ‫∫‬ ‫‪−π‬‬ ‫∞‬ ‫‪‬‬ ‫∑ ‪= C пЈ¬0 +‬‬ ‫‪‬‬ ‫‪n =1‬‬ ‫‪пЈвЂ¬вЂ¬ ‫‪2‬‬ ‫‪p‬‬ ‫‪2‬‬ ‫‪p‬‬ ‫‪ в€ћ n2 ПЂ dx ‬‬ ‫‪= C пЈ¬пЈ¬ ∑ 2 p ∫ ‬‬ вЂ«вЂЄпЈ n =1 n в€’ПЂ ПЂ ‬‬ ‫‪2‬‬ ‫‪p‬‬ ‫‪.‬‬ ‫‪1‬‬ ‫∞‬ ‫‪1‬‬ ‫‪1 + 2∑ 2 p‬‬ ‫‪n =1 n‬‬ ‫‪17‬‬ ‫= ‪, C p2‬‬ ‫‪2‬‬ ‫)‪2 ( p в€’1‬‬ ‫∞‬ ‫∑ ‪= C p2‬‬ ‫‪n =1 n‬‬ ‫∂‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫اﻟﺒﺮﻫﺎن‪.‬‬ ‫ﻣﻦ‬ ‫ﻧﻜпє�ﺐ‪, в€Ђi в€€ N :‬‬ ‫اﻟﻔﺮض‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪≤ M 2 ei‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪An ei‬‬ ‫ﻣﻊ‬ ‫ﻣﻼﺣﻈﺔ‪:‬‬ ‫‪2‬‬ ‫) ‪ {ei}iв€ћ=1 = ID( An‬و п»«п»њпє¬Ш§ ‪fi Anei H ≤ M2 fiei H,в€Ђn =1,2,...‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪nв€€N‬‬ ‫‪2‬‬ ‫‪k‬‬ ‫‪≤ M C ∑ fi‬‬ ‫‪k‬‬ ‫‪∑ f Ae‬‬ ‫‪2‬‬ ‫‪2 2‬‬ ‫‪i n i H‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪M‬‬ ‫‪i =1‬‬ ‫ﻟﻜﻞ ‪. k в€€ N‬و Ш§п»џп»Ёпє�п»ґпє пє” ﻫﻲ‪:‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪. An # ≤ M2, n = 1,2,...‬إذا п»›пєЋЩ† в€ћ = ‪An #‬‬ ‫∞=‬ ‫∞‬ ‫‪∑ f Ae‬‬ ‫‪2‬‬ ‫‪i n i H‬‬ ‫ﻧпє�п»ґпє пє” ‪ .3‬إذا ﻛﺎن‬ ‫‪2‬‬ ‫‪M‬‬ ‫‪i =1‬‬ ‫‪⊂H‬‬ ‫‪R‬‬ ‫‪An # ‬‬ ‫→‪‬‬ ‫‪A#‬‬ ‫ﻣﺎ ‪ ШЊ n в€€ N‬ﻫﺬا п»іпє†ШЇЩЉ إﻟﻰ‬ ‫ﻣﻦ ШЈпєџп»ћ ﻗﻴﻤﺔ‬ ‫و п»Јп»Ёп»Є п»іп»Ёпє�пєћ )‪ An ∉H2(H‬و п»«пє¬Ш§ ﺗﻨﺎﻗﺾ‪.‬‬ ‫} ‪{e‬‬ ‫∞‬ ‫`= ‪i i‬‬ ‫ﻗﺎﻋﺪة ‪⊂ H 2 (H ) ШЊ H‬‬ ‫}‬ ‫‪ {A‬ﺑﺎﻋпє�ﺒﺎر‪:‬‬ ‫∞‬ ‫‪n n =1‬‬ ‫ﻟﻤﺎ в€ћ в†’ ‪ n‬ﻓﺈن п»«пє¬Ш§ п»» п»іпє†ШЇЩЉ ШҐп»џп»° ‪:‬‬ ‫‪H‬‬ ‫→‪ An h ‬ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪h в€€ D( An ), n в€€ N‬‬ ‫∞ в†’ ‪Ah, , n‬‬ ‫ﻣﺜﺎل‪ .3‬ﻟﻴﻜﻦ ‪ A : H в†’ H‬و ) ‪ H = l 2 (C‬ﺑﺎﻋпє�ﺒﺎر‪:‬‬ ‫)‬ ‫إذا Щ€ ﺿﻌﻨﺎ‬ ‫(‬ ‫‪Ax := x1 ,22 x2 ,..., i 2 xi ,...‬‬ ‫‪n n в€’1‬‬ ‫(‬ ‫)‪An x := (в€’1‬‬ ‫‪x1,22 x2 ,...,i2 xi ,...), n = 1,2,...‬‬ ‫‪n‬‬ ‫ﻓﺈﻧﻨﺎ п»§пє пєЄвЂЄ:‬‬ ‫∞‬ ‫‪i4‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫∑ ‪A p =C‬‬ ‫)‪= C ∑ 2 p = Cp ∑ 2( pв€’2‬‬ ‫‪i =1‬‬ ‫‪i =1 i‬‬ ‫‪i =1 i‬‬ ‫‪H‬‬ ‫‪5‬‬ ‫‪1‬‬ ‫) ‪ A в€€ H p (H‬ﻣﻦ ШЈпєџп»ћ > ‪ . p > ⇔ p в€’ 2‬ﻧﻼﺣﻆ п»›пє¬п»џп»љ أن‪:‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫∞‬ ‫و п»«п»њпє¬Ш§ ﻓﺈن‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪,n в€€ N‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪p‬‬ ‫‪Aei‬‬ ‫‪ip‬‬ ‫∞‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪p‬‬ ‫‪ n n в€’1 ‬‬ ‫)‪An x в€’ Ax H = пЈЇ(в€’1‬‬ ‫‪−1пЈє x1,22 x2 ,32 x3,...‬‬ ‫‪n‬‬ ‫‪‬‬ ‫‪‬‬ ‫(‬ ‫)‬ ‫‪≠0‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪lim An x в€’ Ax‬‬ ‫∞→‪n‬‬ ‫‪-5‬ﺑﻌﺾ Ш§п»џпє�ﻄﺒﻴп»�пєЋШЄ п»“п»І Ш§п»џп»”п»ЂпєЋШЎШ§ШЄ ) ‪: H 2 (H‬‬ ‫‪16‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫) ‪(H‬‬ ‫ﻟﺒﺮﻫﺎن )‪ (2‬ﻧﻜпє�ﺐ‪:‬إذا ﻛﺎن‬ ‫‪2‬‬ ‫‪ A в€€ H‬و )‪ Re( A‬ﻛﺜﻴﻔﺔ п»“п»І ‪ H‬و‬ ‫أﺟﻞ п»›п»ћ )‪، h в€€ D( A‬ﻋﻨﺪﺋﺬ ﻣﻦ ШЈпєџп»ћ п»›п»ћ ) ‪ h1 , h2 в€€ D ( A‬إذا ﻛﺎن‬ ‫إﻟﻰ‬ ‫‪≥ 0,‬‬ ‫‪≥ M h1 в€’ h2‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪ Ah H ≥ M h‬ﻣﻦ‬ ‫‪Ah1 = Ah2‬‬ ‫‪0 = Ah1 в€’ Ah 2‬‬ ‫) (‬ ‫وﻫﺬا п»іп»Њп»Ёп»І ‪ h1 = h2 :‬و п»Јп»Ёп»Є п»§пє пєЄ ‪Aв€’1 : D Aв€’1 в†’ H ШЊ D(Aв€’1 ) = Re( A) :‬‬ ‫‪Aв€’1h ≤ M′ h H‬‬ ‫‪H‬‬ ‫‪= M′‬‬ ‫‪H‬‬ ‫‪≤ M ′ ei‬‬ ‫ﻧﻈﺮﻳﺔ‪ .3‬ﻟпє�ﻜﻦ‬ ‫ﻣﻦ‬ ‫ﻛﻞ‬ ‫أﺟﻞ‬ ‫) (‬ ‫‪h в€€ D A в€’1‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫‪ A ei‬و п»«пє¬Ш§ п»іпє†ШЇЩЉ ШҐп»џп»° Ш§п»џп»¤п»„п» п»®ШЁ Щ€ п»«п»® ‪≤ M ′‬‬ ‫‪1‬‬ ‫‪M‬‬ ‫‪−1‬‬ ‫‪H‬‬ ‫‪{ei }iв€ћ=1 вЉ‚ H‬‬ ‫= ‪M′‬و‬ ‫‪−1‬‬ ‫‪#‬‬ ‫‪. A‬‬ ‫ﻗﺎﻋﺪة ‪ H‬و )‪ {An}n=1 вЉ‚ H (H‬ﺑﺤﻴﺚ أن‪:‬‬ ‫∞‬ ‫‪2‬‬ ‫‪Anh в†’ Ah, n в†’ в€ћ, в€Ђh в€€ D( An ), n = 1,2,...‬‬ ‫ﻋﻨﺪﺋﺬ ‪:‬‬ ‫‪→ A#‬‬ ‫‪An‬‬ ‫‪#‬‬ ‫ﻟﻤﺎ‬ ‫∞→‪n‬‬ ‫‪H‬‬ ‫‪ . Anei ‬و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻳﻤﻜﻦ ШЈЩ† ﻧﻜпє�пєђ ‪→Aei , n в†’в€ћ,i = 1,2,...‬‬ ‫‪, n в†’ в€ћ , i = 1,2,...‬‬ ‫‪H‬‬ ‫‪→ Aei‬‬ ‫‪H‬‬ ‫‪An ei‬‬ ‫و пє‘пєЋп»џпє п»¤п»Љ ﻧﺤﺼﻞ п»‹п» п»°вЂ¬ ‫‪, n в†’ в€ћ,в€Ђk в€€ N‬‬ ‫‪k‬‬ ‫‪∑ f Ae‬‬ ‫‪2‬‬ ‫‪i H‬‬ ‫‪i‬‬ ‫‪‬‬ ‫‪→C‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪k‬‬ ‫‪∑ f в‹… Ae‬‬ ‫‪n i H‬‬ ‫‪i‬‬ ‫‪2‬‬ ‫‪C‬‬ ‫‪i =1‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪#‬‬ ‫‪→ A‬‬ ‫‪ An‬ﻟﻤﺎ‬ ‫‪#‬‬ ‫∞→‪n‬‬ ‫ﻣﻊ ﻣﻼﺣﻈﺔ أن‬ ‫∞<‬ ‫ﻧпє�п»ґпє пє” ‪.2‬‬ ‫‪#‬‬ ‫إذا п»›пєЋЩ† ‪{ei}iв€ћ=1 вЉ‚H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪An h H ≤ M 2 h H‬‬ ‫} ‪{A‬‬ ‫∞‬ ‫‪n # n =1‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪ An‬و в€ћ < ‪ A #‬ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪. n в€€ N‬‬ ‫ﻗﺎﻋﺪة ‪ {An}n=1 вЉ‚ H (H) ШЊ H‬ﺑﺎﻋпє�ﺒﺎر‪:‬‬ ‫‪2‬‬ ‫ﻣﻦ ШЈпєџп»ћ п»›п»ћ ) ‪( An‬‬ ‫∞‬ ‫‪ n = 1,2,... ШЊ h в€€ D‬و ‪. M > 0‬ﻋﻨﺪﺋﺬ‪:‬‬ ‫ﻣпє�пє�ﺎﻟﻴﺔ ﻣﺤﺪودة‪.