Electrotecnia Apuntes y Problemas 08-09
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Transcript of Electrotecnia Apuntes y Problemas 08-09
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11
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−
+
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c
O
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ϕ
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HH11OHH11O
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11 11
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# $ A
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ω πω πω πω π
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&&&&3CQ0-E'
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Ω = − Ω
/8G % 1G19@@T$ 11$$ ,>-L@-H5' 1G$'
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(=,H
11
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+
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=O
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.=1 H/ (1N
6
6
6
9 6
+
+
+
= Ω = + Ω= Ω = + Ω= Ω= − Ω
= + Ω = Ω
4# + "/8G % 1 $$1.-T=7 7>--M: $ ,-i$ 1@-H5'+
(
=O
=O
=O
F)$ 1= (== = ,,
*$ 11
1= = =
- $ H= .H= =/
F)$ ,, .= ,,/
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.H= ,/
' 8
' 4
6
6
6
9 6
ω π
ω π
−
−
+
+
= = × × = Ω
= = = Ω× ×
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= − Ω = H(O(, − Ω
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(
=O
=O
=O
F)$ 1= (== = ,,
*$ 11
1= = =
- $ H= .H= =/
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.H= ,/
' 8
' 4
6
6
6
9 6
ω π
ω π
−
−
+
+
= = × × = Ω
= = = Ω× ×
= Ω = + Ω= Ω = + Ω= Ω= − Ω
= − Ω = H(O(, − Ω
&''' !" -./-0
>/!)2.A
O E"%5 ">;"
=OH(O
H(
(,
(,
$
+
−
= = =Ω
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L=O LH(O =H(O
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2 A- 7AH= %AH= 2
2 AP 7A,, %A,, 2
2 AP 7 A11 %A11 2−
Ω
Ω
,O) "
=O LH(O LH(O
L=O LH(O =H(O
( *( =O LH(O
2 A- 7AH= %AH= 2 A .(L+=/2
2 AP 7A,, %A,, 2 A .4(L+HH1/2
2 AP 7 A11 %A−
Ω
Ω
4N=NO
6 =O
11 2A.1(HH4+,N/2
2 .(,L + =/2A(, =
H(OH= +
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N=NO11 −
26A =O(,
&''' !" -./-0
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ω ω ω πω
π
= = = = = =
=
• $T "• $* % ))T"• *$**>"
4# 5#-7#6#@57E@#5)) "
L=O * 4=OP AP .= / .= / 6 6
+1
→ + = −
4%PP*"5))9 ))"/8G $ '?))H1T1`> 1=[ ""1=2)"#& "T ./" TRSR*S"
(((
(
H1T 0T H1T TH1 =
= T= T T
1 > 0> 1 > 1 =
= >= > >
=N
H1 = 1 =
# 8
4# 4
8 4
µ µµµ
π π
−
−
− −
→ ×→ = = ×→
→ ×→ = = ×→
= = =× × ×
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(=O
=O
=O =O =O
=O
=N H1 = 1H(=
1H(=
=N 1 =
1= 1H(= 1H(= .1= =/
.= 1H(=/
.= 1H(=/
.1= =/ 1=
' 8
' 4
9 6
6
6
6
ω π
ω π
−+
−−
+ −
= = × = Ω
= = = Ω×
= Ω+ Ω+ Ω = + Ω+ Ω− Ω+ Ω = Ω
4*F "4; E"
=O=O
=O
1=
1=
$
= = =
Ω
4; E"
=O =O =O
=O =O =O
=O =O =O
