binomial_trigo_logs.pdf
DESCRIPTION
fTRANSCRIPT
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g g 0 0 n s 0 0 0 ns ...... 1
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2n s 0 0 n0 g 0 g 0 0ngs g ns 0 0 1 g g 0
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0 1 g g 111111 g 100 0 0 0 ]
110 11
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g g g 0 0 ( g 0 )0 a00 1 � 0 0 0 � 0 ( � 0 )0
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0 0 0
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g 0 an0 0 bd n n0 n0 g a (0 f f p)d ns( ) 0 ( ) 1 ( ) ( ) d g a0
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öçè
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g s 0 0 Þ 0 p
sn0 ÷ø
öçè
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1 0 0 Þ
1 + 0 0pd 0 Î 0
n0 Î (0d 1) 0
1 + Î ( d ¥) 0 g 0 0
2 0g g ag n00n0n s n 0 ]
f f , f ] ]] ]],]
1111 8e 11
00 D d dn0nd d a 0
Õ
å
g
g 1
g
ns
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02n0 2 0 a0
g a0
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ø
öçè
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11110 4 10
d 0na0s 0 a D ag e gdd 1 gd a00 1 gd g s g n d 1 0 ag a 0 gna0 ns( ) e0 ss gd ( ) 84 ss gd ( ) 7 ss gd ( ) 00 ss gd
02n0 2 ,g 0 g d 0na0 s g a
c 0 1 C n0 a00 1 g c
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1
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ÞÞÞ g a 0 D 0 7 gd ]
1111704 bn0
00 s g 00 gd 0 a0sn 0 aa
a
0
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1
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g 0 · 10
10
a
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a
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0g 10
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0 g
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14
0
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0
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11118e0 11
a 0 g 71
0
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0
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0
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0
ns 2
( ) a ga n 0a 0 db g ( ) ngga n 0a 0 db g ( ) (0 g 0 ) ( ) (0 � 0 )
f f , f ] ]] ]]]]
1111e 0 10
00 g1d g d g0 b ga0nn 0 gngg s 0 gna0 d 0
å
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1
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g
ns s a 2
( ) å
g ( )
g
g å ( ) å
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a0s å
0 å
a0 Þ ]
111 00e bn0
a 0 (4 · 0 1 g 4 · 0
g 40 · 0
0 g 111111 g 40) ns
( ) 0 ( ) 0 g 1 ( ) 0 ( ) 0 - 10 2n0 2 cn 0 0 4 1 0
1 g 4 1 0
g 40 1 0
0 g 111111 g 40 1 0
0
0 (1 g 4)0 - 1 Þ 0 - 1 Þ ]
111 1e0 11
00 m a00 n ag sn n n0 gs sa ns0dn0
1 g g s q g g s 4q g g s 0q g g s 8q g g s 10q 0 q
qqsn0
0sn0·dg s
0 (m g n) ns s a
( ) e ( ) 10 ( ) 11 ( ) 1
00 1 0 0 g s 0° g g s q g g s 4q g 1111111111 g g s 10q 22]...].]]]2...]
sn0q · 0 0 sn0q 0g s0 g g s q g 1111111111 g g s 10q] 0 sn0 q g sn0 q 0 sn00q � sn0 q 0 sn0 q � sn00q 0 sn07q � sn0 q 0 sn0eq � sn07q 0 sn011q � sn0eq���������
sn0q · 0 0 sn011q g sn0q sn0q · 0 0 sn00q · sn0 q
0 0 q
qqsn0
g s0sn0 0
qqq
sn0
dg s0sn0
Þ 0 0 0 a00 d 0 0s1 ]
111 8 sp
s a ns1111111111111111101810141
71 1011
810141
1011
0141
011
41
1¥++++
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+-
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)10 )(10 111111111( 1011
++-
\ 00 0å 0 0
1 �
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++
a 0¥ 0
1]
f f , f ] ]] ]]]]
111 0e8 11
dn0nd d a 0 g ssn 0 sn0
4 sn0 e + 0 g Î (0d p) ns
( ) 0
10( ) 0 ( ) 1 ( )
0
8
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0
sn0
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0 a sn0 ns g 0 n0 s a 0 0 a00 a an0s a p g ng ns g a g a0 0 a 0 p d 0g n d s ak 0 n0 (0d p) ]
111 44 bn0
s d 0 g - 00ngn 0 s 0 a 0 g gs 0 n0 a0sn 0 0 ( - 0 g 1)11 ns( ) 1 010 ( ) 0 1 010 ( ) 011 ( ) 0 0
02n0 2 ( - 0 g 1)11 0 a0 g a
1 g a
g 111111 g a
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g a
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?
