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8
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·
∖ tgm 984 tgm
7
( )9 :
3:.7:
<
∗ K 94 2 7jos3:.7: ∖ K ( <3 )94 P
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-; "
3 G
∃
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1
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∗ K 94 2 \ shm P
∃
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90
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4 … … … … .. ( 7)
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54.7
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y
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744 jos jos :4∖ 644 ΰ 9 4 ∗ K 94 2 744 x
ΰ9 ;<.:<9 ;<.:
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( )9 < 3
4
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4
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pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho cm ao# cnc# cnc# 1 y = lhgergig. lhgergig. Lca jucrpo ahfrc.
jos <4 ´ ∖ Kgj jos:4 ´ 9 4 … . (7) · ∀ Kx 94 2Kj# jos
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75
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7
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78;.694
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64+.-!/$!H.6
70
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x
9
4
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9
4
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q 9 ;6.884
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9
664.67M
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9
6.<6i
78
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4
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9
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64
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4
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67
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66
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76 scm;4
9
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6 scm;4 76 9 :4
4
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9
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9
4
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4.056:
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4
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4
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4
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4
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4
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4
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9
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6-8:. :a jgmlcagfro c#t< #o#tcmhlo por trc# jglcmg# quc #om jomjurrcmtc# cm 6-8:. :a ca pumto 4. &h ag kucrzg cm jglg jglcmg thcmc umg igemhtul lc H4 af, c*prc#c jglg kucrzg joio um cjto cjtorr jgrtc jgrtc#hgm #hgmo o y lctc lctcrihmc rihmc ag igem igemhtul htul y ao#
9
KG .u G
K G
9
H4
+ G jo# 34# + G jo# 34/6
-
+
Gscm34 +
-
+ -Gscm34/6
K G
9
{ 6-.-!# - !H.H + - G.b} af 1
KF
9
KF .uF
K F
9
H4
+ -G jo# 34# + -G jo# 34/6
-
+
Gscm34 +
Hb / +
-
+ -Gscm34/6
KF
9
{ -6-.-!# - !H.H + - G.b} af 1
KJ
9
KJ .uJ
K J 9 H4
+ -H/6
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-
+
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3<
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9
KG + KF
+
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K. 9 ( -!G.-b ) af 1 q 9 ,41 f 9 ,41 e 9 !-41
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KJ
9
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9
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cro #c #gfc por jomlhjhom lc aprofacig quc ) 2$!34af, glcig# quc(
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9
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9
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= tgifhcm( K.,
9
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9
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9
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9
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9
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9
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9
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9
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+ -. .GH6/6
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9
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9
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K
9
-
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4.H 4.H"36 "36 +
-
4.H!H6b / af
{ ".G# - --.6 + - -3.6b} af 1
4.GG44 g 9 H3. 1
jo# g
9
jo# f
9 -
jo# e
4.H"36 f 9 !3! 1
4.H!H6 e 9 !6- 1
9 -
:-<0. Lctcrihmc ag tcm#h'm lc#grroaaglg cm ao# jgfac# :-<0. Lctcrihmc jgfac# GF GF,, GJ y GL y GL quc quc #c rcquhcrc pgrg aoergr ca cquhahfrho lc ag jgng lc 344 af.
&oaujh'm( #cg ag kheurg !.
35
^
F
J K 6k t GF7k t
7k t 6k t
6k t
6k t
KGJ G
X
KGL U9:44 af
P Tgrg ags vcjtorcs !cr"gs#
olcio# c*prc#gr jglg kucrzg lca lhgergig jucrpo ahfrc io#trgmlo cm ag kheurg !, cm ag korig lc cjtor jgrtc#hgmg joio? K GF
9
( -6 - 4)h + (7 - 4) , + (6 ( 6 - 4)& KGF 6 4)6 + (6 - 4)6 ( -6 - 4) + (7 - 4)
6 7 6 9 - KGFh + KGF , + KGF& : : : ( -6 - 4)h + (-6 - 4) , + (7- 4)& 6 6 7 K GJ 9 KGJ KGJ h - KGJ , + KGJ & 9 6 6 6 : : ( -6 - 4) + (-6 - 4) + (7- 44)) : K GL
9
KGLh
!
