INTERNATIONAL CONFERENCE ON MATHEMATICAL ANALYSIS
AND OPTIMIZATION: THEORY AND APPLICATIONS (ICAPTA 2014)
UNIVERSITY OF LAGOS
MARCH 12th – 14th, 2014
S
Edited by
E. P. FASINA
B. A. SAWYERR
S. AKINFENWA
WELCOME ADDRESS
The Mathematical Analysis and Optimization Research Group (MANORG), comprising of related
researchers in the Departments of Mathematics and Computer Science of the University of
Lagos, is borne out of the need to align with the global trend of interdisciplinary research with
optimal applications of the “gown” to the “town”. A step towards achieving the goal is for
experts in related but different disciplines to discuss their work and discover possible areas of
collaboration. Mathematical Analysis and Optimization Theory and Techniques are one of those
related disciplines with a wide application to the industry in which collaboration between
experts in those fields has not been fully explored. I hope the Annual International Conference
on Mathematical Analysis and Optimization: Theory and Applications will encourage this
collaboration. Furthermore, the annual conference will metamorphose into a bi-annual peerreviewed internationally recognized and open access Journal titled International Journal of
Mathematical Analysis and Optimization: Theory and Applications. Presenters in this
conference are encouraged to submit the full text of their publications in the next one month
for possible publication in the Inaugural Edition of the Journal.
The Organizers, the Departments of Mathematics and Computer Sciences will like to appreciate
our invited guest speakers, who are world renowned experts in Mathematical Analysis and
Optimization, for honouring our invitations. They are:

Prof. Mujahid Abass, University of Pretoria

Prof. C. E. Chidume, African University of Science and Technology, Abuja

Prof. Montaz Ali, Witwaterstrand University, Johannesburg

Prof. Christopher Thron, Texas A & M Central University, USA.
Finally, the encouragement, contribution and support of the Vice-Chancellor towards the success of the
conference are highly appreciated.
Thank you.
Professor J. O. Olaleru
Chairman, MANORG and LOC.
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Copyright © 2014 MANORG, except where otherwise restricted.
All rights reserved. No material may be reproduced without
permission of MANORG, Department of Mathematics and
Department of Computer Sciences,
Faculty of Science, University of the Lagos,
Akoka, Yaba, Lagos, Nigeria.
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Programme Schedule
Wednesday, March 12th 2014
Time
Registration opens,
Courtesy visit to the Vice- Chancellor,
Arrival of Special Guests and Dignitaries
8.00am Julius Berger Auditorium
Conference Opening Ceremony
 National Anthem
 Opening Prayer
 Introduction of Dignitaries
 Opening Remarks by the HOD of Computer
Sciences Department
 Welcome Address by the Chief Host, ViceChancellor, Unilag
 Keynote Address by Prof. C. E. Chidume
 Remarks by the HOD, Mathematics
 Closing Remarks by the Dean, Faculty of
Science
 Vote of Thanks by the Chairman, Conference
Organizing Committee.
Coffee/Tea Break
Presentations
Refreshments (Lunch time)
First Plenary Session: Prof. Christopher Thron
Presentations
Wednesday Presentations
Room
11.00am – 1.00pm
E203
B001-B006
Faculty Board
A001-A008
Venue
1.00 – 2 .00
Refreshment
(Lunch time)
9.00-10.30am Julius Berger Auditorium
9.00am
9.05am
9.10am
9.20am
9.25am
9.35am
10.20am
10.25am
10.30am
10.30-10.45am Julius Berger Auditorium
11.00am – 1.00pm E203 Computer Lab &
Faculty Board Room
1.00 – 2 .00pm Faculty Board Room
2.00 – 2.50pm Faculty Board Room
3.00 – 6.00pm E203 Computer Lab&
Faculty Of Science Room
2.00 – 2 .50pm
First Plenary Session
3.00 – 6.00pm
B007-B0014
A009-A0019
Thursday, March 13th 2014
Time
Registration opens
8.00am
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Venue
Faculty of Science Board
Room
Second Plenary Session: Prof. Montaz Ali
9.00-9.50am Faculty of Science Board
Room
9.50-10.10am Faculty Board Room
10.10-1.10am Faculty Board
1.10 – 2 .00pm
2.00-2.50am
Faculty Board
3.00 – 6.00pm E203 & Faculty Board
6.30pm – 7.30pm Faculty Board Room
Coffee/Tea Break
Presentations
Lunch Break
Third Plenary Session: Prof. Mujahid Abass
Presentations
Conference Dinner and Closing Ceremony
Thursday Presentations
Room
10.10am – 1.10pm
E203
B014-B020
Faculty Board A020-A031
1.10 – 2 .00
Refreshment
(Lunch time)
5
2.00 – 2 .50pm
Third Plenary Session
3.00 – 6.00pm
B021-B027
A032-A042
Conference Organizers
Prof. J. O Olaleru, Department of Mathematics, Faculty of Science University of Lagos
(Chairman)
Dr. E. P Fasina, Department of Computer Sciences, Faculty of Science University of
Lagos (Vice- Chariman)
Dr. H. Akewe, Department of Mathematics, Faculty of Science University of Lagos
(Secretary)
Dr. M. Adamu, Department of Mathematics, Faculty of Science University of Lagos
Dr. B. A. Sawyerr, Department of Computer Sciences, Faculty of Science University of
Lagos
Dr. O. A. Sennaike, Department of Computer Sciences, Faculty of Science University
of Lagos
Dr. S. Akinfenwa, Department of Mathematics, Faculty of Science University of Lagos
Dr. E. B. Nkemnole, Department of Mathematics, Faculty of Science University of
Lagos
Mr. G. A. Okeke, Department of Mathematics, Faculty of Science University of Lagos
Mrs. S. K. Eke, Department of Mathematics, Covenant University, Ota.
Mrs. O. V. Olisama, Department of Mathematics, Faculty of Science University of
Lagos
Mrs. B. I. Akinnukawe, Department of Mathematics, Faculty of Science University of
Lagos
Mr. H. O. Olaoluwa, Department of Mathematics, Faculty of Science University of
Lagos
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SCIENTIFIC COMMITTEE:
Prof. R. Okafor, Head of Department of Mathematics Department
Prof. C. O. Uwadia, Head of Department of Computer Sciences
Prof. A. S. Okunuga
Prof. S. O. Ajala
Prof. S. S. Okoya
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8
APPROXIMATION OF COMMON FIXED POINTS OF
COUNTABLE FAMILY OF NONSELF ASYMPTOTICALLY
NONEXPANSIVE MAPPINGS IN CAT(0) SPACES
Abdulmalik U. B.
[email protected]
African University of Science and Technology, Galadimawa junction, Abuja, Nigeria
ABSTRACT:
Let E be a CAT(0) space. Let K be a nonempty, closed and convex subset of E. An iterative
process for a countable family of nonself asymptotically nonexpansive mappings is defined on
K, where strong convergence and Δ-convergence are established. Our result generalizes many
results in the literature.
A NEW FAMILY OF SECOND DERIVATIVE METHOD
FOR STIFF IVPS IN ODES.
Abhulimen C. E
[email protected]
Department of Mathematics, Ambrose Alli
University, Ekpoma, Nigeria.
Adoghe L. O
Department of Mathematics, Ambrose
Alli University, Ekpoma, Nigeria.
ABSTRACT
In this paper, a new family of implicitly 4-step second derivative linear multistep methods for
numerical integration of stiff initial value problems (ivps) in ordinary differential equations
(ODES) is developed. The new approach which is based on exponential fitting methods isof
order six. The stability analysis of the method when discussed shows that it is A-stable. Some
numerical results are reported to illustrate the efficiency and accuracy of the new method when
compared with existing ones in the Literature.
AMS subject classification: 65L05, 65L06
Key words: Four-step, second derivative method, exponential fitting, order 6, stiff IVPS.
9
BINARY POLYNOMIAL REPRESENTATION USING THE
(123) AVOIDING CLASS OF THE AUNU PERMUTATION
PATTERNS OF CARDINALITY SEVEN
Abubakar S. I.
aminualhaji40@gmailcom
Department of Mathematics, Sokoto State
University,P.M.B 2134, Sokoto, Nigeria.
Shehu S.
[email protected]
Department of Mathematics, Sokoto State
University,P.M.B 2134, Sokoto, Nigeria.
Zaid I.
[email protected]
Department of Mathematics, Sokoto State
University,P.M.B 2134, Sokoto, Nigeria.
Ibrahim A. A.
[email protected]
Department of Mathematics, Sokoto State
University,P.M.B 2134, Sokoto, Nigeria.
ABSTRACT
A generating function of binary codes using the (123) - avoiding class of the Aunu permutation
patterns was reported earlier by the authors. This paper reports a polynomial representation
scheme using these binary codes. The purpose of using these binary polynomials is to define
operations on the words and sub-words generated by the Aunu permutation patterns using
conventional polynomial arithmetic-except that the coefficient are taken modulo 2 in the
completed operation. Binary codes have an interesting applications in digital electronic circuits
in which a Boolean variable is used to represents a point in a circuit; hence Boolean algebra can
be used as a design tool for digital electronic circuit. The binary polynomials derived can also be
used for construction of mathematical structures such as groups, rings and fields which have an
important application in cryptography.
10
OPTIMAL PENALTY OF INSIDER TRADING DRIVEN
BY JUMP-TIME LéVY PROCESSES
Achudume C.
Department of Mathematics, University of
Ibadan, Oyo State, Nigeria
Oyem A. O.
[email protected]
Department of Mathematics, Federal
University Lokoja
ABSTRACT
This paper extended the driving force of the price process from Brownian motion to a JumpTime Lévy process for optimal penalty of an insider trading and observed the extinction of
insider trading as the year goes with subsequent change in penalty rate, thereby studying how
optimal market regulatory agency checks insider trading activity with the view ofreducing it to a
zero tolerance through deriving optimal penalty for an insider trading driven by pure Jump-Time
Lévy process. The result shows that under a mild condition, the illegal activity of an insider can
be cube and brought to a zero tolerance.