‬‬ ‫‪15‬‬ ‫ﻫﺬا ﻳﺆدي‬ ‫ﻣﻮﺟﻮد و‬ ‫ﻧﻜпє�ﺐ‬ ‫‪:‬‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫‪2‬‬ ‫)‪(23‬‬ ‫‪ci‬‬ ‫∞‬ ‫∑‬ ‫‪+‬‬ ‫‪2‬‬ ‫‪bi‬‬ ‫‪i =1‬‬ ‫∞‬ ‫∑‬ ‫=‬ ‫‪2‬‬ ‫‪i =1‬‬ ‫‪ai‬‬ ‫∞‬ ‫∑‬ ‫‪i =1‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻧﺴпє�ﻔﻴﺪ ﻣﻦ اﻟﻨﻈﺮﻳﺔ Ш§п»џпє�ﻤﻬﻴﺪﻳﺔ )‪:(1‬‬ ‫‪ (1‬ﻣﻦ ШЈпєџп»ћ п»›п»ћ ) ‪A в€€ H 2 (H‬‬ ‫∞‬ ‫∞‬ ‫‪i=1‬‬ ‫‪i=1‬‬ ‫ﻳﻤﻜﻦ п»›пє�пєЋпє‘пє�п»Є ﺑﺎﻟﺸﻜﻞ‪:‬‬ ‫(‬ ‫)‬ ‫⊥‪AB + A‬‬ ‫∞‬ ‫∞‬ ‫‪i=1‬‬ ‫‪i=1‬‬ ‫= ‪ AвЂ¬п»‹п» п»° )‪ D ( A‬و‬ ‫‪AB + AвЉҐ = A = ∑ai Ei = ∑ai EBi вЉ•EвЉҐi = ∑ai EBi ⊕∑ai EвЉҐii‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫∞‬ ‫∞‬ ‫‪i =1‬‬ ‫‪i =1‬‬ ‫))‪AB = ∑ai EBi в€€ B(D( A)), AвЉҐ = ∑ai EвЉҐii в€€ BвЉҐ (D( A‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫‪ {Ei}iв€ћ=1‬ﻗﺎﻋﺪة п»“п»І ) ‪ . H (H‬ﻟﺒﺮﻫﺎن )‪ (2‬ﻧﻜпє�пєђ ‪ :‬ﺑﻤﺎ ШЈЩ† ) ‪(H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪ AB в€€ H‬ﻟﺬا ‪AB = ∑ai Ei‬‬ ‫∞‬ ‫‪i =1‬‬ ‫∞‬ ‫و п»›пє¬п»џп»љ ) ‪AвЉҐ в€€ H 2 (H‬‬ ‫‪2‬‬ ‫∞‬ ‫∞‬ ‫و п»«пє¬Ш§ ﺑﺴﻤﺢ п»џп»ЁпєЋ пє‘пєЋп»џп»њпє�ﺎﺑﺔ‬ ‫‪i‬‬ ‫‪∑cE‬‬ ‫‪i‬‬ ‫‪i =1‬‬ ‫= ⊥‪A‬‬ ‫و Ш§п»џп»Ёпє�п»ґпє пє” ‪:‬‬ ‫∞‬ ‫‪. ∑ ai = ∑ bi + ∑ ci‬‬ ‫‪2‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪i =1‬‬ ‫} ‪{e‬‬ ‫∞‬ ‫ﻧﻈﺮﻳﺔ‪ .2‬ﻟﻴﻜﻦ ‪i i =1‬‬ ‫‪i =1‬‬ ‫ﻗﺎﻋﺪة п»“п»І ‪ H‬و ) ‪(1 . A в€€ H 2 (H‬ﻋﻨﺪﺋﺬ‪≥ M > 0 Щђ :‬‬ ‫‪#‬‬ ‫‪ A‬إذا‬ ‫ﺗﺤп»�п»– Ш§п»џпєёпє®Ш· Ш§п»џпє�ﺎﻟﻲ‪:‬‬ ‫‪Ah H ≥ M h H‬‬ ‫)‪(24‬‬ ‫ﻣﻦ ШЈпєџп»ћ п»›п»ћ )‪ h в€€ D( A‬ﺑﺎﻋпє�пє’пєЋШ± ‪. M > 0‬‬ ‫‪ (2‬إذا п»›пєЋЩ† )‪ (24‬ﻣﺤп»�п»�пєЋЩ‹ Щ€ )‪ Re( A‬ﻛﺜﻴﻔﺔ п»“п»І ‪ H‬ﻋﻨﺪﺋﺬ‪Aв€’1 : D(Aв€’1 ) вЉ‚ H в†’ H :‬‬ ‫ﺑﺎﻋпє�пє’пєЋШ± )‪D (Aв€’1 ) = Re( A‬‬ ‫‪1‬‬ ‫‪M‬‬ ‫‪Aв€’1h ≤ M′ h H‬‬ ‫و‬ ‫‪H‬‬ ‫= ‪ M ′‬و ШЈп»›пєњпє® ﻣﻦ Ш°п»џп»љ ‪≤ M ′ :‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬إذا п»›пєЋЩ† ) ‪A в€€ H 2 (H‬‬ ‫‪H‬‬ ‫‪−1‬‬ ‫‪#‬‬ ‫‪≥M h‬‬ ‫‪H‬‬ ‫‪.‬‬ ‫ﻣﻦ ШЈпєџп»ћ п»›п»ћ )‪ h в€€ D( A‬ﻋﻨﺪﺋﺬ‬ ‫‪ Aei H ≥ M ei H ,i = 1,2,...‬ﻧﻜпє�ﺐ‪fi Aei H ≥ M fi ei H,i =1,2,3,...:‬‬ ‫∞‬ вЂ«п»§пє пєЄвЂЄв‰Ґ C2M 2 ∑ fi = M 2 :‬‬ ‫‪2‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪h в€€D Aв€’1‬‬ ‫ﻣﻦ ШЈпєџп»ћ ﻛﻞ‬ ‫‪ A‬إذا п»›пєЋЩ† )‪{ei}iв€ћ=1 вЉ‚ D(Aв€’1‬‬ ‫‪Ah‬‬ ‫) (‬ ‫و ﻣﻨﻪ‬ ‫∞‬ ‫‪2‬‬ ‫‪ C ∑ fi Aei‬و п»«пє¬Ш§ п»іп»Њп»Ёп»І ‪≥ M > 0 :‬‬ ‫‪i =1‬‬ ‫‪14‬‬ ‫ﻣﻮﺟﻮد‬ ‫‪#‬‬ ‫‪. A‬‬ ‫و‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ пЈ« i 2 ei 0 пЈ¬ ‫ Щ€ ШЈп»›пєњпє® ﻣﻦ‬C 0 + 2 , p пЈ¬ i c2 i пЈ p 0 j ej + 0 + ... + 0 + p , p j j c2 2 p H H пЈ¶ + 0 + ... + 0пЈ· = 0 пЈ· пЈё T = в€ћ ∑aT i =1 ai = T, Ti =C ∑ Ti 2 p =C j =1 2 p p jej i2ei , j2 i2C2 в€ћ 2 2 =C 2 2 в€ћ Ti e j j =1 jp ∑ в€ћ ∑ ij=1 Tej i 2ei , j 2 i 2c2 1 = C2 , i =1,2,3...,p = 2 i H 2 2 2 H :‫ذﻟﻚ‬ H пЈ« i 2e = C пЈ¬ 0 + ...+ 2 i пЈ¬ i C2 пЈ 2 i i H пЈ¶ + 0 + ...пЈ· = 1 пЈ· пЈё ‫و ﻫﻜﺬا‬ T 2 p в€ћ = ∑ ai i =1 2 в€ћ =∑ i =1 C2 i 2 = C 22 C12 . C2 i 2 пЈ«в€ћ пЈ¶ Tx = ∑ixi ei = ∑ xi ei = пЈ¬ ∑ai в‹…Ti пЈ·x i =1 i =1 i C2 пЈ i =1 пЈё в€ћ в€ћ . x в€€ l ‫ﻟﻜﻞ‬ 2 :‫ﺑﻌﺾ Ш§п»џпєЁпєјпєЋпє‹пєє Щ€ Ш§п»џп»Ёпє�ﺎﺋﺞ‬-4 ‫ ﻋﻨﺪﺋﺬ‬H 2 (H ) ‫{ п»—пєЋп»‹пєЄШ© ﻓﻲ‬Ei}iв€ћ=1 ‫ و‬H ‫ﻗﺎﻋﺪة ﻓﻲ‬ {ei }iв€ћ=1 ‫ﻟпє�ﻜﻦ‬ .(1)‫ﻧﻈﺮﻳﺔ‬ : A в€€ H (H ) ‫ﻟﻜﻞ‬ 2 ШЊ D ( A) ‫ п»‹п» п»°вЂ¬A = AB + AвЉҐ в€ћ AвЉҐ = ∑ai EвЉҐi в€€BвЉҐ(D( A)) ШЊ AB = i=1 :‫ п»‹п»ЁпєЄпє‹пє¬ ﻳﻜﻮن‬AвЉҐ = в€ћ ∑ c E в€€ B (D ( A)) ‫و‬ i =1 вЉҐ i i 13 (1 в€ћ ∑a E i =1 в€ћ i Bi в€€ B (D ( A )) AB = ∑bi Ei в€€ B(D( A)) : ‫( ШҐШ°Ш§ ﻛﺎن‬2 i =1 вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫‪ (2‬أﻣﺎ ﻣﻦ ШЈпєџп»ћ ‪r >1‬‬ ‫ﻓﺈﻧﻪ п»іп»њп»®Щ† п»џпєЄп»іп»ЁпєЋ ) ‪ I в€€ H r (H‬و ﻟﻜﻦ‬ ‫‪1‬‬ ‫‪1‬‬ ‫‪ в€ћ 1пЈ¶2 пЈ« 1 пЈ¶2‬‬ ‫‪. I r = ∑ 2 пЈ· = пЈ¬ 2‬‬ ‫‪ в‰ 1‬‬ ‫‪пЈr в€’r ‬‬ вЂ«вЂЄпЈ i =1 r ‬‬ ‫ب ‪ C‬ﻓﻤﻦ أﺟﻞ‬ ‫‪ (II‬ﻳпє�п»њпє®Ш± Ш§п»·п»Јпє® п»“п»І ) ‪ H p (HвЂ¬п»“п» п»® п»‹пє®п»“п»ЁпєЋ Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І ) ‪ (20‬دون Ш§п»џп»Ђпє®ШЁ ِ‬ ‫‪1‬‬ ‫‪ p = 0‬ﻧﺤﺼﻞ п»‹п» п»°вЂЄ Hp(H) = HS :‬و ﻟﻜﻦ ﻣﻦ أﺟﻞ‬ ‫‪2‬‬ ‫‪1‬‬ ‫‪1 пЈ¶2‬‬ ‫‪ в‰ 1‬‬ ‫∑‬ ‫‪2 p‬‬ ‫‪i =1 i‬‬ ‫‪‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫ﻣﺜﺎل‪ .3‬ﻟﻴﻜﻦ ‪ H = l‬و ‪ T : l в†’ l‬ﺑﺎﻋпє�ﺒﺎر‪:‬‬ ‫∞‬ ‫> ‪ p‬ﻓﺈن ) ‪ I в€€ H p (H‬و‬ ‫‪‬‬ ‫‪= ‬‬ ‫‪пЈвЂ¬вЂ¬ ‫‪. I‬‬ ‫‪p‬‬ ‫)‪T(x1, x2, x3,...) = (x1,2x2,3x3,...‬‬ ‫واﺿﺢ ШЈЩ† ‪ T‬ﻫﻮ пє§п»„п»І п»Јп»ђп» п»– و‬ ‫‪(T ) = l 2‬‬ ‫‪. D‬أذا Щ€пєїп»Њп»ЁпєЋ ‪ ШЊ p = 2‬ﻋﻨﺪﺋﺬ‬ ‫‪1 C22‬‬ ‫‪=C ∑ 2 = 2‬‬ ‫‪C1‬‬ ‫‪i =1 i‬‬ ‫∞‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪Tei‬‬ ‫‪i2‬‬ ‫∞‬ ‫∑‬ ‫‪i =1‬‬ ‫‪=C‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪p‬‬ ‫‪T‬‬ ‫إذا ﻋﺮﻓﻨﺎ‬ ‫‪A : l2 в†’ l2 , B : l2 в†’ l2‬‬ ‫)‪A(x1,x2,..) =(x1,2x2,...nxn,...),B(x1,x2,...) =(0,0,...,0,(n+1)xn+1,(n+2))xn+2,...‬‬ ‫و п»Јп»Ёп»Є ﻧﻜпє�ﺐ‬ ‫‪ . T = A вЉ• B‬إذا п»‹пє®п»“п»ЁпєЋ ШЈп»іп»ЂпєЋ ‪ {T i }i = 1‬ﺑﺎﻋпє�ﺒﺎر‪:‬‬ ‫∞‬ ‫ﻋﻨﺪﺋﺬ ﻣﻦ ШЈпєџп»ћ ‪i < j‬‬ ‫‪+‬‬ ‫‪H‬‬ ‫‪i2‬‬ ‫‪(0,0,...,xi ,...), i =1,2,..., p = 2‬‬ ‫‪C2‬‬ ‫‪Tiei Tjej‬‬ ‫‪,‬‬ ‫‪ip ip‬‬ ‫‪+ ... +‬‬ ‫‪H‬‬ ‫‪Tie2 Tje2‬‬ ‫‪,‬‬ ‫‪2p 2p‬‬ ‫‪12‬‬ ‫= )‪Ti (x1, x2 ,...‬‬ ‫‪+‬‬ ‫‪ T e Tj e1‬‬ ‫‪= Cp2 пЈ¬ i p1 , p‬‬ ‫‪p‬‬ ‫‪ 1 1‬‬ ‫‪пЈвЂ¬вЂ¬ ‫‪‬‬ ‫‪Tiej Tjej‬‬ ‫‪...+ p , p‬‬ ‫= ‪+ ...‬‬ ‫‪‬‬ ‫‪j‬‬ ‫‪j H‬‬ ‫‪‬‬ ‫‪Ti ,Tj‬‬ ‫‪H‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ :‫ﻗﺎﻋﺪة ﻓﻴﻪ‬ {e i }i в€€ I ‫ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ و‬H ‫ ﻟﻴﻜﻦ‬.