1= 1=
1H(= 1H(=
1H(= 1H(=
$
$
$
+ +
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= × = Ω × =
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=+ + + +
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1
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H
$
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1
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= = = = Ω+ + + +
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j4*E )"
= + +
=O
=O=O
=O
4=O=O
=O
L=O=O
(
(=- $ = .= =/
=1
(=F)$ (, .= (,/
N1
(=*$ 1H, .= 1H,/
H
.= N=/ 1(
$ 6 $
$ 6 $
$ 6 $
6 $
+
−
= = = = +Ω
= = = = −Ω
= = = = +Ω
= + =
=O
=O
(=O(=O
(==H1
1(
$
9
$ −= = = Ω
4# + "
P
-
P*
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/8G % 1 !$$1.-T=7 7>--M: $ ,-i$ 1! ,>-/@-H5'+
(
=O
=O=O
=O
4=O=O
F)$ 1= (== = ,,
*$ 11
1= = =
(=- $ NN .NN =/
H=
(=F)$ ,,= .= ,,=/
,,
*
' 8
' 4
$ 6 $
$ 6 $
ω π
ω π
−
−
+
= = × × = Ω
= = = Ω× ×
= = = = +Ω
= = = = −Ω
=O
L=O=O
(NO
=O
(NO(NO
(=$ ,,1 .= ,,1/
11
.NN =1/ H
(=,=N
H
$ 6 $
6 $ $
9
$
+
−
+
−
= = = = +Ω
= − =
= = = Ω
=OA,, $−
=ONN $
6 =O2 A(=
6 (NO7 AH $−
* =O7 A,,1 $+
&''' !" -./-0
?/!)20>
?',' &&& !&''&'4>""5?!%7@6#@578%8#5;%-*7%#57@6#@578%86E6%"4*5?!%@\!#-E5*E!;#:E5"4# 7!;#8%@*7%6E6%"
?'>'!''&'4G .))/ ./4'"4@ )+1= )+ ) # "45 -#5E@%@*7%)) l"PAP*
ω ω ω πω
π
= = = = = =
=
• $T "• $* % ))T"• *$**>"
4# ;%-%#E7@6#@578%8#5)) "E5#%@?%@"
L=O * 4=OP AP .= / .= / 6 6
+1
→ + = −
4%PP*;%-%#Ex"5))9 ))"!3&c4#*E@8#@5%8E- $ @-H5 7@8?*672E*r"
&''' !" -./-0
?/!)20?
/8G $ !'?))H1T1`> 1=[ ; ""1=2)"#& "T ./" TRSR*S"
(((
(
H1T 0T H1T TH1 =
= T= T T
1 > 0> 1 > 1 =
= >= > >
=N
H1 = 1 =
# 8
4# 4
8 4
µ µµµ
π π
−
−
− −
→ ×→ = = ×→
→ ×→ = = ×→
= = =× × ×
(
=O
=O
=N H1 = 1H(=
1H(=
=N 1 =
' 8
' 4
ω π
ω π
−+
−−
= = × = Ω
= = = Ω×
4; E"
=O=O
=O
=O=O
=O
=O=O
=O
=O =O =O
1=
1=
1==H1N1
1H(=
1==H1N1
1H(=
=H1N1 =H1N1
. =/
.= =H1N1/
.= =H1N1/
$
$
$
$ $ $
6 $
6 $
6 $
−
+
+
−
− +
= = =Ω
= = =Ω
= = =Ω
= + + = + +
= + ++ −+ +
=O. =/ 6 $ $= + =
&''' !" -./-0
?/!)20@
(;F$1!$;$ 1$19$C7 7$E=$ G$ $$1 1$G19$C $ $E'
* L=OA=H1N1 $
- =O 67 A 7$ =
6 =O2 A1= 2
4=O7 A=H1N1 %
4# )&& )) ""4)) ) )) &"""4# *r .=O/ )-"F"6"4 FEF7@%578#%#5< =O4=O4=O"
&''' !" -./-0
?/!)20A
?'?'!& 4# +)-#5E@%@*7%;%-%#E+1="
4#+$ ))) 4,1O7 AH1 %
*r "4#*r "4#+*r*.4,1O/A=N=H."/"45 ; )) )) "4# )) "/ 7$9;$ $1; 1$1G12 1=$$G$ 1! I:G127 7$;1;1 $ '
4,1O7 AH1 %
6 =OA(=
A4,1Oϕ
4,1O7 AH1 %A.=4+=/%
6 =OA(=
A4,1Oϕ
=6 6 $+ = +
=6 6 $− = −
&''' !" -./-0
?/!)20B
4# + M+=% L+=%"4 =O"46 ++ )"
,1O
=O
,1O =O
=O
H1 .= =/
= = =
H1 =
.= =/
.= =/
.= =/ =
$ 6 $
6 $ 722 6 $ $
$ $
6 $
6 $
6 $ $
−
+
− +
= = −
− + =
= + = +
= − +
+ +
= + =
4;) "
1(= (H H( =
= 1= (H
H(N
4
$ '
4
ω π
µ
−= = = Ω = = = ×Ω
=
4* )"
*q*4#+*qH(N`>9 ) $
*A`>L((`>AN`>"
4,1O7 AH1 %A.=4+=/%
6 =OA(=
=6 6 $+ = +
=6 6 $− = −
=6 6 $+ = +
=O= $=
&''' !" -./-0
?/!)20.