R -:44 B Y af
9
pahjgmlo K
9
42
K GF + KGJ
+
KGL + ! 9 4
6 7 6 6 6 7 (- K GFh + KGF , + KGF & ) + (- KGJ h + KGJ , + KGJ & ) + KGLh + ( - :44& ) 9 4 : : : : : : 6 6 7 6 6 7 (- K GF - KGF + KGL )h + ( KGF - KGJ ) , + ( KGF + KGJ - :44)& 9 4 : : : : : :
:quhahfrgmlo ag# joipomcmtc# h, n, b. -
7
6 :
K GF
-
6 :
KGJ
+
K GL
9
6 K GF - K GJ 9 4 : : 6 7 K GF + K GJ - :44 9 4 : :
4
(7) (6) (:)
30
2c#oaujh'm lc ag# cjugjhomc# tcmcio#( K GF
9
:;4af
K GJ 9 704af K Gl
9
:;4af
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F J K 6k t GF7k t
7k t 6k t
6k t
6k t
KGJ G
X
KGL U
Tgrg ags vcjtorcs !cr"gs# olcio# c*prc#gr jglg kucrzg lca lhgergig joio ahfrc# quc #c iuc#trg cm ag kheurg !
38
K GF
9
(-6 - 4)h + (7 - 4) , + (6 ( 6 - 4)& KGF 6 4 ) 6 + ( 6 - 4) 6 (-6 - 4) + (7 - 4)
6 7 6 9 - KGFh + KGF , + KGF& : : : (-6 - 4)h + (-6 - 4) , + (7 - 4)& 6 6 7 K GJ 9 KGJ 9 KGJ h - KGJ , + KGJ & 6 6 : : 4) 6 (-6 - 4) + (-6 - 4) + (7 - 4) : K GL
9
KGLh
!
!&
9 -
pahjgmlo ag# jomlhjhomc# jomlhjhomc# lc cquhahfrho, #c thcmc. K
9
42
K GF + KGJ
+
KGL + ! 9 4
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0eugagmlo ao# joipomcmtc# h, n, b. -
6 :
K GF
-
6 :
KGJ
+
K GL
9
4
7
6 K GF - K GJ 9 4 : : 6 7 K GF + K GJ - :44 9 4 : :
(7) (6) (:)
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9
663af
K GJ 9 <34af K Gl 9 :53af
lomlc KGJ
9
663af
1
<34af iuc#trg `hp'tc#h# kuc jorrcjtg jorrcjtg
:-34. Lctcrihmc ag kucrzg mcjc#grhg cm jglg jgfac pgrg #o#tcmcr ag pagtgkorig lc 3"44af. Jom#hlcrc l 9 6 phc#.
;4
&oaujh'm( #cg ag #heuhcmtc kheurg( kheurg !.
6k t 3k t
:k t KGF
74k t
KGJ KGL
74k t
74k t
Tgrg aos vcjtorcs $c !cr"g# Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. !. :m #u korig cjtor jgrtc#hgmg joio #heuc(
;7
K GF
9
KGF (
K GJ
9
KGJ (
K GL
9
KGL (
) 9 4.:350KGFh - 4.6;0:KGF , - 4.08<
) 9 4.7007KGJh + 4.6066KGJ , - 4.8<45KGJ &
-
( -<)6 + 76 + (- 74)6
) 9 -4.:;80KGLh + 4.486<3KGL , - 4.86<3KGL&
K 9 { :344&} af
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho( K GF + KGJ
+
KGL + K 9 4
(4.:350 K GF + 4.7007KGJ
-
4.:;80KGL )h + (- 4.6;0:KGF + 4.6066KGJ
K
9
42
( 4.08<< K GF - 4.8<45KGJ
+ -
-
+
4.486<3KGL ) ,
4.86<3KGL + :344)& 9 4
0eugagmlo ao# joipomcmtc# h, n, b( 4.:350 K GF + 4.7007KGJ
4.:;80K GL
-
9
4
(7)
4.6;0: K GF + 4.6066 KGJ
+
4.486<3K GL
9
4.08<< K GF - 4.8<45 KGJ
-
4.86<3K GL
:344 9 4
-
+
4
( 6) (:)
2c#oahcmlo ag# 3 cjugjhomc# #c thcmc( th cmc( K GF
9
7:;8.38af 9 7:5&hp.
