Радиотехнические и телевизионные системы: Сборник...
Transcript of Радиотехнические и телевизионные системы: Сборник...
! "#"$ ""%
&'"%%
Ñàíêò-Ïåòåðáóðã2000
ÌÈÍÈÑÒÅÐÑÒÂÎ ÎÁÐÀÇÎÂÀÍÈß ÐÎÑÑÈÉÑÊÎÉ ÔÅÄÅÐÀÖÈÈÑàíêò-Ïåòåðáóðãñêèé
ãîñóäàðñòâåííûé óíèâåðñèòåò àýðîêîñìè÷åñêîãî ïðèáîðîñòðîåíèÿ
(
) *(+, -./-0
11 -(,23
+4
+4 ""%" "5" 6" %%"78 , , , / ! ", 1, ,
7'"" 9 !:)!, !,; (<<<, +.2 %,9 5, =>?@ 4A2<22A<<34A4
%" &"% 5" %B; &% CD"" "E"F &5"7
%&CC 65B$ '7#9 %G5 "5" 6A
; """% ""% %%"79 #" "%
& E"C H''" % '7# %%"7, % 7"A
5 %%7 F%C &%; %FD"%C 6 "5" 6
%$% 5C %%"7 7G ,
! """ %BC "65B %%5" $ 7G B &5"6
E7 G %&"#5% ; % C6 % 6$ H%&5#A
"$ "5" 6G C; I" 7 7 %&A
7,
"#"6"8
'" "5" "C "" A!""G%G G%% "G
"%" "5"77#$ 7, &', 1A1" 9 ""%
#"
Ðåäàêöèîííàÿ êîëëåãèÿÁ. Ñ. Òèìîôååâ (ãë. ðåäàêòîð), Í. Í. Êðàñèëüíèêîâ, Î. Ñ. Àñòðàòîâ, Ë. Ä. Âèëåñîâ,
Â. Í. Ôèëàòîâ (îòâ. ñåêðåòàðü)
A!""G%$
G%% "$ "%"
H%7"%G &%"C;
(<<<
©=>?@ 4A2<22A<<34A4
-
!%5""" "%C5"" " "6"%C G77 %I"A
C7 5% '78 ""6 G55BF %"B =JKLMJLK &"%A
5B$ 7&BF" '7#C; &5"C "5 ""% 7 6 %CA
"5"C; & I$ 7, "$ 5B7 %5 %A
%5" C & "; &"6 F; &""" & 657 A
57 % C6; H''" 7 "F; I"F %&CF 6A
I"$, 6I"C7 67F%C &"% %" 5%C
"5 ""%$ "C"5B%, H &C; 7" % &7DBF
6I"$ "5 " &5" &"5FD"" 5"% '7A
#, %CD"7 %" &"% 5" "65B '7"5BA
%%5" $ "5 ""%G 6"C; &% " &
7"%G I"C #" C &7" N" &
% &% &6 ,
% C6 % % E7%C &%5""" "7C &5"77 H5G
5BE G ; 6"5B" 7" "5C"%C 657 %&"A
7 %6C 76 "5" 6 '7# %A
%"7 5C &7G 6 $ & "% % #"5BF I"A
C #" &7" 6GC6"$, !7""" % "7" %A
% "5B # " A7" %" % 7&BF"7
67 %&"#56 7 &G777 &7; &"6A
"7 5C '# C 5 &"" 6A
I"C; &6 5 %D"% B G5%$ &" $ 5B
$ & "% % &5" &CB % A
" "7"" " " 7" & 5 # $ 65
"' G & "%A "D"% ,
%" I" &"% 5" C %"$; N""
"7$ %%5" C IFD"$ %" "A ""%A
7 7"7, %&5B6 " "5" 6 %%"7 H7 %5"
& "7; A6I"C "%B7 '7 &6 5CA
F &" &7B "" "E"C %5I %#C, OA
" """ %"% %5"5B$ " &"&""55 %A
"I" 7G %"$ %; G" C % ""%7 "E"A
C7 & "" I" 5G7 &G77; "65B 6A
I"$ 7"7"%G 7"5 C P,
7" G; %" 7""%C C %"$; &% CD" #A
$ ""%$ "5" 6$ "7"; 7 %5" #""
3
6"EFD"$ %&%%; %IF "'7#; "5" "F
& E"$ "%; A&"#; "% %&6 7 6A
I"$,
!"5I"" IF % " % "7"" &5"7
%'"" %%5" $; % C6 % $ 6I"$;
&5"6 E7 G %&"#5% 65 & 5"$ 5%A
"$ "C"5B%,
4
), *+(,2
&#"%%" 6"C " 6"5BG %&CC; GFD"$ %A
D"% " IF 5B & 6" &" "5" 6A
%%"7 65G 6"C 7 5 & "" %%5" C
67"%"$ I"C &6 C "5 "7A5F"5"7
7"% 6I"$ &%% G G%% E7,
15 &6; 6"5BC %%"7 %D"% 5C" &%% "A
F '5B#F; C & "57 E7" & 6 "% &A
7" 6I"$ C 5C"%C %G5% $ Q+R3S, P7 %%5" A
C7 5 &5I" 5 7 7 & 5"F; 7
G 6 7"5 6"5B$ %%"7 6 "%" 7"A
5 %G5% $ '5B# Q4R+<S, P 7"5 E %&5B6FA
%C %CD"" "7C & &" '7# %%A
"7; & 6" 7"#% G%"% 7", A
&7C" 7"5 " %5$ 7"%G
6"C, 7"%" % "7 5BE% "5B 6I"$ C 5CF%C # "A
7,
T"5BF $ C 5C"%C H%&"7"5BC & " 6A
7I% &7""C &5I"$ " %G5% $ '5B#
6"5B$ %%"7" "5 " &G %5 C 5F"C # "A
6I"$, &% "7 H%&"7" "% " "%
N" %&5B6 5%B %56 " 5B# 5B; "A"A
5$ &6 %, +, "65B; & 7" I";
%C%C %5F; G 67""C # " 5 %A6"5"$ A
5% # " G &%% , 5G" "65B 7"F 7"%
& " I"5A%"$ 5% # " G &%% ,
*
P%&"7" & &5" H%&"7" 7G 6 B I"A
5"7" # " $ C%$ % H 5"# & E"F
'; 7 5F5%B, %" &7" "% N"
& & "" & 5 5F"5C7 & 6 "%, A
"% " &7"; 5 "7$ 6I"C; &7"C5%C A
$ 6"5$ G%% E7; $ "6 5%C %"" A
7 6"C7 C%$ 7"% 7&", "A
% % H 7&" % 5 5%B H%&"7"7 & G"A
"# 6E75" 6I"$, E75"" 6I"C G""A
5%B 7&BF"$ &G77$; 6"7 &"NC 5C5%B 5FA
"5C7 5C &6 C H" 7, "5"$%B 7&5A
$ "% 7; %&5B6 E"G%C &% "7 I"
&; 5 D"5B %" , P%&"7" 5F5 %"C
&CB %"$ & , %" & &C5 %" " %&"7
% 75B7 # " 7 6""7; 5 %&5B6 & +( 65A
"56#$ 6E75" 6I"$,
&" $ %" & "% $ N"; 5I"$ "G
$ 6"5$ G%% E7 %6 5 6I" 5B
C%$ %; " 67"C5 "G # "; $ 5 I"5A6"A
5"7, 6"I" 7&5 G"$ E7 % "%A
G N" 5%C 757, ! 7"%7 &6" (44
"$ C C%B ' &""5C5%B ++. C7 A
C; C%B "% G N" +-. C7 C, ""A
" 6"" E7 σ I" I5%B "# "$ C, "$$ 6 %56 7 5B#" 5B %A
% 5C5 3 %5 &%"5C, "%B 5"" & %5 7 &%"5"7
&7"%C C &5D C G"7""%7 67"
E7 G &C,
"65B" & "" 67""$ 5 &5" 6 %7%B
"C% & 5BG &6 C "% G N" & %""A
G 6"C E7 "5B7 5F"5C7; & ""A
C %, ( 6"C #'$ + U6I"" 7"%";
E7 7"%$V, !%5B &C %5 C & ""C &A
6"5BC %%"7 "5 " "%&" " F I" "C%B
& 5BG &6 C 6E75" 6I"$; &75BA
$ &"7 G"A"5B ; %D"% 5CFD$ %G5% A
F '5B#F; E"7 5B"$E"7 65I" 6 %7%B +
.
7I %%7 B &F; ,", % B % "$ G" H%&"A
7"5B" 6 %7% Q+R3S,
C %"C & 55%B &" $ "7; "$ "%A
$ N"; 5I"$ 6I"" $ 6"5$ GA
%% E7 %6 5 6I" 5B # " $ % & H7
C%" % 6I"C; E7 5 5F, GA
7 %5 7; 6I"C; &"NC 5C E"%C 5F"5C7 5C &6A
C H$ %" & ; 5 % 7"%7, ! H7
%% " E7 '; 7 5F5%B "% " N"; 5
I"5A6"5"7 U W +-.; W +(3V; "% " N" R 6"5"AI"5A
7 U W ++.; W +-<V, "%B ""6 6" %5 "$ A
C; &""5CFD"" "% %B %G 6"5"G %G5"
% "% ", 5C %6C % 7"%G E7 '7FA
D" "G %C 6"5"C 7&" 67"C5%B 67 & &A
5I % H''#"7 + <;((/<;.<* % "% ", "%B 5""
"% %B E7 I"%C ""6 %"" " 6""
"G %$ 7&" σ, 6"I" 7&5 G"$; ""; & & 5%C & "5BE # " %,
H & 5 67"" 6 %7%B "C% & 5BA
G &6 C "% N" %"" G 6"C
E7 5C "5B 5F"5"$; & ""C %, ( 6"A
C #'$ ( U6I"" E7 % 7"%"V, 7
7" ; 6 %7%B ( &""5 &G"E% 67""$
% &" % 6 %7%BF +; &5"$ 5C 7"%; 6E7A
5" 6I"$; ; % F ""B; % &" % 6 %7%BF
"C% & 5BG &6 C 6E75" 7"%
6I"$ &75B7 &"77, 6 HG %5""; &
&6 % 7"% 6I"$ "% N" ; %"
&7" & 6 "%; 6E75" % 7A
"%7 7 6"57 G%% 7 E77; "5 "A5FA
"5B %D"% 5C" %G5% F '5B#F,
"B"$ %" & 5 %%5" %5$; G "% $
N" %6 5 6I" # " $ %; E7 R C%$,
P %5$ ""%" "7; " 67I%B %%5" B "65BA
67"$% C 7"%G # "6% 5 U
7 %5" 5 V 6"5B$ %%"7 "5 " & &6A
6E75" 6I"$, ! & "" & 7 I" A
5 % 757 # " 7 C%7 %7,
2
"65B" & ""C H$ %" & 5 $"; A
7"%$ E7; &C 5CFD$%C 6I" " '5#$
C%; " 67"CFD$ # " " &%"5"$; " &&F
"G %; " 5C" "C%B &6 C & 6I"C
% 7"%G "% G N"; C %"%C $ "A
#" I" & "B % C E7, !5"C 6 %7%B
"C% & 5BG &6 C 6E75" "% N"A
& %"" G 6"C E7 σ 5C HG %5C &A
6 %, ( 6" #'$ - U6I"" % 7A
"%"; E7 7"%$V,
" "C %"C & 55%B "B"$ "7; 7
%5" "% " N" %6 5 6I"C C%$ A
%; "7C $ 6"5$ G%% E7 %6 5
6I"C # " $ %, "65B" &5"C H$ %"
& 5 $"; E7; 67"CFD$ # " 6I"C; "
67"CFD$ "G C%; " 7"BE" "C% & 5BG &6A
C "% N" ; I" "%5 "5, $"C 5C HG
%5C 6 %7%B "C% & 5BG &6 C 6E75"A
"% N" & %"" G 6"C E7 σ
&6 %, ( 6" #'$ 3 U6I"" 7"%A
0
"; E7 % 7"%$V, !%5B H7 %5"; &"A
D"7; E7 "% " N" 67"CF 65" "%A
6I"$; 7I 5 6"" &"&5IB %% "
5C" E7 "C%B & 5BG &6 C "% N"A
,
$ "65B &5"%C 5B 7 %5"; "%5 "5A
"$%B % " $ "% "%& %&5"C; 7
&"NC 5CF%C 6I"C 5F"5C7; D"5B %"A
; %"5B" C% % # " & 5B &""5"
5C %&5B6"7G & "%&, 5" I" "5BE$ "5"$A
%; I" 67"$ &G"E% &""5" %"5B
C%"$ % # " & C 7; # " $ E7 %
&"6"%C 7"%$ E7 5GC H7 6 "
5C" &6 " 7"%G 6I"C "% G N"A
, !" C 5"" %"5%B 5B7 H&" &5" &A
,
P H''" &C 5%C 6 "% & & 7% F "%A
%%5B "E"; %6FD 6I"C C%$
% %%5B7 "E"7; " %6 5 6A
I"C % 7"%$ % Q++S,
&C$ 65F"5B$ %" & "% " N"; A
$ 6"5$ G%% E7; 5 "7$ 6I"C;
%6 5 C%$; 7"%$ %, 7 A
67; H$ %" H%&"7" &6 6E75" # ";
" % 7"%; 6I"$ 5 6"$% A
7"%$ 5; # "6%$; 7 %5" ; 5
6"5B$ %%"7, ! & "" H$ %" & " 7&"A
G%% E7; 6 FD" 67""C C% # " 6A
I"; &"I 5%B 7 & "5"; 5 67
""5 7, "65B" &5" 67""$ 5 &A
5" 6 %7%B "C% & 5BG &6 C "%
N" & %"" G 6"C E7 σ; C &6A
%, ( 6" #'$ 4 U6I"" E7 %"I
C%F; 7"%F 7&"V,
&% 5CC "" $"" 6 %7% + ( % 6 %7%BF 4;
7; & &6 # " 6E75" 6I"$
7"%$; # "6%$ 5 6"5B$ %%"7
F % 7"%; "65B" "G "C%B & 5BG &6A
+<
C 6%", !" "5B" #"" %" &6 A
F; "65BFD"" E"" %G5 E7 ψΣ; &""5CFD"";
"7 %""; "C%B & 5BG &6 C "% G
N" "5 "7A5F"5"7 6E75"7 # "7 6I"A
; %5"" 6 H%&"7"5B ; 6 "%C 7
2 2 2 ,L R G B YΣ − −Ψ = Ψ + Ψ + ΨG" ψ
R E"" %G5 E7 &%5" %G5% $ '5B#
7"%7 5"9 ψR
R E"" %G5 E7 &%5" %G5A
% $ '5B# 5" 9 ψ R!