(2) вЂ«ШЈп»Јпєњп» пє” ﺗﻄﺒﻴп»�ﻴﺔ‬ пЈ± A : D ( A ) вЉ‚ H в†’ H : It is a closed пЈґ в€ћ H p (H ) := пЈІ Aei в€ћ в€— { } вЉ‚ such that e D A : : ∑ i i =1 пЈґ ip i =1 пЈі ( ) linear operator пЈј пЈґ 2 пЈЅ (1 1 < в€ћ, p > пЈґ 2 H пЈѕ :‫ ﺑﺎﻟﺸﻜﻞ‬A, B в€€ H p (H ) ‫ﻧﻌﺮف Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І п»џп»њп»ћ ﻣﺆﺛﺮﻳﻦ‬ A, B p в€ћ пЈ« 1 пЈ¶ = C ∑ 2 p пЈ· Aei , Bei пЈё i =1 пЈ i 2 p в€’ H пЈ«в€ћ 1пЈ¶ , Cp = пЈ¬ ∑ 2 p пЈ· пЈ i =1 i пЈё 1 2 (20) пЈ± A : D (H ) вЉ‚ H в†’ H : A is a closed linear пЈґ 2 в€ћ H r (H ) := пЈІ Aei в€ћ в€— { } пЈґ such that : ei i =1 вЉ‚ D A : ∑ r i , r > 1 i =1 H пЈі operator ,пЈј пЈґ пЈЅ (2 пЈґ пЈѕ :‫ пєіп»®ЩЃ п»іпєёп»њп»ћ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ п»Јпє®п»“п»�пєЋЩ‹ пє‘пєЋп»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»ІвЂ¬H r (H ) ‫ﻋﻨﺪﺋﺬ‬ ( ) в€ћ A, B r = Cr2 ∑ i =1 Aei Bei , ri ri пЈ«в€ћ 1пЈ¶ , Cr = ∑ 2 пЈ· пЈ i=1 r пЈё H в€’ 1 2 (21) operator пЈј пЈ± A : D ( A) вЉ‚ H в†’ H : is a closed linear пЈґ пЈґ (3 2 в€ћ H ! (H ) = пЈІ пЈЅ Aei в€ћ в€— <в€ћ пЈґ such that :{ei }i =1 вЉ‚ D A : ∑ i! пЈґ i =1 H пЈі пЈѕ :‫ пєіп»®ЩЃ п»іпєёп»њп»ћ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ п»Јп»�ﺮوﻧﺎً пє‘пєЋп»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»ІвЂ¬H ! (H ) ‫ﻋﻨﺪﺋﺬ‬ ( ) A, B ! = C 2 ! в€ћ ∑ i =1 Aei Bei , i! i! в€’1 2 пЈ«в€ћ 1 пЈ¶ ,C! = пЈ¬пЈ¬ ∑ 2 пЈ·пЈ· H пЈ i =1 (i!) пЈё (22) :‫( ﺑﺎﻟﺸﻜﻞ‬21) ‫( п»џп»® п»‹пє®п»“п»ЁпєЋ Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І ﻓﻲ‬I :(4)‫ﻣﻼﺣﻈﺔ‬ в€ћ A, B r = ∑ i =1 Aei Bei , ri ri H : ‫ﻋﻨﺪﺋﺬ‬ . H r (H ) = H S ‫ п»іп»њп»®Щ† ﻟﺪﻳﻨﺎ‬r = 1 ‫( ﻣﻦ أﺟﻞ‬1 11 вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫)‪ A h , h в€€ D(A‬‬ ‫‪:= пЈІ B‬‬ ‫) ‪0 , h в€€ H / D ( A‬‬ ‫و п»«п»њпє¬Ш§ ﻧﻜпє�ﺐ‪:‬‬ ‫~‬ ‫‪= AB‬‬ ‫)‪D( A‬‬ ‫‪AB‬‬ ‫``‬ ‫‪AB‬‬ ‫‪ .‬ﻟﺒﺮﻫﺎن )‪ (14‬ﺑﺴﻬﻮﻟﺔ п»§пє пєЄ ﻣﻦ ) ‪ (6‬أن‬ ‫) ‪A # ≤ A B , в€Ђ в€€ B(H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫و п»«пє¬Ш§ п»іп»Њп»„п»І ‪:‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪A # в€’ AвЉҐ # ≤ AB‬‬ ‫‪{e i }i в€€ I‬‬ ‫ﻧﻈﺮﻳﺔ ﺗﻤﻬﻴﺪﻳﺔ‪ .2‬ﻟпє�ﻜﻦ‬ ‫‪2‬‬ ‫‪ H‬و)‬ ‫ﻗﺎﻋﺪة ﻓﻲ‬ ‫≤ ‪.0‬‬ ‫(‬ ‫⋅‪ H (H ), в‹…,‬ﻣﻌﺮﻓﺔ ﻛﻤﺎ ﺳﺒﻖ‪ ،‬ﻋﻨﺪﺋﺬ‪:‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫ﻛﻞ ) ‪ A в€€ H 2 (H‬ﻳﻤﻜﻦ ШҐЩ† п»іп»Њпє’пє® п»‹п»Ёп»Є пє‘пєёп»њп»ћ وﺣﻴﺪ ﻛﻤﺎ п»іп» п»ІвЂЄ:‬‬ ‫) ‪{ai }iв€ћ=1 вЉ‚ l 2 (K‬‬ ‫)‪(15‬‬ ‫)‪(16‬‬ ‫‪= 1, в€Ђi = 1,2,3,...‬‬ ‫) ‪(17‬‬ ‫‪=0‬‬ ‫‪#‬‬ ‫‪#‬‬ ‫‪, {Ai }i =1 вЉ‚ H 2 (H ),‬‬ ‫∞‬ ‫‪iв‰ j‬‬ ‫‪2‬‬ ‫‪ai‬‬ ‫)‪(19‬‬ ‫‪i =1‬‬ ‫‪Ai‬‬ ‫‪: Ai , A j‬‬ ‫)‪(18‬‬ ‫∞‬ ‫‪A = ∑ ai Ai‬‬ ‫∞‬ ‫∑‬ ‫=‬ ‫‪i =1‬‬ ‫‪∀ i, j в€€ N ,‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪A‬‬ ‫‪A, Ai # = ai , i = 1,2,3,...‬‬ ‫أﻛﺜﺮ ﻣﻦ Ш°п»џп»љ ШҐШ°Ш§ ﻛﺎن‬ ‫‪I‬‬ ‫ﻣﺆﺛﺮ пє§п»„п»І ‪Ih = h, в€Ђ h в€€ H :‬‬ ‫ﻋﻨﺪﺋﺬ ‪= 1‬‬ ‫‪#‬‬ ‫‪. I‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻣﻦ ШЈпєџп»ћ Ш§п»џпє’пє®п»«пєЋЩ† اﻧﻈﺮ п»“п»І) ]‪ [2‬اﻟﺼﻔﺤﺔ ) ‪ .( ( p.87‬ﻧﺒﺮﻫﻦ أن‪= 1 :‬‬ ‫‪=1‬‬ ‫‪2‬‬ ‫∞‬ ‫‪= C 2 ∑ fi‬‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫∞‬ ‫‪f i Ie i‬‬ ‫‪H‬‬ ‫‪10‬‬ ‫∑‬ ‫‪i =1‬‬ ‫‪2‬‬ ‫‪= C‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪I‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪I‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻟпє�ﻜﻦ ) ‪ {A}n =1 вЉ‚ B (H‬ﻣпє�пє�ﺎﻟﻴﺔ п»Јпє�п»�пєЋШ±пє‘пє” п»“п»І ) ‪ H 2 (H‬إﻟﻰ ‪A‬‬ ‫∞‬ ‫أن ) ‪ : A в€€ B (H‬ﻣﻦ ШЈпєџп»ћ أي‬ ‫)‪h = ∑ ai ei в€€ D( A‬‬ ‫ﻓﻲ ) ‪(H‬‬ ‫‪2‬‬ ‫‪ . H‬و ﻟﻨﺒﺮﻫﻦ‬ ‫‪iв€€I‬‬ ‫‪Ah H = ( A в€’ An )h + An h H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪≤ ( A в€’ An )h H + Ah H‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪h‬‬ ‫‪2‬‬ ‫‪h‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪(A −‬‬ ‫‪An ei ) H + An‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪+ An‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪ai‬‬ ‫∑‬ ‫≤‬ ‫‪iв€€ I‬‬ ‫) ‪⋅ max ( A в€’ An e i‬‬ ‫‪2‬‬ ‫‪i‬‬ ‫‪iв€€ I‬‬ ‫ﻟﻜﻞ ) ‪( A) ∩ D( An‬‬ ‫‪∑a‬‬ ‫‪iв€€ I‬‬ ‫‪ . h в€€ D‬إذن‪:‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪h‬‬ ‫‪2‬‬ ‫‪+ An‬‬ ‫‪B‬‬ ‫‪.‬‬ ‫)‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪3‬‬ ‫‪i‬‬ ‫‪)∑ a‬‬ ‫‪iв€€I‬‬ ‫≤‬ ‫(‬ ‫) ‪≤ max ( Aei в€’ An ei‬‬ ‫‪iв€€I‬‬ ‫(‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪Ah‬‬ ‫‪= h H max( Aei в€’ An ei ) + An‬‬ ‫)(‬ ‫)(‬ ‫) (‬ ‫‪iв€€I‬‬ ‫‪2‬‬ ‫و п»«п»њпє¬Ш§ п»іп»њп»®Щ† اﻟﻤﺆﺛﺮ ‪ A‬ﻣﺤﺪوداً п»‹п» п»° ‪ D A ∩D An = D A‬ﻷن ‪ An‬ﻣﺤﺪود Щ€ п»џп»њп»ћ ‪. n‬‬ ‫ﺑﺮﻫﺎن )‪ (11) ШЊ (10‬و )‪ (12‬ﻣﻦ ﻧﻈﺮﻳﺔ Ш§п»џп»”п»ЂпєЋШЎ Ш§п»џпє пє°пє‹п»І Ш§п»џп»¤п»ђп» п»– п»џп»”п»ЂпєЋШЎ п»«п» пє’пє®ШЄвЂЄ .‬اﻧﻈﺮ Ш§п»џпєјп»”пє¤пє” )‪ (80‬ﻣﻦ‬ ‫]‪ . [3‬ﻟﺒﺮﻫﺎن )‪ (13‬ﻧﻜпє�ﺐ‪:‬‬ ‫⊥‪AB = A в€’ A‬‬ ‫ﻋﻨﺪﺋﺬ‬ ‫))‪A в€’ AвЉҐ в€€ B(D( A‬‬ ‫و п»«п»њпє¬Ш§ ﻳﻜﻮن‬ ‫)‪≤ M 2 h H , h в€€ D ( A‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪AB h‬‬ ‫و п»«пє¬Ш§ п»іпє†ШЇЩЉ إﻟﻰ‬ ‫)‪≤ M 2 h H , h в€€ D ( A‬‬ ‫‪2‬‬ ‫ﻧﺴпє�ﻄﻴﻊ ﺗﻤﺪﻳﺪ‬ ‫‪AB‬‬ ‫إﻟﻰ ‪: H‬‬ ‫‪9‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪( A в€’ AвЉҐ )h‬‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫)‬ ‫(‬ ‫‪1 2‬‬ ‫‪b + d2‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪A H 2 = a2 + c2 +‬‬ ‫ﺑﻴﻨﻤﺎ‬ ‫‪2‬‬ ‫‪A S = a 2 + c 2 + b2 + d 2‬‬ ‫و‬ ‫‪2‬‬ ‫‪S‬‬ ‫≤‬ ‫‪A‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪A‬‬ ‫‪-3‬اﻟﻔﻀﺎءات Ш§п»џпє пє°пє‹п»ґпє” Щ€ Ш§п»џпє�ﻌﺎﻣﺪ‬ ‫ﻓﻴﻤﺎ п»іп» п»І пєіп»®ЩЃ ﻧﻌﺮف Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І п»“п»І ) ‪ H 2 (H‬ﻛﻤﺎ п»іп» п»І ‪:‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪−‬‬ ‫‪‬‬ ‫‪2‬‬ ‫‪, C := ∑ fi ‬‬ ‫)‪(8‬‬ ‫‪H‬‬ ‫‪iв€€I‬‬ вЂ«вЂЄпЈ iв€€I‬‬ ‫‪‬‬ ‫ﻣﻦ ШЈпєџп»ћ п»›п»ћ ﻣﺆﺛﺮﻳﻦ ) ‪. A, B в€€ H 2 (H‬‬ ‫ﻧﻈﺮﻳﺔ ﺗﻤﻬﻴﺪﻳﺔ‪ . 