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" -# " - .# / ! !
!" #$ " % !" !" & ' (
!" ! ) £ !"" * !" + ( * * ! # , -." / % ! #0." !" $ % % !" + !" ! " / ¼ ¼
( %
!" !" !"
!" % * !" !" ( 1% * !" / #-. !" * ! "
/ *
#0. 1% * % %
/ * %
% ( ) 2
% ! "
/ % !" 3 % !" , ( % #,.
, !" + ( 1 #4 0 4 ,. / 53 + 4 / % #4. !" 1 6 !" -6 -6 6 !" + 3 %
#0. , -6 ' !" + 7 + 8 9 Æ% #,. / %
#8. , 6 !" + :
% #,. 6 4 !" + %
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/ #4. % 0 , , !" + / 9 Æ% 8
8 , !" + / + 8 , 4 !" + ! , 4" % #8 ,. % ( % ( 1 (
% 1
7 * !: " 6 ! !: " ; !: " &
!" + $ & * !!: "" !: " !!: "" !!: "" + #$ " ' !" + $ !" + & ' !" !!: ""
6
" !: " !" !"
/ !" + $ !" + !" +
!" * !" + $ !" + / % !" + $ ( !" + < ( !"
!" + < !" & 7 ! * #4 0." !" % 7 Æ !" % ! " ( 7
* => ! " ? !: " !¼: ¼ ¼" @* ¼¼ ¼ ¼ %' ¼¼ ¼ %' ¼¼ ( !¼¼: ¼¼ ¼¼" !: " !¼: ¼ ¼" ! " ? !: " !¼: ¼ ¼" @* ¼¼ ¼ ¼ %' (
!¼¼: ¼" !: "
!¼ : ¼ ¼" !
" ? !: " !¼: ¼ ¼" !¼¼ ¼" !: " !¼: ¼ ¼" * % %
¼
@ £ ( !£: ¼" !: " !¼: ¼ ¼" !@ " ? !: " @*
¼ % ¼ ¼
4
¼ ¼ ( !¼: ¼ ¼" !: " G
1111111111
0000000000
0000000000
1111111111
x" 1111111111
0000000000
0000000000
1111111111
0000000000
1111111111
0000000000
1111111111
G
y
111111111
000000000
00000000
00000000011111111
111111111
00000000 y’
11111111
00000000011111111
111111111
00000000
x
y"
G’
(a) Parallel construction
x1
G’
(b) Series construction
x3
x
x2
G’
111111111
000000000
000000000
111111111
000000000
111111111
x111111111
000000000
111111111
000000000
y’
y
000000000
111111111
000000000
111111111
x’
G
(c) 3+-series construction
11
00
00
11
00
11
G
00
11
00
11
00
11
00
11
00y
11
y’
(d) Diamond construction
7 / , & % #$ " ! $ " 7 1 1 ( % 7 #$ " # . %
) ! " (
% # . : % # . $ & ' # . # . 7 + 68 % #$8 ,. #,8 $,. 7 (
!# . " % # . % !# . " + : !# . " +
; / #$ " % !" + A !"
8
0
3
[2.5, 0.2] r
1
[0.5, 2] r
2
7 , / + 68 % 7 *
; + ; + 7 ; ; ! #$ ""
¼¼ ¼ !¼¼" + !" !¼"
$ ¼¼ ¼ !¼¼" + !" ; !¼"
# ¼¼ ¼ !¼¼ " + !" ¼ !¼" ; ¼ + % # . # ; . # ; .
% !" !," %
!6" ¼¼ !" + $ !" + !¼" + ( !" !¼" 0
¼ !" ! " ! " # . # ; . # ; . % !" !¼ " # . # ; . # ; .
!" + $ !" + !¼" + ' ¼¼ ? ,, !" 1 & % ? ,6 1 #0.
+ # . + # . !# . " ; !# . " ; + & !# . " ; !# . " ; + # ; ; .