K GJ 9 5<<.7af 9 4.5<<&hp. K GL
9
754:.;6af 9 7.54&hp.
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;6
%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg( kheurg !.
K9:344 af ^ 7k t
X :k t KGF
KGJ KGL
74k t
74k t
74k t
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9
9
9
9
KGF (
<
6
( :)
+ -
6
( 74 )
+ -
: , - 74&
KGJ (
:
6
( 74)
+ -
6
6
) 9 4.605:KGJ , + 4.8350KGJ &
-
KGL (
( -< )
6
+
6
7
) 9 4.:350KGFh - 4.6;0:KGF , - 4.08<
( 74 )
+ -
6
) 9 -4.:;80KGLh + 4.486<3KGL , - 4.86<3KGL&
{ :344& } af
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
K
9
42
K GF + KGJ
+
KGL
+
K 9 4
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+ -
0eugagmlo ao# joipomcmtc# h, n, b( 4.:350 K GF
-
4.:;80K GL
9
4
(7)
4.6;0: K GF + 4.6066KGJ
+
4.486<3K GL
4.08<< K GF - 4.8350KGJ
-
4.86<3K GL + :344 9 4
-
9
4
( 6) (:)
2c#oahcmlo ag# 3 cjugjhomc# #c thcmc( th cmc(
;:
K GF
9
7<;5.<6af 9 7.<5&hp.
K GJ 9 87:.3:af 9 4.87<&hp. K GL
9
7<78.;8af 9 7.<6&hp.
:-36. Lctcrihmc ag kucrzg mcjc#grhg cm jglg umo lc ao# a o# trc# jgfac# pgrg cacgr ca trgjtor juyg ig#g c# lc - ie.
%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg( kheurg !.
<0ji
G 6i
6i 7.63i KGF
:i P
X
:i
7.63i KGJ
KGL 7i
:i
Tgrg aos vcjtorcs $c !cr"g# Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc(
;<
6h - 7.63 , - :&
K GF
9
KGF (
K GJ
9
KGJ (
K GL
9
KGL (
K
{ 50.<0& } BM
9
66 + (-7.63)6 + (- :)6 6h + 7.63 , - :& 66 + 7.636 + (-:)6 7h - :&
-
( -7) 6 + (-:) 6
) 9 4.36<7KGFh - 4. 4 .:65;KGF , - 4.50;7KGF&
) 9 4.36<7KGJh + 4.:65;KGJ , - 4.50;7KGJ &
) 9 -4.:7;6KGLh - 4.8<05KGL &
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho( K
9
42
(4.36<7 K GF
+
K GF + KGJ
+
KGL + K 9 4
4.36<7KGJ
-
4.:7;6KGL )h + (- 4.:65;KGF + 4.:65;KGJ ) ,
( 4.50;7 K GF - 4.50;7KGJ - 4.8<05KGL )& 9 4
+ -
0eugagmlo ao# joipomcmtc# h, n, b. #c thcmc. 4.36<7 K GF
+
4.36<7KGJ
-
4.:7;6 K GL
9
4
4.:65; K GF + 4.:65; K GJ 9 4
( 6)
-
4.50;7 K GF - 4.50;7KGJ
-
-
4.8<05 K GL
(7)
+
50.<0 9 4
(:)
2c#oahcmlo ag# 3 cjugjhomc# #c thcmc( th cmc(
K GF
9
KGJ 9 7;.;BM
K GL
9
33.6 BM
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;3
%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg( kheurg !.