1‬ﻟﻴﻜﻦ ) ‪ H 2 (H‬و ) ‪ B (H‬اﻟﻤﻌﺮﻓﻴﻦ пєіпєЋпє‘п»�пєЋЩ‹ п»‹п»ЁпєЄпє‹пє¬ п»§пє пєЄ أﻧﻪ‪:‬‬ ‫⊥‬ ‫) ‪H 2 (H ) = B (H ) вЉ• B (H‬‬ ‫)‪(9‬‬ ‫‪2‬‬ ‫و п»«п»њпє¬Ш§ п»“пє€Щ† п»›п»ћ п»Јпє†пє›пє® ‪ A‬ﻣﻦ ) ‪ H (H‬ﻳﻤﻜﻦ ШЈЩ† ﻧﻌﺒﺮ п»‹п»Ёп»Є пє‘пєЋп»џпєёп»њп»ћ Ш§п»џпє�ﺎﻟﻲ‪:‬‬ ‫)‪(10‬‬ ‫‪A, B # = C2 ∑ fi Aei , Bej‬‬ ‫‪2‬‬ ‫⊥‪A = AB + A‬‬ ‫‪AB в€€ B(H ) ،‬‬ ‫‪،‬‬ ‫) ‪AвЉҐ в€€ B(H‬‬ ‫⊥‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫)‪(11‬‬ ‫و‬ ‫)‪(12‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫⊥‪+ A‬‬ ‫‪2‬‬ ‫‪#‬‬ ‫‪= AB‬‬ ‫‪2‬‬ ‫‪A‬‬ ‫‪#‬‬ ‫) ‪A в€’ AвЉҐ в€€ B(H‬‬ ‫و‬ ‫)‪(13‬‬ ‫‪( A в€’ AвЉҐ )h H ≤ M h H ,‬‬ ‫‪h в€€ D( A) , M > 0‬‬ ‫و п»‹п»јЩ€Ш© п»‹п» п»° ذﻟﻚ‬ ‫)‪(14‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪A # в€’ AвЉҐ # ≤ AB‬‬ ‫‪8‬‬ ‫≤ ‪.0‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫ﻟﺬا ﻧﻜпє�ﺐ‪:‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫∗‪= A‬‬ ‫∗‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪An‬‬ ‫‪lim‬‬ ‫=‬ ‫∞→‪n‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪An‬‬ ‫‪lim‬‬ ‫=‬ ‫=‪2‬‬ ‫∞→‪n‬‬ ‫‪H‬‬ ‫‪A‬‬ ‫ﻣﻼﺣﻈﺔ)‪ :(2‬ﻳﻤﻜﻦ ШҐпє›пє’пєЋШЄ اﻟﺨﻄﻴﺔ п»џп» п»¤пє†пє›пє® اﻟﻤﻌﺮف ‪ A‬ﻓﻲ )в€—( ШЇЩ€Щ† Ш°п»›пє® ШЈЩ† Ш§п»џпє�ﻤﺪﻳﺪ пє§п»„п»І Щ€ Ш°п»џп»љ ﺑﺈﺿﺎﻓﺔ‬ ‫اﻟﺨﺎﺻﺔ Ш§п»џпє�ﺎﻟﻴﺔ )ШҐп»џп»° Ш§п»џпє�п»Њпє®п»іп»’ اﻟﻤﺬﻛﻮر п»“п»І )в€—( (‪:‬‬ ‫‪m‬‬ ‫‪m‬‬ ‫‪m‬‬ ‫‪nв†’в€ћ i=1‬‬ ‫‪i=1‬‬ ‫‪i=1‬‬ ‫‪m‬‬ ‫‪∑fiО±i Aei = A∑fiaiei = ∑αihi =lim∑αi An fiei , в€Ђmв€€I , в€ЂО± i в€€ K‬‬ ‫‪i=1‬‬ ‫ﻣﻼﺣﻈﺔ)‪ :(3‬ﻳﻤﻜـﻦ ШЈЩ† ﻧﻮﺳـﻊ Ш§п»џп»”ЩЂп»ЂпєЋШЎ ) ‪ H 2 (H‬ﺑـﺄن п»іп»њЩЂп»®Щ† п»›ЩЂп»ћ п»ЈЩЂпє†пє›пє® ‪ A‬ﻣـﻦ ) ‪ H (H‬ﻗﺎﺑـﻞ ﻟﻺﻏـﻼق‬ ‫ﺑـــﺪﻻ ﻣـــﻦ ШЈЩ† п»іп»њЩЂЩЂЩЂп»®Щ† п»Јп»ђп» п»�ــﺎً‪ .‬و ﻟﻜـــﻦ п»іпє ЩЂЩЂЩЂпєђ ШЈЩ† ﻧـــﺸﻜﻞ пє»ЩЂЩЂЩЂп»”п»®п»“пєЋЩ‹ п»Јпє�п»њпєЋп»“пєЊЩЂЩЂЩЂпє” ﻣـــﻦ اﻟﻤـــﺆﺛﺮات‪ :‬و Ш°п»џЩЂЩЂЩЂп»љ пє‘ЩЂЩЂЩЂпєЋЩ† ﻧп»�ЩЂЩЂЩЂп»®Щ„ أن‬ ‫اﻟﻤﺆﺛﺮﻳﻦ‪:‬‬ ‫‪2‬‬ ‫‪ B : D (B ) вЉ‚ H в†’ H ШЊ A : D ( A ) вЉ‚ H в†’ H‬ﻓـــﻲ пє»ЩЂЩЂЩЂп»’ Щ€Ш§пєЈЩЂЩЂЩЂпєЄ )п»Јпє�ﻜـــﺎﻓﺌﻴﻦ( إذا‬ ‫ﺗﺤп»�п»– اﻟﺸﺮط‪:‬‬ ‫‪A в‰Ў B ⇔ Aei = Bei , в€Ђi в€€ I‬‬ ‫ﻣﺜﺎل)‪ :(1‬ﺑﻔﺮض ‪ RвЂ¬п»Јпє п»¤п»®п»‹пє” Ш§п»·п»‹пєЄШ§ШЇ Ш§п»џпє¤п»�ﻴп»�ﻴﺔ‪ .‬ﻧﻀﻊ ‪ H = R 2‬و ﻧﻌпє�ﺒﺮ‬ ‫‪‬‬ ‫{‬ ‫}‬ ‫‪‬‬ ‫‪a b ‬‬ ‫‪, a, b, c, d в€€ R‬‬ ‫‪пЈc d ‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪2‬‬ ‫ﻧﻌﺮف Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І п»‹п» п»° ) ‪ H (H‬ﻣﻦ ШЈпєџп»ћ ШЈЩЉ ﻣﺆﺛﺮﻳﻦ‬ ‫‪H 2 (H ) = A : R 2 в†’ R 2 , linear = пЈІ A = ‬‬ ‫‪b1 ‬‬ ‫‪‬‬ ‫‪d 1 ‬‬ ‫‪b‬‬ ‫‪a‬‬ ‫‪ , B = пЈ¬пЈ¬ 1‬‬ ‫‪d‬‬ вЂ«вЂЄпЈ c1‬‬ ‫‪a‬‬ ‫‪A = ‬‬ ‫‪пЈc‬‬ ‫ﺑﺎﻟﺸﻜﻞ ‪:‬‬ ‫‪R2‬‬ ‫‪1 пЈ«0пЈ¶ пЈ«0‬‬ ‫‪AпЈ¬ пЈ·, B пЈ¬ ‬‬ ‫‪2 пЈ¬пЈ 1 пЈ·пЈё пЈ¬пЈ 1 ‬‬ ‫‪1пЈ¶ пЈ«1‬‬ ‫‪= AпЈ¬пЈ¬ пЈ·пЈ·, B пЈ¬пЈ¬ ‬‬ ‫‪пЈ0пЈё пЈ0‬‬ ‫‪+‬‬ ‫‪R2‬‬ ‫‪H2‬‬ ‫‪A, B‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪1‬‬ ‫‪(b, d ), (b1, d1) R2‬‬ ‫‪2‬‬ ‫‪A, B H 2 = (a, c), (a1, c1 ) R2 +‬‬ ‫‪1‬‬ ‫) ‪(bb1 + dd1‬‬ ‫‪2‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪7‬‬ ‫‪= aa1 + cc1 +‬‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫ﻧﺒﺮﻫﻦ ШЈЩ† ‪ A : D ( A) в†’ H‬ﻗﺎﺑﻞ п»џп»єп»Џп»јЩ‚ اﻧﻈﺮ п»“п»І ]‪ [3‬اﻟﺼﻔﺤﺔ ) ‪ . ( p.22‬ﻟﻬﺬه Ш§п»џп»ђпєЋп»іпє” п»іп»њп»”п»І пє‘пє®п»«пєЋЩ† أن‬ ‫) (‬ ‫∗‪ D AвЂ¬п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ اﻟﻤﺆﺛﺮ‪ Aв€— : D(Aв€— ) в†’ H :‬ﻛﺜﻴﻔﺔ п»“п»І ‪ : H‬ﻟпє�ﻜﻦ‬ ‫ﻣпє�пє�ﺎﻟﻴﺔ п»›п»®пє·п»І Ш§п»џпєґпєЋпє‘п»�ﺔ‪ ،‬ﻋﻨﺪﺋﺬ‬ ‫} ‪{A‬‬ ‫∞ *‬ ‫‪n n=1‬‬ ‫‪2‬‬ ‫اﻋпє�ﻤﺎداً п»‹п» п»° )‪: (5‬‬ ‫} ‪{f A e‬‬ ‫∞‬ ‫‪i n =1‬‬ ‫‪2‬‬ ‫‪H2‬‬ ‫ﻣпє�пє�ﺎﻟﻴﺔ п»›п»®пє·п»І п»“п»І ) ‪ . H 2 (H‬ﻳﻤﻜﻦ ШЈЩ† ﻧﻜпє�ﺐ‪:‬‬ ‫‪2‬‬ ‫∗‪= T‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪n‬‬ ‫‪H‬‬ ‫ﻣпє�пє�ﺎﻟﻴﺔ п»›п»®пє·п»І ﻓﻲ‬ ‫∗‬ ‫‪An в€’ A‬‬ ‫)‪An в€’ Am = T в€€H2(H‬‬ ‫‪ T‬ﺑﺎﻋпє�ﺒﺎر‬ ‫∗‬ ‫‪i‬‬ ‫‪∗ 2‬‬ ‫‪m‬‬ ‫‪H2‬‬ ‫‪= An в€’ Am‬‬ ‫‪H2‬‬ ‫) ‪{An}в€ћn=1 вЉ‚ H 2 (H‬‬ ‫وﻫﻜﺬا п»іп»њп»®Щ† ﻟﺪﻳﻨﺎ‬ ‫‪ i в€€ I‬و ﻛﻤﺎ пєіпє’п»– ﻧﻌﺮف اﻟﻤﺆﺛﺮ‪:‬‬ ‫و ﻟﻜﻞ‬ ‫‪ A : D пЈ«пЈ¬ A пЈ¶пЈ· вЉ‚ H в†’ H‬ﺑﺤﻴﺚ أن‪:‬‬ вЂ«вЂЄпЈ пЈёвЂ¬вЂ¬ ‫~‬ ‫~‬ ‫∗‬ ‫‪f i Aв€—ei := lim f i An ei , в€Ђ i в€€ I‬‬ ‫∞→‪n‬‬ ‫~‬ ‫~‬ ‫ﻛﻤﺎ пє‘пє®п»«п»ЁпєЋ пєіпєЋпє‘п»�пєЋЩ‹ п»“п»І )в€— в€—( ﻳﻤﻜﻦ ШЈЩ† ﻧﺒﺮﻫﻦ в€ћ < ‪ . A H 2‬ﻣﻦ Ш§п»џпє�п»Њпє®п»іп»’ п»§пє пєЄ ШЈп»іп»ЂпєЋЩ‹ ШЈЩ† ‪ D пЈ«пЈ¬ A ‬ﻛﺜﻴﻔﺔ‬ вЂ«вЂЄпЈ пЈёвЂ¬вЂ¬ ‫~‬ ‫ﻓﻲ ‪ . H‬ﻧﺒﺮﻫﻦ Ш§п»µЩ† ∗‪ A = AвЂ¬п»‹п» п»°вЂ¬ ‫‪{ei }iв€€I‬‬ ‫‪, в€Ђi, j в€€ I‬‬ ‫ﻟﺬا ﻧﻜпє�ﺐ‪:‬‬ ‫‪H‬‬ ‫‪= ei , A*e j‬‬ ‫~‬ ‫‪= fi ei , f j A e j‬‬ ‫‪, в€Ђi, j в€€ I‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪Aei , e j‬‬ ‫‪fi Anei , f j e j‬‬ ‫‪i, j в€€ I‬‬ ‫ﺑﺄﺧﺬ اﻟﻨﻬﺎﻳﺔ ﻟﻤﺎ в€ћ в†’ ‪ nвЂ¬п»§пє пєЄвЂЄ :‬ﻟﻜﻞ‬ ‫~‬ ‫‪= fiei , f j Aej‬‬ ‫‪H‬‬ ‫‪fi Aei , f jej‬‬ ‫‪H‬‬ ‫و п»«пє¬Ш§ ﻳﻌﻄﻲ‬ ‫~‬ ‫‪= ei , Aej‬‬ ‫‪, в€Ђi, j в€€ I‬‬ ‫‪H‬‬ ‫ﻷن ‪fi в‰ 0, в€Ђi в€€ I :‬‬ ‫‪∀i в€€ I‬‬ ‫~‬ ‫‪H‬‬ ‫‪ei , Aв€—e j‬‬ ‫‪.