5 + < ; + <
( % ( & % 7 % 8 % , !" + 7 , 6 !" + 3% Æ ( ! "
!B" ? 8 #, . ( # , . / + 4 !B" ! " !" + : 8 ! " ! " !" + & % ! " % !B" ' &% $ ! " + * / ) C
! ! " + " 1 $ $ + & ! " + ? ¼ + ¼ + ( ¼¼
! " + ¼ ¼ 3%
! " ! "
D% ¼ ¼ + ! " ! " + + ¼ !¼¼ " + / ¼ !¼¼ " 8 , ! " + ( ) % ! ! " & ?
6
$ " " !" 8 ! : " , !! "! ," ; "! "
! " + #! ," ! " ! ,".
' ,
! " + <
? % + # # + !: " 7 , -
!" ; + !" + $
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# . # ; ; . # . # ; ; . % 4 (
# , ! ,". % # , ! ,". !" + $ !" + ' (
!" + # , ! ,".
, !" + <
7 , B 6 & % , !! ,"! " ; "! " %
! " + #! ," ! " ! ,".
7 + % , !! ,"! ," ; "! ,"
! " + #! ,"! " ! ," ! " ! ,"! ".
5 !! ,"! " ; "! " !! ,"! ," ; "! ," , !! ,"! " ; "! "
! " + ! " ; !"
+ #! ,"! " ! ," ! " ! ,"! ".
;# , ! ,".
( % ,!! " ! ,"! "" ; ,! ! ,"" + , ,! ,"
/ !! ,"! " ; "! " , ,! ," ! + 4 + , '
+ 4 E" B ? ,,
! " + #! ," ! " ! ,".
8 , !: " ! " ! ; ,"! "
!" + # ! " ; .
F
' ! "
!" + <
& % /
+ !! ," ; " ! " + ! ," &
* ? 6, ( ? 6, / + , + ,! ," ; %
+ !! ,";" 6 ? 66 ¼ ¼ ¼ ? + ! "
( + ! ," ! ," B !¼: ¼ ¼" !" ! ; ,"! "
!¼" + # ! " ; .
? $ ¼ ( $
B ? ,, !$" + < ! ; ,"! "
!$" + !¼ " ! "
+ # ! " ; . # .
+ # ; . # ! " .
7 6 !¼" ! "
[a-1-(b-1)r, br-a+1]
[a-1-(b-1)r, br-a+1]
a/b < r
a/b > r
[1, r-1]
[1, r-1]
7 6 / !¼" ! "
? ¼¼ $ !4"
B 6 ¼¼ ! $ ¼¼"
$
& % ! ; ,"! "
!¼¼" + # ! " .
B ? ,, !¼¼" ¼ !$" + ; ¼ # . # ; . # ; . 4 / # ; .
¼ # ! " . # ! " ; . / # . # ; . # ; . + # ; . # ; .
! ; ,"! " %
! ; " ! ; " ! ! " ; " ! ; " 8
[t-1, t+1]
[t-1, t+1]
[s-1, s+1]
[r-1, 1]
[r-1, 1]
[s-1, s+1]
[s+1, r-1]
[s+1, t-1]
7 4 / % # ; . # ; . ¼ # ! " . ¼ # ;. # ! " .
( # ; . % 8 4 (
!¼¼"
/ # ! " . ¼ # ; . # ; ! " ; ; . / # . # ; . # ; . + # ; . # .
! ; ,"! " %
! ; " !! " ; ; ; " 8
7 % !¼¼"
/ # ;. ¼ # ;. #; ;; .
/ # . # ; . # ; . + # ; .
% ! ; " !, ; " 8 (
# ; . % 8 4 ( !¼¼"
/ # ! " . ¼ # ! " . # ! ," ; . / # . # ; . # ; . + # .
% , , 8 7 % !¼¼ "
[s-1, s+1]
[r-1, 1]
[t-1, t+1]
[t+1, r-1]
7 8 / % # ; . ¼ # ; . ¼ # ! " .
(
!¼¼" + # ! " .
5 / + ; + ; ! " +
! " / ¼¼ B 6 B ? ,,
! ; ,"! " ! ; ,"! "
!" + !¼¼" ; ! "
,
+ # ! " . ; # , ; ,.