Key words: Lévy-Itô decomposition, Jump-Time, penalty, insider trader, semi-martingale,
Brownian motion
11
A NOTE ON JUST-IN-TIME SCHEDULING ON UNIFORM
AND UNRELATED MACHINES
Adamu M.
[email protected]
Department of Mathematics,
University of Lagos
Akoka, Yaba, Lagos, Nigeria
Nigel B.
[email protected]
School of Mathematics,
Statistics & Computer
Science, University of
Kwazulu-Natal, South Africa
Gbolahan I.
[email protected]
Lagos State University Ojo,
Lagos, Nigeria
ABSTRACT:
In this paper, the scheduling to maximize the weighted number of Just-In-Time jobs on Uniform
and Unrelated machines are considered. This problem is known to be NP Complete for when the
due date is at a point in time indicating no efficient optimal solution is feasible in reliable time.
Due dates with interval in time are considered in this work. The problem formulation is
suggested, greedy heuristics are proposed for solving the problem. A numerical example to
illustrate its use and extensive computational experiments performed with promising results are
presented. Likely areas of extensions are provided.
Keywords: Just-In-Time, NP Complete, Uniform Machines, Unrelated Machines, Scheduling
12
APPLICATION OF A LOCATION MODEL TO FIRE STATIONS
IN IJEBU-ODE METROPOLIS
Adekolu A. G.
[email protected]
Department of Mathematics, Tai Solarin
University of Education, Ijebu-Ode, Nigeria
Osinuga I.A.
[email protected]
Department of Mathematics, Federal
University of Agriculture, Abeokuta, Nigeria
ABSTRACT:
This research work is carried out to locate one or more fire stations in view of the many petrol
filling stations in Ijebu Ode metropolis with just one fire service station to combat fire outbreak
within the town. With the aid of a global positioning system (GPS germin 60 version), the
coordinate of the filling station was taken and that of the fire service station. Four major points
were discovered on the map with the aid of the geographic information system (GIS ARC
VIEW) from the existing fire service station to minimize weighted total distance to the demand
points. The single facility location problem considers distance function from facility to demand
as against demand to facility which is mostly considered in location problem. The objective of
this work is to locate one fire sites from the four potential fire sites using a suitable model.
13
TOWARDS AN OPTIMAL MODEL OF SOLID WASTE
COLLECTION AND DISPOSAL BY CLUSTERIZATION
Adeleke O. J
[email protected]
Department of Computer and Information
Science/Mathematics, Covenat University,
Ota, Nigeria.
Omoregbe N. I
Department of Computer and Information
Science/Mathematics, Covenat University,
Ota, Nigeria.
Adewumi O. A
School of Mathematics, Statistics and
Computer Science,
University of KwaZulu Natal, Westville
Campus, Durban, South Africa.
Agarana M. C
Department of Computer and Information
Science/Mathematics, Covenat University,
Ota, Nigeria.
ABSTRACT
A new generic model of solid waste collection is proposed and developed based on the clustering
of waste bins and the limitations of traffic congestion and road characteristics. The techniques of
combinatorial optimization and linear integer programming are used as tools for the formulation
of the model. A combination of exact methods such as Lagrange Relaxation, Branch and Bound
or Dynamic programming; and/or standard optimization solvers such as CPLEX OR AnyLogic,
shall be used to seek an optimal solution to the model. Data of varying sizes generated from
literature will be used to test the robustness and if possible the limit of the exact methods. In
order to compare the effectiveness of recent heuristic methods, this research also seeks nearoptimal solutions for large instances of dataset. The study area is Lagos, Nigeria.
14
QUEUING ANALYSIS OF SALES OF TOASTED BREAD
IN UNIVERSITY OF LAGOS, AKOKA, NIGERIA
SPREEDSHEET SIMULATION APPROACH
Adesina O. S.
[email protected], [email protected]
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos, Nigeria
ABSTRACT
This research explores the queuing theory and the analysis for the sales of toasted bread in the
Faculty of Education eatery in University of Lagos, Nigeria. The recording and observation
were done on a week day; while school was on session. Twenty students (20) customers were
sampled and recorded for inter-arrival time and process time, mean and standard deviation were
calculated as it  7.81 , st  7.61 ,  it  4.01 and  st  1.93 respectively. Parameter Alpha and
Beta Calculated thus as it  3.79 , it  2.06 ,  st  15.55 .Simulation for one thousand (1000)
customers was carried on spreadsheet with M/M/1 Heavy Traffic via Gamma.Inv (Rand(),  , 
).The simulation result reveals that mean waiting time is 23.11, mean time spent in the system is
30.22, mean inter-arrival time is 7.64 and mean process time is 7.21. It shows that customers
wait for an average of 23.11 in the queue while waiting for an average 30.22 entirely in the
system. It is therefore recommended that measure be taken to avoid or reduce queue so as to
enable customers maximize their time in other meaningful activities if they must consume the
snack.
Keywords: Queuing, Simulation, Alpha, Beta, Gamma distribution, inter-arrival and
process time.
15
OPTIMAL CONTROL O F NATIONAL E C O N O M Y
B Y GOVERNMENT SPENDING: AN ANALYSIS O F
SAMUELSON'S INTERACTIVE MODEL
Adewale T. A.
[email protected]
Department of Industrial Mathematics
Adekunle Ajasin University,
P.M.B. 01, Akungba – Akoko, Ondo State, Nigeria
In this presentation an analysis of Samuelson’s model is undertaken. Four discrete
functions are considered in describing a national economy. The simplified model
p r e s e n t e d by Samuelson is modified
imports and exports. A Difference equation
spending is optimalized and predictions
to accommodate
foreign
trade i n terms o f
model is formulated and s o l v e d . Government
are made b y using t i l e m o d e l o n Nigerian
economy.
Keywords: Production propensity to consume, propensity to save, differential equation,
difference equation, development plan petroleum and petrochemicals.
16
AN APPLICATION OF GOAL PROGRAMMING TECHNIQUE
TO LOAN PORTFOLIO MANAGEMENT IN NIGERIA BANKS
Agarana, M. C.
Agboola, O. O.
Adeleke, O. J.
Department of Mathematics,
Covenant University, Ota, Ogun
State, Nigeria
Department of Mathematics,
Covenant University, Ota,
Ogun State, Nigeria
Department of Mathematics,
Covenant University, Ota, Ogun
State, Nigeria
ABSTRACT
Most banks that fail do so as a result of mismanagement of their loan portfolio. In this paper we
examine loan portfolio management of banks. An Operations Research technique, Goal
programming, is applied to the management of loan portfolio in Nigeria banks. With the result
obtained, using a multi objective package provides an answer on how to handle cases of bad
loans or doubtful loans. Bad loan is a major factor militating against optimization of bank goals
in Nigeria.
Keywords: Loan portfolio, Goal programming, Bad Loan, Optimization.
17
NEUTROSOPHIC VECTOR SPACES
Agboola A.A.A
[email protected]
Department of Mathematics, Federal
University of Agriculture,
Abeokuta, Nigeria
Akinleye S.A.
[email protected]
Department of Mathematics, Federal
University of Agriculture,
Abeokuta, Nigeria
ABSTRACT
The objective of this paper is to study neutrosophic vector spaces.Some basic definitions and
properties of the classical vector spaces are generalized. It is shown that every neutrosophic
vector space over a neutrosophic field (resp. a field) is a vector space. Also, it is shown that an
element of a neutrosophic vector space over a neutrosophic field can be infinitely expressed as a
linear combination of some elements of the neutrosophic vector space. Neutrosophic quotient
spaces and neutrosophic vector space homomorphisms are also studied.AMS (2010): 03B60,
15A03, 20A05.
Key words: Weak neutrosophic vector space, strong neutrosophic vector space, field,
neutrosophic field.
18
CONSTRUCTION OF NEW VECTOR SPACES
Ajala S.O
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
Ukenazor V.I
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
ABSTRACT:
We introduce a collection of new vector spaces Vn2 nN of n 2 matrices over the field  of real
numbers with respect to some fixed    under the operations of vector addition and scalar
multiplication different from those of M n 2 () - the vector space of n 2 matrices over  .
This collection of new vector spaces is denoted Vn2 nN and interestingly, it turns out that the
zero of this collection behaves uniquely and also, the zeros follow a pattern.
19
ON THE SPECTRAL THEORY OF SELFADJOINT AND
NONSELFADJOINT OPERATORS IN HILBERT SPACE
Ajibo, A.
[email protected]
Federal University Ndufu-Alike Ikwo, P.M.B. 1010, Ebonyi State, Nigeria
ABSTRACT
This paper is a review of the spectral theory of selfadjoint operators and methods which have
been used to analyze the spectrum of nonselfadjoint operators. It begins with a succinct
introduction of the basic notions in a Hilbert space encompassing unbounded linear operators,
classication of linear operators in terms of their adjoints and the spectral resolution of unbounded linear operators.
Keywords: spectrum, eigenvalue, resolvent, selfadjoint operators, nonselfad- joint operators,
pseudospectra, spectral operator.
20
USING SPHERICAL BESSEL FUNCTIONS TO
COMPUTEBACKSCATTER RADAR CROSS SECTION BY A
PERFECTLY CONDUCTING SPHERE
Akala A. O.
[email protected]
Department of Physics,
University of Lagos, Yaba,
Lagos, Nigeria.
Somoye E. O.
Adewale A. O.
Department of Physics,
Lagos State University, Ojo,
Lagos, Nigeria
Department of Physics,
University of Lagos, Yaba,
Lagos, Nigeria.
ABSTRACT
This study presents numerical computation of backscatter radar cross section (RCS) by a
perfectly conducting sphere, using Mie series. Techniques of series approximations and
recursions of the spherical Bessel functions were used to construct Mie series. Finally, we
analyzed mathematical properties of backscatter RCS by a perfectly conducting sphere, and
calibrated radars at different frequency bands for different sizes of spherical targets.
Keywords: Radar cross section; spherical Bessel functions; Mie series
21
HYBRID ENERGY OPTIMIZATION FOR RURAL
ELECTRIFICATION USING LINEAR PROGRAMMING
Akinbulire T. O.