‬و п»«пє¬Ш§ ﻳﻌﻨﻲ‪:‬‬ ‫~‬ ‫∗‬ ‫‪ Aв€—ei = Aei‬وﻣﻨﻪ ﻧﻜпє�ﺐ‪ A = A :вЂ¬п»‹п» п»°вЂ¬ ‫‪2‬‬ ‫‪H‬‬ ‫∗‪= A‬‬ ‫‪6‬‬ ‫‪{ei }iв€€I‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪A‬‬ ‫‪ .‬ﻧﺜﺒﺖ أن‪:‬‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪1‬‬ ‫‪2‬‬ ‫‪−‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫‪‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪2‬‬ ‫‪i‬‬ ‫∑‬ ‫‪f‬‬ ‫‪iв€€ I‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪пЈвЂ¬вЂ¬ ‫‪≤ C в€’2 A‬‬ ‫=‬ ‫‪.C‬‬ ‫‪-2‬اﻹﺗﻤﺎم‪ :‬ﻧﺒﺮﻫﻦ ШЈЩ† ) ‪ H 2 (H‬ﻫﻮ п»“п»ЂпєЋШЎ пє—пєЋЩ… ‪:‬ﻟпє�ﻜﻦ ) ‪ {An }n =1 вЉ‚ H (H‬ﻣпє�пє�ﺎﻟﻴﺔ ﻛﻮﺷﻲ‪ .‬ﺳﻨﺒﺮﻫﻦ п»‹п» п»°вЂ¬ ‫∞‬ ‫‪2‬‬ ‫وﺟﻮد ﻧﻬﺎﻳﺔ п»«п»І اﻟﻤﺆﺛﺮ ‪ A : D( A) вЉ‚ H в†’ H‬اﻟﻤﺬﻛﻮر Щ€ п»Јпє®Ш§п»“п»�п»Є п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ п»›п»ћ ﻣﻨﻬﻤﺎ ﻛﺜﻴﻔﺔ ﻓﻲ‬ ‫‪ H‬و пє—пє¤п»®ЩЉ п»‹п»ЁпєЋпє»пє® Ш§п»џп»�пєЋп»‹пєЄШ© Щ€ п»іпє пєђ ﺗﻮﺿﻴﺢ ﺧﻄﻴﺔ ‪ A‬و п»—пєЋпє‘п» п»ґпє�п»Є п»џп»єп»Џп»јЩ‚ )п»іп»®пєџпєЄ п»Јпє†пє›пє® пє§п»„п»І п»Јп»ђп» п»–вЂ¬ ‫‪A‬‬ ‫ﺑﻤﺎ‬ ‫أن‬ ‫ﻳﺤп»�ﻖ‬ ‫اﻟﺨﺎﺻﺔ‪:‬‬ ‫) ‪⊂ H 2 (H‬‬ ‫‪<ε‬‬ ‫‪( AвЉ‚ A‬‬ ‫‪H2‬‬ ‫و‬ ‫ﻫﺬا‬ ‫اﻟﻤﺆﺛﺮ‬ ‫} ‪ {A‬ﻣпє�пє�ﺎﻟﻴﺔ ﻛﻮﺷﻲ‪ ШЊвЂ¬п»“п» п»њп»ћ ‪ε > 0‬‬ ‫∞‬ ‫‪n n =1‬‬ ‫‪ An в€’ Am‬ﻟﻜﻞ ‪n, m > n0‬‬ ‫‪<Оµ2‬‬ ‫و п»«п»њпє¬Ш§ ﻓﺈن‬ вЂ«Ш§п»џп»¤п»ђп» п»–вЂ¬ ‫‪H‬‬ ‫‪{ f i Anei }в€ћn =1‬‬ ‫ﻫﻮ‬ ‫ﻳﻮﺟﺪ п»‹пєЄШЇ ﻃﺒﻴﻌﻲ‬ ‫‪2‬‬ ‫‪= ∑ fi‬‬ ‫‪2‬‬ ‫‪H2‬‬ ‫‪iв€€ I‬‬ ‫‪An в€’ An‬‬ ‫ﻣпє�пє�ﺎﻟﻴﺔ п»›п»®пє·п»І п»“п»І ‪ H‬و ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪ . i в€€ I‬ﻟﺬا ﻧﻜпє�ﺐ‬ ‫‪H‬‬ ‫‪ fi Anei пЈ§пЈ§в†’ hi‬ﻟﻤﺎ в€ћв†’ ‪n‬‬ ‫و ﻣﻦ ШЈпєџп»ћ п»›п»ћ ‪ . i в€€ I‬و п»Јп»Ёп»Є ﻧﻌﺮف اﻟﻤﺆﺛﺮ‪:‬‬ ‫‪A : D(H ) в†’ H‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫‪fi Aei = lim fi Anei в€Ђ i в€€ I‬‬ ‫)в€—(‬ ‫∞→ ‪n‬‬ ‫و п»«пє¬Ш§ Ш§п»џпє�ﻤﺪد ﺧﻄﻲ‪ .‬ﻋﻨﺪﺋﺬ ﻟﻜﻞ‬ ‫‪ε‬‬ ‫‪i‬‬ ‫‪2‬‬ ‫= ‪< Оµi‬‬ ‫‪H‬‬ ‫‪iв€€I‬‬ ‫‪f i An ei в€’ f i Aei‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪<Оµ 2‬‬ ‫‪H‬‬ ‫ﻳﻤﻜﻦ أﺧﺬ‬ ‫‪ε‬‬ ‫‪2i‬‬ ‫= ‪ Оµ i‬ﺑﺎﻋпє�пє’пєЋШ± أن‬ ‫ﻟﻜﻞ ‪ . n > n 0‬و п»«п»њпє¬Ш§ ﻳﻜﻮن‪:‬‬ ‫‪= ∑ f i Aei в€’ f i An ei‬‬ ‫‪iв€€I‬‬ ‫‪2‬‬ ‫‪H2‬‬ ‫‪A в€’ An‬‬ ‫ﻟﺬا п»іп»њп»®Щ† п»џпєЄп»іп»ЁпєЋ ﻣﻦ ШЈпєџп»ћ ‪ n в€€ N‬ﻣﺜﺒﺖ ﻟﺤﻈﻴﺎً ‪:‬‬ ‫)в€— в€—(‬ ‫∞<‬ ‫‪H2‬‬ ‫‪n0‬‬ ‫‪.‬و п»Јп»Ёп»Є ﻧﻜпє�ﺐ‪:‬‬ ‫‪( An в€’ Am )ei‬‬ ‫‪2‬‬ ‫‪A‬‬ ‫اﻟﻨﻬﺎﻳﺔ‬ вЂ«Ш§п»џп»¤п»„п» п»®пє‘пє”вЂЄ.‬‬ ‫‪+ An‬‬ ‫‪H2‬‬ ‫‪A H 2 ≤ A в€’ An‬‬ ‫ﻣﻦ пє—п»Њпє®п»іп»’ ‪ A‬ﻳﻤﻜﻦ ﻣﻼﺣﻈﺔ ШЈЩ† п»џп»Є п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ пє—пє¤п»®ЩЉ п»‹п»ЁпєЋпє»пє® Ш§п»џп»�ﺎﻋﺪة‪.‬‬ ‫‪5‬‬ ‫ﺑﺤﻴﺚ أن‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ = ∑ f j Bв€—hj , Aв€—hj 2 jв€€I H = ∑∑ f j Bв€—hj , gk 2 jв€€I kв€€I gk , Aв€—hj H Agk , hj H H = ∑∑ fk hj , Bgk 2 jв€€I kв€€I = ∑ fk 2 k в€€I Ag k , Bg k (f ∑∑ jв€€ I k в€€ I H . H 2 в€’ fk j 2 )в‹… a jk = 0 :‫ﻟп»�пєЄ Ш§пєіпє�п»Њп»¤п» п»ЁпєЋ اﻟﺨﺎﺻﺔ‬ :‫ﺑﺎﻋпє�ﺒﺎر‬ a jk = h j , Bg k H Ag k , h j H , j, k в€€ I ‫( Щ€ ذﻟﻚ‬3 ) ‫ Щ€ п»›пє¬п»џп»љ ﻣﻤﺎ пєіпє’п»– ﻧﺴпє�п»Ёпє�пєћ пє—пє¤п»�ﻖ‬.‫و п»Јп»Ёп»Є п»§пє пєЄ ШЈЩ† Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І п»Јпєґпє�п»�п»ћ ﻋﻦ Ш§пє§пє�ﻴﺎر Ш§п»џп»�ﺎﻋﺪة‬ : A, B в€€ H 2 (H ) ‫ﻷن ﻣﻬﻤﺎ ﻳﻜﻦ‬ A, B H =∑ fj ‫ﻓﺈن‬ BA 2 H 2 = ∑ fi 2 iв€€ I Bв€—h j , Aв€—h j ‫و‬ H2 B в€€ B(H ) ‫ ﻣﻬﻤﺎ ﻳﻜﻦ‬: (4) ‫ﻟﺒﺮﻫﺎن‬ 2 2 2 2 Aei iв€€I B H = A* , B* H B ( Aei ) H 2 B Ae i , Be i A в€€ H 2 (H ) ≤ B B ∑ fi = 2 iв€€I 2 jв€€I := ∑ f i 2 A H 2 H 2 . ‫ﻓﺈن‬ A в€€ H 2 (H ) ‫ ﻣﻬﻤﺎ ﻳﻜﻦ‬: (4) ‫ﻟﺒﺮﻫﺎن Ш§п»џпє пє°ШЎ اﻟﺜﺎﻧﻲ ﻣﻦ‬ A H 2 = ∑ fi Aei 2 2 iв€€I 4 2 H ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ اﻟﻤﺤﺪودة‬ ‫‪2‬‬ ‫)‪(6‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪B‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪≤ A‬‬ ‫‪H‬‬ ‫‪2‬‬ ‫‪BA‬‬ ‫‪H‬‬ ‫) ‪≤ c в€’ 2 A B , в€ЂA в€€ B ( H‬‬ ‫‪2‬‬ ‫) ‪(7‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪A‬‬ ‫‪H‬‬ ‫‪−1‬‬ ‫‪‬‬ ‫‪2 пЈ¶ 2‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫∑ ‪. C := ‬‬ ‫‪fi‬‬ ‫‪‬‬ вЂ«вЂЄпЈ iв€€ I‬‬ ‫‪‬‬ ‫‪ (5‬إن Ш§п»џп»”п»ЂпєЋШЎ ) ‪ H 2 (H‬اﻟﻤп»�пє�пє®Щ† пє‘пєЋп»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І ‪:‬‬ ‫‪:= ∑ f i‬‬ ‫‪2‬‬ ‫‪Aei , Bei‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪iв€€I‬‬ ‫‪H‬‬ ‫‪A, B‬‬ ‫ﻳﺸﻜﻞ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ п»“п»®Щ‚ Ш§п»џпє¤п»�п»ћ Ш§п»џпє�пєЋЩ… ‪. K‬‬ ‫اﻟﺒﺮﻫﺎن‪ .‬ﻧﺒﺮﻫﻦ أن‪ в€ЂA в€€ H 2 (H ) :‬و п»›пєЋЩ† ‪ A H 2 = 0‬ﻓﺈن ‪ A = 0вЂ¬п»‹п» п»°вЂ¬ вЂ«п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»”п»Є )‪ : D( A‬ﻣﻬﻤﺎ ﻳﻜﻦ )‪ в€Ђh в€€ D ( A‬ﻓﺈن‪،‬‬ ‫‪i‬‬ ‫‪∑a e‬‬ ‫‪i‬‬ ‫= ‪ h‬و ﻣﻦ ﺟﻬﺔ ШЈпє§пє®Щ‰ ﺣﺴﺐ‬ ‫‪iв€€I‬‬ ‫ﺗﻌﺮﻳﻒ اﻟﻨﻈﻴﻢ‪:‬‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪Aei‬‬ ‫‪0 = ∑ fi‬‬ ‫‪iв€€I‬‬ ‫و п»Јп»Ёп»Є п»§пє пєЄвЂЄ:‬‬ ‫‪2‬‬ ‫‪Aei‬‬ ‫‪2‬‬ ‫‪ 0 = f i‬ﻣﻬﻤﺎ ﻳﻜﻦ‬ ‫و ﺑﻤﺎ ШЈЩ† ‪ f i в‰ 0‬ﻣﻬﻤﺎ ﻳﻜﻦ ‪ i в€€ I‬ﻓﺈن ‪Aei = 0‬‬ ‫‪= 0‬‬ ‫‪i‬‬ ‫‪∑ a Ae‬‬ ‫‪i‬‬ ‫ﺑﻔﺮض‬ ‫‪Aei = 0‬‬ ‫و‬ ‫= ‪Ah‬‬ ‫‪iв€€ I‬‬ ‫} {‬ ‫ﻟﻜﻞ‬ ‫‪I‬‬ ‫∈ ‪ . i‬إذن ‪:‬‬ ‫‪.