R E"" %G5 E7
&%5" %G5% $ '5B# 5" R!,
&%" I"" %& "5 5C %5C; G E7 6A
"5B 5 ""5 %G5%"%C % #"&#"$ &75BA
G 5F"5C,
15G'"%$ %&%
+, 5C" E7 %F % "5BA
%B 6"EFDF %&%%B &"7$ "5" 6$ //
" "5" "C, +042, &, (4, , (*R3-,
(, "#$%& &% 65"A
5F"5"7 6E75" 6I"$ // 7"C, +0.<,
X -, , (<R(4,
-, "#$%& &%'()* 65A
" "5 "7 6I"$ G%% 7 E7" // 7"C, +0.-,
X +, , .R+3,
3, "C &"" %&CC 6I"$,
,8 % C6B; +02*, (3. %,
4 +,-Y./&01230&-4 Z[K\]L^ _`aKLMY `J ]bc[J d`Y`eJ // ?`ea,
fghLMJLK`\Y, +0.*, X ((, i, +2+R+22,
*, 15,617&8,9YY:2,&;,Y,9/9 feJKM[YK YLJY`K`d`Kg [Y [ _bJ\K`eJ
e_ [ Yj[K`[a _MLkbLJ\g; d`Ll`Jm ^`YK[J\L [J^ L\\LJKM`\`Kg l`K] [J^ l`g]ebK
Yj[K`[a Je`YL //n`Y`eJ oLY, +00(, nea,-(, i, *-+R*3<,
., ;,Y,9/9&<-..19/9+&15,617 >j[K`[a `JKLmM[K`eJ e_ h[J^Aj[YY
_`aKLML^ j[KKLMJY `J Je`YL //n`Y`eJ oLY, +00-, nea, --, X ., i, 0<-R0++,
2 15,61 7& -9=:9/9>&;,Y,9/9 Ze^La`Jm K]L ^LjLJ^LJ\L e_
\eJKM[YK YLJY`K`d`Kg eJ mM[K`Jm [ML[ [J^ Yj[K`[a _MLkbLJ\g //n`Y`eJ oLY, +00-,
nea, --, X +2, i, (..-R(.22,
++
0, &?@AB p#5BC 7"5B
6"C // &"%$ I5, +00., , *3, X (, , .(R2(,
+<, &?@AB&*C p5BA
#C 6"5B$ %%"7" "5 " %5 C &G G 5F"A
C // &"%$ I5, +000, , **, X +, , 4R+3,
++, D/E,21-Y <<&>F:=./Y G >`cbaK[JLebY c[Yq`Jm `JKLM[\K`eJY
hLKlLLJ \]Mec[K`\ [J^ rbc`J[J\L mM[K`Jm // s, tjK, >e\ uc, +02-, nea, .-,
X +, i, ++R+2,
+(
), *+(,2
&*C
!"##
%CD"" "7C& 6" 65 '7#
%%"7; %" &"6" 5C &"" 6I"$; EA
%&5B6F '#5B" 7"5 6"C, 15BEF 5B
GF '65G 6"C; G" &6 5CF %6 B " 7"A
%%5" C 6"5BG %&CC &" B &&A
5C 5"%G %&5B6 C, 15BE% 7"A
5"$; %" 7"5"$ &7"C"7 I""$ &"; %A
F%C #"&# "5BG 5F"5C, " 7"5 %A
6F%C % 5C &G %5 $ 5F"C; & %A
D"% "" 5C" "C%B & 5BG &6 C A
6 " &%% " E7 65G &%I"C, ! H7 &A
G " %5 C 5F"C 7G B %5 5" "A
7 E77 6"5B$ %%"7; E77 %77 %7 6A
I"; 7"" 7"%; &7"; & 5F" 5#A
6I"$, ! H%&"7"5B %%5" C 6"5BA
$ %%"7 "5 " 5 67""; C" %5" "CA
%B & 5BG &6 C UI"CV "% N"
"5B7 5F"5C7 &G %5 C 6 "%C I";
"7 "C%B &6 C UI"CV "5B7 5FA
"5"7 & 7 I" " E7, 5C " %I"C H H%&"A
7"5B 5 "" 6 "7$ H''#" H'A
'" % η UL__`\`LJ\gV, H''#" H''" % "5BG5F"5C &""5CF %5"FD7 678
2
2
,Ψ
η =Ψ
G" Ψ5
R E"" %G5 E7; & 7 "5B$ 5FA
"5B &6" UI "V "% $ N" % $ I" "CA
%BF; "5B$ 5F"5B & E" %G5 E7
Ψ,
+-
H''#" H''" % η & % "7 &""5"F; "%5 " GA
B &G"E%C &; " 7I" B 5BE" "# Uη ≤ +V;&"7 %5 C & " %5C "G "5 7I"
B %D"% " 7"BE" "#,
!" C G&& &; 6 FDC 7"BE"" H''#"
H''" %; %5 5" "% "E"% 7 6"5B$ %%"7
"5 ", !7"7 G "% "E"% C 5C"%C ';
5B 5 +<v % "; &CD"G ""6 6 G56;
&G5D"%C "#"&7 %"; "7C 5 0<v %%"A
"%C &"% %" G56 &G5D"%C "7 &G7"A
7 H&"5 Q+S,
! GG ; & CD" 6"5B7 7"BE"A
F η; %5 5" "7; %5 C; "5B$ 5FA
"5B &6 5F"C; & 5; %D"% " 5F%C
%5 $; &C 5C "5BG 5F"5C, ; & % "7
&""5"F; "5B$ 5F"5B; % 7 % "%C "A
5B$ 5F"5B; & %5" H''#" H''" %A
%&5G" &5$ &$ '7#"$ %" &7"
6I"$ 5F"7 "% N" ; "7C "5BA
$ 5F"5B $ '7#"$ 5BE% " %5" &A
" %&5G", %% " &$ '7# &7"A
5F"7 "% N" "5BG 5F"5C &A
"%"% " 7"BE"F "C% & 5BG &6A
C &; %" & 5BE7 " E7; %5" "5B;
& 7"BE"F H''#" H''" %;
5C "5"C & G C; $ "%&" " "5BA
$ 5F"5B; "7 "5B Ψ5
,
7 67; ""$ $ 5"" "7 wA
H''#" H''" %x &"% 5C"%C " &5" 7,
"$% "5B; & %5 %G5; G" %D"% "F 5B GA
F & &" G ; 7I G B "% "E"% "
6"5B$ %%"7; 6; 7"BE"$ "5" "" H''" A
% & % "F % "5B7 5F"5"7, %"%C
& G ; % C6 I" " % "% "E"% 7
6"5B$ %%"7; % %% "7 &5$ &$ 'A
7# 5F"77 N""; H "6"I & %A
I"F "C% &6 C,
+3
P%&"7"5B" %%5" C &6 F; %% "
5F"5C &$ '7# 65 &7" 5FA
"7 N" 65 %6 "%C H''#"" H''" A
%, %% " &$ '7# 67" "% G N"A
75 5C" "5 η; "7C %% " &$'7# ; &""5CFD &5I"" "% A
G N" &5%% 6I"C; 6 " %5B" 5C"
"5 η, P %C"5B% " %"G 5I7 67 A"%C & #"" 7"5"$ 6"5B$ %%"7; G &
E7#"7 Q(R3S,
T"5BF &% "7 I" H%&"7" 5 %%5" " 6 A
%7% H''#" H''" % %"" G 6"A
C G 6"5G G%% 7"%G E7; 5I"A
G 7"%" 6I"C "% N" & %5 ;
"% G N" &5%% 6I"C 6 A
5%B % %BF ± 9 %5 &%"5"$, "%B 5"" & %5 A
7 &%"5"7 &7"%C C &5D C G"7""%A
7 67" E7 G &C,
%%5" C & 5%B 7"5 6"5B$ %%"7;
"56FD"$ 5G7 G"A"5B ; $; 6 "%A
; % 7"5" 6"5B$ %%"7 &A
G %5 C; % %&5B6 "7 "5B 5F"5"$
Q4R2S, "5B 6"5B$ %%"7 5 "56 " 7&BA
F"$ &G77; &%$ & y`J^elY, %%5" C & A
5%B % %&5B6 "7 "% N" " %56
5"# 5B, 6I"C H "% N" & ""
%B" w%%5" " &%% "$ '5B# 6"5B$
%%"7" "5 " & 5F" # " 6I"$x; &7"D"A
$ H7 I" %", ! &5" H%&"7" 6A
I"C7 "% N" 5C5%C $ 6"5$ GA
%% E7; %G"" $ &G777 %&%7; &%5" "G
&6 5%B &6 ", "65B 67""$ &; &5"A
+( 65 "56#C 6E75" 6I"$ 5C
IG C E7 I$ "5 "&""5"% %A
"5B &6 "7G "% G N"; 6&% 5%B;
6"7 5 %&5B6 5C %" H''#" H''" A
%, "5 E"C %G5 E7; &""5CFDC "A
+4
7 G" "C%B & 5BG &6 C "% G N"
6E75"7 6I"; %% 5%B; %C 6 %5"FA
D 6 "% &7" 8 &""& %G5 7"I '7 "%A
7 N"79 %"" G 6"C E7 67" 6A
%56 7 5B#" 5B; $ %% 5C5 3 %A
5 &%"5C,
!""& %G5 %"" " 6"" E7 IA
5%B %5" "$ C, &% "7 & &""&
%G5; %5 5"$ "% 7 N"7; %% 5C5 (+ "B
C & 7"%7 &6" (44 "$ C,
%, + & "" 6 %7% H''#" H''" %
%"" G 6"C G 6"5G G%%A
E7; &5"" "65B" H%&"7"5B
& % 7"5BF 5C C 6"$ &$ "&""A
5"% E" ; &""5CFD &5I"" "%A
N" &5%% 6I"C, 6 %, + %5""; A
H''#" H''" % η %5"; G 9 z <; %5B 6 % %"" G 6"C E7; 5I"G 6I"C;
I" "5 "&""5"% &5I"C "% G N"A
η
σ
+*
&5%% 6I"C 9; & H7 "5 η 67"C"%C "B E &""5,
5G" 6 %7% 5 &5" H%&"7" %
7C "5B7 5F"5C7 U%, (V, " "B; "B
56 "65B7; &5"7 7"5,
15G'"%$ %&%
+, p65GC %"% %%"7, , +, p65GC 6"C /! ",
HHI( ,8 ; +0.+, 3+* %,
(, ;,J,9/9&<-..19/9+&15,617>j[K`[a `JKLmM[K`eJ e_ h[J^Aj[YY
_`aKLML^ j[KKLMJY `J Je`YL //n`Y`eJ oLY, +00-, nea, --; X ., i, 0<-R0++,
-, A$&% C"C%B I"C N"
H" 7 &AH5"$ %%"7 5F"C //&A
"%$ I5, +003, X ., , -R.,
3, A$&% C "C%B %&6 C N"A
H" 7 &AH5"$ %%"7 5F"C //&A
"%$ I5, +003, X ., , .R++,
4, 5C" E7 %F % "5BA
%B 6"EFDF %&%%B &"7$ "5" 6$ //
" "5" "C,+042, &, (4, , (*R3-,
σ
η
+.
*, "#$%& , &% 65"A
5F"5"7 6E75" 6I"$ // 7"C, +0.<,
X -, , (<R(4,
., "#$%& &%'()* 65"A
"5 "7 6I"$ G%% 7 E7" // 7"C,+0.-, X
+,, .R+3,
2, "C &"" %&CC 6I"$,
,8 % C6B; +02*, (3. %,
+2
) *(+,-0.
! ! $
5C I"C & "%C 65 "'
G 6GC6"$ E %&5B6F "5" 6" 7",
7&BF"C A6I"$ &6 5C" 5%%'A
# B 75; &""5CB #" B 7%A
E, A%%"7; % 5"" 5""5B &&A
; 7%; &5 , ,; "%&" F %5" "
E &5D"$ 7%E" "5BG "7", %&5B6A
" % "7" %"% % C6 " 67I%B N"B
; 7 %5" &%"" & 657 &#&7;
"F %%"7 %#G 7G IFD"$ %"A
, 56 5" ; I" & &%"C &A
%%"7 &6 F; 5C %&" %5" C I
&5B C &%5" "5B &#" Q+S8
&"" 6 &%% 5F"7 6I"$ &%A
% &6 ; &6 5CFD$ "6 %B N"7 "A
7 9
%"5"#C I" 'G7" &C" "E"C
&5"I% 7 5 7 5%%9
%5"" G"7""% "% 'G7" ; #"
G &7" U5D &5"; N"7 65$ "' &,V9
'7 " '7#G %D"C 5C &5B6 "5C %A
%"79
&"6 " U%I"V %D"C "G &"" & 5 % CA
69
7" " &5" %D"$,
"'CC &5" & "% 6" "'""#A
$ '5B; &A67 IFD$ &G5DFD$ H5"7GA
" 5"C % 657 57 5, !H7 &7"CF
5G7 56 # " A6I"$; 6FD"%C %&"A
65B &6, "% " G 6 &6 %&5B6A
F K''W U+;
(; ,,,; ΛV; G"
+0
max
min
max
min1
( ) ( )
,
( ) ( )
i
i
ii
S d
c
S d
λ
λλΛ
= λ
ϕ λ λ λ
=
ϕ λ λ λ
∫
∑ ∫U+V
6"%B ϕUλV R %&"5BC &5%B I"G $ & "A% H5"7GG 65"C9 L
:UλV R %&"5BC % A
"5B%B :G 5 "" 65"C9 Λ R %5 5 U5C
A7" Λ W -V9 λc`J
; λc[
R 775BC 7%75BC 5
5; "G%"7" ""7 65"C,
%&5B6 " "% " &6 # "% &6 5C" &5B
5G7 6I"$; & $ 67""C7 C%
&"" "7 N" E &""5, 7""5B I"A
U+V 7"" '6"%$ %7%5 "% % 65"C, !H7
# "% : R "667"" "5; " 6 %CD"
C% N" , 6 I"C U+V %5""; %77 H''#"A
+ |
( |
- W +, P " 67I%B &6B 67"%B "A
# "% ; "$ H5"7" %"G 7I" B A
%5" 6 %5B8 - W + R
+ R
(,
# "7 "5" " C &C" )K'A7"A
7 Q+S, "% " A7" 7G B &A
C 5B K'; ; " &" %&6A
C " # "%"$ % "% FD 7 5F7' "%A
&", % A&"7 %&5B6F % " # " ;MLN
UO; &C; V GN U" &"$%$ %V, # " 7A
7&BF" %&5"C &7"CF 7""" %D""; 6
5"" C" # " O((; PLO , , % &% % &7 "57
# "7 U & 5 D*4V " % " # " 6F
F 57""%F %%"7 !
! !,
" # " % # " &G "5G
# " 57""%$ %%"7" Q!R&6 5CF %%B 7A
# &""%" # " 6 %%"7 Q!R %%"7 !
! !
; I" " (#)@', %5 H "
%&6 "" " "% %&"5B$ % "5B%
# ""5" 5 7" T UλV;
UλV
UλV; C 7"
57""% " &""5C" # "
(<
max max max
min min min
( ) ( ) ; ( ) ( ) ; ( ) ( ) .R G BR s d G s d B s dλ λ λ
λ λ λ
= ϕ λ λ λ = ϕ λ λ λ = ϕ λ λ λ∫ ∫ ∫ % "% % I""7 U+V # "%
; , R G
r gR G B R G B
= =+ + + +
# "%B 7I &"% B " # " 7 G'"
U%, +V,
&" 7 H&" 56 "56F &"" 6 &%% %A
6I"$ &%% &6 , H$ #"5BF # " 7
G'" C 6 #@(K''&G"F I%A
BF; &C7G5B7 5 $ G$ 67$ 'G$, 6A
I" "5CF 5%B % # "%C7; &&FD7 B 6
&%,
" Q(S &"5I" '7 B S'(TS'
% "% % & 57
4
1 2 31
( ) 1,j j jR G
j
a u a u a T=
Θ = + + = c U(V
G" O R &"; &7FD$ 6"" ΘUV W + %5" A&5"C %5 $ O5 ΘUV W < %5" " &5"C9 -
; -
- R %G5; % "% FD" "7 # ""5"7 6I"A
C79 MU - | -
| -
9 ,
: R H''A
#"; &""5CFD" ""
&C7" "G5B" # "
U%7, %, +V G FD" &CA
7G5BF 6 &% # "A
%B,
D7 "%7 57"A
"% %%"7 Q!R C 5CA
"%C ; %%C" 7"I # "A
7; "7 H &A
%% ; D"7 %5" " %A
"% " %&7"77 "A
5 "7 65F 7"I 6A
7 # "7, #"5BF &"5"C
(+
HG "% 7"I$ 7%%"$ & % "D"% UV
"" 6 "7" ''# " " &%% -5
,VQ-S) "C % C6 %G &%%
,V% 7 %$ 57""%$ %%"7 Q!R GA
5CC %5"FD7 678
1/ 3
1/ 3 1/ 3
1/ 3 1/ 3
25( / ) 16;
500[( / ) ( / ) ];
200[( / ) ( / ) ],
W
W W
W W
L Y Y
a X X Y Y
b Y Y Z Z
= −
= −
= −
G" # " Q0 ; !