[email protected]
Department of Electrical/
Electronics Engineering,
University of Lagos, Akoka,
Yaba, Lagos, Nigeria
Oluseyi P. O.
[email protected]
Department of Electrical/
Electronics Engineering,
University of Lagos, Akoka,
Yaba, Lagos, Nigeria
Babatunde O. M.
[email protected]
Department of Electrical/
Electronics Engineering,
University of Lagos, Akoka,
Yaba, Lagos, Nigeria
ABSTRACT:
There are several of ways of designing an optimal hybrid power system, each with varying levels
of certainty. These methods vary from the basic pencil and paper analysis and calculation by
means of rules of thumb to sophisticated computer simulated programs. Sizing of any hybrid
energy systems involves putting in place a number of constraints, and decision variables to be
optimized. This leads to the problem of determining many unknowns and hence a long iterative
process. Considering the long iterative process and multi-objective function to be optimized,
computer simulations are more accurate and recommended. In a nutshell, optimization and
system modeling programs are imperative for minimizing the cost of power systems utilizing
renewable energy. This work presents the mathematical models involved in the optimization of
hybrid energy for rural electrification. The optimization problem in this case consists of
minimizing a cost function while satisfying the load demand of a typical community. In solving
the optimization problem, linear programming is used to determine the optimal system
configuration which more economically satisfies the load.
Keywords: Optimization, Mathematical model, Linear programming, Hybrid energy
22
RABBIT WEIGHT PREDICTION USING BODY
MEASUREMENTS: A NEURAL NETWORK APPROACH
Akinsola O. M.
Animal Science Deptartment,
Faculty of Agriculture, Ahmadu
Bello University
Omole O. O.
Department of Computer
Sciences, University of
Lagos
Abanikannda O. T. F.
Adepeju A. A.
Department of Zoology, Faculty
of Science, Lagos State
University
Department of Mathematics,
Lagos State University
Sennaike O. A.
Department of Computer
Sciences, University of
Lagos
ABSTRACT
An Artificial Neural Network (ANN) model has been developed for predicting body weight
of eight-week old New Zealand White purebred and crossbred rabbits. Five predictor variables
were used viz, breed, sex, heart girth, body length and height at wither as input variables and
body weight was considered as dependent variable from the model. Observation data set within
the same age group was randomized and split into a training set (comprising of 60% of the data
set) and test set (comprising of 20% of the data set) and the remaining 20% to test the
effectiveness of the model. The ANN used was multi-layer feed forward network with back
propagation. Our ANN models performed better than traditional multivariate linear regression
(MLR) models indicating that the ANN models were able to more accurately capture how the
variations in input variables explain the variations in body weight. It was concluded that ANN
models are more powerful than MLR models in predicting animals’ body weight. Nonetheless,
we recognize that fitting an ANN model requires more computation resources than fitting a
tradition MLR model.
23
GEOMETRIC ERGODICITY OF THE MIXTURE
AUTOREGRESSIVE MODEL
Akinyemi M. I.
Department of Mathematics,
University of Lagos
Boshnakov G. N.
Department of Mathematics
University of Manchester
ABSTRACT:
Geometric ergodicity is very useful in establishing mixing conditions and central limit results for
parameter estimates of a model, it also justifies the use of laws of large numbers and forms part
of the basis for exploring the asymptotic theory of the model. Geometric ergodicity is very useful
in examining the consistency and asymptotic normality of the parameter estimates of a model.
The class of mixture autoregressive (MAR) models provides a exible way to model various
features of time series data and is well suited for density forecasting. The MAR models are able
to capture many stylized properties of real data, such as multi-modality, asymmetry and
heterogeneity. We show here that the Mixture Autoregressive model (MAR) model is
geometrically ergodic and by implication satisfies the absolutely regular and strong mixing
conditions.
24
ON THE ERROR ANALYSIS OF A ONE STEP CONTINUOUS
IMPLICIT HYBRID METHOD
Anake T. A.
[email protected]
Department of Mathematics Covenant University,
Ota, Ogun State, Nigeria
Bishop S. A.
[email protected]
Department of Mathematics Covenant
University, Ota, Ogun State, Nigeria
Oghonyon G. J.
Department of Mathematics Covenant University,
Ota, Ogun State, Nigeria
Edeki S. O
Department of Mathematics Covenant
University, Ota, Ogun State, Nigeria
ABSTRACT:
The application of linear multistep formulae poses important questions bordering on the degree
of accuracy of these formulae. The accuracy of the result obtained from a multistep formula
depends largely on the local truncation error. In this paper, we shall establish a bound using the
generalized remainder theorem and the mean value theorem on the total error induced by the
local truncation errors of a one step continuous implicit hybrid method proposed for the solution
of initial value problem of second order ordinary differential equations. The method shall be
experimented on a typical electric circuit problem where the absolute errors obtained from the
implementation at selected grid points shall be compared to values of the error bound at similar
points.
25
EFFECT OF COMBINED CONTROL POLICIES ON THE
OPTIMAL CONTROL OF A HOST-VECTOR MODEL
FOR MALARIA WITH INFECTIVE IMMIGRANTS
Bakare E.A
[email protected]
Federal University OyeEkiti,
Ekiti State Nigeria
ABSTRACT
We formulate and analyzed a compartmental deterministic model on the effect of combined
control policies on the optimal control of a host-vector model for malaria with infective
immigrants. We provided sufficient conditions for the sensitivity analysis for the basic
reproduction number with respect to the model parameters for the host-vector model without the
control. We also applied optimal control theory to study optimal strategies for controlling the
epidemiology of malaria disease in the presence of infective immigrants using quarantine,
treatments and Insecticide treated BedNets as our system control variables and by deriving its
necessary conditions for optimal control of the malaria disease using the Pontryagin’s
Maximum Principle (PMP). With the applications of optimal control theory, the optimal levels of
the three controls are characterized. We carried out the Numerical simulations and extend the
analytical results.
26
PREDICTIVE MODELS OF CURRENT, VOLTAGE AND
POWER LOSSES ON ELECTRIC TRANSMISSION LINES
Bamigbola O.M.
[email protected]
Department of Mathematics, University of Ilorin,
P.M.B. 1515 Ilorin, Nigeria
ABSTRACT
Energy is a basic necessity for the development of any nation. Although, there are different
forms of energy, the most important of them is electrical energy. A modern and civilized society
is so much dependent on the use of electrical energy because it has been the most powerful
vehicle for facilitating economic, industrial and social developments. Electrical energy produced
at power stations are transmitted to load centres from where they are distributed to its consumers
through the use of transmission lines run from one place to another. As a result of the physical
properties of the transmission medium, some of the transmitted power are lost to the
surroundings. The power losses could take off a sizeable portion of the transmitted power since
the transmission lines usually span a long distance, sometimes several hundred kilometers. The
overall effect of power losses on the system is a reduction in the quantity of power available to
the consumers. Therefore, an accurate knowledge of power losses on transmission lines will be
useful in the planning and maintaining of an efficient electric power system. An accurate
knowledge of transmission losses is hinged on the ability to correctly predict the available
current and voltage along transmission lines. Therefore, mathematical physics expressions
depicting the evolution of current and voltage on a typical transmission line were formulated,
and derived therefrom were models to predict available current and voltage respectively at any
point on the transmission line. Recasting the power loss function as a mathematical physics
problem eventually yielded the predictive model for power losses along the line. The predictive
models evolved as explicit expressions of the space variable and they are in close agreement with
empirical data and reality.
27
CONVERGENCE OF A HYBRID ITERATIVE
SCHEMEFORFIXED POINTS OF NONEXPANSIVE MAPS,
SOLUTIONSOFEQUILIBRIUM AND VARIATIONAL
INEQUALITIES PROBLEMS
Bashir A.
[email protected]
Department of Mathematics
Bayero University Kano,Nigeria
ABSTRACT
In this paper, convergence theorem is proved for infinite family of nonexpansive mappings,
solutions of equilibrium problem and solution of variational inequality problem in a framework
of a real q-uniformly smooth Banach space with weakly sequentially continuous duality map.
The result presented here is an improvement of several results recently announced.
28
ON EXISTENCE AND UNIQUENESS OF MILD SOLUTION OF
IMPULSIVE PERTURBED QUANTUM STOCHASTIC
DIFFERENTIAL EQUATIONS AND THE ASSOCIATED
KURZWEIL EQUATIONS
Bishop S. A.
[email protected]
Department of Mathematics Covenant
University, Ota, Ogun State, Nigeria
Agboola O. O.
Department of Mathematics Covenant
University, Ota, Ogun State, Nigeria
ABSTRACT:
Existence of mild solution of impulsive Lipschitzian quantum stochastic differential equations
(QSDEs) associated with the Kurzweil equations are introduced and studied. This is
accomplished within the framework of the Hudson-Parthasarathy formulation of quantum
stochastic calculus and the associated Kurzweil equations. The solutions of a QSDE are
functions of bounded variation that is they have the same properties as the associated Kurzweil
equations introduced in the literatures. This generalizes similar results for classical initial value
problems to the noncommutative quantum setting. This work would have applications in the
theory of quantum continuous measurements.
29
AN n – WAREHOUSE STOCK ALLOCATION MODEL
USING DYNAMIC PROGRAMMING TECHNIQUE
Chikwendu C.R.
Emenonye C.E
ABSTRACT:
The
dire need for optimum distribution of goods at minimum cost is vital to
manufacturing organisations. This work develops a mathematical model that ensures
efficient allocation of goods and services. The Dynamic Programming technique is used
to develop a model that maximizes returns through optimum allocation. If r i(Q) is the
total returns from the ith activity with the resourse
Qii, , then we seek to maximize
R(Q1 , , Q2 , …………… , Qn ) = r1(Q1 )) + r2Q2 +…..rn(Qn) given that
Q = Qi
0 and I =
1, 2, …………, n. Related literature and relevant theorems are included while illustrative
example of a firm with n – distribution outlets , n
30
2 is used to buttress the model.