‬‬ ‫‪{ei }iв€€ I‬‬ ‫ﻧﺒﺮﻫﻦ ШЈЩ† Ш§п»џпє пєЄШ§ШЎ Ш§п»џпєЄШ§пє§п» п»І اﻟﻤﻌﺮف п»Јпєґпє�п»�п»ћ ﻋﻦ Ш§п»џп»�пєЋп»‹пєЄШ© اﻟﻤﺨпє�ﺎرة‬ ‫‪jв€€ I‬‬ ‫‪iв€€I‬‬ ‫ﻓﻲ ‪. H‬‬ ‫‪ {g k }k в€€ I ШЊ h j‬ﻗﺎﻋﺪﺗﻴﻦ ‪ . H‬ﻋﻨﺪﺋﺬ ﻣﻦ ШЈпєџп»ћ п»›п»ћ ﻣﺆﺛﺮﻳﻦ ) ‪A, B в€€ H 2 (H‬‬ ‫‪Ae i , Be i‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪‬‬ ‫‪hj , Bei ‬‬ ‫‪H‬‬ ‫‪‬‬ ‫‪H‬‬ ‫‪H‬‬ ‫‪Bв€—hj , ei‬‬ ‫‪fi‬‬ ‫∑‬ ‫=‪:‬‬ ‫‪iв€€ I‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪A, B‬‬ ‫‪2‬‬ ‫‪= ∑ fi пЈ¬пЈ¬ ∑ Aei , hj‬‬ ‫‪iв€€I‬‬ вЂ«вЂЄпЈ jв€€I‬‬ ‫‪ei , Aв€—hj‬‬ ‫‪H‬‬ ‫‪3‬‬ ‫‪2‬‬ ‫‪∑∑ f‬‬ ‫‪i‬‬ ‫‪iв€€I jв€€I‬‬ ‫=‬ вЂ«п»‹пє п»®Ш± Щ€ ﺑﻴﻜﺮد‬ ‫)‪(2‬‬ ‫∞‬ ‫‪A, B S := ∑ Aei , Bei‬‬ ‫‪H‬‬ ‫‪i =1‬‬ ‫)ﻣﻦ ШЈпєџп»ћ ШЈЩЉ ﻣﺆﺛﺮﻳﻦ ) ‪ ( A, B в€€ B (H‬ﺟﺪاء ШЇШ§пє§п» п»І п»“п»І ‪ . HS‬اﻧﻈﺮ ﻓﻲ‪ [6] ):‬اﻟﺼﻔﺤﺔ ) ‪ ( p.87‬و‬ ‫]‪ [3‬اﻟﺼﻔﺤﺔ )‪.( ( p.123‬‬ ‫ﻧﻌﺮف ШЈп»іп»ЂпєЋ Ш§п»џп»¤пє п»¤п»®п»‹пє”вЂЄ:‬‬ ‫)‪(3‬‬ ‫‪A : D( A) вЉ‚ H в†’ H : A: is a closed linear operator‬‬ ‫‪‬‬ ‫‪ H (H ) := ‬ﻣﻦ ШЈпєџп»ћ п»Јпє�пє�ﺎﻟﻴﺔ‬ ‫‪2‬‬ ‫‪2‬‬ ‫∗‬ ‫‪‬‬ ‫=‪such that: A 2 :‬‬ ‫{‬ ‫}‬ ‫‪,‬‬ ‫‪f‬‬ ‫‪Ae‬‬ ‫‪e‬‬ ‫‪D‬‬ ‫‪A‬‬ ‫<‬ ‫∞‬ ‫⊂‬ ‫∑‬ ‫‪i‬‬ ‫‪i H‬‬ ‫‪i iв€€I‬‬ ‫‪‬‬ ‫‪‬‬ ‫‪iв€€I‬‬ ‫) (‬ ‫‪2‬‬ ‫أﻋﺪاد пєЈп»�ﻴп»�ﻴﺔ п»ЈпєЋ ‪ { fi }iв€€I вЉ‚ K‬ﺑﺎﻋпє�пє’пєЋШ± ‪fi в‰ 0,в€Ђi в€€I‬‬ ‫و‬ ‫∞<‬ ‫‪2‬‬ ‫‪i‬‬ ‫‪∑f‬‬ ‫‪iв€€I‬‬ ‫) (‬ ‫‪ .‬ﺣﻴﺚ ﻗﺼﺪﻧﺎ ШЈЩ† )‪ D( A‬و ∗‪ D A‬ﻫﻤﺎ п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ п»›п»ћ ﻣﻦ اﻟﻤﺆﺛﺮ ‪ A‬و‬ ‫ﻣﺮاﻓп»�п»Є ∗‪. A‬‬ ‫ﻣﻼﺣﻈﺔ)‪ :(1‬ﻣﻦ اﻟﺴﻬﻞ ﻣﻼﺣﻈﺔ ШЈЩ† )‪ D( A‬ﻛﺜﻴﻔـﺔ п»“ЩЂп»І ‪ . H‬و ﺑﻤـﺎ ШЈЩ† ‪ A‬ﺧﻄـﻲ п»“ЩЂпє€Щ† п»Јпє®Ш§п»“п»�ЩЂп»Є ﻣﻮﺟـﻮد‪،‬و‬ вЂ«п»Јпє п»¤п»®п»‹ЩЂЩЂпє” пє—п»Њпє®п»іЩЂЩЂп»’ اﻟﻤﺮاﻓــﻖ ∗‪ A‬ﺗﻜــﻮن ﻛﺜﻴﻔــﺔ ШҐШ°Ш§ Щ€ п»“п»�ЩЂЩЂп»‚ ШҐШ°Ш§ п»›ЩЂЩЂпєЋЩ† ‪ A‬ﻗﺎﺑــﻞ ﻟﻺﻏــﻼق‪.‬اﻧﻈــﺮ п»“ЩЂЩЂп»І ]‪ [3‬اﻟــﺼﻔﺤﺔ‬ ‫) ‪. ( p.22‬‬ ‫ﻧпє�ﺎﺋﺞ‪ (1 :‬إذا п»‹пє®п»“п»ЁпєЋ п»‹п»¤п» п»ґпє” Ш§п»џпє п»¤п»Љ ﻣﻦ ШЈпєџп»ћ ШЈЩЉ ﻣﺆﺛﺮﻳﻦ ) ‪A , B в€€ H (H‬‬ ‫) ‪( A + B )h = Ah + Bh, в€Ђh в€€ D( A) ∩ D(B‬‬ ‫‪2‬‬ ‫و п»‹п»¤п» п»ґпє” Ш§п»џп»Ђпє®ШЁ пє‘п»ЊпєЄШЇ ﻣﻦ Ш§п»џпє¤п»�ﻞ‬ ‫)‪(О»A)h = О» ( Ah ), в€ЂО» в€€ K , h в€€ D( A‬‬ ‫ﻓﺈن ) ‪ H 2 (H‬ﻳﺸﻜﻞ п»“п»ЂпєЋШЎ пє·п»ЊпєЋп»‹п»І п»“п»®Щ‚ Ш§п»џпє¤п»�п»ћ ‪. K‬‬ ‫‪ (2‬ﻧﻌﺮف п»‹п» п»° ) ‪ H 2 (HвЂ¬Ш§п»џпє пєЄШ§ШЎвЂЄ:‬‬ ‫)‪(4‬‬ ‫‪Aei , Bei‬‬ ‫‪H‬‬ ‫ﻣﻦ ШЈпєџп»ћ ШЈЩЉ ﻣﺆﺛﺮﻳﻦ ) ‪(H‬‬ ‫‪2‬‬ ‫‪:= ∑ f i‬‬ ‫‪2‬‬ ‫‪ . A, B в€€ H‬ﻋﻨﺪﺋﺬ )‬ ‫‪iв€€I‬‬ ‫⋅‪⋅,‬‬ ‫)‪. (unitary space‬‬ ‫‪ (3‬ﻣﻬﻤﺎ ﻳﻜﻦ ) ‪(H‬‬ ‫)‪(5‬‬ ‫‪ (4‬ﻣﻬﻤﺎ ﻳﻜﻦ‬ ‫‪2‬‬ ‫‪Aв€€ H‬‬ ‫ﻓﺈن‬ ‫‪∗ 2‬‬ ‫‪H2‬‬ ‫) ‪B в€€ B(H‬‬ ‫‪2‬‬ ‫‪A H2 = A‬‬ ‫و ) ‪ A в€€ H (H‬ﻓﺈن‬ ‫‪2‬‬ ‫‪2‬‬ ‫‪H2‬‬ ‫‪A, B‬‬ ‫‪(H (H ),‬‬ ‫‪2‬‬ ‫ﻳﺸﻜﻞ п»“п»ЂпєЋШЎШ§Щ‹ أﺣﺎدﻳﺎً‬ вЂ«Ш§п»џп»¤пє п» пєЄ ‪ ШЊ16‬اﻟﻌﺪد ‪ ШЊ2007 ШЊ1‬ص ص‪24-1 .‬‬ ‫اﺑﺤﺎث اﻟﻴﺮﻣﻮك "пєіп» пєґп» пє” Ш§п»џп»Њп» п»®Щ… اﻷﺳﺎﺳﻴﺔ واﻟﻬﻨﺪﺳﻴﺔ"‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» п±ЄШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ п»ЏпІ‘ اﳌﺤﺪودة‬ ‫أﺣﻤﺪ ﻣﺤﻤﺪ п»‹пє п»®Ш±* Щ€ رﻳﻨﺮ‬ ‫ﺑﻴﻜﺮد**‬ ‫ﺗﺎرﻳﺦ ﻗﺒﻮﻟﻪ‪2006/10/19 :‬‬ ‫ﺗﺎرﻳﺦ Ш§пєіпє�п»јЩ… اﻟﺒﺤﺚ‪2004/8/30 :‬‬ вЂ«п»Јп» пєЁпєєвЂ¬ ‫ﻓﻲ п»«пє¬Щ‡ اﻟﻤп»�пєЋп»џпє” ﻧﻌﺮف ) ‪ H 2 (H‬ﻛﺼﻒ ﻣـﻦ اﻟﻤـﺆﺛﺮات اﻟﺨﻄﻴـﺔ ﻏﻴـﺮ اﻟﻤﺤـﺪودة Щ€ Ш§п»џп»¤п»ђп» п»�ـﺔ‪ ШЊвЂ¬п»Јпє п»¤п»®п»‹ЩЂпє”вЂ¬ ‫ﺗﻌﺮﻳﻒ п»›п»ћ п»Јпє†пє›пє® ﻣﻦ п»«пє¬Ш§ Ш§п»џпєјп»’ Щ€ п»Јпє п»¤п»®п»‹пє” пє—п»Њпє®п»іп»’ п»Јпє®Ш§п»“п»�п»Є п»›п»ћ ﻣﻨﻬﻤﺎ ﻛﺜﻴﻔـﺔ п»“ЩЂп»І п»“ЩЂп»ЂпєЋШЎ п»«п» пє’ЩЂпє®ШЄ ‪ H‬و ﺗﺤـﻮي‬ ‫ﻋﻨﺎﺻــﺮ Ш§п»џп»�пєЋп»‹ЩЂЩЂпєЄШ© п»“ЩЂЩЂп»І ‪ . H‬ﺛــﻢ ﻧــﺪرس Ш§п»џпє�п»ЊпєЋп»ЈЩЂЩЂпєЄ Щ€ Ш§п»џп»”ЩЂЩЂп»ЂпєЋШЎШ§ШЄ Ш§п»џпє пє°пє‹п»ґЩЂЩЂпє” п»џп»”ЩЂЩЂп»ЂпєЋШЎ п»«п» пє’ЩЂЩЂпє®ШЄ ) ‪ H 2 (H‬اﻟﻤﺆﻟــﻒ ﻣــﻦ‬ вЂ«п»Јпє п»¤п»®п»‹ЩЂЩЂпє” اﻟﻤــﺆﺛﺮات اﻟﺨﻄﻴــﺔ ﻏﻴــﺮ اﻟﻤﺤــﺪودة )ШЈЩ€ اﻟﻤﺤــﺪودة пє‘ЩЂЩЂпєёп»њп»ћ п»‹ЩЂЩЂпєЋЩ…(‪..‬ﺛــﻢ ﻧﺤــﺴﺐ ﻧﻈــﻴﻢ п»«ЩЂЩЂпє¬Ш§ اﻟﻤــﺆﺛﺮ ﻣــﻦ‬ ‫) ‪ . H 2 (H‬ﻧﻌﺒﺮ ﻋﻦ п»›п»ћ п»Јпє†пє›пє® ﻣـﻦ ) ‪ H 2 (HвЂ¬п»›п»¤пє п»¤ЩЂп»®Ш№ пє§п»„ЩЂп»І ﻟﻤـﺆﺛﺮﻳﻦ ﻣـﻦ ) ‪ H 2 (H‬إﺣـﺪاﻫﻤﺎ ﻣﺤـﺪود‬ ‫‪.‬ﺛﻢ ﻧﺒﻴﻦ ШЈЩ† ШЈЩЉ п»ЈЩЂпє†пє›пє® ﻣـﻦ ) ‪ H 2 (H‬ﻳﻌﺒـﺮ п»‹п»ЁЩЂпє” п»›п»¤пє п»¤ЩЂп»®Ш№ пє§п»„ЩЂп»І п»џп»Њп»ЁпєЋпє»ЩЂпє® Ш§п»џп»�пєЋп»‹ЩЂпєЄШ© п»“ЩЂп»І ) ‪. H 2 (H‬و أﺧﻴـﺮاً‬ ‫ﻧﻮﺟﺪ п»‹п»јп»—пє” ﺑﻴﻦ اﻟﻄﻴﻒ اﻟﻤﻨﻔﺼﻞ п»џп» п»¤пє†пє›пє® ﻣﻦ ) ‪ H 2 (H‬و ﻧﻈﻴﻤﻪ‪ .‬ﻣﻊ пє‘п»Њпєѕ Ш§п»·п»Јпєњп» пє” أﻳﻀﺎً‪.‬‬ ‫ﻣп»�ﺪﻣﺔ‪ :‬إن ﻧﻈﻴﻢ اﻟﻤﺆﺛﺮ Ш§п»џпєЁп»„п»І اﻟﻤﺤﺪود п»» ﻳﻤﻜﻦ ﺗﻮﺳﻴﻌﻪ п»џп»Ёп»®пєџпєЄ ﻣﻌﻴﺎراً ﻟﻤﺆﺛﺮ пє§п»„п»І ﻏﻴﺮ п»Јпє¤ЩЂпєЄЩ€ШЇ Щ€ ﻛـﺬﻟﻚ‬ ‫إن اﻟﻨﻈــﻴﻢ اﻟﻤﻌــﺮف п»‹п» ЩЂЩЂп»° п»“ЩЂЩЂп»ЂпєЋШЎ п»«п» пє’ЩЂЩЂпє®ШЄ ﺷــﻤﺖ اﻟﻤﻌــﺮف п»»пєЈп»�ЩЂпєЋЩ‹ п»» п»іЩЂЩЂпє†ШЇЩЉ Ш§п»џп»ђЩЂЩЂпє®Ш¶ ШЈп»іЩЂЩЂп»ЂпєЋЩ‹ пєЈпє�ЩЂЩЂп»° ШЈЩ† ﻗﻴﻤــﺔ ﻧﻈــﻴﻢ‬ ‫اﻟﻤﻮﺛﺮ اﻟﺤﻴﺎدي ﻓﻴﻪ ﻏﻴﺮ п»Јп»Ёпє�ﻬﻴﺔ‪.‬‬ ‫ﻟﺬا أوﺟﺪﻧﺎ п»“п»ЂпєЋШЎ п»«п» пє’пє®ШЄ ﻣﻦ اﻟﻤﺆﺛﺮات اﻟﺨﻄﻴـﺔ ﻏﻴـﺮ اﻟﻤﺤـﺪودة ﺿـﻤﻦ пє·ЩЂпє®Щ€Ш· пєіпє�ﻔﺮﺿـﻬﺎ п»џЩЂп»Ђпє®Щ€Ш±Ш© Щ€ пєџЩЂп»®ШЇ و‬ ‫إﺗﻤﺎم اﻟﻔﻀﺎء‪.‬‬ ‫‪ - 1‬ﺗﻤﻬﻴﺪ‪ :‬ﻟﻴﻜﻦ ‪ H‬ﻓﻀﺎء п»«п» пє’пє®ШЄ п»—пєЋпє‘п»ћ п»џп» п»”пєјп»ћ п»Јп»�ﺮوﻧﺎً пє‘пє¤п»�п»ћ пє—ЩЂпєЋЩ… ‪ K‬و ‪ {ei }iв€€I вЉ‚ H‬ﻗﺎﻋـﺪة ﻓﻴـﻪ Щ€ ‪I‬‬ вЂ«п»Јпє п»¤п»®п»‹ЩЂЩЂпє” ШЈШЇп»џЩЂЩЂпє” п»—пєЋпє‘п» ЩЂЩЂпє” п»џп» п»ЊЩЂЩЂпєЄ п»‹п» ЩЂЩЂп»° اﻷﻛﺜــﺮ‪ .