0 R
0&""5CF # " &G "5G
# " UN5D*4V; 6G %&"5B7 %&""5""7 5%$
H"G,
T " " 65C C & '75"
2 2 2( , , ) [( ) ( ) ( ) ]E L a b L a b∆ = ∆ + ∆ + ∆ ;
C "56 7G &G77 &" #' $ A
# " 6I"$ U&7"; N1/2D,F; PW1V/OX1=1LX1
,V,
! ""7 "&"B &"%$ &7" "56# 5G7 %"GA
7"# 6I"C $ & "% % "'C7 &C7 U%, (V
& &6 # "%, %%77 G%G77 %&""5"C A
"$ %G5 # " $ %%"7" ,V5C %$ $ & "%
"'C$ &5" U%, -V, ; 6I"C "'C$ &5"
%$ %D"% " 5A
F%C & %&""5"C7 "$
C% U V; # "A
%"$ U5 , VV,
5" C% &%
%7"D"" %""G C % -0;+
42;<2, "7 %77 "D" 6 &A
"I"%C 6 "%$ ' 6A
"5B 5BE"G H''#"
I"C "'C$ &5" &
% "F % %$ $, 5"A
" $ & "% 6 %A
7%B H''#" I"C
G5 &5I"$ % %A
((
"D"C "G% 65"$ & %D"% "7 %
%"" "%G 5"C "$ %" 6"$ U% 0;-+
(-;.+V, %E"" G%G77 %&""5"C "$ C%
7I" %5IB &5"5B7 &67; &6 5CFD7 & "%
%"G7"#F 6I"$ $ & "%,
D" 5"" %D"% " 5C 5 # "%"$ U%, -V,
5" ,%""" 6"" %G5 %7"D"%C % <;2+ +;20; %A
" 5"" "$ %G5 "5 "%C % (;(- +<;-2, 5A
G 5" V8 % R(;-* R+-;<< % -;<+ +.;((, !"% 7 6
%&""5"C %G5 # "%
" H55&% % 57 &5%"$
7 % "% FD7 6"A
C7 7%75B 5"$ A
"$ %G5 U%, 3V, ; H
6 " &""%"F%C; &6 5CA
" "5B "'C" &C '"
% "C%BF "#,
! ""7 "&"B "65B %"GA
7"# 6I"C & "%
% "'C7 &C7 U%7, %,
(V, U%, 4V; "'C" &CA
% "" "5",
%
&
(-
P &6 5C" & "% 67""A
" G"7""% "%A
8 &5D %"5"
5%"$; 5"$ 67"
U5; EV, ! "
&%5" "5B% A ;
&5" ""6 6 "%" &A
7"I "7"; 7I 67"A
B %%B &""7"D"C &CA
",
O G%G77 %&"A
"5"$ "$ %G5 # "A
% I" '; 6A6
5"C $ & "% % &5" %&5GF%C & 6A
7 G57 & E"F % % "D"C "G% 6A
5"C, "65B" %6"%C E$ %&" # "%"$ U# "
&"I5%V; $ C 5C"%C &5"5B7 &67 5C
6GC6"$, &"% B G$ &"7" $ & "%A
; %6FD$ % 7$ % "'C$ &5"$ %&" # "%"$, !A
H7 H &6 I" 5"" "I"; "7 #" 6
# "% U%7, %, -V,
! &""7"D" "'CG &C "G # " C G77 67"
7"C"%C, &7"; 5C A; %CG 6 "" "7C &A
6G %, (; %&""5"" "$ %G5 5 # "%A
" "%5B 7, """ 6"" %G5 5 , V
%% 5C"; % "% " - R+(; 6% "$ %G5 *;3(
+<;*3,
T " "'C$ &5" 6 % "" 5D; &G %5 $;
"7" C % %N"7, !H7 C" %5" &"&F
%&6 B "'C" &C %5 C &$ "&""5"%
% '7 "7 Y'"S'K''" " "C %
%"7 5F"5C Q(S, "65B" "C C H''#A
" ,: I" U(V; " % &% 6F H5F
5%B # "%"$ U%7, %, (V, )%" 5F"5C & E" %A
"%B "65B 67""$; " %"G & , !H7
5C "E"C H$ 6 5E" 5 B %%"7 I"C
75$; &%"" & 67 &#&7,
'
(3
I$ &5"7$; F I "EB & &" %A
FD"G "G% 65"$; C 5C"%C 'K'@
Z#[, "5 7; "5B" "% %&"5B$
% "5B% # ""5" 5 A7" U%, *V 67"
5F%C ""7, p7 5B &" 7 &5I"A
& C" G5 " " "5B 7&", %% A
F I" " #"5B" &5I"5B" %; &A
5I"5B" % 6"5"G %"G 5 5B "A
, "65B7 "% "% C C 5CF%C "%B7 6"5BA
" E %&6 "" # " ,
5C %I"C E # "&"" %% A%%"7 5FA
F '\" K''; '7FD$ " %G5
# ""5" 5 -; -
-
6 6 "E" %77 /
; /
/ % "% % %%"7$ 5"$ "$
1 2 3
1 2 3
1 2 3
,R R R R R
G G G G G
B B B B B
u e
u e
u e
α α α = α α α × α α α
G" α:] R H''#",
:, "$G"H Q-S &"5I5 #" B 5"C ∆L: "7
%&"5B$ % "5B% 56FD"G %$%
J:UλV "5B 7&" η
:UλV 6""7 "G5 A
6% H '#$
max
min
2[ ( ) ( )] .i iS s d
λ
λ
∆ = η λ − λ λ∫
λ
λ
λ
λ
(
(4
,p,FE &65; % &7DBF $ 7" 7I #"A
B " %&"5B$ % "5B% 5EB % 6"C "A
% "#$ 7"7"" # " Q3S, "" ∆L:&6 "
5B 5"" %&"5B "% ""7; "
#" " 5"% " 6FD" & H7 %I"C # " ,
!H7 D" &7" 7G U5"$GV # ""
%% F8 V &"7 776# E # "
%&6 7 # " 9 V &"7 776# E "5" A
"%G5 ; &5"7 & &""" "%A5#; %"ID"$
H5 # " , $ 7"; &"5I"$ &" " , I%7 Q4S;
5"%C G5C%BF &%$ % " % 7"7;
776F E %&6 7 # " Q*; .; 2S,
5C #" "% # "&"" 7"I$ 7%%"$ &
% "D"% UV &"5I" % &%B # " 8 75$ %A
D"% !M+; !M(; M; NM+; NM(; NM-;; OM+; OM(9 %""$ %D"%A
!^; ^; ^; ^9 7%75B$ %D"% L; L; L; OL+;
OL(& >L; G'" Q!R 6 "% Q0S, A7""
&"NC 5CF "%A5#; %% 5"F 6 H5 # " ; % A
F %G5 "" % %"7 6"C7, H''#"A
# "" α:] &F 7; 776 B A
%5F" 6"C 6% H %G5 , "65B # ""A
# U%, .V &6 F; %""7 E # " %&6 ""C
! ! ! "! # # "# # # $#%
)
(*
%65%B; " # "
U%7, # " LV E I" 6%5,
"5B 5BE" %"
E; &5"" "65B" "5A
6# 5"$G # "";
NC%CF%C %D"% "7 5C7
%&"5B$ % "5B%
# ""5" 5 A7"
""7 , 5C & E"C H'A
'" % # ""# 7I
&"5IB %&5B6 B 3A $ # "" Q+<S, !5%%B
# "%"$ U5"$ # "6% %G5 R!; R!V 6 F
"" % "% % 7 5, +,
6 % &% +0 H5 # " + &&F # "
L; OL+; NM-; OM(; OL(9 ( ROM+; ^; L; >L; !M+; !^9
- R ^; M; L; !M(9 3 R NM(;NM+; ^, 5C IG
%% F &75B" 6"C H''#" #"A
" & 7""; &C$ 5C %" 5"$G # "A
", "65B" &5F "" 7# H''#" # "A
"; " &""5FF 6 %7% &"" "7A
G $ 77" # ", "65B 3A $ # ""A
SK _
& ! ! ! "! # # "# # # $#%
*
(.
# U%, 2V &6 F %D"% "" %I"" E # "&""A
, !H7 #"5"%6 &5B %F A7" A
67 # ""7 5C "E"C 6 %"G7"# 6I"A
C $ & "% & # " 7 &67, 5"" 7"B;
# ""#C 7I" B %D"% 5" &G77 " A
# "G 6I"C,
15G'"%$ %&%
+, " T " # "7 "5" ", ,8 % C6B;
+022, -.< %,
(, B&\a G%&"5BC " C %%"A
7 I"C 67""C &7" N" // 6 "%C 6
%%, H5", +002, &, +, , 4<R43,
-, bc##b&IKH T " " ""8 !", % G5, ,8
; +0.2, +* %,
3, a'TId % %&6 ""C # " 'G';
&5G', ,8 %%% ; +0.<, (+< %,
4, 7"%C &76#C &7" # "A
" 7" T // " %"% % C6, ", " "5" A
"C, +00+, &, -, , (<R-(,
*%"% "" &6"5 # "G 6I"C/
, ,; +023, *4 %,
.('a&%e"B C # ""#C A
7"//" "5" "C, +0.2, X +, , 4+R4.,
2SK[C"#C # "&"" "&I 7" %
&7DBF 67""C # "6% %G5 // " "5"A
""C, +02+, X +<, , (*R-<,
0 @('H $ # "" 5C A7"//L
"5" "C, +0.0, X +(, , -+R-3,
+<#'aH& %&"5B # "
5C "# # " %I"$ // " "5" "C, +02<,
X *, , 30R4+,
(2
) *(+,-0.
a*S()
! !##
% "7" %5 C; G GG%" 6 " &7E5"%A
%$ "B 6# & C "6 $ 7
G7 7"E"5B% "5 " &; %" 5B7
% %C "E"" 6 H5G"%G 5C, "%&""" &"A
G EG U& "V 5C "" 6A
% "% FD ""% %"% %%"7,
% $ %BF H5G"%G 5C C 5C"%C 5B %A
& "%"$, 7 "E"C H$ 6 &"5G"A
%C &G77A&&C %%"7 &" G I"C "'CA
7%5C &C"; I" G 6GC6"C ,
%"7 5F" %"C "7"; % 5"F 5"A
"5BG &&; 7&BF" % % "% FD7 &G777 "%A
&"""7,
%"7 %D"% 5C" 5B % 9 & %N"7
% 6GC6"C9 &""" &5"" 6I"" 7&BF" 5C
&%5"FD"$ 9 '7" '7#$ ; $ 6A
"7 7I" B &"" G5 $ 5B$ &,
'7#$ U%, +V &"% 5C" %$ '$5; 5FFD$
%"C "% " G'"%" "; "6FD" 6GC6"",
%"I ; "7C 7"% & ""C 5F"C; 'G'F
&C 6GC6"C; "5 "G &5D & "7% "% $
77"$; 7$ &"7 %%"7 " 7 "I7",
!5DB &C 6GC6"C 7I" B $" "7C %&%79
6 %7% '7#$ '7"%C " A
7; 76 7 5 7"%7 "I7",
*@# @f# @[' Ze[Z[ ''
c p7"7$ '7#$ % 6I""7 &C A
%C H 7, 5C &""5"C &5D &C "G 6A
I"" 5 "%C %G"" C % &7DBF %&"#5BG &A
G77G "%&""C 67""5BC %", &" &7"" 7A
EBF C"$ %" % 5 &5%BF 6C" &C7 6GC6"A
C , 67" C"$ %" 6 "%"; 6 &5I"$ #" &5A
D &C; N" 5F"C; 5"G "E"%C,
(0
67" C"$ 67""5B$ %" &""5CF%C %$; %
$ &6 5%B %N"7; "#"$ 7" %"5B & "A
% , 5" "5B; & '7 67""5B$ %" "A
7 "%&"B 7%E " %" 6 %7% %
%N"7 % "% " %%"7 7" %%"7"
N" 5F"C, " H 6 "EB; %&5B6C 7" A
Q+;(S; $ &6 5C" 6B %" &"A
6 $ U"7" 5C &""%" 6 $ %%"7 A
GF V &"# $ % &7DBF "$ 7# Z 67"%BF 3×3 , 7%E C %" % "E"%C ""6 &"#A
" %" &5%%B $ & "%, %&5B6"%C #"A
5BC &"#C, T" &"# 5" $ &5%% U A
$ & "% V %%C" W; " %" %N"7, # &A
"# C 7""
1 0 0 0
0 1 0 0
0 0 0 1/
0 0 0 1
Md
= −
G" W R % %N"7,
-<
5G7 '7 C 7%E$ %" %% 6 %5"FD
EG , C 67" ; %"ID"G &C 6GC6"C; 6 A
E%B EG7 X U6 7 67"7 C"$V; &""5CF "
65 %"
[ ] ,, , , , 1.. 1, 1.. 1, 1, i j
x y z w i N j N W= + = + =
G" ;e; ;
R %5 C"" & G65 "59 0 R C
,
657 &7"CF #"5B" &"# " & C A
7 % 0 W +
[ ] [ ][ ]
, , ,1 * , , , / 1
/( / 1), /( / 1),0,1] .
x y z
x z d y z d
= − + ⇒ − + − +
%&5B6C "%" "" &C7$; &""5CF A
" %" 7"I 657,
65I"" %& "5 ; "%5 %N"7 5 &6 "" & "A
# 7" %G &"&"5C $ & "%,
&" "#C 7" %"5B $ & "%
5 %G &"&"5C$ &""5C"%C "7C G57 8 α;ϕ; γ R 677; GI7 "7 5""5BG &&,
7""7 " %%"7 8 N" 5F"C 7", 6A
I"" &C '7"%C %%"7" 7", 5C "A
% 67""$ 7%EC %" &"" 5I""7 6I"" 5A
I B %'7 8 "7 &""%B %";
6" %%"7" N"; %%"7 7",
%"7 N"8 #" %C N""
5F"C; %B R &"&"5C &5%% $ & "%;
%B ! % &" % & 5""7 I"C 5""5BG &&; %B
Q "%C 6 %5 C '7 C & %"$ %%"7 A
, %"7 7"8 #" %C 7A
E" 7"; %B R % 7"D" % %BF 6 C; % Q ! % "A
% F 5" %"$ %%"7" , !5I"" 7" %%"A
7" N" &""5C%C 7 5""5BG &&A
Q<;!
<;R
< G57 α; ϕ; γ U%, (V,
%B ! %%"7 N" % &" % & 5""7 I"A
C 5""5BG &&; &H7 G5 α Q< <; R
<
%" %N"7" W9 0 tgY d= ϕ ,
×
-+
# &"6 C ; % C6 FDC %%"7 7"
N"; " &"% 5CB %$ &6 """ "" 7#
[ ] [ ] [ ] [ ] * * * , = ϕ π γ G"
R % 7"D"" #" %%"7
7" % #"7 %%"7 N"A
9
R % 7"D"" % g %%"7 A
7" % %BF R %%"7 N"
& 7 G5 ϕ %"5B % Q9
R &"" 6 5" %"$ & %FF
%%"7 9
R % 7"D"" % h %%"7
7" % %BF Q %%"7 N"A
& 7 G5 γ %"5B % !,
[ ]
0 0
1 0 0 0
0 1 0 0
0 0 1 0
0 0
T
Y Z
= − −
[ ]
1 0 0 0
0 cos sin 0
0 sin cos 0
0 0 0 1
R
ϕ ϕ ϕ = − ϕ ϕ
[ ]
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
R
− − π =
[ ]
cos 0 sin 0
0 1 0 0
sin 0 cos 0
0 0 0 1
R
γ − γ γ = γ γ
××
× ×
ϕ γ
-(
7 67; & '7 7%E$ %" "A
7 &""%B 65 %" &5B #"5BA
" &"# ", 77" &"6 " " 7"B
[ ] * . Σ =
5C 7"BE"C 5"% E; %7 &"7; C"$
%" 6I" 5I B E , "7; A
# " %" 5 %" # " 6I"C; " %"A
5 "%C, T " & "% % &C7 6GC6"C 7"C"%C
E &""5; &H7 %" 7 &%C7 # "A
7; " 6 %CD7 # " 6I"C; C 5C"%C 75H''" A
7, "A % %" %5 B%C % 6I""7 "A
CB%C "7, T"5"%6 7"CB # " %" 6 %7%
6I"C, 5C HG & 7 65 %% F A
%" &7"I "; 6FD %", !"" A
7 I$ %" &""5CF # " 6I"C; A
F 5 "%C %", ! H$ '7# 6F # "
%"; &5"5B$ # " 6I"C,
!5"" 7 67 #" &5D &C 6GC6"C
7"F 5BEF &G"E%B, D"% "7 %7 &G"EA
% C 5C"%C 5" % 6C &C7 6GC6"C C""
7%E$ %"; " & &""5" &5D F%C
&5%BF 6&5"", 5C &"5"C HG "% #"A
5"%6 67"B %"%B %"8 6B C"$ &NCA
"$ 7"BE"G 67", ! H7 %"%B 5I B "A
5" 5B &G C"$ R C"$ % 5I"A
&C 6GC6"C % %F ,
*@#@f#@['Ze[Z[''Z
''\ c) ! 7"%7 76A
7 %&%" &""5"C &5D &C G5 $ C 5C"%C 6A
I"C "5"C &C 6GC6"C &5"7 %A
7 6I", %" 6I"" &"% 5C" %$ A
F 8 % &%B &%"5"$ "6 &5"IA
% 7A5 N" 6I"C, % "$ '7A
#"$ C 5C"%C # " IG &%"5C; &"% 5"$ "G AA
7 U& '7 6I"C "I7" "&%"% "A
$ # "&"" R KMbL \eaeM R IF %C 2
×
--
V Q-S, 5" "5B; ""7; & 7 &C 7I" B $A
"; C 5C"%C "G # ",
5G7"% 6 "E"%C %5"FD7 67, ! C &A
&%"5B" % " 6I"C &""5CF # " IG &A
%"5C, 5C %5F"C C%$ %% 5CFD"$ %&5B6F "# "A
" U7 "V # "
/( ),
/( ),
/( ).
r R R G B
g G R G B
b B R G B
= + += + += + +
"7 & "CF &&" # " IG &%"5C # "A
$ " 5; % "% FD$ &C 6GC6"C, 77F %A
5 &%"5"$; # " " &&5 # " $ "A
5, C 6"E"" U%5 &%"5"$ "# 5V 67" A
; &""5CF &5DB &C 6GC6"C,
"I%B H''" %B 5G7 6"5B$ %"A
&" 6 % "% &""5"C # " G " 5; %A
"% FD"G &C 6GC6"C, 76 7 "I7" H
'#C 65G"%C &", &" 7EBF &7"" &C;
&% % " # " &%"5C; 6 "7 &5"ID"G &CA
6GC6"C; '7 " "G % " # " G " 5,
5C &D"C 5G7; "5"C "G % "I%
#"5"%6 GB 6 &%, &" 5I" &5"5BA
&7"" &C 6B 7EBF 56"7F 5%B, P 5
6 6 %%7 C % %E "; && E" 6I""8
%5F &%"5; &&FD" 6$ # " $ " 5; "
&5"ID" $ & "%, "% "; 7"BE%C "7C
& %%C %B &""5"C &5D,
5C "5"C &C 6GC6"C &""5"C "G &5D A
7"%7 "I7" "7 7"B EF 6 # "A
" 5 ; % "% FD &C7 6GC6"C; 6 %7%A
" &C" U"'C"; 7%5C" ,V; 5D &5";
% "D"% &G %5 $, 5G7 H7 %5" &"% A
5C"%C %5"FD7, !"" 57 5C 6 F%C "G &A
7"8 "7C %; &G" %5 C , "7C &6 A
%C &%$ E" &&%"5B$ 56 6I"C % "7
7"FD%C 6" 7"5"$ 6 &7" 5C,
-3
6" 6 7I" B &5" % " 7A
6 G 7", 5C HG 5I" B &5" 67I%A
BF %7"C %%"78 "&%"% " &%5" &"A
7 &C 6GC6"C '7 C "C &%5"$ % %"7
"77 7 6%%C 6 ,
15G'"%$ %&%
+, C%&'a "7"C 7&BF"C G',
,8 % C6B; +004, ((3 %,
(,dbc&YbYa % " $ 7E$ G',
,8 ; +024, , +, -*. %,; , (, -*2 %,
-, ap7 G'"% '$5 , " 8 !p wA
' ,x; +004, 32< %,
-4
) *(+,-0.,-
$
!