^ 7.63i 53i 3i
6.3i
KL 3i
6.3i
KJ 6.3i X
KF
:i
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Tgrg aos vcjtorcs $c !cr"g# Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc(
: , + 6.3& ) 9 4.5;06KF , + 4.;<46KF & :.843 4.53h - 3 , + 6.3& KJ 9 KJ ( ) 9 4.7::4KJh - 4.00;3KJ , - 4.<<:6KJ & 3.;<4 -7. 63h - 3 , - 6.3& K L 9 KL ( ) 9 -4.6706KLh - 4.0568KL , - 4.<:;
9
KF (
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
;;
K K K K
42
K F
+
KL
x 9
42
4.7::4 KJ
-
4.6706K L
9
y 9
42
4.5;06 KF
-
4.00;3KJ
-
9
-
9
42
-
+
KJ
4.<<:6 KJ
+
-
K 9 4 4 4.0568K L
4.<:;< K L
-
9
4
<834 9 4
2c#oahcmlo ca #h#tcig lc cjugjhomc# #c thcmc(
78.6BM
1
KJ 9 74.< BM
1
K L
1
K F
9
9
;.:6 BM
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;5
%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg!
^
L J
6i 7.3i
:i
KL 6i
KGJ
#i G
KGF X
P U934(.07!"
Tgrg aos vcjtorcs $c !cr"g# Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc(
;0
K GF
9
KGF ,
(6 - 4)h + ( -; - 4) , + (: - 4) & 6 ; : 9 KGJh - KGJ , + KGJ & 6 6 5 5 4)6 (6 - 4) + (-; - 4) + (: - 4) 5 (-7.3 - 4)h + (-; - 4) , + (6 - 4)& : 76 < K GL 9 KGL KGLh - KGL , + KGL& 9 6 6 6 7: 7: (-7.3 - 4) + (-; - 4) + (6 - 4) 7: K GJ
9
!
R -34(8.07)& Y M 9 R -<84.3& Y &
9
KGJ
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
K
9
42
K GF
+
KGJ
+
KGL + ! 9 4
6 ; : : 76 < K GF , + ( KGJh - KGJ , + KGJ & ) + (- KGLh - KGL , + KGL& ) + ( -<84.3& ) 9 4 5 5 5 7: 7: 7: : 76 < 6 ; : 4 < 8 4 . 3 K K h + K K , + K + K & 9 5 GJ 7: GL 5 GJ 7: GL 5 GJ 7: GL
0eugagmlo ao# joipomcmtc# h, n, b. #c thcmc.
6
:
K GL 9 4 7: ; 76 K GL 9 4 - K GJ 5 7: : < K GJ + K GL - <84.3 9 4 5 7: 5
K GJ
-
(7) ( 6) (:)
2c#oahcmlo ca #h#tcig lc cjugjhomc# #c thcmc(
K GF
9
7677.06 M
9
7.67BM
K GJ 9 ;4; M K GL
9
534 M
:-33. &h ag ig#g lc ag a g igjctg c# lc "4be lctcrihmc ag tcmjh'm lc#grroaaglg cm jglg jgfac pgrg aoergr lc cquhahfrho. Jom#hlcrc x 9 6i y - 9 7.3i .
;8
%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg!
^
L J
7.3i :i
6i 6i
KL KGJ
#i G
KGF X
P U934(.07!"
Tgrg aos vcjtorcs $c !cr"g# Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc( 54
K GF
9
KGF ,
(6 - 4)h + (-; - 4) , + (: - 4) & 6 ; : 9 KGJ h - KGJ , + KGJ & 6 6 5 5 4)6 (6 - 4) + (-; - 4) + (: - 4) 5 (-6 - 4)h + ( -; - 4) , + (6 ( 6 - 4) & < 76 : K GL 9 KGL KGLh - KGL , + KGL& 9 6 6 6 7: 7: (-6 - 4) + ( -; - 4) + (6 - 4) 7: K GJ
9
!