‬ﻧﺮﻣــﺰ п»џп»”ЩЂЩЂп»ЂпєЋШЎ اﻟﻤــﺆﺛﺮات اﻟﺨﻄﻴــﺔ اﻟﻤﺤــﺪودة ﺑــﺎﻟﺮﻣﺰ‪ . B (H ) :‬ﻧــﺬﻛﺮ‬ ‫ﺑﻔﻀﺎء п»«п» пє’пє®ШЄ ﺷﻤﺖ‪:‬‬ ‫)‪(1‬‬ ‫ﺑﺎﻋпє�ﺒﺎر‬ ‫‪{ei }iв€ћ=1‬‬ ‫‪‬‬ ‫‪< ∞‬‬ ‫‪‬‬ ‫‪2‬‬ ‫‪H‬‬ ‫‪‬‬ ‫‪HS := пЈІ A в€€ B(H ) : ∑ Aei‬‬ ‫‪i =1‬‬ ‫‪‬‬ ‫∞‬ ‫ﻗﺎﻋﺪة п»“п»І ‪ H‬و‬ ‫© ﺟﻤﻴﻊ Ш§п»џпє¤п»�п»®Щ‚ ﻣﺤﻔﻮﻇﺔ п»џпє пєЋп»Јп»Њпє” اﻟﻴﺮﻣﻮك ‪.2007‬‬ ‫* п»›п» п»ґпє” اﻟﻬﻨﺪﺳﺔ اﻟﻜﻬﺮﺑﺎﺋﻴﺔ Щ€Ш§п»№п»џп»њпє�ﺮوﻧﻴﺔ‪ ،‬ﺟﺎﻣﻌﺔ пєЈп» пєђвЂЄ ،‬ﺳﻮرﻳﺎ‪.‬‬ ‫** ﻋﻤﻴﺪ п»›п» п»ґпє” Ш§п»џпє�пє¤п» п»ґп»ћ п»“п»І Ш§п»џпє пєЋп»Јп»Њпє” Ш§п»џпє�п»�ﻨﻴﺔ ﺑﻤﺪﻳﻨﺔ درزدن‪.‬‬ ‫ﻣﺤпє�п»®п»іпєЋШЄ اﻟﻌﺪد‬ 1 ‫أﺣﻤﺪ ﻣﺤﻤﺪ п»‹пє п»®Ш± Щ€ Ш±п»іп»Ёпє® ﺑﻴﻜﺮد‬ ‫اﻟﺒﺤﻮث пє‘пєЋп»џп» п»ђпє” اﻟﻌﺮﺑﻴﺔ‬ ‫ﺗﻄﺒﻴп»�пєЋШЄ п»“п»І п»“п»ЂпєЋШЎШ§ШЄ п»«п» пє’пє®ШЄ п»џп» п»¤пє†пє›пє®Ш§ШЄ اﻟﺨﻄﻴﺔ ﻏﻴﺮ‬ * ‫اﻟﻤﺤﺪودة‬ ‫اﻟﺒﺤﻮث пє‘пєЋп»џп» п»ђпє” Ш§п»»п»§пє п» п»ґпє°п»іпє”вЂ¬ * Use of X-ray Diffraction and Mud Master Program in the Evaluation of Crystallite Size and Size Distributions of Illite and Kaolinite at Various Depths of Rock Formations in Jordan Ibrahim M. Odeh, Waleed A. Saqqa and Denis Eberl 1 * Assessment of Background Radiation Dose due to Radon in Kharja Village, Irbid Governorate, Jordan Khitam M. Khasawinah and Khalid M. Abumurad 19 * Determination of the Specific Activities of Radioactive Nuclides of Surface Soils of Some Hadhramout’s Valleys in Yemen Using GammaRay Spectrometry Awad Ali Bin- Jaza and Abdulazize Omer Bazohair 27 * Origin and Migration of Primordial Germ Cells in Mosquitofish, Gambusia affinis Janti S. Qar and Mohammad A. Al-Adhami 39 * The Role of Selenium and Lycopene in the Protection of Mice Against Microcystin Toxicity Saad Al-Jassabi and Ahmad Khalil 49 * Geoeletrical and Hydrochemical Investigations in the Hallabat Area, North Jordan Ghunaim S. Nasher, Hakam A. Mustafa and Nabil Abderahman 59 * Environmental Impact Assessment of Hiswa Clay Deposits, South Jordan Talal Al-Momani 93 * Performance Evaluation of One UMTS Cell by the New Modelling Specification and Evaluation Language MOSEL-2 Aymen Issa Zreikat 105 * A Generic Parallel Map: Extending the List Map Higher Order Function to Arbitrary Data Structures Mohammad M. Hamdan 123 * Effect of Access Point Moving on the Wireless Network Performance Using Opnet Modeler Sameh H. Ghwanmeh 135 * New Techniques for Improving H.263 Videoconferencing Ammar M. Kamel and Moh'd Belal. Al-Zoubi 147 ‫اﻟпє�ﻮﺛﻴﻖ‪:‬‬ ‫أ‪ -‬ﺗﻮﺛﻴﻖ اﻟﻤﺮاﺟﻊ واﻟﻤﺼﺎدر اﻟﻤﻨﺸﻮرة‪ :‬ﻳпє�п»ў Ш°п»џп»љ ШЇШ§пє§п»ћ اﻟﻤпє�ﻦ пє‘пєЋпєіпє�пєЁпєЄШ§Щ… ﻧﻈﺎم Ш§п»џпє�ﺮﻗﻴﻢ ]‪[ 1‬‬ ‫ﺑﻴﻦ ﻗﻮﺳﻴﻦ‪.‬‬ ‫• пє—п»ЊпєЄ ﻗﺎﺋﻤﺔ ﺑﺎﻟﻤـﺼﺎدر واﻟﻤﺮاﺟـﻊ اﻟﻤﻨـﺸﻮرة п»“ЩЂп»І ﻧﻬﺎﻳـﺔ Ш§п»џпє’пє¤ЩЂпєљ пєЈЩЂпєґпєђ Ш§п»џпє�ـﺮﻗﻴﻢ Ш§п»џЩЂп»®Ш§Ш±ШЇ ﻓـﻲ‬ ‫اﻟﻨﺺ‪.‬‬ ‫إذا п»›пєЋЩ† اﻟﻤﺮﺟﻊ п»›пє�пєЋпє‘пєЋЩ‹ п»іп»њпє�пєђ ﻫﻜﺬا‪:‬‬ ‫] [ ﻋــﺰوز‪ ،‬درﻳــﺪ‪ .‬ﻣﻴﻜﺎﻧﻴــﻚ اﻟﻤﻮاﺋــﻊ‪ ،‬ﻣﺪﻳﺮﻳــﺔ Ш§п»џп»њпє�ЩЂЩЂпєђ واﻟﻤﻄﺒﻮﻋــﺎت‪ ،‬ﺟﺎﻣﻌــﺔ пєЈп» ЩЂЩЂпєђвЂЄ ШЊвЂ¬пєЈп» ЩЂЩЂпєђвЂЄШЊвЂ¬вЂ¬ ‫‪.1979‬‬ ‫واذا п»›пєЋЩ† اﻟﻤﺮﺟﻊ пє‘пє¤пєњпєЋЩ‹ п»“п»І ШЇЩ€Ш±п»іпє” п»іп»њпє�пєђ ﻫﻜﺬا‪:‬‬ ‫] [ ﻣﺤﻤﺪ‪ ،‬ﻧﻮري ﺻﺎﺑﺮ‪ ،‬ﻗﻴﺎس ﺣـﺴﺎﺳﻴﺔ Ш§п»џпє�пєЁпє®п»іЩЂпє° ШЈпє›п»ЁЩЂпєЋШЎ п»›ЩЂпєґпє® Ш§п»џп»”ЩЂп»®п»»Ш° اﻟﻜﺮﺑـﻮﻧﻲ‪ ،‬دراﺳـﺎت‪:‬‬ вЂ«Ш§п»џп»Њп» п»®Щ… اﻟﻬﻨﺪﺳﻴﺔ Щ€Ш§п»џпє�ﻜﻨﻮﻟﻮﺟﻴﺔ‪ ،‬ﻣﺞ‪ ШЊ12‬ع‪ ШЊ1985 ШЊ9‬ص ‪.24‬‬ ‫واذا п»›пєЋЩ† اﻟﻤﺮﺟﻊ п»Јп»�пєЋп»џпє” ШЈЩ€ п»“пєјп»јЩ‹ п»“п»І п»›пє�пєЋШЁ п»іп»њп»®Щ† п»›пєЋп»џпє�ﺎﻟﻲ‪:‬‬ ‫] [ п»‹пє’ЩЂпєЄ اﻟﺤـﺎﻓﻆ‪ ،‬ﺳـﺎﻣﻲ ﺧـﻀﺮ‪ .‬اﻟпє�ـﺸﺨﻴﺺ اﻟﻤﺨﺒـﺮي п»џп» п»„п»”п»ґп» п»ґЩЂпєЋШЄвЂЄ ،‬ﻃـﺮق ШІШ±Ш№ Ш§п»џп»„п»”п»ґп» п»ґЩЂпєЋШЄвЂЄШЊвЂ¬вЂ¬ ‫ارﺑﺪ‪ ،‬ﺟﺎﻣﻌﺔ اﻟﻴﺮﻣﻮك‪ ШЊ1986 ،‬ص ‪.181-175‬‬ ‫ب‪ -‬ﺗﻮﺛﻴــﻖ اﻟﻬــﻮاﻣﺶ واﻟﻤــﺼﺎدر ﻏﻴــﺮ اﻟﻤﻨــﺸﻮرة‪ :‬ﻳــпє�п»ў Ш°п»џЩЂЩЂп»љ п»“ЩЂЩЂп»І اﻟﻤــпє�ﻦ пє‘пє€пє›пє’ЩЂЩЂпєЋШЄ п»›п» п»¤ЩЂЩЂпє” )п»«ЩЂЩЂпєЋп»Јпє¶(‬ ‫ﻣпє�пє’п»®п»‹ЩЂЩЂпє” пє‘ЩЂЩЂпєЋп»џпє®п»—п»ў اﻟﻤпє�пєґп» ЩЂЩЂпєґп»ћ п»џп» п»¬ЩЂЩЂпєЋп»Јпє¶ ШЇШ§пє§ЩЂЩЂп»ћ ﻗﻮﺳــﻴﻦ‪ ،‬ﻫﻜــﺬا‪) :‬ﻫــﺎﻣﺶ‪ .(1‬وﺗــﺬﻛﺮ Ш§п»џп»¤п»Њп» п»®п»ЈЩЂЩЂпєЋШЄвЂ¬ ‫اﻟпє�п»”пєјп»ґп» п»ґпє” п»џп»њп»ћ п»«пєЋп»Јпє¶ п»“п»І ﻧﻬﺎﻳﺔ Ш§п»џпє’пє¤пєљ пє—пє¤пє– п»‹п»Ёп»®Ш§Щ† اﻟﻬﻮاﻣﺶ Щ€п»—пє’п»ћ ﻗﺎﺋﻤﺔ اﻟﻤﺮاﺟﻊ‪:‬‬ ‫ﻫﺎﻣﺶ‪ :1‬ﺧﻀﺮ‪ ،‬ﺑﺴﺎم راﺷـﺪ‪ ،‬ﻗﻴـﺎس ﺗﺮﻛﻴـﺰ اﻟـﺮادون‪ 222‬ﻓـﻲ п»«ЩЂп»®Ш§ШЎ п»Јп»ЁЩЂпєЋШІЩ„ п»ЈпєЄп»іп»ЁЩЂпє” ارﺑـﺪ‪ ،‬اﻷردن‪،‬‬ ‫رﺳﺎﻟﺔ п»ЈпєЋпєџпєґпє�ﻴﺮ ﻏﻴﺮ ﻣﻨﺸﻮرة‪ ،‬ﺟﺎﻣﻌﺔ اﻟﻴﺮﻣﻮك ‪ ШЊ1990‬ص ‪.11-8‬‬ ‫ﻣﺮاﺟﻌﺎت Ш§п»џп»њпє�ﺐ‪ :‬ﺗп»�пє’п»ћ п»џп» п»Ёпєёпє® п»“п»І Ш§п»џп»¤пє п» пє” п»Јпє®Ш§пєџп»ЊпєЋШЄ Ш§п»џп»њпє�пєђ Ш§п»џпє¤пєЄп»іпєњпє” Ш§п»џп»�ﻴﻤﺔ‪.‬‬ ‫اﻟпє�ﺼﺮف‪ :‬ﻳﺤﻖ ﻟﺮﺋﻴﺲ Ш§п»џпє�пє¤пє®п»іпє® ШҐпєџпє®Ш§ШЎ Ш§п»џпє�ﻐﻴﻴﺮات Ш§п»џпє�п»І п»іпє®Ш§п»«пєЋ пєїпє®Щ€Ш±п»іпє” п»·п»Џпє®Ш§Ш¶ اﻟﺼﻴﺎﻏﺔ‪.‬‬ ‫اﻟﻤﺴпє�ﻼت‪ :‬ﻳﻤﻨﺢ п»›п»ћ ﻣﻦ п»іп»ЁЩЂпєёпє® пє‘пє¤пєњЩЂп»Є ﻧـﺴﺨﺔ Щ€Ш§пєЈЩЂпєЄШ© ﻣـﻦ п»‹ЩЂпєЄШЇ Ш§п»џп»¤пє п» ЩЂпє” Ш§п»џЩЂпє¬ЩЉ п»іп»ЁЩЂпєёпє® ﻓﻴـﻪ اﻟﺒﺤـﺚ‬ ‫ﺑﺎﻹﺿﺎﻓﺔ ШҐп»џп»° ﻋﺸﺮﻳﻦ п»Јпєґпє�п» пє” ﻣﻨﻪ‪.‬‬ ‫ﺗﺮﺳﻞ Ш§п»џпє’пє¤п»®Ш« واﻟﻤﺮاﺳﻼت إﻟﻰ‬ ‫رﺋﻴﺲ пє—пє¤пє®п»іпє® п»Јпє п» пє”вЂ¬ ‫أﺑﺤﺎث اﻟﻴﺮﻣﻮك "пєіп» пєґп» пє” Ш§п»џп»Њп» п»®Щ… اﻷﺳﺎﺳﻴﺔ واﻟﻬﻨﺪﺳﻴﺔ"‬ ‫ﻋﻤﺎدة Ш§п»џпє’пє¤пєљ Ш§п»џп»Њп» п»¤п»І Щ€Ш§п»џпєЄШ±Ш§пєіпєЋШЄ Ш§п»џп»Њп» п»ґпєЋвЂ¬ ‫ﺟﺎﻣﻌﺔ اﻟﻴﺮﻣﻮك‬ ‫ارﺑﺪ‪-вЂ¬Ш§п»џп»¤п»¤п» п»њпє” اﻷردﻧﻴﺔ اﻟﻬﺎﺷﻤﻴﺔ‬ ‫ﻳﻤﻜﻦ Ш§п»џпє¤ЩЂпєјп»®Щ„ п»‹п» ЩЂп»° ШЈпє‘пє¤ЩЂпєЋШ« اﻟﻴﺮﻣـﻮك ﻣـﻦ п»—ЩЂпєґп»ў Ш§п»џпє�пє’ЩЂпєЋШЇЩ„ п»“ЩЂп»І п»Јп»њпє�пє’ЩЂпє” пєџпєЋп»Јп»ЊЩЂпє” اﻟﻴﺮﻣـﻮك‪ ،‬أو ﻋﻤـﺎدة‬ ‫اﻟﺒﺤﺚ Ш§п»џп»Њп» п»¤п»І Щ€Ш§п»џпєЄШ±Ш§пєіпєЋШЄ Ш§п»џп»Њп» п»ґпєЋ п»џп»�пєЋШЎ ШЇп»іп»ЁпєЋШ± п»џп» п»ЁпєґпєЁпє” اﻟﻮاﺣﺪة‪.