+ #! ; " !! ; " " ! ; " ! ; " ; .
+ # ! " ; .
/ ; , ¼¼¼¼ + ! "! " + ! " B £ !¼¼ ¼¼" !¼¼ ; ,"!¼¼ "
!£ " + #¼¼ !¼¼ " ¼¼ ¼¼ ; .
? ¼¼ £ B ?
6 B ,, ! ;
,"! " ! ; ,"! "
!" + !¼¼" ; !£"
+ # ! " . ; #¼¼ !¼¼ " ¼¼ ¼¼ ; .
+ #! ; ¼¼" ! ; ¼¼ " ! ; ¼¼ " ! ; ¼¼" ; .
+ # ! " ; .
( ? 66
, B ? 66
!" + # ! " ; .
? ( ! " + # . ? ,, % ! " + < ( ! " + (
( 6
¾
¿
( , 6 ( ) / * %
#8. % #. / % ( % 1 E ! "
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!, 6" ! " + !: " ! ,"! "
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' !" + <
7 + !, ; " , / ! " + , ? + % , , / % , !" + <
5 % ! , !% " + #,! !! " ! ,! .
/ * !% " + # . % % %
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, !% " + #,! !! " ! ,! .
% % % %
!% " + !% " ; !%" + #,! !! " ! ,! . ; #, ,.
( #,! !! " ! ,! . 1 ,!! ,! " #, ,. 1 ,! ," 1 !,! ; ," !4! ; 4" ,!!;;6 (
(
!,! ; ," 4! ; 0
!,! ; ," !4! ; 4" , #,! !! " ! ,! . ; #, ,. + #,!! ; " ! !! ; " ,!! ; ".
4
%
!% " + #, , ! ," ! " !, ,".
+ # 6 ! ," ! " ; 6.
& % ? 4 !, 6" / + , ! " + , + , ; % % 6 ! " + + ,
B ¼ !" ! ,"! " %
!¼" + # 6 ! ," ! " ; 6.
7 % ! "! " , ! ,"! " ! ,"! " ! ,"! " 1
!¼" + # 6 ! ," ! " ; 6.
? ¼¼ ¼ % B ! ,"! " %
!¼¼ " + !¼" ; !%"
+ # , ! " ; ,.
? ¼¼ !" + # ! " .
7 # ! " . !"
B Æ #$ . ! " 7 $ * !¼" + $ !¼" + !" + ; !" + !" !" !¼¼" ) ' ¼¼ % # ! " . , & % !¼" + $ !¼" + ' ' !¼¼" +
# , ! " ; ,. !" !" , ! " / !" !" % #$ . , , , & !" !" (
8
% 4 #$ . # !". #
!" !". #
!" $. + ; !
!" " ; !
!" !"" ; ! !""
; ; ! , ! "" ; ; ; ! , ! "" ; + % ( ? ! " + ¼ ¼ / ¼¼ 6 ' ¼
¼
!" + #¼ 6 !¼ ," !¼ " ¼ ; 6. ! ¼ " ¼ ,
¼
!" + < ! ¼ "
/ ¼¼ + 6 + ! %'"
!" + $
& / %
!" + ! " ; !"
+ # ! " . ; #¼ 6 !¼ ," !¼ " ¼ ; 6.
+ #! ; ¼" 6 ! ; ¼ ," ! ; ¼ " ! ; ¼" ; 6.
+ # 6 ! ," ! " ; 6.
( ? 4
, 6 ! " + " B ? 4 !: "
! " ! ,"! "
!" + # 6 ! ," ! " ; 6.
!" + <
0
? % ( ! " ! ,"! "
! " + !" !%"
!% " + #6 , 6. % ! " + < ! " + 7 6 4 ! " + ( 6 (
( 4 % #8.
#,. % , 4 ( E #. G B G H
( !FF$" 4CF
4-,
#,. B B I J ( B
( / ,4!FF-" CF
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+ G H (
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#4. I J ( .
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#8. I J ( B D 8F!FFF" -6
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#0. I J ( @ D
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