% 7 6GC6"5"7 %%"$ C 5CF%C & "A
'; "; 5"G" ; 6F "" & "% &5"
65$ "% %, "'C" 6GC6"C % %&%A
CF%C E" " , )% 5" Q+S; + G "'"A
& 6" & "% &C; 7" G 7A
I" %GB 6 %7% "'"& + ( 7, "% A
7 %&%"F %&%% " ; & "'
7"F 75" H''#" "C; 5GC "7 &C "'"&A
%" 5"G % %&%CF%C & $ & "%;
6C " &5", !%5""; C%B 7"I 7C "%B7 & IA
7 %"7 R 6; %7 &"F 5BEF 7%B;
"$'C & & "% & 6"$% "7 " ""C,
7 6 I H& B % 6GC6""7 $ & "%A
C 5C"%C %6" %# 7" I"C "'
"'"& & "% , %CD"" "7C %6
C '6"% 7" 5C &""5"$; % 7"FA
D"7 7"% 65 &"% "&5 % $% ; 6GC6A
"$ "'"&7; %$ $, ! 56" &C" "'
"'"& Q(;-S "7 &""5B8
G# 6 %&%"C9
'7 67" &C" "'"& 9
G% &C" U%"&"B &C &C7 $ & "%V9
"% %B &C"9
G# 6 % 65$ G%$ &C"9
G# 6 % 65$ "% %BF &C"9
%%B %&%"C &C"9
& 5"" %&%"C &C",
! 5C"7 "&%C "7" &%% " 5"A
& ; &%D &G7 %"7 R 6; &5" "'A
"& 6 "%C; 6C "5B" &C 65 67"A
; '7; "% % G%, "7 5BE" 7%B H
%"; "7 7"BE" 67" &C, 5BEC &5DB &C" & &A
-*
%5 C 5F"%C & E5C %&$7 %%C
$ & "%,
%#" 7" I"C "'"& 7I 6"A
5B &%% " ", " 7" 5C %&5B6F
I"G 56"G 65"C, 5F %$
% "5B%BF; " 7G B &7; ""7F 5C &CA
C "E"C &5D 6GC6"C, !H7 &5CF &%% A
7 7"7 5C, !%% " 7" % "G%#
"&5 G 65"C U"&5 6V 5 C%G % U"5" A
6" 7"V,
!5" "'"& " "5C"%C '" %$ % 7
% "5B C7 "5"% 7 7; %" C%F 75 ""A
F &G; "%5 %7"B &C & G57 6"C -<R.<,
!5" "'"& 67"CF &"%" % $% & "%A
R # " C%B, %"I%C "D"% G"%G
&%I"C; " & "$% "7 5B'5" 5"$ A
F '5F"%# B,
%%5" C; & """ C7 Q(4S; &65; %
"5""7 5D &5" "5 "%C 5"% '5F"%#A
FD "D"% ; , ", "5 "%C 65"", 6 & ""G
%, + G' Q-S ; 5% 7G 65"C 7"BA
EC C%B 6&CD '#$ "' U"%; G65"$" 7%A
5; C -V, 15"" C" % """ 7"F "% %5C " 7%5
U C +V; &7"I" 6"" 67F "% "6 UA
C (V, 5D &5" 7"C"%C # " "7 '5" G U"A
6V C7 % "5A'5" 7 U"%V,
"%
%B
-.
P%&"7"5B % 5"; "'"& 5"" A
"% &G5DF 5B'5" " 5 -*--*4 7; " 6A
IF % """ 5 $ % %&", %77 %&"A
&%C '5" A%$ % 3<<34< 7,
%B &5" "'"& &""5C"%C " 5B %% "A
7 65""7; I"5B$ %&%%BF & "%,
P %&%%B "6"%C &6"5"7 &"575"C +;-.+;33
5C 5"G '#$ +;33+;4- 5C 7%"5, 67""" "% %
% "; &E"E"G ""6 &5" "'"& &65; &A
&%" + +<v &FD"G "" & "%B % " 6 %7%
5D, 5" "5B; 5BEC %B &FD"G % " %%"A
"%C &G5D"%C &5"$,
7 67; %% "" 65""; I"5BC
%&%%B &5" "'"& &""5C"%C; G5 7 67;
5D$ %% 7; , ", "% %BF &5", !H7 "5A
C% 7I" B %&5B6 "% " &6"5C "% A
% &5",
" 7""" "5 &5" %" % %7 %$
& 5 C; !%5"CC & %5 " 7"% %A
&%"C &5" " 6"%C, ! %5B7 "" CB &C 5C"A
%C % $ & "%; &$ &5"$; H7
%5" 5F"%C 67"" %G5I " 5 C, 1"5"% $
" "'C &5" %5$ "% % NC%C"%C "7;
%G5I"C & "%B 7"% %&%"C &5" A
I" % "% 6"5B 5BE"$ %"&"; "7 %
%$ , 15GC 5BE"$ 6" 5 C; 6FD"$%C
% %$ ; &C7" %5"" 5 IF%C "" &
6"5B 5BE7 G57 5 G6; "7 %%" %A
; & "'C$ &5"$, !H7 C%F &G & %A
5BE$ %" %5# I"" C %5"" 5 A
5B "5BE7 5" " %CD%C; &""5 FD%C
", 5 I" % C &"% 5CF%C %"5B "77
&C7, % %G5I"$ & "% ; &"
&5"$; IF %5"" 5 & 7"BE7 G57 5 GA
6 &&F 5F"5F 5B 6"5B7 5"
, !H7 &C &5" "'"& 56 I%C 5"" "7A
7; "7 IFDC %C ,
-2
!%5B 7%77 5F7"%#"G 65"C 5"I A
5 $ 5% 7$ % %&"; % C 7%% &C" "'A
"& 7"" # " 5% %"G; , ", I" 5 $
% %&"; %&"5BC "% "5" 6$ 7"A
5I 7"B 7%77 H$ I" 5% %&"; 5"
7"; &7"C"7 5C "D"5BG "5" "C, &"5BC A
"% Q4S %B7CA#"6" G ' & "" %, (,
5C C 5"C &C" "'"& 7I %&5B6 B "&5 A
6" 7"; FD" &6" 2+- 7; & H7 C 5CA
"%C %5F "7 "57 UH''#" "&5 G 65"C 5A
6 +V,
! 5 & "% &5" "'"& 65"5BC
%&%%B E"%C, P % C6 % "7; "'C$ %5$
67"C" %5 C "77"%G "%C & A
6 F "7&"$ 75 R "7&"7 % 7"I
%$ $ $; 6GC6"$ "'"&7, 75C %A
5 5"8
7"BE""7 %% %&"C % & "% 6A6 & A
5"C "'C$ &5"$ %% C 59
%I""7 65"5B$ %&%% 6A6 5"" %G H'A
'#" I"C "'"& 9
5"" 6$ "&5& %BF "' "'"& U -4
6V "&5"7%BF U +;4(;4 6V & % "F % %$ $,
"65B"; &6 F %"; 5"" "C %5"A
FD" 5C # "7&" "' %$ 8
%5"$ "B +( ; BF <;4+ ,
%
"5BC
% "5B%B
-0
6 %"G %6G ; C%B &5" "'"& 7A
I" %5IB "%$ 6GC6"C, & H7 %5""
7"B ; %7 C%B %5B 67"C"%C 6 %7%
%"&" % "D"% &5"; &H7 "&%"% " %&5B6 B
C%B "% " "% % &5" 67I 5B
& %5 ; "%5 %5F" 5"C C%; %5 5""
67"""7 % "D"%, PG 7I B%C; "%5 %&5B6 B
7" C%G % Q*S,
5F"" 5FG N" " % C6 % &""5""7 6A
# C% %7G N" "G IFD"$ %" Q*S,
1,R R R
KR R
−= = −
G" !
pR % "% " C% &5" '; 67""" A
"7" & $ $ I" % "D"%; < R '7""%$
%, ! %"" % %% 5CFDC % "D"% &A
"% %5F"%C U '75 E"" C%"$V
% " &""5CB%C 5B %% "7 65""7 &5"
"'"& ,
E""
Rr
R= % 6 " %"5BG H''#"
C%; %% " &""5C" %,
C & "%B %"G & $A5 &5"$;
$ %F ; %"5B $ 67"CF %; ,
!H7 "% " H5 %&5B6F F 7G; 5FA
DF % "5B &%C7 I"5B7 % $% 7 UH'A
'#" I"C <;2 R <;24V,
%B HG H5 %"G E" C% &C"; "A
% " %"5BG H''#" C% %&5B6F E""
Rr
R= ,
C" H%&"7"5B" 6 %7%; &6 F % C6B A
%"5BG H''#" C% % "% %BF &C" 5A
5 U%, -V,
7 6 "% C 5C"%C % "5B 75C % "5BA
%B 7D7 65 7 C$ %A$ %$ "'; &%5B;
3<
I" C%5%B; && " &6" '5" A%A
5,
5G" 6 %7% &5" & %&5B6 "&5 A
6$ &&, H$ &&" &7"7; &""5CFD7
"% %B &C" C 5C"%C % "7&" U%, 3V,
!%5" G; 5 &5" '7#$ ; , ", "%GA
5 % "% FD"" "7 6I"" 6GC6"G % A
; "6 %7 U"5" 6C 5 "&5 6C
7"V; % C 6 5B"$E"$ %% "5"
&C "'"&, P& "5"C C 5C"%C 5FA
" 7 "E" 6 56 '7#G , "
"5"C % 7G, O %&5B6"7" &C"
wx I"% 5C"%C % % &%BF " 6I"A
C % % 67"CFD"$%C C%BF, G" 6 F A
7 w5 %G G" C% 6I"x; G"
%
"5B$
H'
'#"
C%
&
%
"7
&"
$
%
3+
%C 7 w 6I"C; " 6F 5
&%C 6"5B" &""& C% 5 # "x, !A
"7; "%5 G#7 6I" C%$ &""& &""A
5 &5I"" 6; &C" &5 G 6A
I"C; 7 C 5C"%C &5"$ '7#$ ; %C"
% $ "% "$ " Q.;2S,
!H7 5C 7GG#G 6I"C 7I"% "
7I" B 6"5B G"; "%5 5C &""5"C %&5BA
6 B %E"C
( ) 1,k kgrad B X Y > δ5
( ) 2,k kB X Y∆ > δ ,
67"CC "5 δ; 67I &5"" 6I"C %65$ C%BF, "5 δ#"5"%6 B % "A% % E5$; IFD"$ "% %B C%"$ 6GC6"C "'A
"&7, 5B"$E"7 7I" "%%B & I7
"5"7 "5B%; I" & ; "6A
FD"7 7%75BF &5DB &C "'"& ,
!5DB L 7I &""5B; &7"; %77 "7 5"5BA
%"$ "7&5B% ; 6FD &""%""C 6I"C &CA
%FD7 57 &""FD"$ "5" 6$
2
1
,n
oi
i
S DS t
ZT F =
= ∑G" L
1 R &5DB '" &""FD"$ 9 R R %5
% 65I"C9 5"5B%B &C7G %$
6 "9 DR %%C" N" "5"7"9 8R '%" %A
%C" N" 9 =:R 5"5B%B "7&5B% ,
%B" %%7" 5B "" 67I% &5"C
&C" "'"& %5"" %5B "%A
6GC6"C &&7 %"% 7, % C 6 %%
&5" '7#G , %" %5B" %5"C; 7"C
5 '7#$ ; 7I &5B 7"% % &A
7DBF P,
3(
15G'"%$ %&%
+, 'a, GC6"" 7C "'BF, ,8 :7""6A
; +0.-, 4< %,
(, $'$ %#" 6 " "'C 6GC6"A
$ $ // , G7""5G"%$ '7#, A
%, +00., +24 %,
-, #" 5F"C 5B 6GC6"%BF ;
%E 7"$, ""%" 6C, ,8 :7""6; +0.4, +0( %,
3, a% #" 5C "'C &C" & "A
% "; 5F"7 % %7"% %"5"$ 77 A
&6" %&" // %%5" " "75 6 %7%, +004, X -, , *3.(,
4, Z $& a &d#?b, %#"
H%&"%% " 7" &""5"C 6GC6"C IFD"$ %",
,8 :7""6; +0.., +0< %,
*, #'i&(Zaa&%Z#[b, %#A
" I"" 6GC6"$ %%"$ '&5 &A
"%7 7"7 // " "%%, +0.(, X 2, , *4.4,
., @\&$C&jIba, 1%$ 5GA
7 C N" 6I"C // 7"C, +00<, X +,
, +++*,
2, ?a &5 6I"$ // &%
" &" C "5" 6 %%"7 &""; &"7;
I"C '7#8 "I 6, %, / !, ,; +0..,
, 4(4*,
3-
) *(+, -0., +-
d'
# #!##
!& E" "'"& U!V G" 6GC6CFD" "D"A
% % """7 "7" &""&" F C &%5" "5B &" A
D"$ & 6"$% "7 5"%; %5"$ #; "
G G7""5G"% 7"% ' , 5 4<v
5"% %&C"%C " 5"G '#$; (-(2v 6" CA
I"5" %"FD" G"G; +4v % C"%C " 5B +4+.v
%"%C &5"$ '6" Q+S, !5"" %%C" 6 &" A
5B '7 %D"% C 6GC6"$ $ %"" 5""
C$ 7&" "'CG 6GC6"C, p7 "% %B &CA
" &5" !; " C 5CF%C %77 %&%"7 7 6GA
C6"$ $ & "%; &%% "" &5I"" 6A
"5B 67"CF%C & 6"$% "7 G7""5G"% 'A
,
! 5C"7 "&%C "7" &%% " 5"A
& ; &%D &G7 %"7 6; &5" !
6 "%C; 6C "5B" &CC 65 67" ; '7;
"% % G%, "7 5BE" 7%B H %"; "7
7"BE" 67" &C", &C 5"" I" %5G " ""C &5"A
! 6 "%C "5B" &C; " % CG FA
%C; &"C &5G " '7, ! 7"" %5"C " 5 "A
"C 5 H &5% "5 "%C; E 7"BE"%C,
6 %7% %5 $ % "D"C & 5"C 6 C
&5" ! 7I" % " "5CB%C '" %$
% 7 % "5B C7 "5"% 7 7; %" 75 "A
"F &G, " 7""" "5 &5" 7I" % B %
%7 %$ & 5 C,
6A6 5BEG 5"% 66 ' ; 5CFD
"% A5C 67I%B 7"%$ A
6I"$; "77 %5 "7 & E"C % "&"A
# "65B 67""$ C 5C"%C 5" H%&"7"5B A
G5 7 %&""5" H''#" %&"5B$ C%
33
UV 6 %7% " & "%G 5"C, 5C
C 5"C 5E %5 $ A5C 67""C &7"
6GC6"C $ & "%; 5C "7"#$ & %A
&5B6 F A&& "7 &" 5F"C %&5BA
6"7%C "65B7 & "" %%5" $ Q(*S,
5"" Q(S & "" " 5BEG 5"% %75"A
5F"$ &5" !; "A"5 'G'$; &5" &
65 %5 C %N"7; 5%%'#C &C" ! & "% %A
; 7" & ""C #G %&" C
#" %"&" 7 6GC6"C $ & "%, #"5BF
%5F"C 6 %7% C% &5" % "D"% 67"C5%C
C%$ % &5" %"5B %$
1 ,R R R
KR R
−= = −
G" & C%B &C !
' C%B ' U%$ V; 67""A
" & $ $ I" % "D"% & G57 0<~ & "%
, 5%%'#; $ "5" % " G&& &CA
"; 5BE" 6"" 7"" 6" &6 ; "7%FD &CA
!, H7 &67 "%" % &C9 # "9
%% " C %G5I " 5,
!C 75$ "% %; C%$ % " 3
+(v; 7"FD" "5"% $ 5 "5"% A%"$ " G %
%57 7%5C%7 5"%7; 5"" " &%7 F%C %
% 5# & " & G57 34~.<~ "5,
!C %""$ "% % % C%7 %7 (<-<v 7"F
%" " 5 %" A%5B" &5" &"F C%F &GA
C$ 6"5B$ & "% & % 5BE G5
6"C "5,
!C 5BE$ "% %; C%$ % 5""
34v; # " " "% 7G 7"CB%C 55 A'5"A
"7A6"5" U %5" "'CG 6GC6"CV % "A
7 I7 U&""5 FD7%CV 7; " & G5 6"A
C 7"BE 34~ "5, ! 5BE G5 " &C C%F
&G 7G 7"B C$ 6"5B$ & "%, 7"7;
% "5B C$ % "5A'5" $ # " &5" % ""5B% "
5 "$ 7&" "% ; "7A'5" $ "6 ,
34
%77 65"C & %" 7&" ; CD
&5" ! &%C '5" A%$ % 7G
%&" % 57 5 &7" 3<<34< 7 Q(S, %B &5"
! &""5C"%C " 5B %% "7 65""7; IA
"5B$ %&%%BF & "%, P %&%%B "A
6"%C &6"5"7 &"575"C; $ 6 % %% A
#"# !,
5I"$ )p 7$ 5%C %&" "'C" &5" A
5F 5FD7%C %$ %&"7 %%"CC U6A6
5CC %% " &5% &G5D"C "'V I"C Q4S,
7" G; "'B 7I" '5"%# B, A5% H''A
#" &"575"C "' 5BE"; "7 %$ ; &
5"" %7 H''#"7 I"C "'C &5",
77 &6" %&" E7 &6" G5 6A
C 6"C H''#" I"C $ & "% A
%% ; & 5 &5" ! " &" E" "%5B &A
#" Q-S, "'B 7"" 5BE$ H''#" I"C; "7 %C
U5C 8 3v %5" "'; (v %5" %$ V,
7" G; CD"" 6A& 65"" & "5"F
C% %$ Q*S,
5C % "C %5 $ 5F"C "% " "C
"5 % "'C$ &5" '" %$ ; %%A
"7G & '75" Q-S
,max ,
I IK
I I
−=
G" k "% %B 65"C "'C$ &5"; k
%$
, 15 &5" 6 %7% % < "5BG G5
6 C Θ 5C 65 6" G5 5# Θ< ;675BA
G5 6 C ϕ %&"5B &6 U334; 30<; 4*4;*.<; .*4 7V, 56 & "" G' &6 "8
77 %&"5B7 &6" 7%75B$ % U
C" "'V %&""5C5%C &7"I" G5 Θ W -<~ R *<~ ; &"7
5BE% " #$ 7%77 < &5%C Θ ≈ 34~9 A&6" U 56 2<< 7V "'B C" ; 7%75B"
6"" < % G"%C Θ W <~ U& 5"" 6 C &"&"A
5C & "% V,
3*
!5I"" A7" %"5B % 6I""7 6A
"%" G5 6 C U5F"CV & 5"C %5"A
G % "D"C & "" %, +; G" Θ "5B$ G5 6A
C9 Θ< 6"$ G5 5#9 ϕ 675B$ G5 6 A
C; % "7$ &5%% %5"G "5 Uϕ W < &A 5#; ϕ W +2<~ & 5#V,
P%&"7"5B" "; %CD"%C G5 7 %&""5"A
F "5 5F"7G %; & "" 5"" Q3S,
675BC 6 %7%B % 5C 65 "5B GA
5 6 C &65; 5BE$ % %G"%C & ϕ56 34~ , %7%B "5 % G5 6 C
&5%% %5"G "5 &65 %"5B" &%C%
5F"7G % " 5" G5 Θ W < R 3<~ &%5"FD""
"G 7"BE"" & Θ z 3<~,
C 56C "65B H%&"7"5B %%5" A
$; &5" % &7DBF 5F"$; % &7A
DBF 7EG 7"5 C; 7I &$ %5"FD7 7
& 5"" H''" G 67"D"C A7" 5C G5%A
G 5C 6 %%C"7 & "% ""8
!