‬‬ ‫اﻻﺷــпє�пє®Ш§Щѓ اﻟــﺴﻨﻮي‪ :‬دﻳﻨــﺎران وﻧــﺼﻒ п»“ЩЂЩЂп»І اﻷردن‪ ،‬وﺛﻤﺎﻧﻴــﺔ دﻧــﺎﻧﻴﺮ ШЈЩ€ Ш§пє›п»ЁЩЂЩЂп»І п»‹ЩЂЩЂпєёпє® ШЇЩ€п»»Ш±Ш§Щ‹ أﻣﺮﻳﻜﻴ ЩЂпєЋЩ‹ ﻓــﻲ‬ ‫اﻟﻮﻃﻦ اﻟﻌﺮﺑﻲ‪ ،‬وﺛﻤﺎﻧﻴﺔ п»‹пєёпє® ШЇЩ€п»»Ш±Ш§Щ‹ أﻣﺮﻳﻜﻴﺎً ШЈЩ€ п»ЈпєЋ ﻳﻌﺎدﻟﻬﺎ п»“п»І Ш§п»џпє’п» пєЄШ§Щ† اﻷﺧﺮى‪.‬‬ ‫ﺑِﺴﻢ пєЌп»џп» п± п»Є ﺍﻟﺮﹼﺣﹾﻤﻦﹾ ﺍﻟﺮﹼﺣﹺﻴﻢﹾ‬ ‫أﺑﺤﺎث اﻟﻴﺮﻣﻮك‬ вЂ«пєіп» пєґп» пє” Ш§п»џп»Њп» п»®Щ… اﻷﺳﺎﺳﻴﺔ واﻟﻬﻨﺪﺳﻴﺔ‬ вЂ«п»Јпє п» пє” п»‹п» п»¤п»ґпє” ﻣﺤﻜّﻤﺔ‬ ‫ﺗﻨﺸﺮ Ш§п»џп»¤пє п» пє” Ш§п»џпє’пє¤п»®Ш« Ш§п»·пє»п» п»ґпє” Ш§п»џпє�п»І пє—пє�п»®Ш§п»“пє® ﻓﻴﻬﺎ‬ вЂ«Ш§п»џп»¤п»Ёп»¬пє п»ґпє” Ш§п»џпєґп» п»ґп»¤пє”вЂЄ ،‬واﻟпє�п»І п»џп»ў пє—п»�пєЄЩ… п»џп» п»Ёпєёпє® п»“п»І ШЈЩЉ п»Јп»њпєЋЩ† آﺧﺮ‬ ‫ﻗﻮاﻋﺪ Щ€ШҐпєџпє®Ш§ШЎШ§ШЄ اﻟﻨﺸﺮ‬ ‫• Ш§п»џп» п»ђЩЂЩЂпє”вЂЄ :‬ﺗﻜпє�ЩЂЩЂпєђ Ш§п»џпє’пє¤ЩЂЩЂп»®Ш« пє‘пєЋп»џп» п»ђЩЂЩЂпє” اﻟﻌﺮﺑﻴــﺔ ШЈЩ€ пє‘пєЋп»џп» п»ђЩЂЩЂпє” Ш§п»№п»§пє п» п»ґпє°п»іЩЂЩЂпє” Щ€п»» пє—ЩЂЩЂпєґпє�п» п»ў Ш§п»џпє’пє¤ЩЂЩЂп»®Ш« ﺑﻐﻴــﺮ‬ ‫ﻫﺎﺗﻴﻦ Ш§п»џп» п»ђпє�ﻴﻦ‪.‬‬ ‫• пє—п»�пєЄп»іп»ў اﻟﺒﺤﻮث‪ :‬ﺗп»�пєЄЩ… Ш§п»џпє’пє¤п»®Ш« п»“ЩЂп»І ШЈШ±пє‘ЩЂп»Љ ﻧـﺴﺦ п»Јп»„пє’п»®п»‹ЩЂпє” пє‘п»”пє®Ш§п»ЏЩЂпєЋШЄ п»Јпє°ШЇЩ€пєџЩЂпє” Щ€п»‹п» ЩЂп»° وﺟـﻪ‬ ‫واﺣﺪ‪ ،‬وﻫﻮاﻣﺶ пєЈпє п»ў Ш§п»џп»®Ш§пєЈпєЄ ﻣﻨﻬﺎ ‪2.5‬ﺳﻢ‪.‬‬ ‫ п»іпє ЩЂЩЂпєђ ШЈЩ† п»» п»іпє°п»іЩЂЩЂпєЄ п»‹ЩЂЩЂпєЄШЇ пє»ЩЂЩЂп»”пє¤пєЋШЄ Ш§п»џпє’пє¤ЩЂЩЂпєљ ﺑﻤــﺎ п»“ЩЂЩЂп»І Ш°п»џЩЂЩЂп»љ Ш§п»»пє·ЩЂЩЂп»њпєЋЩ„ Щ€Ш§п»џпє®пєіЩЂЩЂп»®Щ… Щ€Ш§п»џп»¤пє®Ш§пєџЩЂЩЂп»ЉвЂ¬вЂ«Щ€Ш§п»џпє пєЄШ§Щ€Щ„ واﻟﻤﻼﺣﻖ ﻋﻦ )‪ (30‬ﺻﻔﺤﺔ‪.‬‬ ‫ п»іп»�пєЄЩ… Ш§п»џпє’пєЋпєЈпєљ п»Јп» пєЁпєјп»ґп»¦ п»џпє’пє¤пєњп»Є п»“п»І пє»п»”пє¤пє�ﻴﻦ п»Јп»Ёп»”пєјп» пє�ﻴﻦ أﺣﺪﻫﻤﺎ пє‘пєЋп»џп» п»ђпє” اﻟﻌﺮﺑﻴﺔ Щ€Ш§п»µпє§пє®вЂ¬вЂ«пє‘пєЋп»џп» п»ђпє” Ш§п»№п»§пє п» п»ґпє°п»іпє” п»“п»І п»ЈпєЋ п»» п»іпє°п»іпєЄ п»‹п» п»° ‪ 200вЂ¬п»›п» п»¤пє” п»џп»њп»ћ ﻣﻨﻬﻤﺎ‪.‬‬ ‫ п»іп»њпє�пєђ п»‹п»Ёп»®Ш§Щ† Ш§п»џпє’пє¤пєљ Щ€Ш§пєіп»ў اﻟﻤﺆﻟﻒ Щ€Ш±пє—пє’пє�ЩЂп»Є Ш§п»џп»Њп» п»¤п»ґЩЂпє” واﻟﻤﺆﺳـﺴﺔ Ш§п»џпє�ЩЂп»І ﻳﻌﻤـﻞ ﺑﻬـﺎ п»‹п» ЩЂп»°вЂ¬вЂ«пє»п»”пє¤пє” п»Јп»Ёп»”пєјп» пє”вЂЄ ،‬ﺛﻢ п»іп»њпє�пєђ п»‹п»Ёп»®Ш§Щ† Ш§п»џпє’пє¤пєљ п»Јпє®Ш© ШЈпє§пє®Щ‰ п»‹п» ЩЂп»° Ш§п»џЩЂпєјп»”пє¤пє” Ш§п»·Щ€п»џЩЂп»° ﻣـﻦ اﻟﺒﺤـﺚ‬ вЂ«Щ€п»‹п» п»° пє»п»”пє¤пє” п»›п»ћ п»Јп» пєЁпєєвЂЄ.‬‬ ‫ п»іп»�пєЄЩ… Ш§п»џпє’пє¤пєљ пє‘п»ЊпєЄ اﻟﻤﻮاﻓп»�пє” п»‹п» п»° ﻧﺸﺮه п»Јп»„пє’п»®п»‹пєЋЩ‹ وﻣﺤﻔﻮﻇﺎً п»‹п» п»° п»—ЩЂпє®Шµ ﻛﻤﺒﻴـﻮﺗﺮ ﻗﻴـﺎس‬‫‪ 3.5‬إﻧﺶ п»Јпє�п»®Ш§п»“п»– п»Јп»Љ أﻧﻈﻤﺔ )‪IBM (Microsoft Word 2000, XP‬‬ ‫اﻻﺷﻜﺎل واﻟﺮﺳﻮﻣﺎت‪:‬‬ ‫• пє—п»®пєїп»Љ Ш§п»·пє·п»њпєЋЩ„ Щ€Ш§п»џпє®пєіп»®п»ЈпєЋШЄ Щ€Ш§п»џпє пєЄШ§Щ€Щ„ п»“п»І ﻧﻬﺎﻳﺔ Ш§п»џпє’пє¤пєљ п»Јп»Љ Ш§п»№пє·пєЋШ±Ш© ШҐп»џп»° أﻣﺎﻛﻨﻬﺎ اﻟﻤﻨﺎﺳـﺒﺔ ﻓـﻲ‬ ‫اﻟﻤпє�ﻦ‪ ،‬ووﺻﻒ ﻟﻬﺎ пє»п»”пє¤пє” п»Јп»Ёп»”пєјп» пє”вЂЄ.‬‬ ‫• пє—п»�пєЄЩ… Ш§п»·пє·п»њпєЋЩ„ Щ€Ш§п»џпє®пєіп»®п»ЈпєЋШЄ Щ€Ш§п»џпє пєЄШ§Щ€Щ„ п»Јпє®пєіп»®п»Јпє” пє‘пєЋп»џпє¤пє’пє® Ш§п»·пєіп»®ШЇ п»‹п» п»° Щ€Ш±Щ‚ пє·ЩЂп»”пєЋЩЃ ‪(Tracing‬‬ ‫)‪ ШЊPaper‬وﻓــــﻲ пє»ЩЂЩЂЩЂЩЂп»”пє¤пєЋШЄ п»Јп»Ёп»”ЩЂЩЂЩЂЩЂпєјп» пє” ﺑﺤﻴــــﺚ п»» пє—пє�пє ЩЂЩЂЩЂЩЂпєЋЩ€ШІ ШЈпє‘п»ЊЩЂЩЂЩЂЩЂпєЋШЇ п»«ЩЂЩЂЩЂЩЂпє¬Щ‡ Ш§п»»пє·ЩЂЩЂЩЂЩЂп»њпєЋЩ„ واﻟﺮﺳــــﻮﻣﺎت‬ ‫)‪19‬ﺳﻢ×‪12‬ﺳﻢ(‪.‬‬ ‫• أﺳﻤﺎء Ш§п»·п»‹п»јЩ… اﻷﺟﻨﺒﻴﺔ‪ :‬ﻋﻨﺪ Щ€Ш±Щ€ШЇ أﺳﻤﺎء ШЈп»‹п»јЩ… أﺟﻨﺒﻴﺔ п»“п»І Ш§п»џпє’пє¤п»®Ш« اﻟﻤп»�пєЄп»Јпє” ﺑﺎﻟﻌﺮﺑﻴﺔ‬ ‫ﻓﺈﻧﻬﺎ пє—п»њпє�пєђ пє‘пєЋп»џп» п»ђпє” اﻟﻌﺮﺑﻴﺔ пє—п» п»ґп»¬пєЋ اﻷﺳﻤﺎء пє‘пєЋп»№п»§пє п» п»ґпє°п»іпє” ﺑﻴﻦ ﻗﻮﺳﻴﻦ‪.‬‬ ‫ﻫﻴﺌﺔ Ш§п»џпє�ﺤﺮﻳﺮ‬ ‫رﺋﻴﺲ Ш§п»џпє�ﺤﺮﻳﺮ‬ ‫اﻷﺳпє�пєЋШ° Ш§п»џпєЄп»›пє�п»®Ш± ﻋﺒﺪاﻟﺮﺣﻤﻦ ﻋﻄﻴﺎت‬ ‫اﻷﻋﻀﺎء‬ ‫اﻷﺳـــــــпє�пєЋШ° Ш§п»џЩЂЩЂЩЂЩЂЩЂЩЂЩЂпєЄп»›пє�п»®Ш± ﻋﻤـــــــﺮ اﻟﺮﻳﻤـــــــﺎوي‬ ‫اﻷﺳــــــــпє�пєЋШ° Ш§п»џпєЄп»›пє�ЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂп»®Ш± ﻣﺤﻤــــﺪ أﺑﻮﺻــــﺎﻟﺢ‬ ‫اﻷﺳـــــــпє�пєЋШ° Ш§п»џЩЂЩЂЩЂЩЂЩЂЩЂЩЂпєЄп»›пє�п»®Ш± пєЈпєЋп»ЈЩЂЩЂЩЂЩЂЩЂЩЂЩЂпєЄ ШІШ±п»іп»�ـــــــﺎت‬ ‫اﻷﺳـــــــــــــпє�пєЋШ° Ш§п»џпєЄп»›пє�п»®Ш± ﻣﺸﻬﻮر اﻟﺮﻓﺎﻋﻲ‬ ‫اﻟﺪﻛпє�ЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂп»®Ш± ﻣﺤــﻤـــﺪ اﻟﺸــــــﺒﻮل‬ ‫اﻟﺪﻛпє�ЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂЩЂп»®Ш± ﻣﺤﻤﺪ пє‘п»јЩ„ اﻟﺰﻋﺒﻲ‬ ‫ﺳﻜﺮﺗﲑ Ш§п»џпє�ﺤﺮﻳﺮ‬ ‫ﻋُﻼ пє·пєЋп»›пє® п»‹п»�п» п»ЄвЂ¬ ‫© ﺟﻤﻴﻊ пєЈп»�п»®Щ‚ Ш§п»џп»„пє’п»Љ ﻣﺤﻔﻮﻇﺔ п»џпє пєЋп»Јп»Њпє” اﻟﻴﺮﻣﻮك ‪2007‬‬ ‫ﻻ п»іпє п»®ШІ ﻧﺸﺮ ШЈЩЉ пєџпє°ШЎ ﻣﻦ п»«пє¬Щ‡ Ш§п»џп»¤пє п» пє” ШЈЩ€ Ш§п»—пє�пє’пєЋпєіп»Є ШЇЩ€Щ† Ш§п»џпє¤пєјп»®Щ„ п»‹п» п»°вЂ¬ ‫ﻣﻮاﻓп»�пє” ﺧﻄﻴﺔ п»Јпєґпє’п»�пє” ﻣﻦ رﺋﻴﺲ Ш§п»џпє�ﺤﺮﻳﺮ‬ ‫ﻣﺎ п»іпє®ШЇ п»“п»І Ш§п»џп»¤пє п» пє” п»іп»Њпє’Щ‘пє® ﻋﻦ ШўШ±Ш§ШЎ أﺻﺤﺎﺑﻪ‪ ،‬وﻻ п»іп»Њп»њпєІ آراء‬ ‫ﻫﻴﺌﺔ Ш§п»џпє�пє¤пє®п»іпє® ШЈЩ€ ﺳﻴﺎﺳﺔ пєџпєЋп»Јп»Њпє” اﻟﻴﺮﻣﻮك‬ ‫اﻟﻤﺮاﺟﻌﻪ Ш§п»џп» п»ђп»®п»іпє”вЂ¬ ‫اﻻﺳпє�пєЋШ° Ш§п»џпєЄп»›пє�п»®Ш± اﺑﺮاﻫﻴﻢ ﺟﺒﺮﻳﻞ‬ ‫ﻗﺴﻢ اﻟﻜﻴﻤﻴﺎء – пєџпєЋп»Јп»Њпє” اﻟﻴﺮﻣﻮك‬ ‫ﺗﻨﻀﻴﺪ واﺧﺮاج‬ ‫أﺣﻤﺪ أﺑﻮﻫﻤﺎم Щ€п»Јпє пєЄЩЉ اﻟﺸﻨﺎق‬ ‫‪ISSN 1023-0149‬‬ ‫أﺑﺤَـﺎث اﻟﻴَﺮﻣـﻮك‬ вЂ«пєіп» пєґп» пє” Ш§п»џп»Њп» п»®Щ… اﻷﺳﺎﺳﻴﺔ واﻟﻬﻨﺪﺳﻴﺔ‬ вЂ«п»Јпє п» пє” п»‹п» п»¤п»ґпє” ﻣﺤﻜّﻤﺔ‬ вЂ«Ш§п»џп»¤пє п» пєЄ Ш§п»џпєґпєЋШЇШі ﻋﺸﺮ‬ ‫اﻟﻌﺪد اﻷول‬ ‫‪1428‬ﻫـ‪2007/‬م‬
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