ROW-WISE REPRESENTATION OF ARBITRARY
RHOTRIX
Chinedu P.
[email protected]
Federal University Dutsin-ma. PMB 5001, Dutsin-ma. Katsina State
ABSTRACT
This paper identifies some various methods of representing an arbitrary rhotrix. One of the
methods - the row-wise method - has been chosen as it is observed to be flexible in analysing
rhotrices for mathematical enrichment. A relationship between the location of the heart of a
rhotrix and the dimension of the rhotrix and also a relationship between the location of the heart
of a rhotrix and the order of the principal matrix of the rhotrix have been determined. The
flexibility of the representation has paved way for two formulae, one for row-column
multiplication of arbitrary rhotrices and the other for heart-oriented multiplication of arbitrary
rhotrices. Some examples have also been given as a way of demonstrating the application of the
proposed formulae. Finally, the paper introduces the concepts of subrhotrix and submatrix of a
rhotrix which can be exploited for further study of various algebraic properties of rhotrices.
Keywords: rhotrix, principal matrix, complementary matrix, inscribed matrix, row-wise
representation, row-column multiplication, heart-oriented multiplication, subrhotrix, submatrix.
31
NUMERICAL SOLUTION OF THE BURGER’S EQUATION USING HIGHER
ORDER SEMI-DISCRETIZATION SCHEMES WITH THE BACKWARD TIME
CENTERED SPACE
Ehigie J. O.
Department of Mathematics,
University of Lagos, Akoka, Yaba.
Nigeria
Okunuga S. A.
Department of Mathematics,
University of Lagos, Akoka, Yaba.
Nigeria
Aderibigbe L. Y.
Department of Mathematics,
University of Lagos, Akoka, Yaba.
Nigeria
ABSTRACT
In this paper, the Burger’s equation is tranformed to a system of nonlinear Ordinary Differential
Equations (ODE) by some newly introduced approximations to the derivative terms using higher order
semi-discretization schemes. The nonlinear ODE is consequently transformed to a system of nonlinear
equations by the Backward Time Centered Space (BTCS) formula. These resulting nonlinear equations
are finally solved by Newton’s formula to obtain numerical solutions to the Burger’s equation. Some
graphical results are hereby presented.
32
INTUITIONISTIC FUZZY SETS IN CAREER
DETERMINATION
Ejegwa, P.A.
[email protected]
Department of Mathematics, University of
Agriculture, P.M.B. 2373, Makurdi Nigeria
Awolola J.A.
[email protected]
Department of Mathematics, University of
Agriculture, P.M.B. 2373, Makurdi Nigeria
ABSTRACT
We proposed the application of intuitionistic fuzzy sets (IFSs) in career determination. Solution
is obtained by looking for the smallest distance between each student and each career.
Keywords: Fuzzy sets, Intuitionistic fuzzy sets, Career determination.
33
ON THE COMPARISONS OF OPTIMAL SOLUTION
METHODS OF SECOND-ORDER CONIC PROBLEMS VIA
BARRIER AND PRIMAL-DUAL INTERIOR POINT
TECHNIQUES
Eze, E.O
[email protected]
Department of Mathematics,Michael Okpara
University of Agriculture, Umudike,
Umuahia-Abia State. Nigeria.
Ezeme, C. N
[email protected],
Department of Computer Science and
Information Technology,
Caritas University, Amorji-Nike, Emene
Enugu, Nigeria
ABSTRACT
We considered the optimal solution of second order conic problems via barrier and primal-dual
interior point technique on comparative basis. The results showed that both techniques provided
an optimal solution and was further confirmed by the duality gap which gave zero.
We therefore concluded that primal-dual interior point technique should be used when solving
second order conic problems for non linear optimization because it is more efficient and effective
with high degree of accuracy and minimal error term than the barrier method, even without
extensions to global convergence property.
Keywords: Second order conic problem, Barrier method, Primal-dual interior technique, optimal
solution, Global convergence property.
34
A NEW DISCRETE PARTICLE SWARM ALGORITHM FOR
SOLVING OPTIMIZATION PROBLEMS
Fasina E. P.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Sawyerr B. A.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Edagbami S.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
ABSTRACT
The Particle Swarm Optimization algorithm has been applied successfully to a wide variety of
continuous and combinatorial optimization problems. However its efficiency may be severely
limited when used for combinatorial optimization problems because of its origin seeking bias
(Monson and Seppi, 2005) and its bias along paths parallel to the coordinate axes (Spears et al.
2010). Unlike optimization problems in continuous spaces where global best positions attract
particles to promising region in the search space thereby limiting the effect of position biases,
combinatorial optimization problems are best solved when the problem space is searched
uniformly without unintended biases. In this paper a new discrete Particle Swarm Algorithm is
proposed that supports the use of uniform or non-uniform discretization functions that explicitly
map particle positions in uniform continuous spaces to non-uniform discrete spaces. The
positions of particles are mapped dimension by dimension from a continuous space to a discrete
solution space thereby limiting or eliminating biased search. The effectiveness of the new
discrete PSO algorithm is demonstrated for the multiobjective optimization of combinational
logic circuits. Using integer encoding schemes introduced by Coello Coello (1997) and Miller
(1998) the proposed discrete PSO algorithm was found to generate good and feasible ReedMuller logic circuits optimized for low transistor counts and low propagation delays.
Keywords: Origin-Seeking Bias, Combinatorial Optimization Problems, Particle Swarm
Algorithm,
Monson C. K. and K. D. Seppi (2005) ―Exposing Origin-Seeking Bias in PSO‖, Proceedings of the 2005 ACM
Conference on Genetic and Evolutionary Computation (GECCO 05), pp. 241-248, June
Spears W. M., D. T. Green and D. F. Spears (2010) ―Biases in Particle Swarm Optimization‖, International Journal
of Swarm Intelligence, vol. 1, no. 2, pp. 34-57
35
Coello Coello C. A. , A. D. Christiansen, and Arturo Hernandez Aguirre (1997) ―Automated Design of
Combinational Logic Circuits using Genetic Algorithms‖, In D. G. Smith, N. C. Steele, and R. F. Albrecht, Editors,
Proceedings of the International Conference on Artificial Neural Nets and Genetic Algorithms, pages 335–338.
Springer-Verlag, University of East Anglia, England
Miller, J. F. P. Thomson, and T. Fogarty (1998) Designing Electronic Circuits Using Evolutionary Algorithms.
Arithmetic Circuits: A Case Study. In D. Quagliarella, J. P´eriaux, C. Poloni, and G.Winter, editors, Genetic
Algorithms and Evolution Strategy in Engineering and Computer Science, pages 105–131. Morgan Kaufmann,
Chichester, England
36
THE ELITIST MAX-MIN PARTICLE SWARM OPTIMIZER:
TOWARDS AN EXPLORATION CENTRED SEARCH OF
COMPLEX MULITMODAL PROBLEM SPACES
Fasina E. P.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Sawyerr B. A.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Ojiako C.
[email protected]
Department of Computer
Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
ABSTRACT
The Particle Swarm Optimization (PSO) algorithm first proposed by Kennedy and Eberhart
(1995) is one of the most widely deployed, studied and extended Swarm Intelligence
paradigms. PSO is easily implemented and it has been demonstrated to have good performance
over a wide range of continuous and combinatorial optimization problems. The inefficiency of
PSO caused by its problems of unstable particle trajectories and premature convergence
remains a major limitation in its widespread adoption as a problem solver of first choice. In this
work, the Elitist MAX-MIN Particle Swarm Optimization (EMM-PSO) algorithm is proposed.
EMM-PSO leverages on the unstable trajectories of particles for aggressive search, discourages
premature converges through the use of extreme elitist exemplars and encourages slow
convergence through a dynamic cycling of the clamping velocity, Vmax. Other attributes of
EMM-PSO eliminate stagnation and prevent other parameter induced deceleration of particle
speed. EMM-PSO is compared with the Standard Particle Swarm Optimizer (SPSO) on some
functions in the CEC2005 benchmark suite. Results demonstrate the effectiveness of
intensifying and leveraging on the exploitative advantage of PSO while inducing exploitation
through a gradual reduction in the spatial distribution of particles that is effected by an
adaptive and dynamic Vmax.
Keyword: Clamping velocity, Elitist, Particle Swam Optimization
37
Kennedy, J. and R. C. Eberhart, (1995) “Particle Swarm Optimization”, in Proceedings of the IEEE International
Conference on Neural Networks, Perth Australia, vol. 4. pp. 1942-1948
Eberhart, R. and J. Kennedy, “A New Optimizer using Particle Swarm Theory”, in Proceedings of the 6
th
International Symposium on Micro Machine and Human Science (MHS ’95)., Nagoya, Japan, October, pp. 39-43
FIXED POINTS OF MAPS SATISFYING PARAMETRIC
IMPLICIT RELATIONS IN METRIC-TYPE SPACES
Hallowed Olaoluwa
[email protected]
Department of Mathematics, Akoka, Yaba, Lagos, Nigeria
ABSTRACT
In an attempt to unify, extend, and generalize the exhaustive literature of common fixed points in
metric type spaces, we establish fixed point theorems for maps satisfying implicit parametered
relations. The operators used in the implicit relations correspond to contractive, expanding Cirictype conditions in literature.
38
39
A COMPARISON OF PARTICLE SWARM OPTIMIZATION,
DIFFERENTIAL EVOLUTION AND BACKPROPAGATION
ALGORITHMS ON THE TRAINING OF NEUROFILTERS FOR
FINGERPRINT IMAGE BINARIZATION
Fasina E. P.
[email protected]
Department of Computer Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Sawyerr B. A.
[email protected]
Department of Computer Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
Agho A.