"#$%
"#&%
Θ
'('(
Θ
ϕ
3.
+, 77 &6" %&" " " "7C A7" #"5"%A
6 & 5CB F & "%B & G57 Θ W 34~,
(, "% 5F"" % &7DBF A7" I"5"5B % $ %A
; C 5BEF %B C C 5C"%C 6""$ ""$,
-, "7" "7C % "7 %&5B6 B A&6;
A7" %&5GB "5B % Θ W <~,
3, %&5B6 " &5C6# '5B 5C "5"C A
% &5" ! & "% " & 6"5B7 H'A
'" Q.;2S; 6 "" &%CG &%% C "5 "A&",
15G'"%$ %&%
+,df(bi& &C$ GC6"" "G
6 %G 7"$ &5"7 "'"& // " "%%, +00*, ,
(-, X -, , -*+R-.4,
(, #" 5F"C 5B 6GC6"%BF ; %E
7"$, ""%" 6C, ,8 :7""6; +0.4, +0( %,
-,a% , #" % "'C &C" &A
"% "; 5F"7 % %7"% %"5"$ 77
&6" %&"// %%5" " "75 6 %7%, +004, X -, , *3R
.(,
3,a&%'T)&fH %5 $ A
%#G 6 C ""% 6 $ 7$ 5A
% %&" % "7 H''" ""G $ 6 // %%5" " "75
6 %7%, +02., X 4, , 4*R*4,
4, ZC$& a &d#?b %#"
H%&"%% " 7" &""5"C 6GC6"C IFD"$ %",
,8 :7""6; +0.., +0< %,
*,R>=g/6V, u K]`J e`a _`ac \edLM`Jm K]L YL[ YbM_[\L [Y [ ce^`_`LM e_ K]L
^elJl[M^ KM[JYc`YY`eJ e_ a`m]K // t\L[Jeaem`[, -0U3V, +00., , -0.R3++,
.,(Zaa %#C #C 6GC6"$ &A
"% 7C &5C7""%7 7"7// " "%%, +0.4,
X -, , +(2R +-(,
2,a%&#I&' a H''" A
% &5C6# 67""$ & &%% 7 %#7 6A
" 7$ 5% %&" // %%5" " "75 6
%7%, +02., X 4, , **R.3,
32
) *(+,-0.
*a''&CC'
"
" % " & &6 5CF %# I B &5"A
"'; "'"& 5 & "% "D"% U!V
& "% , !" C 67""" &"% "%
& "%; & CD"" 67""F I"5B % $% "" 6A
5 5%C % " G %&", C 67""" '6"%G
%%CC & "% %5"% " 67""C 5"C; &"6 A
C; %&"C , , & 5C"7 &5" Q+S,
%%77 &"" F &, &5"%C %F
& "%B "'B % %""%C & 6"$% "7 & "A
%G CI"C &C; % 7"FD"" %5, "'CC &5"A
67"C" %7 "I7 5"C & "% , 7"F "A
%5B 7"67 HG C 5"C8
+, :E"" 5 % C6 % "77 &GA C67 &#"%A
%7; &%CD7 %7$ &5"",
(, :E"" 6 "%C C6$ %%&#"$ 5D" %7$ ,
"C NC%C" GE"" 5"C &5&"7 75"5 !
& "% , !5&" &"&C% " 6 F " 5A
&#"%% ; 76 , !" $ 7"67 & "5"F
$ &5"" 5BEG 5"% C6$ H"G, $ %&%A
" %5$ ; $ 6 F%C 5 " &#"%%,
"$% "5B%; "C; F 7"67; % A
" 6""; "%7"; 7"" $, C6C H"GC GE"C %5EA
7 "5; B 556 $ 5B $ &5""; &
H7 &5" &% %&5%B, G &5" "' %&"G"%C
"5B" %#; &% 67""" %'# ""G
%5C 7C, "% " 67"CF%C %&"%" %E"C
5C ; H I" 7I" & B GE"F 5"C,
7 67; C & "C "'; "'"&
D" ! %#7 &"%7 7"7 % C6 % 'A
7 "7 G7"%G % $ & "%; &A
$ &5"$ !, "$% "5B; 5F"C &6 F;
30
% " "$% " %% GE" &55C 5, G"
& "% &% '7 " %5 % % %"5B
75$ "% %BF & "%G 5"C Q(S,
"65B 5F"$ 6 C %5 7I % "% %5"A
FD"78
7"67 6 C %5 ; % C6 % GE""7 G #
&55C$ C &5"$ !9
%5 " &5% 5FF%C & %% " 42 7/%;
&"7 E &5% % %5""7 " 7"BE"%C9
G5I " & "% "6"%C 7"BE""7
%5" %"" G 5 " 5; % 7 &C A
5CFD""%C %%$ % %&",
!7"7 &5"; "6FD GE"" G #AA
&55C$ C; C 5CF%C 8 #"#C !:; & "%" CA
I"" ( )σ H''#" &G%
d
d
σ= − ; $ 7A
I" 7"CB%C 5C % 5BE 6"$, %%7 C
&5" ! &%% F &7"%B; 67""" : 7I 6B; %C
6 E 6 "%G 7"G "C %"C "D"%
21 1
0 2
UD
t x x
∂ ∂∂+ =∂ ∂ ∂
"%B8 :< "%" 6"" #"#9
:+ W :
R :
< R 5"A
" "%G 6"C; %5 5"" &I""7 59 4
G65BC %%B %# 5"9 D RH''#" 5"A
% 5 75"5C$ ''6,
&6 " 56; 67"G G5I C & "%
" &%; "%5 &7" " &" E" 6"C 5 <;<4 &
%" 67""C #"# :, G5I " "%C % C 5A
$ ++;4 %7, !5"" H%&"7" " &6 F Q(S;
%5" "$% "5B &% %"5B" %55"" %" %&"A
5B %% 5CFD & "%G 5"C E7 &6A
" %, %, + 6I" '#C lU3V WL?U3V/L
iU3V; "6A
FDC %"5B" 67""" %&" 5% %5 U C +V &
% "F % IFD"$ ' $ CBF U C (V OU3V WLiU3V/L
U3V,
6 $ lU3V ; %"$ &5%" % (-< :# %&"5BC
&5%B %5" 7"BE"; "7 IFD"$ ' $ C,
4<
!7 &%% "$ 75C# C% & "%
& H7 C 5CF%C; A&" ; "%B & G5 C% 6"5B
I"G '%"$ & "%BF % "; A ; 6 %7%B
H''#" p""5C G5 &"C % " IFDF '%",
"7 %""; 7" 5 IFD"$ &5D &""5CA
" "" C%B, !H7 56 6I"C & "% "
&"I" %"G &%% "$ %&" !L U.;mV U &5C A
V 5 H5"7" & "% U"" %&" 75C G"
& "% V, H7 '7#C " G "%C8 "%5 %&"
5 &"5B 5 G %5 .; &5%C #"
%&" 6 E"$ & "%
( ) ( )2, ,Sk k kΨ θ = Ψ θ ,
5C &5"C '7# %&"" 67I 5BE"7 " A
5" 6"$ 5 %"5 "7 &5B 6I"" & "A
% % %7 6"E""7 & &%% ,
&55C" 5 & "% ; "%7C % F 7A
F%B; GF IF 5B C" %D"% " C 5"$,
7G7 &""5CF I"5BF %&%%B & "%
77 % "" &H7 5" 5 %% " U &%5""" %5A
I 7 C 5"$ G5I CV 7I" B 6'%
7 %5" %# % %75" 5 ,
7 67; &67 5C &C" ! 7I" %5IB A
%% " %% %% 5CFD %&"" 5 &55CA
$ C & 5 &%5" %$ ", I" "7C 6 "%A
; C%B %5 5 6 % "5B"' 'G'A
"%" 6I"" 5 "5" 6$ %G5; C 5CFD"%C " A
7 I""7 %G % " G %&""5"C; "% %""
'7#F %" % " G &%% "G %&""5"C,
%"% "7 " "7; &"NC 5C"77 A%%"7"; C 5C"%C
!
! "#
4+
H7 %5" ; "" 6"EFD"$ %&%% 5I B %A
5C %&6 ""C 5C % " G 65"C &55CA
$ C,
I"C &C ! H7 %5" 7I" B "E"
&"7 &5"C "D"G &%% "G %&" pB" "A
6I"C Q-S &""5"C %% C "7 %% %A
% 5CFD &55C$ C, ) C '; 5C C 5"A
C &55C 5"$ ""%C 67I 5BE"" 6"E""
A%%"7; 5C 56 5"" & C%C %% 5CFDC
A%G5; "%DC '7#F 7"5% "5C &""A
"7G 6I"C,
D"7 %5" "A"5" 6I""; 7"CFD""%C "7"A
; "%B %&""5"" % " $ H"G &5%% Uh; nV 77"
"7" = *Uh; n; = V, G 7I 6B ""6 $$ "G5 pB"
( ) ( )
( )
1, , , ,
2
exp ,
x y
x y x y
O x y t S
j x y t d d d
= ω ω ω ×π
× ω + ω + ω ω ω ω
∫∫∫
G" ωh; ω
n &%% "" G " %; % C6" % 5$
5 λh; λ
n % %57 &" - ; n "# 5 & 5" %"$
Uh; nV %E"C7 2 2x xuω = π = π λ ; 2 2y yyω = π = π λ 9 ω AG C % U "7"CV9 LUω
h; ω
n; = V "&" $ &%% "A
A "7"$ %&" 6I"C *Uh; n; =V8
( , , )
( , , )exp[ ( )] .
x y
x y
S
O x y t j x y t dxdydtω
ω ω ω =
= − ω + ω + ω∫∫∫ %5" %""C & 6I"$ & % "7" 5F$ 7A
7" =; % %C "& I7 C 5C"%C 5B '#"$ A
&5%% Uh; nV
1( , ) ( ,, )exp[ ( )] ,
2 x y x y x yO x y S j x y d d= ω ω ω + ω ω ωπ∫∫
( , ) ( , )exp[ ( )] .x y x yS O x y j x y dxdyω ω = − ω + ω∫∫
4(
!"% 5CC 6I"" 5C P #' $ '7"
"$ 6'% $ 77" "7"; "G 7I 6&%B
" 7%% %" 3 U9;6V "$ &C7G5B$ 5%, 1A
5"" R " &C7G5B$ 7# +WQ8U9;6VS; G" 9 &7A" 6"C 5% <; +; ,,,; ;+; 6 5% <; +; ,,,;^+, H7
%5" &C7" 7"" %"" &"6 " pB" U!pV
6&% "%C '75$
( )1 1
210 0
1, ,
N Mln km
lkn m
f n m W WNMc
− −
= == ∑ ∑
G" 7&5"%" C &"6 C,
21
1
2
( , , , ) ,
2exp , 0,1,..., 1,
2exp , 0,1,..., 1.
l n kmW l k n m W W
W j l NN
W j k MM
=
π = − ∈ − π = − ∈ −
6"57 5" C" %5 F G5B%,
%5 C 7"G !p 6"57; &C7" &"6 "
7I 6&%B 7$ '7"
[ ] ( ) [ ],c f , ,l k Rn m = A A
G" ,cl k 7# %&"5B H''#" U%'7V !p;
( )f ,n m 7# 6"$ U%" V %G5; [ ]A C
7# &"6 C 67"7 U; h ; V 5C ; W (9; 9W +;(;,,,
[ ] ( )
( )( )
0 0 01 1 1
0 1 11 1 1
2 10 21 1 1
1 10 11 1 1
...
...1,
...
...
N
N
N NN
w w w
w w w
N w w w
w w w
−
−
− −−
=
A
[ ]RA 5GC C 7# &"6 C 67"7
U^ × ^V 5C ^W(6; 6W+;(;,,,
4-
"&"C &5"" I"C; &5"7 %&"5B" A
H''#" U%'7V 7"G !p "65B &%5"A
"5BG &5"C 7" &"6 $ 7"G
%G5 & %7 & %5#7 U7V, !" " 7"" &"A
6 " U7I"" 7# Q,S %5" V % "% " !p %5A
# %G5B$ 7# Q_U9;6VS, " 7"" &"6 "
U7I"" 7# %&"5B H''#" Q\2;6SWQ,SQ_U9;6VS
%& 7# Q,S V % "% " &"6 F & %7;
&#"%%" G &""5CF%C %&"5B" H''#" U%A
'7V Q\2;.S !p,
7# C !p %77" & E"F "" G5 $
G5; 7# QuS QuS C 5CF%C 7 & &""5"F
QuS+WQuhSWQuS;
QuS+WQuhS
WQuS
;
G" QuS; QuS R 7&5"%%&CI""; QuS; QuS
%&A
" 7# QuS; QuS, % " HG " 7"" !p
7$ '7" 6&% 7""
Q_U9;6VS W QuSQ\2;.SQuS
,
%&5B6C E"%6"; 5C I"C ""6 pB"A&"6A
" %&"5B$ &5% A%G5 "G "5C# 'A
#$ 7I &%B 5G7 &""5"C 5C %5 "5" A
67 %G5" $ & "%,
6 "%; 7&5$ %&" Q\2.S " 7I" %5IB % "A
$ "%$ %%5""7G &#"%%; &%5B 6 %
77" 67""C, &$ 6" I"C %5; "A
7; A&" ; "EB 6 &5"C % "$ #" %&"A
; A ; "5B "G 5"" "F 5%B ; A"BA
; "%&"B 756#F &5"$ #"; %5FFDF 5CA
" 7"EFD ' R % "D"%; "% % 5"C ,&,
% "F #" &%% "G %&" " %"""
Q\2.S % 5"5B7 "7"7 " 5"; " &"A
EFD7 &5 "7"G " 5 5F"C %5,
%5 H " 5 "%" 67I &"5"" 7A
G 5G78 5" &6 %C %""" 6
Q\2.S H''#" & G&&" %%" &%% " %;
6"7 %""" & "7",
*
*
43
%&5B6C &5"F #"; 6 "E "7 %&"5B H''A
#" 7I "5B 5"" '7 F %B; & $
67I &C" "E"C 5 %5, 5C %5F"C 5CC
7"EFD ' "7 & "% 7 &5"G
"" &6 5 %&"%F %G5; 5 5G %'A
7 $ &6 & 5"" %$ $ % %&",
I"" 5C %5 67I &"7 % "C " 5
"5C# "D"G 6I"C 5"7$ & "%
% 6 "7 %$ $ & "% UH5GV, %% A
$ #" "%5B% %%; % "5B%B
%&" %&"5B7 7",
"5C#G 5G7 U%, (V "%C % 56 A
%G5 & %7 & 7 U% "% " "CC ICC "A
%$ %"7V, 5 + + %5CF%C "5C#A
" '# & %7 7; 5 ( ( &""5CF%C
% "% FD" H''#" "5C#, 5"" 5 - -
%5CF%C " 5 "5C#, 6&7FD %$% A
C%C 6"C " 5 "5C# H5 ; &5""
&" "5B, 5 % "C 3 3 "56"%C % ""
"D " 5 "5C# % H57 "65B % "C
&""%5"%C "EFD$ 5; 7 &7"%C "E""
5 %G5 %5,
"5 " %%7"G 5G7 7I "56 B A
E 6 "% 7"5FD &G77 &" [Kf[^ 5
Z[Kr[h,
$ $ $ $
%&
'(
'(
44
15G'"%$ %&%
+,& " / ! ", $a ,8 ; +02-, -+( %,
(, @a &"%" 7" %& $ G'6
U%%5" " IFD"$ %" % 7"% %%% "
%& "75V, " 8 7; +02*, (2. %,
-,bei%&i"C 7 7%G 5"C &A
" %"%" %G5, " 8 7; +02(, (32 %,
4*
), *(+,-2-,-
b
" # #
FC %%"7 "5F"C &"6" 5C 56 A
IFD"$ % &CC % "% FD"G "E"C, I" %A
%7 "%C & %"6 I"5C %%"7" "5FA
"C; &"6"$ 5C H5G"%G 5C 6 "'C7 6GA
C6"C7 $ & "%, 6I"" $ & "% &A
5" % &7DBF # "G A,
7 6 % &6 ; $ &6 5C" 5B 6A
I"" "'C$ &5" IFD"$ $ & "%; C 5C"%C
5" # " 6I" "'C$ &5" "G "6"5B"
&C 5"" $ & "%, 6 "%; # "" 6I""
C 5C"%C "7 %% 6 " 7&" 8 ; ; R %$;
6"5"$ %$ % "% ",
%"G7"# 6I"$ "'C &C" "E5%B C"
, 7"" Q+S; # "6%" %G5 UR!V U R!V; G"
! R %G5 C%; 7%75B '7 %"5B &6A
; 5FD "'CF &5" $ & "%, 5C $
& "% R Y B Y− ≈ − ; 5C "'CG &C R Y B Y− ≠ − , "A
Q+; (S %"G7"#C "'CG &C "E" % %A
"7 &"; $ &%5" I"C &C %$%
67""" "G # " " "%,
7"%G I"C " 7""" 5B, I"
"E"%C &%% " &6 UR!V U R!V,
T "6%" 6I"C 1( )R Yx x− = r 2 ( )B Yx x− = r ; 6A
" ; &"% 7 "
21 2 0( ) [ ( ), ( )] ( ) ( ) ( ) ; x x R R= = + + ∈ ⊃x r r r S r n r n r r ; U+V
G" 1 2( ) ( ( ), ( ))S S=S r r r R %G5 "'C$ &5"; %%7 "A
7" &D"C % %"5B ' $ & "%
1 2( ) ( ( ), ( ))n n=n r r r # "6% 5 U R !V U R !V9
0 0 01 2( ) ( ( ), ( ))n n=n r r r R E7; IFD$ "6"5B" # " "
4.