R -34(8.07)& Y M 9 R -<84.3& Y &
9
KGJ
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
K
9
42
K GF
+
KGJ
+
KGL + ! 9 4
6 ; : < 76 : K GF , + ( KGJh - KGJ , + KGJ & ) + (- KGLh - KGL , + KGL& ) + ( -<84.3& ) 9 4 5 5 5 7: 7: 7: < 76 : 6 ; : 4 < 8 4 . 3 K K h + K K , + K + K & 9 5 GJ 7: GL 5 GJ 7: GL 5 GJ 7: GL
0eugagmlo ao# joipomcmtc# h, n, b. #c thcmc.
6
<
K GL 9 4 7: ; 76 K GL 9 4 - K GJ 5 7: : : K GJ + K GL - <84.3 9 4 5 7: 5
K GJ
-
(7) ( 6) (:)
2c#oahcmlo ca #h#tcig lc cjugjhomc# #c thcmc(
K GF
9
7:40 M
9
7.:7BM
K GJ 9 5;:M K GL
9
540.3M
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%oa!j&'(# #cg %oa!j&'(# #cg ag #heuhcmtc kheurg!
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KL
Tgrg aos vcjtorcs $c !cr"g#
56
Lcfcio# rcprc#cmtgr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc(
734(8. 8.07 07))& p 9 734(
K F
<
;
7<
7<
KF , -
76
KF & 7< ; < 76 KJ 9 - KJ h - KJ , - KJ& 7< 7< 7< < ; 76 K L 9 - KLh + KL , - KL& 7< 7< 7< 9
KFh -
7<57 7<57.3 .3&
9
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
K
42
K
42
x 9
y 9
K
-
9
42
< 7< -
KF
; 7< 76
-
7<
-
; 7<
KF -
K-
< 7< 76
K F -
7<
< 7<
KJ
+
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-
K L
; 7< 76 7<
9
4
K L
9
4
K L
9
4
2c#oahcmlo ca #h#tcig lc cjugjhomc# #c thcmc(
K F
9
030M
K J 9 4 K L
9
030M
5:
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U
KJ KF
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Tgrg aos vcjtorcs $c !cr"g# 5<
grg ao# cjtorc# kucrzg polcio# c*prc#gr jglg kucrzg lca lhgergig lc jucrpo ahfrc io#trglo cm ag khe. :m #u korig cjtor jgrtc#hgmg joio #heuc(
!
9
K F
!& ; 76 < KF h , - & 7< 7< 7<
9
; h - < , - 76 & 7< 7< 7< - < h + ; , - 76 & K L 9 KL 7< 7< 7< KJ
KJ -
9
pahjgmlo ag# cjugjhomc# cjugjhomc# lc cquhahfrho(
K
K y
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+ % G9 <44 <44 shm ΰ ( : ) + <44 <44 jos jos ΰ ( 6)9 7644shm ΰ + 044jos 044 jos ΰ *% G *ΰ
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+ % F 9<4jos63 ´ ( 6.3 )984.; a#.), + % J 934jos:4 ´ (:.63 )97<7 a#.), <-:4. &h ) F $ 34 af y )J $ G" af, lctcrihmc ca ioicmto rc#uatgmtc jom rc#pcjto ga pcrmo aojgahzglo cm .
+ % G9:4jos :4jos 63´ ( 6.3 ) + <3jos:4 ´ ( :.63) ¿ 783 a#.),
747
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+ % G9 04jos64 ´ ( 4.73 scm ;4 ´ ) ∖04 scm 64 ´ (4.73 4.73 jos jos ;4 ´ ) ¿ 5.57 M . $
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