[email protected]
Department of Computer Sciences
University of Lagos
Akoka, Yaba, Lagos
Nigeria
ABSTRACT
The binarization of fingerprint images is critical in the extraction of useful features that are used
in later stages of the fingerprint identification process. The capturing of fingerprint image is a
non-linear process due to the variations introduced during the capture process (e.g. varying light
intensity, noise, varying pressure, etc.). Global and local thresholding techniques which are
commonly used in image binarization do not perform well on greyscale fingerprint images since
they are based on simple averages and entropy distribution of image intensity. This work
introduces an efficient way of binarizing greyscale fingerprint images using Artificial Neural
Networks trained by the Backpropagation (BP), Particle Swarm Optimization (PSO) and
Differential Evolution (DE) algorithms. An object-oriented and connection-based model was
employed in designing and implementing a robust artificial feedforward neural network
codenamed NeuroMax. Object-oriented implementations of the training and optimizing
algorithms were developed and integrated with NeuroMax. Networks trained by the different
algorithms were compared by the Mean Square Error (MSE), Misclassification Error (ME) and
Region Non-Uniformity (NU) evaluation criteria. Although BP converges faster and gives best
results over a small number of iterations, PSO and DE techniques perform better over large
iterations. PSO on average produced the best quality of binarized images for different fingerprint
images of varying qualities, followed by DE. For good quality fingerprint images, the DE
produced the best results.
40
GENERALIZED COUPLED COMMON FIXED POINT
THEOREMS FOR MIXED WEAKLY MONOTONE
MAPPINGS IN PARTIALLY ORDERED B-METRIC
SPACES
Ibrahim Y. S
[email protected]
Department of mathematics
Kano university of science and technology
Wudil, Kano.Nigeria
ABSTRACT
The idea of an S-metric space as a generalized metric in 3-tuplesS: X3! [0, 1), where X is a
nonempty set was introduced by Sedghi etal. [S. Sedghi, N. Shobe, A. Aliouche, A
generalization of fixed point theorems in S-metric spaces, Mat. Vesnik Vol. 64, no.3, pp 258 266, 2012.]. In this article, we introduce the concept of n-tuples metric B: Xn! [0, 1) and prove
some generalized coupled common fixed point theorems for mixed weakly monotone maps in
partially ordered B-Metric spaces by imposing a few suitable requirements on the contractive
conditions obtained in Gordji et al. [M.E. Gordji, M. Ramezani, Y.J. Cho, E. Akbartabar,
Coupled common fixed point theorems for mixed weakly monotone mappings in partially
ordered metric spaces Fixed Point Theory Appl. 2012:95.]. Our results generalized the main
results of Dung [N.V. Dung, on coupled common fixed points theorem for mixed weakly
monotone maps in partially ordered S-metric spaces. Fixed Point Theory Appl., 2013:48],
Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in
partially ordered metric spaces and applications, Nonlinear Anal. Vol. 65, no.7, pp 1379 - 1393,
2006.] and many others.
41
NORMALIZATION OF INTUITIONISTIC FUZZY
MULTISETS (IFMSS)
Ibrahim A.M.
[email protected]
Department of Mathematics,
Ahmadu Bello University, Zaria
Ejegwa P. A.
([email protected] )
Department of Math/Statistics/Computer
Science, University of Agriculture,
Makurdi, Nigeria
ABSTRACT
In this paper, we introduced the normalization of IFMSs as an operation that retains the property of
IFMSs whenever the hesitation margin is negligible. This idea is deduced from Supriya et al. [6]
definition of normalization of intuitionistic fuzzy set (IFS) since IFMS is an extension of IFS. The
concept of normalization in IFS was later challenged by Zeng and Li [7]. Nonetheless, Ibrahim and
Ejegwa [9] stated that in order for the normalization of IFS to preserves the property of IFS, the hesitation
margin must be restricted to an insignificant value i.e. tending to zero. We gave the definition of
normalization of IFMS and some propositions. We as well deduced a corollary and proved.
Keywords: Fuzzy sets; Intuitionistic fuzzy sets; Intuitionistic fuzzy multisets; Modal operators.
42
A TRAPEZOIDAL APPROACH TO THE NUMERICAL
SOLUTION OF ONE-DIMENSIONAL TIME DEPENDENT
SCHRODINGER EQUATION
Johnson O. Fatokun
[email protected]
Department of Mathematical Sciences and
Information Technology, Federal University,
Dutsin-Ma, P.M.B. 5001, Dutsin-Ma.
Akpan, I. P
Department of Mathematical Sciences,
Nasarawa State University, Keffi, Nigeria.
ABSTRACT
In this paper, the 1-dimensional time dependent Schrodinger equation is discretized by the
Method of Lines using a second order finite difference approximation to replace the second order
spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is
solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative
maximum error of order 10-4 in the interval of consideration. The performance of the method as
compared to an existing scheme is considered favorable.
Key words: Schrodinger’s equation, partial differential equations, Method of Lines (MOL), stiff
ODE, trapezoidal-like integrator.
43
Mandah O. C.
[email protected]
University of Ibadan, Ibadan, Oyo, Nigeria
ABSTRACT:
The aim of this paper is to find an optimal strategy   ( , ) and a minimal cost for an arbitrary
contigent claim denoted by H. In our model, the discounted asset price X is a semi martingale
i.e.
X  X0 M  A
Where X 0 is adapted and G 0 -Measurable, M belongs to the set of squared integrable local
martingale null at zero and A is a predictable process with finite variation. In finding an optimal
strategy for H, we just need to look for the FS decomposition of the contingent claim, which is
given as
T
H  H 0    oH dX s  LTH
0
and by [2], the integrand  sH in * gives the optimal strategy while the remaining summands
H 0  LTH is the minimal cost.
44
ITERATIVE ALGORITHMS FOR ZEROS OF MULTIVALUED NONLINEAR MAPPINGS IN BANACH
SPACES WITH APPLICATIONS TO CONVEX
MINIMIZATION
Minjibir M. S.
E-mail: [email protected]
Department of Mathematical Sciences, Bayero University, Kano, Nigeria.
ABSTRACT
Let
and let E be a q-uniformly smooth real Banach space and K be a nonempty, closed
and convex subset of E. Let
Suppose that
→
be the collection of all closed and bounded subsets of K.
is a multi-valued bounded continuous pseudo-contractive mapping
with a nonempty fixed point set. A recent efficient iteration algorithm for approximating zeros of
important nonlinear operators is studied and the sequence of the algorithm is proved to converge
strongly to a fixed point of T. Furthermore, the ideas of the iteration algorithm are applied to
approximate zeros of continuous bounded accretive maps. Finally, an application of our
theorems to convex minimization problems is given.
45
A NOTE ON GENERALIZATION OF CLASSICAL
JENSEN’S INEQUALITY
Mogbademu A. A
Department of Mathematics,
University of Lagos, Nigeria.
Olanipekun P. O
Department of Mathematics,
University of Lagos, Nigeria.
ABSTRACT
In this note, we prove that if
integrable on [a, b] such that
are any two convex functions and f is Riemann-Stieltjes
, then
(∫
)
∫
CONTROLLABILITY FOR A NONLINEAR
DIFFERENTIAL EQUATION WITH NONLOCAL
CONDITIONS IN BANACH SPACES
Ndambomve P.
African University of Science and Technology, Abuja, Nigeria
Mathematics Institute, P.M.B 681, Garki, Abuja F.C.T
ABSTRACT
This work concerns the study of the controllability of some semilinear differential equation with
nonlocal initial conditions in Banach spaces. We give sufficient conditions that ensure the
controllability of the system by making use of the measure of noncompactness and the Sadovskii
fixed-point Theorem. In particular the compactness of the semigroup operator is not needed.
Keywords: Controllability, Nonlocal Initial Condition, Semigroup Operator, Measure of
Noncompactness, Sadovskii Fixed-Point Theorem.
46
THE MÖNCH FIXED-POINT THEOREM AND
APPLICATIONS IN BANACH SPACES
Ndambomve P.
African University of Science and Technology, Abuja, Nigeria
Mathematics Institute, P.M.B 681, Garki, Abuja F.C.T
ABSTRACT
This work concerns the study of the Mönch fixed-point theorem, which is an extension of the
Leray-Schauder fixed-point theorem, and its applications to controllability problems in Banach
spaces. We give the statement and the proof of the Theorem and look at some of its applications
to evolution equations and the controllability of such systems.
Keywords: Controllability, Evolution equations, Mönch Fixed-Point Theorem.
47
THE EFFECT OF TWO TREATMENTS ON THE
SURVIVAL TIME OF GASTRIC CANCER PATIENTS.
Njoku K.F
[email protected]
ABSTRACT
Stomach cancer (also known as gastric cancer) is a common cancer, which affects more men
than women and is rare in people under 50 years of age. This present study was undertaken to
examine the survival times in days of two groups of 43 patients suffering from gastric cancer and
receiving two different treatments. Group 1 received chemotherapy and radiation; Group 2
received only chemotherapy. Data were analyzed by plotting the Kaplan-Meier survival curves
of each group and using Log-rank, Breslow and Tarone-ware test to test the equality of survival
distributions for the different levels of groups at 95% confidence interval. The survival functions
curve shows that patients receiving chemotherapy have a longer survival time than patients
receiving chemotherapy and radiation.The mean and median for chemotherapy was higher than
that of chemotherapy and radiation. Log-Rank (Mantel-Cox) shows no significant difference,
while Breslow (Generalized wilcoxon) and Tarone-ware shows a significant difference at 95%
confidence interval. Thus, the results show that chemotherapy only is the best treatment for
gastric cancer patients when compared to chemotherapy and radiation combined.
Keywords: Gastric cancer - survival - Kaplan Meier - Log-Rank - Breslow - Tarone-ware.
48
FORECASTING VOLATILITY OF STOCK INDICES WITH
HMM-SV MODELS
Nkemnole E. B.
[email protected]
Department of Mathematics,
University of Lagos, Nigeria
Abass O.
[email protected]
Department of Computer Sciences,
University of Lagos, Nigeria.
ABSTRACT
The use of volatility models to generate volatility forecasts has given vent to a lot of literature.