'5# ' $ & "%; I" %%7 "7$ "A
5$,
) C %%"%F "6 %7%B # "6% %&"A
5B 7&" 6I"C; 6&E"7 '#5 & &A
C 7&"G 6I"C
2
1
22 2
0 1
( / ) ( )
2exp [ ( ( ) ( ) ( ) ) ],
R i Ri
i i ii R
p p x
k x S n dN
−
=
Θ = =
= − − −
∏
∑ ∫
x
r r r r U(V
G" 0N R %&"5BC &5%B # " '5#$ ' # "A
6% 59 .(R &%C$ H''#"9 Θ R " "A
6 "% &7" ; $ 5F" %"C "6 "%$ '
$ & "% 1 2( ) ( ( ), ( ))n n=n r r r "6 "%$ %G5
1 2( ) ( ( ), ( ))S S=S r r r 8 ( ) ( ) ( ).Θ = = +m r n r S r"7"$% %&""5"$ "G 6I"C 67
( / ) : Rp Θ Θ∈Ωx , U-V
!7""%" &%% Ω %% 6 &%% GA
" '#$ 1( )m r 2 ( )m r 8
1 2 ( ), ( ) mm m LΩ = ∈r r , U3V
I"C "'C$ &5" %'75"7 & "
%5I G&"6 +< +
+8
0 1 2 o
1 1 2 1
: ( ) ( ) ;
: ( ) ( ) .m
m
H m m L
H m m L
Θ∈ = ∈ = ΩΘ∈ ≠ ∈ = Ω
r r
r r U4V
5C "E"C 6 %&5B6"%C &#& % Q-S; A
$ % &"% 5" &$ "&""5"% " "A
G &"6 C 6 G&& 7 7,
! 6"$% "7 &"6 $ &% 67""" &7"A
%G %"7"$% %&""5"$; , ", &"6 " A
#" &7""%" &%% Ω "" &"6 "
, %5 % &%B %% 5C" G&& 8 g G= ; g G∗ ∗= "%B
I" G&& Q-S,
42
5C &7""C &#& % 6" I"C "A
7 &5"" %5"FD %5 $ Q-; 3S8
+, "7"$% %&""5"$ ( / ) : Rp Θ Θ∈Ωx 5" % $A
% 7 %77" %"5B G&& ; ,", I7 H5"7" g G∈
o $"%C $ H5"7"
,; g∗ Θ ∈Ω
( / ) ( / )
R
R RR
gp g g p∗
∂Θ × = Θ∂
xx x
x; U*V
G"
R
R
g∂∂
xx
R 7# ,
(, # C G&& o &"6 $
, &%% Ω %A
C" G&"6 +< +
+8 ; 0,1ig i∗ Θ ∈Ω = 5C %" iΘ∈Ω g G∗ ∗∈ ,
!""C "E"F &% 5"$ 6; 7"7; &"6A
C % G
1( ) ( ) ( ) ; ( ) ( ) ; ( ) ;
1g L R∆
= − ∆ ∆ = ∆ ∆ ∈ ∈
x r x r r r r r r ; U.V
G" ∆ R &%% G" '#$ % 6"C7
U ; V−∞ ∞ ; &% FD"" %F &F "&""5"%B A
%"5B ', " &6B; % &%B 5" C"
%5 C7 G&&, P G&& #" &7""%" &%A
% Ω G&& o &"6 $
1
2
( ) 1( ) ( ) .
( ) 1
mg
m∗
Θ = + ∆
rr r
r U2V
! H7 " & "B &5"" %5 C %77" U*V
%"7"$% %&""5"$ U-V; U3V %"5B G&& ; #A
C G&& %C" G&"6 +< +
+; &""5C"7" 6 U4V 5C
%" iΘ∈Ω g G∗ ∗∈ , 7 67; &5" "7" %5A
C; " &6 5CF $ 6" &7"B &#& A
%,
5"FD7 EG7 "E"C 6 C 5C"%C &""5"" 7%A
75B UV G&& o Q3S,
%%7 "77 &7"" %%
1 2[ ( )] ( ) ( )z x x= −x r r r U0V
C 5C"%C G&& &"6 $ % G U.V,
40
# $ G&& o "
1 2( ) ( ) ( )z m m mΘ = ∆ = −r r r , U+<V
"7; %5"C 7 7"; 6 I"C %'7A
5"7 & " G&"6 %"5B G&& o
0 0 1 1: ( ) 0 ; , : ( ) 0 z zH m H m∆ = = Ω ∆ ≠ = Ωr r ,
G '#5 & &C "
22( / ) exp [ ( ) ( )]R z
o R
p z k z m dN
Θ = − − ∆
∫ r r r , U++V
5G7 &CC "E"C 7 6 % "C 5G'7 A
E"C & &C 5C % &G7, ) C; G&"6
1H %"5B zΘ C 5C"%C %"$; % "" % "A
% % ""7 "$7A!% %D"% 5C"%C % 7C &A
G7 p+ p
(
2 1( / 0)
( ) ln ln ( ),( / 0)z
R z
R z
p zc l c
p zΘΘ ≠α < = < αΘ = U+(V
G" α R "C%B 5I$ " G,!% 5CC U0V; U+<V; U++V U+(V &57 & 5 &CC "E"A
C
1 2 1[ ( ) ( )] ( )R
x x m d c− ∆ >∫ r r r r , U+-V
!5"" "EFD"" & 5 C 5C"%C 7; 7"A
5"" 7D7 "%7"D"7 Q3S; , ", &75B7 5%%"
"EFD & 5, '7#C "% $ 'A
# ( )m∆ r %% "; "" #"5"%6 67"B "%F;
,", &CB $ m const∆ = ,
%, + ( &6 P "5BG 6I"C
$ & "%; %"ID"G "'CF &5"; % "% %
5G77 U+-V, %, + %"I # "6%" 6I"C U!V
U%5" V U !V U%& V, %, ( &6 %" # "" 6A
I"" % 7C "'C7 &C7 U%5" V "65B "G
U%& V; " "G5B$; 5G7" U+-V; 5C IG H5"A
7" 6I"C,
*<
"65B H%&"7" & "IF 67I%B %&5B6 A
C # " G &6 R Y B Y− ≠ − 5C 7"%G I"A
C "'C &C" $ & "%,
15G'"%$ %&%
+, 76 " A%%"7 &" G
5C & "%"$ // " & ; <(00<<<-2-0 /
!:)!, !,; +002, , *(R.<,
(, B&\a G%&"5BC " C %%A
"7 I"C 67""C &7" N" // 6 "%C 6
%%, H5", +002, &,+, f, 4<R43,
-, q! " %%"% G&"6, ,8 ; +0.0, -3+ %,
3, b&rb """%C %%, ,8 ; +0.2, 4*< %,
*+
) *(+,-0.
*a''& a*S()&
-
% "% % I"C G" & "7%A
& E"C ""%$ %D"% 5FD %5I,
5#" 67""5 %%; "GFD" 5EB A
5"" % ID""%C %&" %"% &"; 7G
B 5"G I" 7 " &6 5CF 7"A
B "65B 67""$, !%5B "5" 6C %%"7
UV C 5C"%C &%% $; "" %5I IB, 5C "" %A
" ""%C % B I" &" U 5" "A
" % $ 7$ '"67V, 7" HG; %A
% 7 C 5C"%C %C '7 %B; C &6 A
5C" '% B DF IF % ; 7"$ 6
5# "5CAE"5C; "'# B %&" %"A
% ; &5B 6B %% I & , %A
% 5EB 7; 6 5"B H " % &7DBF #' $
"5" 6G %G5, %"% 67""C
5F %$ 6"EFD"$ %&%%BF 5BE$ &" A
%BF,
! &" %%"7 5C IG I"C IA
"%&"B %F % "%B &5"$ '7#; &"A
%B 67I%B 6 C 6 %" % %5 55BA
%%"7 % "E"% C &G77G "%&""C, %A
B" %IF%C "5" 6" 7" 5C %& &A
&"#6 67""$ &7" I"C %&A
%"% ; I" 5%%'# 7" C, "A
65B %%5" $ 7G B &7"" I"5"6I7
7 %&"; 5C 5C 6E$ % 6"
H& ,
"5" 6" %%"7 76 G 5C %&A
& U !V 5FF %"C 5 "%5B "5"A
7"; %&CI" % %5"5B$ %%"7$; 7G "EB %5"A
FD" 68
*(
67""C %% I"C %& %"% ; 7 %5"
&"; % '%#"$ E"5"$ %%G "I79
7" C 6I"$ E"5"$ & 5 IG A
I"C U6&%B %I7 " 6I"C %&G %"% ;
7"G 6 5# "5CV9
%% IG I"C % 5%%'#"$ %&
%"% & &67 UG7; &7; # " ,V9
'%#C 6I"$ "E"G 7" 6 &"6IFA
D"G ""6 5B$ &% %& #C %I7 "
&7C 7&BF" 5 "7G',
"%G5 % "5"7" F %5"5" % #"5BF
S(c[ N" & 5 ' %% " E7 9 5C
Z\[ &5"6 7"EFD N" %&5B6F % &%B
&6 , " H%&5# %%"7 ! &&% N"
"&%7; %" 5I" " G $" "I"5"5B;
%IF % "%B &C "E"$, )5E"" %E"C
7"I "C%C7 & 5BG I"C N" 5I$ "A
G %G"%C 6 %" " &$ '7# % &%
&6 ; 5FD &5"6$ 7"EFD" N", I 7"A
B %5"FD" "" &68
7&5$ &6 P; 5FD$ N" IFD"G '9
67"$ &6 O; "6FD$ G"7""%" 67"
N" 6 5%% 9
$ &6 <; &6 5CFD$ 5B N" 6
5%% & %&5I"F 6"7$ & "%9
"$ &6 M; &6 5CFD$ &6"5B N" & &A
5"I% " I"C9
%%$ &6 N ,
%B "56# 5G7 %&6 C % C6 % GA
""7 '7#F &6 "5B%B %5"5B
%"% ; %&5B6 5 67""5"$ &6 , P %A
"%B & 7; %5 "7 %G5 &A
7" 5 65"C 5I B G", ! H7 7&5A
7 5" UI"5"V "7 56 B %F 'A
7#F; &%&FDF % A , 67""5 &6
%5"" & B I" &"I"F '7#F; &E"EF ""6
7&5$ 5, C 67"G 5 "G;
*-
%5 %5"5B &"#$ 6%"; &H7 5C 5B"$E"G
&"I C "7$ '7# I"5"5B 5FB
&%5" "5B, '7#C 7 "7 5
6"5B$ %"&" I" &"I" 7I" B
&%5" "5B; &55"5B Q+S,
!%5" I"C ID"G%C N" &5" 6"C "5"7"
"EF%C 6 67""C "G %%, %5 67""A
C %%B E&" E" &G " 6"" E&
; &7"%C "E"A
" '%# 6I"C %&G %"% , 5 6A
7I "'# B 7"$ 6 5%B "5C; 6A
I"" %5"" &B "6 &" 6"EFD"$ %&%% A
#" B,
%5"" h&n&g N" &%% " &6 5CA
F "% 7"; &"" 6I"C %GF 67"A
""7 '%G %%CC N" '5B$ "5"7" 5
&"7 %&5B6 C &5"5B$ 7", I$ %7 %A
IF %5I"$ '7#"$; %"ID"$ " "7C %N"7A
; 6"" %% ; & "7%; 77" &",
%6 E"; IF % 56F % &7DBF
5 5BE"G %5 7" U%, +V Q(S, N"C C
%%"7 Q!R & C6 '\@K[; RA
& 5" ", 5 H h_n_g_&h
snsg
s; ,,,; h
;
n;g; % 5 F #" 7"; % "A
*3
F N"7 &%% " & "" 7", h&
n& g "$ H$ %%"7" 7G B &""%
N"F Q&!&R ""6 7# '' &"6 $, A
5BE"" %&%"" 5C 6 7E$ G' &55 '#
##)#'&$ &6 5C" 6B %" &"A
6 $ U% G; & &"#V % &7DBF 7# .6A7"%BF 3×3; &5"$ &"7 &6 ""C 7# % &"A6 $ Q-S
Uh; n; g; +V W UQ; !; R; +V×Z9 UQ; !; R; +V W Uh; n; g; +V×ZR+,
I"C N" "EF 7"7 %% Q3S &"A
""% 5$ U%, +V; &CD ""6 '% 7" 3<+;
3<( 7" N" " '7E"C Q
++&!
++&Q
(+&!
(+, %5
6; " 6 F "5"; 7G 7"BE"; "7 H5"A
7" 65I"C, !%5" &" G I"C N" %A
C%C 6 "%7 5B % "% FD" 7 7" 6 :] "
7", "65B" 775B" %%C" 7"I 5C7 &A
"% G " " 5F; "B &% &""%"FA
%C 5 H 5 &%% " 7I 5EB &5I", "5B6C A
I" "&%"% " $ &""%""C 5$, !"A
5I" "EB H 6 "#7 7"7; &"7 B A
C " Q; !; R; &5"ID 7I"% " &" $
5; %" 5C I$ $ "" %%CC $ 5A
Q4S, ! &% % C%C 6 "%7 775B" %A
%C" 7"I 5C7 Wc`J
#"5 N"7 &%A
% " Q# ; !
# ; R
#, "E"" I" #"5 &7F & %5A
&5"C " "% Wc`J
ε, "" LL F %C 6
& 6 "% 775B 6A
7" %&G %"% G5A
G 6"E"C 5 I"C,
! 7 &" "C%B
& 5BG I"C N" A
&6 ""F 5G "CA
%"$ 5C " "5"7", 5C &A
E"C % "5B% %%"7
% 5 F 6" &G A
I"C; &%5" "G I$ 6 7"
% % 6F 5I"
*4
7" N" , ! &"5I"7 5G7 & "CF %" 6A
7I" %"C H 7" " 7" &A
7F "E"" I" #"5 5B %5" &5"C A
6G E" " "% , "65B" "6 %I"%C "C%B
5I$ " G; 7" #"5"$ F 5B %G5%A
6 Q*S,
"5 " &65; E"" "C%"$ & 5BG
I"C #"5 5I$ " G 5E"%C %""7 -- 6 &
% "F % %5"7 %% C '5B U%, (; '5B X <V, A
" I"$ #"5 " 67I%B " B N"A
; CD"%C 6 &""57 IG &5; &6"7"; 5C
g <, 5"" B I" G"" &
%"8 %&" %"% " 7I" B E" U3;4R4V 7" ,
"65B" &5"5B %I"%C "C%B 5I$ " G
GE %% 5C" 4( 6 U%7, %, (; '5B X +V, A
N" &%5" "5B% " 67I%B &%A
B "F "G &""7"D"C, )" G '; "C
I"C N" "&" ; &6 5C" "5B H E""
*0* 6 U%7, %, (; '5B X (V, "65B" &7""C 6
'5B #"5B "" I F & %" 6I"C
N" U+R(Vv; "%&" " 67I%B H%&5# %%A
"7 & &5 &G %5 C 6 % "D"%C,
""7C %B 67""C %% %% 5C" ≤ 4 7/% &6" 67""C %%"$ U3<R+-<V 7/%, &5"" HG "A
C 6 % &7" %%"7; 67" %&5A
I"" 7" 7"%%; G5 6; %5 6; " 6
, 5C &76# H &7" 5 &"&C 7E"
7"5 " %%"7,
"65B" 7"5 C
5 $"; 7%A
75B" E & 67""A
%% " &" EF
( 7/% 775B
&6" %%"$ .<
+<< 7/% U%, -V9 %""
E " E" + 7/%;
&5" 5" C"
&% 5"7 " A
4<
*<
.<
2<
0<
+<<
++<
+(<
+-<
)$&$*+
E; 7/%
%
**
C7, &75B" G5 6"C 7" %% 5CF ≈-<< 5C 7"
G 6 + ≈(<< 5C '5B$ 7" ( U%7, %, +V,$ 6 % 6; 6FD & 6 " 7GA
7"$ A%%"7; C 5C"%C C & C6 7" 7"%%
Q.S, %5FB "7" " 67""C #"A
H %%"7 U" %&5I"C 7"V; C G"
H%&"7" & &""5"F H % &% ^"A
6 %7 "&" ; 67"D" 7"%% % "% % &A
75B7 &57, "&" "5B6C %&5GB $ &5%%9
N"" Q+; !