45 ;`>==`>"4#*r &.=O/ "?'@'&!c'(&!c!& '4# *r "4#& 4=O=O L=O"* *r$ $/0-R -C19 E' $-R C$$19 E' $Q0-R -CG19 E'/!1 ;9 %-C19 E-='''-=@'''-=0C'E'''C$$19 E'''-=0CG'E'''-=@'''-='''-CG19 E/ : 4 $G1 $17 7$$1) $c19 $$1 $$1$:$1 $1 $=99$: $GP7 '/ 1$ $ G$ $cG11G 1 11G$$1 1 2419'$1 $ 71 $1 $$1$;$ $2$ $ $24'4* )) '$• 2419% ^ .^f/
)+"7 """• 2419%^ .^2%/
& ))"4#' F)* ; "4; ' $• ;*r "5 "• 5 ))"# $
!) " ) &)" !& "
• 5' *r =H7""4*r $
&''' !" -./-0
?/!)200
• G$9$ +
"• G$21 )1$0
*r "• # )+
"#+$* )1Hf *rA=1"5 (=2M1=") )) "
*) +$
1H==H
(= =1
;)+*
* A=1 A*=1A =O
.* / A4=O
.5
$
ϕ
ϕ
ϕϕ ϕ
ϕ
=×= = =
→ ±
=O
'L=O/
#; )) $
7 ==H $
ϕ
−=
4; ) "
1
=O
(=(,N
=HN(
=H =
1= (,N
5
7 ==H .=1=, =HN(/
=HN(
$
: ' 4 '
$ 6 $
7 7 6 $
ω π−
−
= = = Ω
= = = ×Ω
= = −
+
@
@
*
6 =O
=O
$
* =H
*
)) $
7 .= =HN(/
7 .=1=, = / =1=,
7 ==H .=1=, =HN(/
4
4
6 $
6 $ $
2
$ 6 $
µµ
−
<=
= +
= + =
= = −
==H =1=, "
"
% $ $ 6
'
&''' !" -./-0
?/!)2,--
?'A'K &3&& ''K'45 ) "# "" "4; '0"• *' $& "
d2A-7A.2/#""
2A- 7A.2/#"".0 /
2A- 7* A.2/#"".0/ϕ
∆
∆
159 G F ;$)$#)15• * :$8)
)&"#' "$1$ $52;'';$ $1 1)F'I''
d;A-7
A.f/
&''' !" -./-0
?/!)2,-
?'A''K !*&&3& '
4*' ' "4#-F6' 0 "4#+$7 "76*F6"; """5 "*' "
" 2$(I "
" E $ (I%)"1I "
(" 7 %"6"
,"1I)"1I "
45$ d2A-7*r
% 0
(
ρ ϕ ∆ =
8+5 $
(
ρ ϕ = ∆
$$#;''G [ $c
(
ρ ϕ=∆
&&I &&
=O*A==H
ρ Ω×
=O*A==
ρ Ω×
,=O*A==,
ρ Ω×
,=O*A==(((
ρ Ω×
4#' "> 0"
5A5
oA-
Ω× =O*
A ' ./7A7 %.%/d2A*' 2 .2/*rA* "
&''' !" -./-0
?/!)2,-,
?'A','K !KJ'& '
4# : "# 0 )+ "
/1 1)F ,-'?A-'@/@,> 9',--?