However, it is known that volatility persistence, as indicated by the estimated parameter  , in
Stochastic Volatility (SV) model is typically high. Since future values in SV models are based
on the estimation of the parameters, this may lead to poor volatility forecasts. Furthermore, this
high persistence, as contended by some writers, is due to the structure changes (e.g. shift of
volatility levels) in the volatility processes, which SV model cannot capture. This work deals
with the problem by bringing in the SV model based on Hidden Markov Models (HMMs), called
HMM-SV model. Via hidden states, HMMs allow for periods with different volatility levels
characterized by the hidden states. Within each state, SV model is applied to model conditional
volatility. Empirical analysis shows that our model, not only takes care of the structure changes
(hence giving better volatility forecasts), but also helps to establish an proficient forecasting
structure for volatility models.
Keywords: Forecasting, Hidden Markov model, Stochastic volatility, stock exchange.
49
TESTING RANDOM WALK BEHAVIOUR AND
EFFICIENCY OF NIGERIAN STOCK MARKET USING
PARAMETRIC AND NONPARAMETRIC METHODS
Nwoseh D. A.
Department of Mathematics, University of Lagos,
Lagos, Nigeria
ABSTRACT
This project examines the weak form efficient market hypothesis for the Nigerian stock
exchange (NSE) market. Different parametric and nonparametric tests of random walk model are
used. The daily stock indices of Nigerian Stock Exchange (NSE) ranging from the
period January 2011 to December 2012 are considered for investigating the weak form
efficiency. The return series was found to be non-normal in the aspect of skewness and kurtosis.
The Jarque-Bera test also detected the violation of normality in the return series. The hypothesis
of randomness in return series of NSE market is also rejected with auto- correlation test. The
results revealed that stock return series do not follow the random walk model and the significant
autocorrelation rejects the hypothesis of weak form efficiency.
50
AN OPTIMIZATION MODEL FOR POSSIBLE
ELIMINATION OF HIV/AIDS IN NIGERIA
Ochoche J. M.
[email protected]
Dept. of math/stat/comp.sci
University of Agriculture, Makurdi, Nigeria
ABSTRACT:
In 2012, Nigeria with an estimated 3.5 million people living with HIV/AIDS overtook India to
become the country with the second highest burden of the disease worldwide. The number of
persons requiring ARV stands at about 1.5 million; unfortunately less than 30% of these people
have access to the treatment thereby facilitating the spread of the disease since ARV treatment is
capable of reducing transmission rate. Nigeria currently habours a staggering 10% of HIV/AIDS
infected individuals globally, next only to South Africa. In this paper we proposed a
mathematical model for possible elimination of HIV/AIDS in Nigeria. We introduced four time
dependent optimal controls to the model namely, condom use, screening, counseling and
treatment. To investigate the optimal level of effort that will be needed to control the disease, we
formulated the objective functional J, which is to minimize the newly infected (unaware
infectives) and the cost of applying the controls u_1,〖 u〗_2,u_3 and u_4. We applied
Pontryagin’s maximum principle which provides necessary conditions for an optimal control
problem. The principle converts the model equations and the objective functional into a problem
of minimizing an Hamiltonian, H, pointwisely with respect to u_1,u_2,u_3 〖and u〗_4.
Results show that if all control measures are implemented with maximum effort, HIV/AIDS can
be eliminated from Nigeria in finite time. Further, we note that condom use alone cannot
eliminate the disease, however in the presence of limited resources it is a better strategy
compared to the other three control measures combined.
Keywords: HIV/AIDS, Modelling, Nigeria, Optimization, Pontryagin’s maximum principle.
51
SIMULATION OF STOCK PRICE WITH GEOMETRIC
BROWNIAN MODEL
Ogbaji E.O.
Department of Mathematics and Statistics,
Federal University Wukari, Wukari,
Nigeria.
Ochoboju A.
Department of Mathematics and
Statistics, Federal University, Lafia,
Lafia, Nigeria.
ABSTRACT
In this study we study the behave of stock price in the capital market by using geometric
Brownian model. Over the years many financial institutions had crashed because of failure in
stock price in the capital market.
Through the years a lot of work has been done in this area of financial mathematics.
Mathematicians and financial engineers developed many mathematical models and the geometric
Brownian motion is now widely used in stock price. The financial market laws and rules which
this model is base only the present information about a stock efficient to determine the future
price of that stock.
According to geometric Brownian motion model, the returns on a certain stock in successive,
equal period of time are independents and normally distributed.
In stock price simulation, it is shown using geometric Brownian motion model is preferable for
modelling stock price over a long period of time than a shorter time.And it will be more accurate.
This is due to the fact that the expected rate of return and volatility of a stock are assumed to be
constant. To assess the accuracy of the model, it is preferable to model this parameter as
stochastic function of time and not as constant.
Key words: Stock price, rate of return, volatility.
52
OPTIMAL STRATEGY FOR INVESTMENT IN AN OIL FIELD
PROJECT:A STOCHASTIC ANALYSIS OF CRUDE OIL
PRICE"
Ogbogbo C.P
[email protected]
Department of Mathematics,
University Of Ghana. Legon. Accra. Ghana
ABSTRACT
The income demand elasticity is known to be much higher and more significant than the price
elasticity for crude oil. As a result the world economy growth rate keeps pushing world oil
demand upward. As the demand for crude oil rises in the global market, and in the face of market
uncertainty and price fluctuations, the investor in oil field faces a challenge. When, and how to
invest in order to obtain optimal returns, is a challenge faced by an investor in an oil field
project. Determining the value of the field in the face of various constraints is important,
identifying the process that describes the price movements is necessary, to generate the optimal
strategy for investment. This problem is formulated mathematically as an optimization problem,
with oil price as a stochastic process. Two price thresholds are obtained which explain how and
when to invest in an oil field project. Describing optimal stopping time and an application of
optimal singular control.
53
STOCHASTIC SIMULATION AND ANALYSIS OF THE
DYNAMICS OF TUBERCULOSIS
Omame A.
[email protected]
Department of Mathematics,
Federal University of Technology,
Owerri
Inyama S. C.
Department of Mathematics,
Federal University of Technology,
Owerri
ABSTRACT:
In this work a stochastic differential equation model is developed and analysed for the dynamics
of Tuberculosis. The model, which is a multidimensional diffusion process, includes susceptible
individuals, latent, infected and removed individuals. The model used in this work was based on
the deterministic model developed by Adetunde (2008). The model was modified by introducing
a vaccination parameter. The resulting deterministic model was transformed into a stochastic
differential equation model using the second modelling procedure proposed by Allen et al (2008)
and solved using the Euler Maruyama method. Real data for the simulation are based on the
immunization exercise administered on 41 children at Ahmadu Bello University Teaching
Hospital (ABUTH), Zaria between the months of November and December, 2003
(Wammanda,et al, 2004). The result shows that increased vaccination rate will lead to
Tuberculosis disease reduction and possible extinction.
Keywords and phrases: Stochastic model, tuberculosis, transition probability, wiener process,
vaccination.
54
Modelling and Analysis of a Three-Tier Supply Chain System
with Fuzzy-Reliability Parameters
Ogunwolu L.
[email protected]
Department of Systems Engineering,
Faculty of Engineering, University of
Lagos, Nigeria.
Onyedikam C.
[email protected]
Department of Systems Engineering,
Faculty of Engineering, University of
Lagos, Nigeria.
ABSTRACT
A Mathematical Programming Model and Analysis of a three-tier (supply, production and
distribution) supply chain in which decisions are made on choice of suppliers and quantities of
production and distribution based on adjudged reliabilities of the different supply chain players
under uncertainty is presented. Uncertainty in the adjudged reliabilities of the Supply Chain
players are modelled using triangular fuzzy numbers used to specify the Supply Chain players’
reliabilities. The central thrust of the work is to examine and analyse on conceptual and
analytical bases the effects of fuzzy-reliabilities of the systemic components of the Supply Chain
on the overall cost of the Supply Chain. To this end, a linear cost-minimization Mathematical
Programming Model of the three-stage supply chain is built, solved and results analysed under
varying alpha-cuts of the base fuzzy reliabilities. Test experiments were designed as trade-offs of
costs and reliabilities incorporated into the nine variants of the Mathematical Programming
Model to study combinations of effects reliabilities and their variable levels of uncertainties at
selected alpha-cuts. Results vindicate the novel approach of using Supply Chain reliabilities
under fuzzy uncertainty to allocate supplies, production and distribution and point a vast
application of the novel concept in Supply Chain modelling and Analysis and logistic problems
in general.
Keywords— Supply Chain, Fuzzy, Alpha-Cut, Reliability, Distribution, Production, Supplies,
Mathematical Programming
55
AN OPTIMIZED MATHEMATICAL MODEL FOR
ESTIMATING THE WEIGHT OF NIGERIANS AND
PROVISION OF MEDICAL AID: (A CASE STUDY OF
FEDERAL UNIVERSITY WUKARI, TARABA STATE OF
NIGERIA COMMUNITY)
Ogwumu, O.D
[email protected]
Department of Mathematics
and Statistics,
Federal University, Wukari
P.M.B. 1020, Wukari,
Taraba State, Nigeria
Adeyefa, E.O.
Department of Mathematics
and Statistics,
Federal University, Wukari
P.M.B. 1020, Wukari,
Taraba State, Nigeria
Amoo S.
Department of Mathematics
and Statistics,
Federal University, Wukari
P.M.B. 1020, Wukari,
Taraba State, Nigeria
ABSTRACT
The research is concerned with the development of a mathematical model for estimating the
body weight of Nigerian in relation to their height and Waist sizes. The model was optimized to
know whether it is possible for humans to have a maximum or minimum body weight. However,
the optimization result showed that there is no specific body weight that could be called a
maximum or minimum. Emphasis was laid mainly on a particular proportion of Nigerians from
the north- East geopolitical zone in order to be able to make a generalization about the entire
country and beyond. Hence, the population sample for the research was the Federal University
Wukari, Taraba State of Nigeria’s Community. Moreover, several recommendations were made
at the end of the model analysis which when adhered to, would bring about some medical
breakthroughs to the entire human populace.
56
EXISTENCE OF FIXED POINTS OF SOME CLASSES
OF NONLINEAR MAPPINGS IN SPACES WITH WEAK
UNIFORM NORMAL STRUCTURE
Okeke G. A.