+; R
+; ,,, ; Q
^; !
^; R
^ 5I B
6 "% "%&" B EF %5 5"%B "E"7$ 6A
9 %5 "&" 5BE" 5 %5 "6 "% &7"A
U^ ≥ *V, CD" 7# .+ ,,, .
; "6 "%" &7"
&""5CF % 7"% 5C ;7", ! F% " %%"7 &"A
&""5CF H" "&" h+.; n
+.; g
+.; ,,, ; h
^q; n
^q;
g^q %" 7"; &5" 6"C C%C, "7 &A
6 C %" & 65I"$ E" 7"" ; % "% A
FD "&"7 #"5"$ N"7 &%% ", "%&5I"C #"A
H %%"7 7" C " 776# & &7"A
7 Q<. ; !
<. ; R
<. #"5" $ '#
1
, min,M
i i i ii
r c r c=
− − =∑ U+V
G" /:W Uh
:; g
:;
:V R " N" "&" "9 0
: W
Uh#:; g
#:;
#:V R $" % "% FD 7 #"5"$9 G5A
" % z 6F %5C" &6 """,
%B & C6 7" 7"%% 5C" 6"EFDC %&A
%%B 7"; I"C; &7"; %5" %" H5"7"
U&%"5"$V ", %7%B E %5 %" A7"A
" &6 %, 3, 6 &5"$ "65B" 7EG 7"5A
C G%G77 ; & 5"G %I7$ 6"EFD"$
%&%% 7"; % "% FD"$ 65I"F (4* ×(2. H5"7"A ; &5F &5" &"75"7F %B8 E " &" E"
<;+4 7, ! % 5C %%"7 #' G "5" "C .<3 H5"A
7" & %" ""%%7 65I" 4.* %
E %I"%C <;<4 7,
*.
"5"5B %6B %5 67""$ 7"%% 777, %5
" " B &G 6C "&" GB%C 5EB
% 7"%7 67"""7 7" '7E"C "
7"; 6 "C" &""5"%B, 76#C #"5" $ '#
2
1 1
min,M N
kik k
d= =
=∑ ∑ U(V
%% 5"$ 6 %77 %%C$ 7"I %"7 &5"7
6 & 7"7 "&" '7E"C 7" " &% %A
&"; "5B"' #"5" $ '# 65" 55B7 H%"A
777; &% G55BG 777 $" 6"Q2S,
& %B &""5"%B 6 7"BEB %5 55BA
777 ; &"5I" &5"5B B N"" A
A" "&" " 776 B #"5" F 'A
#F; %% 5"F 6 7# I"$ U+V U(V, 7%B &A
#"%% 776# $ #"5" $ '# 6"5B$ %"&"
6 %C $ 5BG &5I"C &%A
% " &7" ; &H7 "7""%C %5"FD$ 5G7 %A
" 8 +V &" "5B & C C G" 67""C 7"%A
% 5 &""5CF & " N"" 7" %A
5 F % %&5I"9 (V % 5 F
7"%% "&" G &#"5 C & 7""7 &5;
× × × ×)**+
E; 7
&
*2
&"7 67"CF C P N"" C
"&" 9 -V "F 7" &#"5 C9 3V 67"CF
H" 7" %" "&" " 7"9 4V A
CF N"" 7" " 776# 7 A
$ #"5" $ '#, "65B" 7"5 C &5"; G5A
5B$ 777 7I" B $" &%5" %&% 6 ≥ (< 5B"; %&""5" & %5$7 6 A
%"5B 5BG &5I"C,
"65B" & "" %%5" $ &5" %" "7" A
"; &6 5CFD"" %B &75B" "5" 6" 67""5B"
%%"7 5C & E"C "6&%% I"C %& %"% ,
15G'"%$ %&%
+, b&" &a %&5B6 " 6A
% 6" I"C %G5 & 5 ' % 67I"A
7 "%C7 // , , 0AG %7&67 & &5"7" 6A
% '7# %%"7, ,8 6A ,; +02*,
, +(2R+-<,
(, G7"" "5" 6" " %%"A
7// " "5" "C, +00., X 2, , -<R--,
-, 'a&C% "7"C 7&BF"C G'A
, ,8 % C6B; +004, ((3 %,
3, "5" 6" %%"7 76 G A
5C %& & // "6, 5, *A$ 7"I, wA
!""G%$ "C7"x, !,; +00., , -3,
4, "5" 6" 7" "65B
%&$ 5""5B && // "5" ""; ""8 ,
, , / !:!, !,; +00*, , +(R+.,
*, a''*&@H&`(\(% ""
%&" "5"C ID%C N" "5" 67 7"A
7 // &""FD" "5" 6" %$% / !, ,;
+0.4, , +0R(-,
.,8:-/7&/3/:/O uJmaL LKLMc`K[K`eJ e_ [`Mja[JLY hg cbaK`\eMMLa[K`eJ
KL\]J`kbL l`K] ejK`c[a KM[^LAe__ YgJK]LK`\ ^`Y\M`c`J[JK _`aKLMY // tjK`\[a
Jm`JLLM`Jm, sbJL, +003, nea, --; X */+2(+, i, -3R3+,
2, 7"%C %$ "5" 6 %%A
"7 % &7DBF 7P, ,8 % C6B; +022, +*< %,
*0
) *(+,-0.
B&dt
1-#
6"EFDC %&%%B &"6 "5"$ 6I"$ &""A
5C"; "7 %""; %&%%B "5" 6$ %%"7 &""A
B %&6 B % 67 %7 7"5" "5 6A
I"C, % C6 % "7; &5"7 6"EFD"$ %&%% "5" A
6$ %%"7 %%C %5 I"$E; &""5CFD 6
G5 7&" "% "5" 6G 6I"C; & ""
'7"5B" %%5" C 7G%5"" &5" A
H$ 5% Q+S, 7"%" % H7; % " 7" %%5" "A
5"$ %%"" "% &"" %"% U"&A
IV 6I"$, ; &% CD"" %"%C7 &""
7"% U& IV 6I"$; % C6 % 7 % 5A
67 C 5"$ "#%; %I"$ G"7" 'G7" 6A
I"C; %I"C7 # "&"" "6 G# & I
N" , ! E"" " $ "% '7"7 6A
I"$ #' "5" 6 %%"7 Q(S; I" """
%" &"6 "5"$ 6I"$ & 7# !; 'A
7# Q-S , , & "5 "7% & ""C 56
' ; &""5CFD 6"EFDF %&%%B &"6 "A
5"$ 6I"$ & &""" " 5B %"%; 7"%A
N" ,
67""" 6"EFD"$ %&%% %"% 6I"$
D" %"G & C & E 7 5#7; %"ID7 "5BA
" G65B" E; 7"FD" 65$ EG % &C7G5BA
7 5 %%5B7 &"%7 &'5"79 C" %5" %A
&5B6F 5#; 5FFD" 6 p""5C Q-S, 5C #" 6"A
EFD"$ %&%% &"6 "5"$ 6I"$ & &""" A
7"% N" 7 5 %&5B6 7"5B 6I"C; %A
"IDC 'G7" 5# % "5B7 E7 %%A
5BG &'5C, ! &"# "& IG 6I"C A
$ 5# %&""5"" % "D"% Guhv 5B % % U%
hV 7I &"% B
.<
( )0( ) 1 sin 2 lE x E f x= + π ; U+V
G" G< R %""" 6"" % "D"% 6I"C9 l
lnf l= ; 9
2 R
%5 w"A"5x E E 6I"C2
5C C 5"C % 67"%"$ %5F"C 5CC
&" %I"$ 7 %%7 5%B % 6%A
" E; " & C &"% +<<A&#"$ 7A
5C# %G5 & "& I7 6I",
"% " &"6 "5"$ 6I"C %CD"" "7C;
5 7"" E"; %&5B6F ""5B" 7# ! 5
'" 7# % 5"$$ "%$ &"6 C Q-S,
'7 " 7# %"" 6C " &" &"A
"%C%C 7 %$% % F%C; '7C A
" &%5" "5B%B 7&5B% %G5 6I"C; &BA
%"7 '# U+V % "% % $ %"$ 7A
#, "% " &7" %, + %"5B "#
( )max
1( ) s
s
i xh x i= &6 'G7" %G5; % "% FD$ "6
% h W <R(< H5"7" 6I"C; & &""" %"%$ EA
$ 5# % %$ E 32U<;-4< U 3<< 5V,
%%77 7"67 '7 C %G5 6I"C 5"$A
7 &"6 "5"7 & "&" 7 &""7"D" E $ A
5# %"5B % 7# % %%BF 5 & 5" h,
! 7 I" 5# %&""5"" % "D"% Guh&=v 5F$
77" "7" = " 7"B ( )0( , ) 1 sin 2 lE x t E f x t= + π + ν ;
, -
.+
'7"7$ %G5 6I"C :J 7I" B &"% 5" %5"FA
D7 67 Q+S8
( ) ( ) 10( , ) 1 2 cos2 cos2 ,s c l c l l ci x t I f t f x f x t
−= + π ν π − π + ν U(V
G" =p R "7C &5"C U % &"6 "5C 7#
! 7I" 67"CB%C &""5 <R<;<3 %V,
E"" U(V "" 6B %"5B "#
( ) ( ) 1( , ) 1 2 cos2 cos2 .c l c l l ch x t f t f x f x t−= + π ν π − π + ν U-V
" % "5B7 H5"7"7 7# !; &5" %A
" ' % $% " "#%B U%5 5" %A
7 6C7 &"5B H5"7" &%5" 6 "E"C &#"%%
&""%V, "#%B &"6 "5C 6I"C; &6A
" 56; 7I" I" "% 67"$ 5 %I"" "5BA
% 6I"C, %"5BC "5 %G5; '7"7G
&"6 "5"7; %%7 "77 %5" &"" E $ A
5# 7I" B &""5";
( )
( ) ( )
'' '0 0
' ''0 0
( , ) 1 sin 2 sin 2
1 sin 2 2 .
c l l c
l c
h x t f x f x t
f x t
= + ξ π + ξ π + ν ++ − ξ − ξ π + ν
G" 0 0,′ ′′ξ ξ R "#%B &"6 "5C &" 7 7 "
% "% " U 7# ! 7I" %% 5CB +;<vV,
15 %%7" &#" '7 C %G5 65A
"I7 &"6 "5C, %5 75% "5 00 ,ξξ ′′′"#%B &"6 "5C & "" I" %" "
5%B, %, ( &6 GFD" %G5 Xuhv 5C
32U<;-4< U 3<< 5V; =
pW <;<3 % & 65 %%C I"A
C %&"5B$ 5#8 X_uhv R 5U+< H5/% U%%B; %A
"% FDC %7"D"F 'G7" 5# %F E %A
2 6 "7C ∆=2W .* %V9 Xsuhv R 5U.4 H5/% U∆=
2W +< %V9 Xwuhv R
5U+4< H5/% U∆=2W 4 %V, 6 G' ; %5"% " "&"A
% &#"%% &5"C & "5" %% I"A
C 5# &% %D"% "" 7"BE"F G5 7A
5C# %G5,
.(
"&"B 5CC I"C '7 %G5 6I"C & %A
% 5U.4 H5/% 65 % E $ 5# 55F%A
" %, -; G" Xsuhv% "% " %" 32 W <;-4< U 3<< 5V9Xxuhv
32W <;+.4 U(<< 5V9Xyuhv3
2W <;<2. U+<< 5V,
D"" "7" &5"C; %5"" 6 I"C U-V; 5IA
& "% & E"F G5 75C# 7"5 "5C IA
D%C 'G7" 6I"C, 5C" "7" &5"C G5
75C# %G5 6I"C & 3: W <;-4< U 3<< 5V; 5U .4 H5/% 55FA
%F G' %, 3; G" &6 GFD" %G5 ; % "A
% FD 3<< 5, %" 6"8 X(uhv=pW <;<3 %; X(uhv=
pW
W <;<( %; X.uhv=pW <;<<3 %, 6 G' ; "%C" 7"BA
,-
,-
,-
%
,-
,-
,-
.-
E"" "7" &5"C & E"C %7 &
%%7 "7 %5 C &"% +<<A&#"$ G5" 7A
5C#, )6" % $% &"5"$ %G5 6I"C EA
%&5B6F%C &'"%%5B$ 5F"5B%$ &&",
%"% " %5"" %B%C % %D"% "7 7"BE""7 % A
"5B% "7" H %5 C %N"7,
15"" &5" &"% 5"" "% &"6 "5C
F 6 %7% G5 75C# P]%G5 6I"C EA
$ 5# %% "" &""7"D"C 5; "7" &5"C =p;
% E 32
( ) ( ) ( ), , 0,5 max , , min , ,j c l c l c lA v t f h v t f h v t f= − ,
%, 4 & "" 6 %7% G5 75C# P] %%
U5U_z: H5/%V 5C 65$ % E 5#8 P_]3U <;-4<
U 3<< 5V; Ps]3U <;+.4 U(<< 5V; Pw
]3U <<2. U+<< 5V,
%7% G5 75C# P]%G5 6I"C E $
5# % 3U <;-4< U 3<< 5V %% U5U_z: H5/%V 5C 65A
&
,-
,-
,-
x0 5 1 0 1 5 2 0
0
1
2
'
.3
G "7" &5"C Px]=
pW <;<3 \;Py
]=
pW <;<( \;P
]=
pW W <;<<3 \
& "" %, *,
; & &""" E % %$ 3U <;-4< U 3<< 5V
&% &5" %"6 "" &5"6$ 75C# %G5 & %A
% I"C55# 5 4+ H5/%, 5"% "7 5B"$E"G "A
5"C %%; 6 G'; C 5C"%C &C 5"" %G5"
6I"C 5I 7&", D"" "7" &5"C U&A
"7 & 5"C 7#"$ !V %D"% " 5E" "%A
"% ID%C 'G7" 6I"C,
!5"" "65B F 5"% "F #" 5F"77
C 5"C7, 15BE" 7"; " "5C"%C %CD"" "7C
"% &"" 7"% 6I"$ #' "5" 6A
%%"7; & "5 6" 7"% "5" 6 %A
&"5B 5# %&"#5B 7" 67""$; &7"; M/J=
N,W|^'7 L9/22~0:2p1h Q3S,
65F"" "7 %"5B %5"FD" 8
+, "65B" & "" %%5" $ 7"67 '7 A
C %G5 &"6 "5C7 6I"$ 6" ! "I7"
&"" ID%C 'G7" % 5" 5"% "C % C6B
6"EFD"$ %&%% &"6 "5C % "G &"%7 H5"A
"%7 "I77 U%E"C (; -V,
(, %%5" C 6 %7% G5 75C# %G5 6A
I"C %% ID%C 'G7" "7" &5"C &"A
6 "5C &6 5CF % B "I7 "G UGA
' %, 4;*V,
(
.4
15G'"%$ %&%
+, B """%" % "5" "C, !,8 6A
wBx; +002, ((2 %,
(,, T' " "5" "" / !:)!, !,; +002,
30 %,
-, !"6 "5 6I"C ! / B&aa$K
'& '@&Ha q"e#' ,8 % C6B; +00(, +23 %,
3,0,22,9WO iM[\K`\[a L\]J`kbLY _eM Z[`JK[`J`Jm K]L b[a`Kg e_ `m`K[a
M[JYc`YY`eJ >gYKLcY // ]L `MYK feJ_, u^d[J\LY [J^ bKbML LdLaejcLJK
e_ f[haL [J^ >[KLaa`KL n, Z, (3R(. LhM,; +000, , *+R*(,
.*
) *(+,-0.,.8*2+,.,<+-,2
CK"&CaC
1 " !!$ # !! ,
56 67I%"$ 75B&5 G 5G7 Q+S; & "A
"$ % "% % 6 "%7 7"7 Q(S; &65;
$ % "$ 5G7 " 5" C" " C7; A
G"77 ""$ "% " 5B &"%&" ; 7"FA
D%C $ 77" """% %%"7 UV, ; A
&7"; 7%75BC &G"E%B 5G7 5% %G
"G5BG "% 6I"C 7I" %GB -<v %"$
E5 #",
!& & %B %B 75B&5 G 5G7 &A
"5 "G 7'#C7 Q-S; 67" H''" & H7
" &5",
T"5BF %CD"$ C 5C"%C & E"" % 75BA
&5 G 5G7 6 &""5"C "G "G5BA
G "% """% %%"7, "7%B "E"C
H$ &5"7 % C6 % I"%""7 " $ 7""%A
7 "%&""F " "% H''" % % C6 %
6%FD7 &"%C7 &; %5 5"7
%"7"5B7 6 "7 " "5G$,
7 6 67I %&% &"5"C 6G "%
C 5C"%C 7"6#C 75B&5 G 5G7,
" 7"6# "F 6 G; 6 %7%B &G"EA
% 7" &G "G5BG "% `
7""
$; 5"$ % `
&""%"FD"$ H %B "$
" Q+S,
T"5BF 7"6# 75B&5 G 5G7 C 5C"%C 6A
7I%B & 5CB E"6$ 6 %7%BF; 7"8 &""A
7"DB & % `
5" F &6" < ≤ `
≤ +,"5B H 7I %5"FD7 678
+, "% '75 75B&5 G 5G7 &%CF
%% 5CFDF < ≤ ≤ +,
..