7'@,/7$ FF".;2*P;#/ 4;)0 $
' 71G $1'
/-F676*F6 ,-'?A-'@/@,> 9'-?$1 $1 I''4-F6476*F6=H7 ) F"6"4-F6476*F6=7 &F"6"
,' $1'
4F+ ) )+ K45 7'@,/7$ $IC7G E=I,C71G =2E"
>' G $1 '59
,1=3N1=2' =3^2"
6 0 )+4;2*]$N=O*"@ ,1=3N1=24#;-P;#$=O*"@ =3^2
?' P 1 $19 $'#
@ "" "/, 1 $G4$'':4$'' #)$'4( ' ""
@' G 41$'
45) ' )!, J!, 0 "
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70" p7$)
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?/!)2,->
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%)(I2 d2A (===
(=
" * "
(1 == N===(=,(
(= (=
$
ϕ
ϕ×
= ⇒ = = = =×
(" *' " ( )
==,= (= ,( ( , 5 A,
( $
ρ ϕΩ×
= = × × = ⇒∆
," *) 0"?@#=",="141(4==,"6)%"1"4)" F"
5A,;2*)+ )
• 7C107A10(=,(%A(H=,% 7A,=%• ;2*,70AN%≥/ 7A,=% .@E*?!;#/
VVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVV4* ! )"
/ 5) ;2*")/ ) #;-P;#
"/ 5@E*?!;#) "
/ 5) ;2*"*)' "
;2*_70A(%≥/ 7A,=% C !E
,!-,_)FR@-kGR?- C !E)/ #;-P;#"
5)' ) ( )
=== (= ,( ,=( 5 A
( $
ρ ϕΩ×
= = × × = ⇒∆
*) ,! J!A,_)FR?0kGR?- C !E
4; ' 0$• ;2*=• #;-P;#
&''' !" -./-0
?/!)2,-?
?'A'>'&3&!''
G $G1 $'7 %
• $%5 .))/<
"*rA_rA=O
• &$2%5 .))/"# ) 25"""
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1 $'' • #)$ $%$Q1 '• #)$ $%>$$
%)) *r " 5 *r+" 5)*r)"% ) 0 ))"# ' + *r7"
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? $701 2 $ 8 $
76A701.! /L7.8 / ; $
701.; /L7.8 /
4T "
$ $''4 )) "
4#*r L=O"/!) $$ $$ $FC=@=.E'I?.!1 ','>'
&''' !" -./-0
@/!)2,-@
L! @' ''&'K'& 3'@''K&'&' @'''$ $#$:1$ $4' @'',' 1$#$= 1$4: 11 ' @''>'$ $ $I8$$G[ '@','!K' @','')2 ;7 ' @',',')2 $;7 @','>'$1;7M M ' @','?'$1$;7M ' @','@'$1$;7M '@'>'"&!I *! I&& I&'@'?'K &&*!K I&'@'@'!3&cK' @'@'' $ $$1 )2 '
@'@',') $ $#8 $ 714$1 )1$G G 119'@'A'K &K& 3'4# "" ")+ $ 1""* "
1""* ">;"1"("5) ' )) "1","* )"2"1"1"**r "1""* "" "
&''' !" -./-0
@/!)2,-A
@''K&'&'4 ) F"6"+ "4# % 6. )/F+6. /"46 '%"6" )F"6" "" (>@ "4* @ "; F"6" # @ "4 "" $
@'''$ $#$:1$ $4'$# $1'4#;6-#56#@57E@#56-7>k57*%567#@#@#!75!E2%E-8#6#@57l@;#-E#@6-##%557#!;-#T%G?@8#5>%5#8#=O• 6- >>".6'/"
2-5A,==2 256A,==2 26-A,==2
• 6- >@ ".6>/" 2-@A(=2 25@A(=2 26@A(=2
4#; =O"$=O=O,=O• 6- >>".6'/
-5 =O
56 =O
6- ,=O
2 A,==
2 A,==
2 A,==
(
(
&''' !" -./-0
@/!)2,-B
• 6- >@ ".6>/
-@ =O
5@ =O
6@ ,=O
2 A(=
2 A(=
2 A(=
L - @ L L 5 6
45 '>),==2(=2 "
=O =O
(=O
=O ,=O
,==(=,
(
(=, (=,
.(=, =/ . 1,N ==/ .(,, ==/ ,==
(=, (=,
. 1,N ==/ . 1,N =
, (, ,
( , (,
( (, ,
6 6 6
6 6
−
= = = =
= − = − =
+ − − + = − =
= − = − =
− + − − −
=O
,=O =O
=O
=/ .= ,==/ ,==
(=, (=,
. 1,N ==/ .(=, =/ . (,, ==/ ,==
, ,
6
6 6 6
+= + =
= − = − =
− − − + = − − =
4 ' 4(=O >"# "
(,
,
,
&''' !" -./-0
@/!)2,-.