[email protected]
Department of Mathematics, Akoka, Yaba, Lagos, Nigeria
ABSTRACT
In this study, we introduce the class of -nearly Lipschitzian mappings. This class of nonlinear
mappings is a generalization of those defined by Sahu [23]. It is also established that in a Banach
space
with weak uniform normal structure, every demicontinuous asymptotically regular
nearly Lipschitzian self-mapping
compact convex subset
of
with
satisfies the
→
√
-
defined on a weakly
-fixed point property. Our results generalize the
results of Sahu [23], Sahu et al. [25] and several other authors in literature.
57
CONVERGENCE THEOREMS ON ASYMPTOTICALLY
DEMICONTRACTIVE AND HEMICONTRACTIVE
MAPPINGS IN THE INTERMEDIATE SENSE
Okeke G. A.
[email protected]
Department of Mathematics, Akoka, Yaba, Lagos, Nigeria
ABSTRACT
In this study, we introduce two classes of nonlinear mappings, the class of asymptotically
demicontractive mappings in the intermediate sense and asymptotically hemicontractive
mappings in the intermediate sense and prove the convergence of Mann type and Ishikawa type
iterative schemes to their respective fixed points. Our results are improvements and
generalizations of the results of several authors in literature.
ON THE PALAIS SMALE COMPACTNESS CONDITION AND
THE MOUNTAIN PASS THEOREM
Okpala M. E.
[email protected]
African University of Science and Technology Abuja
ABSTRACT:
In 1963, Palais and Smale introduced a global topological criteria for the existence of minimizer
for a certain class of functional on Hilbert spaces. This condition, known as Palais Smale (PS)
Condition, and some of its variants have been essential in the development of critical point
theory on Banach spaces. In what follows, we study the presence of this condition on Mountain
Pass Theorem.
58
A COMPARISON OF THE RATE OF CONVERGENCE OF
SOME MULTI-STEP ITERATION SCHEMES FOR QUASICONTRACTION MAPS
Olaleru J. O.
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
Awosola A. O.
Department of Mathematics, University of
Lagos, Akoka, Yaba, Lagos,
Nigeria
ABSTRACT:
Some iterative schemes have been recently introduced and proved to be efficient with respect to their
rate of convergence. The most common of these schemes are: Picard, Mann, Ishikawa, Noor, multistep schemes and recently, Picard-Mann Hybrid (two steps); CR (three steps) and SP (three steps)
iterative schemes.
In this research, the multi-step version of CR and SP schemes, called CR and SP multi-steps
respectively, are introduced and their convergence to the fixed points of the quasi-contractive maps,
mostly used in literature, that is,
,
proved and their rates of convergence with their lower steps, already known in literature, are
compared. Afterwards, the rates of convergence of CR and SP multi-step schemes and the usual multistep are compared analytically.
It was shown that the SP multi-step iteration introduced converges faster than all the iteration schemes
in literature.
Numerical examples are given to confirm the results.
59
COUPLED BEST PROXIMITY POINTS FOR GENERALISED
HARDY-ROGERS TYPE CYCLIC (Ω)-CONTRACTION
Olaleru J. O.
[email protected]
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
Olisama V. O.
[email protected]
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
ABSTRACT:
A new class of map, called generalised Hardy-Rogers type cyclic (ω)-contraction, which
contains the cylic, Kannan, Chatterjea, Reich and Ciric quasi contractions as subclasses, is
introduced. The existence, convergence and uniqueness results of coupled best proximity point
for this map in a b-metric space are proved. Examples follow to support our main result.
2000 AMS subject classi_cation: 47H10
Keywords: coupled best proximity point, generalised cyclic contraction, Kannan cyclic
contraction,, Chatterjea cylic contraction, Reich cyclic contraction, gereralised Hardy-Rogers
type cyclic (ω)- contraction, Ciric quasi cyclic contraction, b-metric space.
60
A COMPARISON OF THE RATE OF CONVERGENCE OF
SOME MULTI-STEP ITERATION SCHEMES FOR QUASICONTRACTION MAPS
Olaleru J. O.
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
Showunmi S. O.
Department of Mathematics, University of
Lagos, Akoka, Yaba, Lagos,
Nigeria
ABSTRACT:
In this study, some known and recently introduced iteration schemes like those introduced by
Noor (2000), Agarwal (2007), Phuengrattana and Suantai (2011), Shaini and Neeta (2009), and
Kumar et al are generalized to multi-step iterations. Furthermore, two new multi-step iteration
schemes are introduced. The five multi-step iteration schemes are used to approximate the fixedpoint of quasi-contractive maps. The rate of convergence of the schemes is examined analytically
and numerical examples are given to corroborate the results on the rates of convergence. Many
results in literature are improved and generalized.
61
OPTIMIZATION TECHNIQUES FOR RESOURCE
PLANNING: A REVIEW
Oluwafemi J. O.
[email protected]
Kogi State Polytechnic Lokoja, Kogi state, Nigeria
ABSTRACT
This paper presents a review of some important optimization techniques useful for
resource planning and allocation. Allocation of resources, in general, depends on
certain decisions which may either lead to Minimizing or Maximizing certain imputes
and outputs. The problem to solve will determine the optimizing technique used.
SOME CONVEX FUNCTIONS FOR HERMITE-HADAMARD
INTEGRAL INEQUALITIES WITH APPLICATIONS TO
SPECIAL MEANS
Omotoyinbo O.
[email protected]
Department of Mathematics,
University of Lagos, Akoka, Yaba, Lagos,
Nigeria
Mogbademu A.
[email protected]
Department of Mathematics, University of
Lagos, Akoka, Yaba, Lagos,
Nigeria
ABSTRACT:
In this paper, we employed a simple analytical method to obtain some new integral inequalities
of Hermite-Hadamard type involving two different classes of convex functions. Some
applications of our results to special means were considered.
62
RIEMANNIAN GEODESICS - AN ILLUSTRATION FROM
THE CALCULUS OF VARIATIONS
Opara, U. M.
[email protected]
African University of Science and Technology,
Km 10 airport road, Galadimawa, Abuja.Nigeria
ABSTRACT:
This paper aims to shed light on the essential characteristics of geodesics, which frequently occur
in considerations from motion in Euclidean space. Focus is mainly on a method of obtaining
them from the calculus of variations.
ON THE EXISTENCE OF
ORDER √
,√
DIFFERENCE SETS WITH
IS AN INTEGER
Osifodunrin S. A.
Department of Mathematics
University of Lagos,
Lagos, Nigeria
ABSTRACT:
Difference sets are useful in communication sciences and closely related to designs. The study of
difference sets is the epitome of elegance of combination of techniques in geometry,
combinatorics, group, representation and number theories.
Lander (1983) states that symmetric design admitting a group G as a regular automorphism
group is isomorphic to the development of the difference set. To date, the biplanes (also called
symmetric designs) are known to exist for some integer values
the existence of
√
difference sets for
, where √
. We investigate
is an integer,
using representation, group and algebraic number theories. Our results indicate that most of these
parameters do not exist.
63
AN ALGORITHM FOR MINIMIZATION OF A
NONDIFFERENTIABLE CONVEX FUNCTION
Osisiogu U. A.
[email protected]
Department of Industrial
Mathematics and Applied
Statistics,
Ebonyi State University,
Abakaliki, Nigeria.
Ezeora J. N.
[email protected]
Ituma V. E.
[email protected]
Department of Industrial
Mathematics and Applied
Statistics,
Ebonyi State University,
Abakaliki, Nigeria.
ABSTRACT:
In this discussion, we present an algorithm for minimization of a nondifferentiable proper closed
convex function. Using the second order Dini upper directional derivative of the Moreau-Yosida
regularization of the objective function, a quadratic approximation is obtained. It is also proved
that the sequence of points generated by the algorithm converges to a point which satisfies the
first order necessary and sufficient optimality conditions.
64
MARKET EFFICIENCY AND MEAN-VARIANCE
OPTIMIZATION OF PORTFOLIO RETURNS IN THE
NIGERIAN STOCK MARKET
Owoloko, E. A.
[email protected]
Department of Mathematics Covenant
University, Ota, Ogun State, Nigeria
Eke, P. O.
[email protected]
Department of Accounting & Finance, Lagos
State University, Ojo, Lagos State, Nigeria
ABSTRACT:
The concept of optimal portfolio forms the centre theme of Markowitz (1952) theory of security
selection, which is necessary for investment planning towards optimizing returns while
minimizing risks. The Nigerian capital market has witnessed declined patronage from both high
and retail portfolio holders since the market crash of 2008, following poor portfolio performance.
This paper fills a gap in the investment process of portfolio selection and choice among retail
portfolio holders, due to inadequate analysis of the mean-variance nexus and inadequate
information, contending with the belief that portfolio risk could be driven to zero through
sufficient diversification (William, 1938; Rubinstein, 2002; Sollis, 2012). The study suggests
that herd investors should have equivalent utility appetite for risks within an ordered optimal
portfolio of securities and the Markowitz (1952) ―expected returns- variance of returns‖ rules.
Keywords: Efficient market, Mean- variance optimization, Utility
65
RESEARCH ON ROBUST LOGISTIC REGRESION
MODEL IN INSURANCE RISK CLASSIFICATION
Oyetunji M. O.
Department of Mathematics, Akoka, Yaba, Lagos, Nigeria
ABSTRACT
Data were collected from International Energy Commission and analyzed using Robust Logistic
Regression to classify risks in Insurance data. The research shows the claims of customers on the
insurance policy on fire, motor etc. The data were actually analysed using R-program to
determine the risk involved in the customers that got their property insured with the insurance
company. Recommendations were made for the insurance company to ensure integrity of a
client’s policy by putting some measures to examine the client.
TESTING RANDOM WALK BEHAVIOUR AND
EFFICIENCY OF NIGERIAN STOCK MARKET USING
PARAMETRIC AND NONPARAMETRIC METHODS
Essessinou A. R.