(, )7IB %F % " "5 U+RV; #"
`
" 5 6 &""5 7%75B &%7G,
-, 6 "% %"&"B ν %" &6"5 "% `:;
7I 5 & 5CB 57 6 %7% &G"E% 7"
"G5BG "% `
5CB &5I"" 5" $
G',
! &"5G"77 7"" % "E"% C '75 7"A
6 G 75B&5 G 5G7 G5C %5"FD7 A
678
1
(1 )m
ii
P ν
== + − ∏ ;
G" `
R 7 $ "G5B$ &6"5B "% 6I"A
C " """%$ %%"79 `: R 7 $ %A
$ &6"5B "% 9 : R 7" %G &6"5C9 6 R %5
% &6"5"$9 R "FDC 9 ν R "FA
D$ &6"5B %"&",
"% " &$ 7"7"%$ 7"5 "G5BG &A
6"5C "% ; '$ &57 G &A
C; &5"$ 7G7"$ &&%7#"$ "65B 7A
G7" H%&"6 "% 6I"C " ""A
"%$ %%"7; & "" & %75F G7" ; &6 A
5C" %%5" B &6"5 "% 75B&5 G 5GA
7 %"7 &6" "G5B #" "% 5F$ A
" HG &6, ! """ %%5" C &65; "65BA
56 75B&5 G 5G7 "6"5B 6 %C
& &57 G7" "G5BG "% , "A
%5B 7"BEC %5B%B "65B %%5" $ 5FA
"7C & 67"" %5 ' &$ 7"7"%$ 7"A
5 "G5BG &6"5C "% 7I" B %" &"7
&&G ""%G N""C % #",
'@[ #ZK[ ('@'e e' A
%7% %" &G"E%"$ 7"6 75B&5 A
5G7 UpW <; ν W d[MV ∆`%U`
V; %%" % "%
% 6 "%$ 7"$ Q(S; 5C 65 6"$ &6"5C %"&"
ν; &"% 5" %, +,
.2
5, + & "" 6"C %" &G"E%"$ ∆`% 7"A
6#$ 7" $ &6 %%5" C,
SK _
'
.
.
.
.
.
∆ ν /
.0
7%C ""7 67I% %&5B6 C 75B&5 A
G 5G7 6 #" "G5BG "% 6I"C
∆ %
≤ <;<4,
&6 "G5B #"; 7"6 $
75B&5 $ 5G7 UpW <;ν W d[MV 7I" %&5B6 B%C %AG5% 7 "F; & "" 5, (,
SKs
%@K[#ZK[('@'ee'
56 A7"6#$ UpW d[M; ν W +V 5G7 %D"% 5C"%C
5G E"& ""7 56 νA7"6#$, %7% %" &G"E%"$ 7"6 G 75B&5A
G 5G7 UpW d[M; ν W +V ∆`%U`
V 5C 65 6"$
&6"5C ; &"% 5" %, (, 5,- & "" 6"C
%" &G"E%"$ ∆`% 7"6 G 7" $ A
&6 %%5" C,
SKw
+' ν
,-
./ / /
/
/
/
/
/
2<
&6 "G5B #"; 7"6 $ 7"A
UW d[M; ν W +V 7I" %&5B6 B%C 6 #" "G"G5BG "% %G5% 7 "F U∆ `
% ≤ <;<4V;
& "" 5,3,
SKx
56 % 7"6 75B&5 5GA
7 &65; &"5I"$ 7" "# % H''"A
",
"6 " 5G7 U W <; ν W d[MV 6 &""5"AC "G "G5BG "% 7G %&5B6 B%C8
& 3 ≥ ν ≥ + R 5% 6 #"9& + z ν ≥ <;4 R 5% %" #"9& ν <;4 R 5% % #",
∆
' .
.
.
.
.
.
.
.
/'
2+
"6 " 5G7 Uν W +; pW d[MV 6 &""5"AC "G "% 7G %&5B6 B%C8
& W <R<;+ 5% 6 "G5B #"9
& W <;+R<;3 5% %" "G5B #"9
&z <;3 R 5% % #",
IC 6 7"6#$ 75B&5 G 5G7 & W d[M
ν W d[M "%&" " H''" " & E"" % 7" 5EB
% &6 "G5B #" "% , !H7 5C %&5BA
6 C 5G7 $ 5 $ 5% "G5BG "% 6A
I"C "7 &""5CB &75B" 5C H$ 5% &6A
"5 7"6# ν %% B %F "G5BF #"A
"% 6I"C % "% % '75$ U+V,
5B"$EC 7 & 5" 5I B #"5"
%%5" " 7 $ 7"6# 75B&5 G 5A
G7 6 7" "" &"%G &7""C 6A
&""5"C "G5BG "% % "7" &"%&" A
"""% %%"7,
15G'"%$ %&%
_K"C&CCa 56 7" "G5B$ #"
"% %&6 CD % $% """% %%"7 / !:),
+000, "&, p, X +4<AA02, +<* %,
sK"C&CCa, " %%5" C 7"
"G5B$ #" "% %&6 CD % $% 65BA
%%"7 / !:), +000, "&, p, X +30AA02,
4< %,
-,%Z$, "% # " "5" 6 6I"$, ,8
% C6B; +022, ((3 %,
2(
) *(+,-0.
a*S()
-! $
"% A6I"C 6"5B$ 7"" &""5C"%C %$A
$ " 6 "B" A%%"7 R A&"7 , 5C & E"C
"% %$ A&"7 "7 "EB 6 N"A
$ #" "G "% " &6"5"$, P &6 58
"56 B %&5E$ 5B %"'#F IG &%"A
7G 6"5C %5 C "$"G &6 % 9
%6B 67F 7"%F %%"7 w%$ R 67""A
"x 5C A&"7 E"%G &5"C % %%"7$ E$; %A
&$ P,
7 "E"C &% 5" 6 &"5I" 7" 7A
"%G #" C % &7" A&"7; % $
D"7 " "% %&6 ""C " G5 7"I
"7 H5G '"%G 6I"C Q+S, "$ "A
% %&6 ""C '756 " &" &%% "A
$ % " &"% &
/ 2 / 2
/ 2 / 2
( , ) ( , ) ,h b
h b
k U x y U x y dxdy− −
= ∫ ∫ U+V
G" X R % H; V R E H,
&&$ "56#"$ "C C 5C"%C &"%$ 5 % 'A
H5""%7 &"6 "5"7, % %G5 4 R 6I"A
" H" A&"7; % %G5 4H R H5" 6A
I"" "G ", " $ &; 6 $ "% 7 6I"A
"7 H" A&"7; '%"%C N" 7 "G ",
"65BFD$ % " $ & 6 "G 7 &"% 5C" %$ "A
65B &""7I"C "5BG H5G 6I"$,
5C & ""C 67""$ &7"" 7&"%#$ 7" % A
% "7$ 7"5BF Q(S , p6"%$ 7"5BF C 5C"%C & 5C"A
7$ G"" H5G %G5 U):PV; &6 5CFD$ B A
7 " %IFD" %G5 H5$ %G5, %5"% " A
%% C 67I% 67"CB H5" 6I""; &5""
2-
" %5$; 67""C & C & %5"FD"$ %"7", P5$
%G5; % ""7 "G %IFD7 %G57; &"%C A
&"7; &""5C"%C %"&"B % &"C 6I"C H"
A&"7 "% G 6I"C "G " %G5% '75"
U+V, !7" 7G H5$ %G5 %IFD"G %G5
&F%C ; B%C 7%75BG % &"C 6A
I"C H" A&"7 "% G 6I"C "G ",
77" 7%75BG % &"C &7" 7 %IFA
D %G5 C 5CF%C #"7 &7" %IFD %G5
A&"7,
C %"7 %%"7 67""C % %I"$ &A
"" %, +,
%5"% " G"% "&" % %IFD %GA
5 &""5 % 7"5B %IFD"G %G5 7I" B &"A
% 5" " 65I"C C & %%"7" 6% '#$
0
( , , ) ( , ), , ,k
j j ij ii
=
α = α Φ =∑6"%B .R 67"%B 6%9 p
:Uh;nV R 6%" '#9 α
:]R &A
7" 7"5,
0"1&$
234) 4"5 6 7 &
81
9$&+$:
&& 7
;
<$
=+$:$&&&
23
" %B 7"5 &% "" 5B"$E"G %&5B6 C "%A
&" "%C &7"""7 &575BG 6%; &% &&A
$ "56# 67""$ R %&5B6 "7 7&5B%G 6%,
5C %G5% C H &5I"$ 67""C & C 7&5B%7
6%"; 6"7 &""5CF &7" 7"5"$ %IFD %G5
&575B7 6%",
2 30 1 2 3 4
2 3 2 25 6 7 8 9
( , , )
, , .
j j j j j j j
j j j j j
y y xy xy x y j
α = α + α + α + α + α +
α + α + α + α + α =
"65B7 67""$; & "" 7&5B%7 6%"; C 5CA
F%C " ∆h; ∆n 6"$ %IFD %G5 CeUh;n;α
eV; C
Uh;n;α
SV
; %,
7 67; 6 "%8 Uh:;n:V; : W +R+* " %;
& 5%B 67""C9 ∆h; ∆n R 6"C %IFD"G %GA
5 H ; C 5CFD"%C %5$7 "579 6 %A
7% %IFD"G %G5 % U(V, "A
7 #"B &7" H$ 6 %7%, !% 5"C 6 &"A
% 5C" %$ 6 "G"%%G 56; %'75 F %5"A
FD7 678 & "% ""6 ; & "I" %5$7 EA
7 %" .A&7""%F & "%B U. R %5 H''#"A
&575B$ 7"5 %IFD %G5 V ; %7A
7 5"$ H%&"7"5B 5 775BA
$, "7 "G"%%G 56 " % R
&"; "5 %I"$ R 5; &57A
5BC 7"5B %IFD"G %G5 R "" "G"%%, ;
F "7 "EB R #" H''#" "G"%%,
"% " 7" #" C H''#" "G"%% %A
&5B6F 7" 7"BE UV Q-S; &6 5CFD$ &5B
#" H''#" "G"%%; & "56"%C %5 "
2
1
minN
ii=
ξ =∑ ;
G" ξ: R 6%B 7"I H%&"7"5B7 %5"7 & A
"F "G"%% 6""7 :A$ H%&"7"5B$ ",
7$ '7" &#" &5"C #" H''#" "GA
"%% %G5% 7""
24
0 1( ) ,t t−α = ∆X X X x U-V
G" 2 R 7# H''#" 5 "6 %7 &""7"; , ", 7A
# % H5"7"7 ,X (x , y )l j l j j= Φ 1.. , 1..j N l k= = 9 α< R " #"A
H''#" "G"%% U&7" 7"5V9 ∆h R " 6"A$ 5 U "5 %IFD"G %G5V,
&%$ 7" G" &5"" %%C"5B; "%7"D"A
H''" #" H''#" "G"%% %5"; "%5 &"A
C 5CF%C ""7 7 "57 5 "%5 "&"A
"5"%B &" " "5, & 7 %5" 6"C #"
&7" 7G 67" 5B%C "$% "5B "5,
"E"7C "G"%%C 6 7"" %D"% "F %"%B8
&" C 5CF%C %5$7 "57, P NC%C"%C %5"FA
D7 %"%C7 ""%$ "56# 67""$ " %,
P5C "5BC 6 %7%B 7"%&5I"C 5 "%&
"7" &6 %, (,
!%B =+;=(; ;=
; R ; &5"%C & B 67""A
C; 7 % "% F 6"C 1 2, ,.., x x x , G5%
7" 67""$ %IFD"G %G5; , ,.., Nx x x %A
∆
∆
∆
∆
∆
2*
7"DF % 7 1 2, ,.., x x x &"7 ""C "7" 6A
"I" H5$ %G5, &7"; 5C =3 6"C h
3 h
H3
% & & """ 6"I ∆=3; C & E W \eJYK " %A
"% B "5" %IFD"G %G5 G %I"C
∆h3 U∆h
W E
h∆=; G" E
hR 75BC %%B 6 "V, 67"""
7 67 6"" " % "% B " " =3; "
'4 4 4t t t= − ∆ ,
5" "5B; ; & C%C 67""C; %7"%C%C
%"5B &" 5BG &5I"C; &"7 "5 %7"D"$
"57 67"" %I"$, "5A
67"" %I"$ C 5CF%C %5$7 "5A
7; %5" "5B; "; & C%C 67"A
"C; C 5CF%C %5$7 "57,
%5" 6"5B$ "&""5"% & '%# &"
%&5B6"%C "#$ 7" Q3;4S #" &7" "G"%%
α, "#$ &#"%% %C %5"FD7 67 U& &%
&%"C "#$ %%7 "%C 5B %5$ #" &7"A
%IFD"G %G5 & G65 ( , , ) α V,
+, % 5CF %77
2 00 0 2 2
1
[ ( , , ) (1/ 2)*( )] ,N
i
i
S x =
= ∆ − α − ∇ ϖ∑ d
G" ( , , ) α R "" "G"%% U7"5B %IFD"G %G5V9
ix∆ R 5 :A$ "9 h:;n:R 6"C &" :A$ "9
0 2 ,i i−ϖ = σ G" 2
iσ R %&"%C "5 5 " Uh:;n:V9 2id R "A
#"5B 77" %5$G " Uh:;n:V9 2i∇ R "A
&6 "C "G"%%,
(, &""5CF 6"C α<e; & %G"%C 777 >
<,
-, !% F "5 21 0( )i ∇ α U 1i∇ R " &" &6A
"C "G"%%; & %" "% " &7" "GA
"%% "%C 6"C α<GV 2id ,
3, % 5CF %77
2 11 1 2 2
1
[ ( , , ) (1/ 2) *( )] ,N
i
i
S x =
= ∆ − α − ∇ ϖ∑ d
G" 1 2 2 1
1 1 0 2[ ( ( ) * )]i i i−ϖ = σ + ∇ α d ,
2.
4, &""5CF 6"C α+e; & %G"%C 777 L
+,
&"# -;3;4 & CF % "% " & α+e ; α
(e ,,
%5"C &"DF; "%5
( 1) ( 1)max ( ) / , 1..js j s j s j k− −α − α α ≤ γ = ;
G" JR 7" "#; γ R 6" 75" &5I"5B" %5,"C α
Je; 5C G &5C"%C H %5 "; &7F 6
#" "6 "% &7" 0α ,
D"% " "$; &6 5CFD$ &""5B $ 7" #"A
C &7" U 5 "#$ V %5"" %&5B6A
B 6 %7% "5 "&""5"% & '%# &"A
, %5 5C %" " &5C"%C %5 "
2 21 2max[( * ) / ] 1i i i
i∇ σ <<d
2 2 0max ( * ) /(2* ( , , )) 1i i i
∇ α <<d
5 5"" G
2 202
1
( , , )( ) * 1
L
jj ijj
d d
dx−
=
α σ <<∑ U3V
210
2 021
( , , )( ) * ( , , ) 1,
L
jj jj
d d
dx−
=
α α <<∑ U4V
G" R %5 &" 9 h:;n: R 6"C &" :A$ "9 2 jjd R
%&"%C ]AG &"; &7"CB "#$ 7" " "A
7%,
5C "G &#" #" C &7" "G"%A
% 5 & "" 56 %5$$ E &" 5
$" " U3V; U4V,
5$C E 5 U&" V 6"%C "65B"
5I"C % 5BEG %5 "6 %7 G G 'A
7"" 75B" %&""5""; %G5% #"5B$ &"A
"5B$ ""7",
5C IG 5 5 $" #" 7"7"%G IA
C %&"% & 7; &5"7 "65B" (+ H%&"A
22
7" & % 7"D"F H5G "5BG 6I"$ +*
% U& %" % %I"C +<vV,
"7 5 &5" 5C &" , "5 &"A
&""5" %G5% '757
0 0,j j j ji ii i i ix x x y y y= − ∆ = − ∆ 1 16, 1 21,i j= − = −
G" h<:;n
<:R &$ %" :A$ "9 ,j j
i ix y∆ ∆ R "5
5 U " %I"C & Q !V :A$ " %; &5A
"" "65B" ]RG 67""C9 ,j ji ix y R "5 &" ,
! &5"7 7 $" #" 7"7"%G IA
C %&"% 5C IG &"; 5C %" " 5 %A
% " U3V U4V, %75B" 6"" "C U3V %%A
58 5C ( , , ) α R <;<<(3(9 ( , , ) α R <;<<34, %75B"
6"" "C U4V %5C " 5"" 6− ,
% &5" 5 %"5 ; & 7"FA
D"7%C E"$ 6" %E" 7"I %&"%C7 &"
"57 &" &6 &7"7 7" A
G "G"%%G 56 U-V,
G5% &"5I"7 7"; & &""5" % %A
I"$ & &575B$ 7"5 %IFD %G5 "%&" A
"%C %5"FDC %B8 5C "%77" 6I"C R <;<+v; 5C
"5"$% R <;*v; 5C %5B %I"$ R <;+v 67"A
%,
15G'"%$ %&%
+, 7"%C %$ "5" 6 %%"7
% &7DBF 7P, ,8 % C6B; +022, +*< %,
(, q")% "5 " "'#C %%"7, ,8 ;
+0.+, (*3 %,
-, a"Z[a&BTC&$Iab, !5C %A
%, %%5" " 6 %7%"$, ,8 p% %%; +024,
32. %,
3, d# "C &75BG H%&"7" U &5 "
"G"%% H%&"7" V, ,8 :5, ", '6, 7, 5,; +0.+, -+( %,
4, [BC&\ &d# " "GA
"%%G 56 & 5 E &" &""7",
,8 ; +0.0, -3 %,