487% -%!%2#*6E-7%8#6#@57E@#58#h@#%G8#>%5#
6- >@ ".6>/ (,
-@ =O
5@ =O
6@ ,=O
2 A(=2
2 A(=2
2 A(=2
4 ' >> > >@ "/1$1$ $4:$$$%
,==(= ,== .(H= / (= .= /
( (
(=(( (= .= / (( .1 /
( (
4
4
5
5
= = =
= = =
,
,
,
(,−
(
(,
,−
(
,
,−
&''' !" -./-0
@/!)2,-0
@'',' 1$#$= 1$4: 11 '$# $1'4# '>"• * '$ "7-7576"• * >$))"7-@75@76@"• * @ $ @ "7@"• # # )"
7-
7-@ L - @ 7@ L L 75@ 76@ 76 5 6
75 4* @ >'# "
, ( , (, , = + + = + +
45 I&==O @ "
• #) (,
-@ =O
5@ =O
6@ ,=O
A . =/
A . (/
A . (/
= .= =/,
$ 6 $
$ 6 $
$ 6 $
$ 6 $
= +
= − +
= − −
= = +
,
,
&''' !" -./-0
@/!)2,-
45 & I&= 3 =O"
• 8)"5)" (,
-@ =O
5@ =O
6@ ,=O
1O
A . =/
A .= /
A . (/
. =H/ =(1,
$ 6 $
$ 6 $
$ 6 $
6 $ $
= +
= +
= − −
= + =
,
• 8)"5)"
-@ =O
5@ =O
6@ ,=O
=O
A . =/
A1 . 1 1/
A . (/
. =1 =,((/ =1,
$ 6 $
$ 6 $
$ 6 $
6 $ $
= +
= − +
= − −
= − + =
• 8)"5)"
-@ =O
5@ =O
6@ N=O
,O
A . =/
A1 . =N1 (/
A .= /
.1 =N/ ,(,
$ 6 $
$ 6 $
$ 6 $
6 $ $−
= +
= − +
= −
= − =
4) )@ "5)O+ 1%)=1% )+ @ "
,
,
,
,
,
,
,
(,
(,
,
&''' !" -./-0
@/!)2,
@''>'$ $ $I8$$G[ '4 )+6-"F"6"#- # &F+6 ) ' """6 F"6"4F+6""1= ===2"45$• !)+ $ ?@q1=2• 6$ 1=2q?@y1==2• 6$ 1==2q?@y===2
4 $• (=2 "• (=2 ,==2 , "
4; @''' 6#@57E@#56-7>k57*%5 6#@57E@#5!E@E>k57*%5
-5 =O
56 =O
6- ,=O
2 A,==
2 A,==
2 A,==
-@ =O
5@ =O
6@ ,=O
2 A(=
2 A(=
2 A(=
@','!K'4 ) ))"4 #J?77F-%8E5 )) )) =O =O"#+ )$• ! $ ))"• 6 $ ))"• T + $ "• F ' $ "• 7 1= ) $1=
"4 8#5#J?77F-%8E5 "#+ )) """# ) 3"
&''' !" -./-0
@/!)2,,
#+ )$• 7 $
) "• 2$
)&) "• #
) ) @ "4 +) ,==2) @ "@','')2 ;7 '4# )$• '>"• #) 0 "• ')"• >)"• ' >"
?--=>j + +>
+,
4%Di ' "
( (
( ( ( ( ( (
( (
+ = → = −
+ = → = −
+ = → = −
4; ]]](E
(
( ( ( (
9 9 9= = =
(
(
(
&''' !" -./-0
@/!)2,>
4? '"4 '$$1;7 $
(
4
=
4#+$? ,==2 1=[ < ';"
=O=O
=O
=O=O
=O
,=O,=O
( =O
,==H
1=
,==H
1=
,==H
1=
((
((
$
9
$
9
$
9
= = =Ω
= = =Ω
= = =Ω
45) ) ) "!=O4 '> $
=O ,=O
(=O
=O =O
1=O
,=O =O
H H .H =/ . , H/
. H/ (H1
H H . , H/ .H =/
. H/ (H1
H H . ,
(
( ( (
(
$ $ 6 $ 6 $
6 $
$ $ 6 $ 6 $
6 $
$ $ 6
= − = − = + − − − =
= + =
= − = − = − + − + =
= − + =
= − = − = − −
N=O
H/ . , H/
.= (H1/ (H1
$ 6 $
6 $
− − + =
= − =
45) ' )$
(H1H
( (
4
$ $= = =
&''' !" -./-0
@/!)2,?