[email protected]
IMSP-UAC 496, Abomey-Calavi, Benin
66
NEW SUBCLASSES OF ANALYTIC FUNCTIONS OF
BOUNDED BOUNDARY ROTATION
Saliu A.
Department of Mathematics
Gombe State University, Gombe
ABSTRACT:
Let p( z )  1  b1 z  b z 2  b3 z 3   be regular and analytic in
U  {z  C : z  1} and satisfies the condition
Re p( z )  0, p( z ) 
1  Az
,  1  A  1,  1  B  A
1  Bz
then this function is called anowski function (see Janowski, 1973). The class of this function is
denoted by P [ A , B]
A function p is in Pk [ A , B] if and only if
p( z ) 
k 2
k 2
p1 ( z ) 
p 2 ( z)
4
4
for some p1 , p 2  P [ A , B]
In this work we introduced certain iterations of Pk [ A , B] and with them we investigate two
subclasses of analytic and univalent functions in the unit disk U having bounded rotation
67
SOLVING THE QUADRATIC ASSIGNMENT PROBLEM USING
DIFFERENTIAL EVOLUTION
Sawyerr. B. A.
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
Akhuemonkhan, I. E.
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
Fasina E. P
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
ABSTRACT
Over the years, numerous studies have been conducted with respect to the Facility Location Problem
(FLP) with varying interests due to its practical application in challenging decision or optimisation
problems which cut across multiple domains ranging from factory layout, backboard wiring, hospital
layouts and location of warehouses etc. The computational complexity involved in obtaining nearoptimal solutions to certain FLPs make them suitable for testing meta-heuristic algorithms.
In this paper, a Differential Evolution (DE) with modified crossover operator and quantisation strategy is
introduced. The new DE is applied to a suite of Quadratic Assignment Problem (QAP) benchmarks from
the QAPLib. Experimental results obtained are presented and discussed.
68
EXPERIMENTAL COMPARISON OF SOME DIFFERENTIAL
EVOLUTION VARIANTS ON A SUITE OF UNCONSTRAINED
GLOBAL OPTIMIZATION PROBLEMS
Sawyerr. B. A.
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
Fasina E. P
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
Enenim A. B
[email protected]
Department of Computer
Sciences, University of Lagos,
Akoka, Yaba. Nigeria
ABSTRACT
Experimental comparison of some DE variants on a suite of unconstrained global optimization
problems B. A. Sawyerr, and Abstract In this paper, an experimental comparison of ten
Differential evolution (DE) variants was carried out on a set 30 test problems. DE is a
metaheuristic for solving problems with non-smooth, non-linear, non-differentiable and multimodal characteristics. DE operates through similar computational steps as employed by a
standard evolutionary algorithm (EA). However, unlike traditional EAs, DE variants perturb the
current generation population members with the scaled differences of randomly selected and
distinct population members. DE is robust, easy to use and requires few control variables. A
statistical analysis of the performances of the ten DE variants was also carried out. Results
obtained show that the binomial DEs (BDEs) are faster than exponential DEs (EDEs) since
BDEs use fewer number of function evaluation (NFE). BDE are less successful than EDE for D
≤ 10 (where D is the dimension of the problem search space) but recorded better success
performance for D > 10 across the test problems
69
THE APPLICATION OF OPTIMAL THEORY IN
ENTREPRENEURSHIP FIELD OF RESEARCH: A
REVIEW OF THE LITERATURE
Shittu, A.I
Dongwu Business School & Centre for
Enterprise, Innovation, and Development,
Soochow University, Suzhou, Jiangsu
Province, P.R. China.
Dosunmu. O
The Ministry of Energy, Bayelsa State,
Nigeria.
ABSTRACT
This study seeks to establish the relevance of applying Optimization Theory in Entrepreneurship
field of research. Progressive debate on the nature and context of entrepreneurism has
consistently argued that Entrepreneurship theory and practice is still in its embryonic stage.
Generally, entrepreneurs perceive themselves as extra-ordinary individuals whose goal is to
pursue opportunities, amid existing resources. So, entrepreneurs, also known as optimistic
martyrs,use mental models to structure their activities because they engage in the interpretations
of equivocal situations that are linked with reflections of perceived opportunities in the
environment. Thus, researchers in the field of Entrepreneurship are employing a social cognitive
process, embracing the role of perception, and are vigorously enacting the reality. These suggest
that optimizing decision making remains a challenge among the optimistic martyrs. Despite these
efforts, the field of Entrepreneurship is currently battling with legitimacy and the increasing
demand for capability development in order to probe interesting issues surrounding the decision
making ability of the entrepreneurs. Will the application of optimal utility theory spur a
difference in the field of Entrepreneurship research? Hence, in this study, we embrace the
Webster-Watson (2002) and Levy-Ellis (2006) methodology of literature review for the purpose
of identifying the potency of Optimal Utility Theory and the extent of its applications in the
context of Entrepreneurship research.
Keywords: Optimization Theory, Optimization Problem, Utility Theory, Entrepreneurship,
Entrepreneurial Intention, and Decision making.
70
CUSTOMER RELATIONSHIP MANAGEMENT MODELS
FOR SMALL AND MEDIUM ENTERPRISES IN NIGERIA
Tyokyaa K. R
[email protected]
Department of Mathematical Sciences
and IT, Federal University Dutsinma,
Katsina state, Nigeria.
Obunadike N. G.
Department of Mathematical Sciences
and IT, Federal University Dutsinma,
Katsina state, Nigeria
ABSTRACT
The need to maintain existing customers as linked to expanding business is paramount in the
economy and organizations of today, a base for this would be the cost of acquiring a new
customer which is higher than maintaining an existing one. The easiest way to achieve this is by
customer relationship management (CRM). According to Anderson 2006, CRM system is an
information system that is meant to tract customer’s interactions with the company or enterprise
and to enable the organization’s employees to have access to the customer’s past and present
records as well as response to the customer’s complaints and perceived wants. CRM as a system
has many benefits to the firm or organization that implement it. Small and Medium Enterprises
(SMEs) on the other hand are basically companies that hire less than 250 employees or there
about, although the specification varies from countries to countries but the general ideal lies on
the population of workers in the organization’s establishment. This work attempts to propose a
framework for adoption by Nigeria SMES for design of CRM model.
Keywords: Customer Relationship Management, Small and Medium Enterprises, Model,
Nigeria.
71
A CONVERGENCE THEOREM FOR APPROXIMATION
OF COMMON FIXED POINTS
Ugwunnadi G.C
[email protected]
Mathematics department, Michael Okpara
University of Agriculture, Umudike , Nigeria
ABSTRACT:
A new strong convergence theorem for approximation of common fixed points of family of
uniformly asymptotically regular asymptotically nonexpansive mappings, which is also a unique
solution of some variational inequality problems are proved in the framework of a real Banach
space. The Theorem presented here extends, generalizes and unify many recently announced
results.
A THREE-TERM CONJUGATE GRADIENT METHOD FOR
SOLVING LARGE-SCALE SYSTEMS OF NONLINEAR
EQUATIONS
Waziri M. Y.
[email protected]
Department of Mathematical Sciences
Faculty of Science, Bayero University Kano,
Nigeria
Aisha H. A.
Department of Mathematical Sciences
Faculty of Science, Bayero University Kano,
Nigeria
ABSTRACT:
Broyden’s method is the famous quasi Newton’s method that approximates Jacobian matrix into
less computational cost n × n matrix and stores every component of it, which can be updated in
each iteration. Nevertheless, still some shortcomings of its Newton’s counterpart persist. In this
paper, we suggest a new three term conjugate gradient (CG) method for solving nonlinear
system’s of equations via memoryless Broyden’s update. The attractive attribute of this method
is due to its low memory requirements, global convergence properties and simple to be
implement. The effectiveness of our proposed scheme is appraised through numerical
comparison with some well known conjugate gradient (CG) methods.
Keywords: Two-step, Secant, Single-point, Equations approximation.
72
AN ECONOMIC ORDER QUANTITY MODEL FOR
ITEMS THAT EXHIBIT DELAY IN DETERIORATION
USING WEIBULL DISTRIBUTION TO REPREESENT
RATE OF DETERIORATION-ANALYTIC SOLUTION
Yusuf A. A.
[email protected]
Kano University of Science and Technology, Kano, Nigeria
ABSTRACT
This research work considers an Economic Order Quantity inventory model for items that exhibit
delay in deterioration with Weibull distribution deterioration rate while applying incomplete
Gamma function to derive an exact solution for the optimal ordering policies. Demand is
considered to be a constant both before and after deterioration sets-in. The study is an extension
of Yusuf and Sani (2012) who developed an approximate model for such items of inventory. The
purpose of the study is to determine an exact solution or a more accurate approximation for items
of inventory whose deterioration follows a Weibull distribution. Numerical examples are also
given and compared with result of Yusuf and Sani (2012).
73
STATISTICAL QUALITY OPTIMIZATION OF BOREHOLE
WATER QUALITY PARAMETERS THROUGH MULTIRESPONSE SURFACE METHODOLOGY: THE DESIRABILITY
APPROACH
Yusuff K. M.
[email protected]
Federal University of Agriculture, Abeokuta, Ogun State
ABSTRACT:
In many processes, quality is multidimensional, so it is expected to observe multiple responses in
parameters of the outputs or results of the final product(s) of such experimental processes. It is
believed that product parameter optimization in such multi-response designs is very crucial and
plays an important role in meeting quality of a desired model and of taste of consumers. A
survey of different optimization methods found that global optimization, goal programming
among others applied to various areas in Science, Engineering and Technology subject to
different response requirements have very simple structure with low convergence, fewer
optimization points and clustering solution points. It is assumed that parameter quality
characteristics of water from borehole varies for different human consumptions and uses where
all responses and factors must fall or meet desired limits of acceptance for optimal condition. In
this study the desirability function approach proposed by (Harrington, 1965) is used to maximize
quality of responses of selected borehole water parameters with respect to their specification
limits.
Keywords: Multi-Response Surface Methodology, Optimization, Water Quality Parameters,
Desirability Function.
74