@',',')2 $;7 '4# )) ))"4# )$• '>"• 8) @E0 "• ')"• >)"• ' >"
?--=>j + +>
+,
4%Di ' "
( (
( ( ( ( ( (
( (
+ = → = −
+ = → = −
+ = → = −
4; ]]](E
(
( ( ( (
9 9 9= = =
4? '"
(
(
(
&''' !" -./-0
@/!)2,@
4#+$? ,==2 1=[1[ < ';"
=O=O
=O
=O=O
=O
,=O,=O
( =O
,==H
1=
,==
1
,==H
1=
((
((
$
9
$
9
$
9
= = =Ω
= = =Ω
= = =Ω
45) ) ) "8 =O4 '> $
=O ,=O
(=O
=O =O
(O
,=O =O
H H .H =/ . , H/
. H/ (H1
H . H (H1/ .H =/
. (H1/
H .
(
( ( (
(
$ $ 6 $ 6 $
6 $
$ $ 6 $ 6 $
6 $
$ $
= − = − = + − − − =
= + =
= − = − = − + − + =
= − + =
= − = − = −
NO
, H/ . H (H1/
., =NH,/
6 $ 6 $
6 $−
− − − + =
= − =
45) 8#5#J?77F-%8E@E '' )"
(
(
(
&''' !" -./-0
@/!)2,A
@','>'$1;7M M '/# @ > ) )# "# (=2 ))"4- @ $;7 $ (=2"* + )"#+ )$• 7 $
) "• 2$
)&) "• #
) ) @ "4# ) @ .+ /) >@ @ &"4* # )@ $• "• #) 0 "• ')"• >)"• % '"• >' )
$
,==(=
( (
4
= = =
J+ 6# "
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&''' !" -./-0
@/!)2,B
+
+, +>
4%Di ' "
( , (,
( (, ,
, ,
= −
= −
= −
4; ]]](E
(
, (, , ( ( (
9 9 9= = = = = =
4* >7:%5 )& '"4 '$$1;7 $
,==(=
( (
4
= = =
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(
(
=, $=
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@/!)2,.
4#+$? ,==2 1=[ < ';"5(=2 @ "
=O=O
=O
=O=O
=O
,=O,=O
( =O
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1=
(=,
1=
(=,
1=
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,
$
9
$
9
$
9
= = = =Ω
= = = =Ω
= = = =Ω
45) ) ) "!=O45) ' )$
,4 $= =
4 )*#-E @ & ) "#+$! '"
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@','@'$1$;7M '/# @ > ) )# "# (=2 ))"4- @ $;7 $ (=2"* + )"#+ )$• 7 $
) "• 2$
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4
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=O=O
=O
=O=O
=O
,=O,=O
( =O
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1=
(=
1
(=,
1=
"
, (
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,
,
$
9
$
9
$
9
, 4
= = = =Ω
= = = =Ω
= = = =Ω
=
=O =O ,=O
=O
, ,
., =/ . , NN/ . ( (H(/
. ( (H(/ ,
( $ $ $
6 $ 6 $ 6 $
6 $
+ + = + + == + + − + + − − == − + =
4 @ ) ) ),%=O @ "45) ) ) "8 3 =O
(
(
(
=, $≠
&''' !" -./-0
@/!)2,,
@','A'$1$;7M '4# )8) $ 1 1 = ) $ ,>-# " >@ ))+ (=2 "4# # 8) 68) '"
+
+, +>
4# 6$
(
(( (
( ( (
(
(
9 99 9 9 9
9
9 99 9 9 9
9
9 99 9 9 9
9
×= = + +
×= = + +
×= = + +
4? # 668)"
(
(
(
&''' !" -./-0
@/!)2,,,
4#+$? ,==2 1=[1[ @ < '; >"• ; # 8)68)"
=O =O =O =O =O
( =O
=O =O (( ( =O =O =O
=O
=O =O( ( ( =O =O =O
=O
1= 1=1= 1= ==
1
1= 11= 1 ==
1=
1 1=1 1= ==
1=
(
(
9 99 9 9 9
9
9 99 9 9 9
9
9 99 9 9 9
9
Ω× Ω×= = + + = Ω+ Ω+ = ΩΩ
Ω× Ω×= = + + = Ω+ Ω+ = ΩΩ
Ω× Ω×= = + + = Ω+ Ω+ = ΩΩ
?--=>j ,--T+, +>--T
--T +,>
=O=O
=O
=O=O
( =O
,=O,=O
( =O
,==
==
,==,
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