0 g 0
0 0 , (1) 0 0 - (1) g g ,( ) 0 ( � 0 g 1)11
0 - 0
0 0 , (- 1) 0 011 - ( )Þ 0
0 011 Þ 0
0 0 1 010 ]
111 117 sp
s d å= ++
100
1k 4 1kk
k ns s a
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4e 0( )
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k
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f f , f ] ]] ]]]]
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td
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g s1
g s1
g s
dt
abg= 0
g 1
g 1
g
00 a gna0 Õ
g 0 å
g ]
111 7 bn0
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ee · ee]
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Þ dn0nd d 000 as as g 0n n s1 Þ ( ) ]
111 887 sp
gngg 0 ga0n s g ns n0sggnb 0 n0 a ss ag 1 dn0 n0 s 0 sn0 s 0 ss ag a b 0
g 00 g 0 bd n0 s d 0 a00 a 0 g ss ag g s 01 sn0 s 0 g s n0 ss ag g g a s
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n0sggnb 0 n0 0 ss ag ns
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01
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00 n0 a D d g s ·g s g sn0 sn0 sn0 0 1 0d s a d 0 g ng ns n0g gg g d ns( ) D ns ns sg s b 0 gn a0 0 ( ) D ns ag a0 0
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1-
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sn0 sn0
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0
8
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p4
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1110007 10
g 0 g 0 agn d ng d a0 0 0 s 0 sn0 s 0 a gna0 a00 agd 0ng d a0 0
0 s 0 a n 0 s 0 gna0 ns s a 2
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0 2n0 2 a 1 0 b
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0 (40 g 1)
pa00 0 dp Þ 0
d p(dd 0 Î 0)
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p 0
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104
d4
+\ Î ga n 0a ... ]
1110 88 10
00 a gna0 d Ð 0 1 0°d 0 0 a00 0 41 00 g 00ng ag g 0s g g 0 0 sn0 a a00 sn0 a d s a 0 ns s a
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d
b
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0
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f f , f ] ]] ]]]]
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00 abg0 0 1 g g ad bd gd 0 ag sn n g a s 0 dn0nd d a 0
a g b g g g 0 g ab g ag g a0 g bg g b0 g g0 ns
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22]........]2]]]]2..]]]
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1110470 10
gna0 as bas 10 gd 0 a00 bas a0 s 0 0° a00 70°1 00 gnd g 0 gna0
n s
g d g s t° g g t Î (0d e0) 0 a 0 g d g t s a s( ) 00 ( ) ( ) 0 ( ) 40
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0 °00sn0
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\ , 0 10 g 0 g s 10°
\ 0 10 d 0 0 t 0 10
g d g t 0 40 0s1 ]
1110 48 bn0
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10
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g g 0n0 gna0 d 0n00 g 0g b g 0 ag a 0 0ngs gna0 a00 sn gna0 ns e08 0
ss ag 0n 1 gnd g 0 0ngs gna0 ns
( ) 10 ( ) 1 ( ) 10 ( ) 18
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0
0
f f , f ] ]] ]]]]
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gnd g 0 1 0s1 ]
11107ee 10
b a gna0 gn Ð 0 0
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1
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+
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0
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00 ad b a00 g ag g g 0s g n sn n gds 0 a c1,1 0 ga 0 d 0 a g b g g ns
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10 Þ 0
g ³ 0
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11140110 sp
C g g ng sn n n0 gs n ns ga n d
å
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f f , f ] ]] ]]]]
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0 0 sn0 0 1d a00 da 0n 0 s 0 a0 s d d d 0 gd a0 agn d ng
g g ssn 01
11141410 10
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p( )
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f f , f ] ]] ]]]]
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0
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n1 1 0
4
b 0 g g 0 0 f
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f f , f ] ]] ]] ]
(nnn) a an0 k g1
0 8 k · k · k
k 0 8
k � 1 · k � 1 · k � 1
k � 1
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11111(1)
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Þ 0 f k f 7 Þ 0 a00
7 gd as g a s g 00ngn 0
Þ k 0 0 g 7 Þ s d 0 0 g 7 0 10 .....]
].............]........]....2]]....2].
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f f , f ] ]] ]],]
0
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0
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åg
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-------
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1 ... ]
].............].............2].....2]2
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gngg dgngg 0 gna0 a 1
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00 ns g 0 g 0 gngg gn ga0n s 0 a0 s a s
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0 1 a00 0
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a0 0 1
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01
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g 0 0
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1
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111 0004 sp
.........]2. 00 7 abg ³ (a g b g g)0 a00 0a g 4b g g 0 1 0 a
1 g 0b
1 g g
1 0 10
g g ad bd g ag sn n g a 0 db gs1
.........]2. C g sn n g a 0 db gs 1 1 ³ c1 1
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns 0a s 1
( ) 0 a d 0 11 ns 0a s d s a d 0 1 ns g 1
00 1 cn 0 (abg)1 0 ³ 0
gba ++Þ a 0 b 0 g (c ³ g ng ns ssnb 0 d n0 c 0 )
\ 0a g 4b g g 0 1 Þ a 0 b 0 g 0 1 222..]..]]..]2..]].]]2]
\ a
1 g 0b
1 g g
1 0 0 ]
111 400 10
b a0 ag gna0 g s g g 0 g ns a 21 n 0 0g d ns g 0 g 0 d
gngg dgngg 0 gna0 a 1
.........]2. 0ns a0g 2 0 4 g s g s g g ns gngg dga0n s 0 gna0 1
e......
.........]2. 0da 0 g g 0 g 2 n0 a0d sn0 0 a0 ag gna0 n s 0 n s gngg dgngg 1
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns 0a s 1
( ) 0 a d 0 11 ns 0a s d s a d 0 1 ns g 1
00 1 D 2 a00 ag g 0 g 0
\ 2 0 0 g s g s
\ 2 0 4 g s g s ] 22]..].2.]2.]2..]].]]2]
f f , f ] ]] ]]]]
111 00 sp
.........]2. 0n00 g 0g b g 0 s d 0 0ngs 100 0 0a ga 0 db gs a00
s d 0 0ngs 100 00 0a ga 0 db gs ns 1001
e......
.........]2. 0n00 g 0g b g 0 s d 0 0ngs n 0 0a ga 0 db gs a00 s d 0 0ngs
n 00 0a ga 0 db gs ns n1
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns 0a s 1
( ) 0 a d 0 11 ns 0a s d s a d 0 1 ns g 1 222..].2.]22]2..]].]]2]
111 0007 10
b a0 ag a0 gna0 a00 d d C ag 0 0 g 00ng ag 0g d d d
sn0 s d a00 g s g n d1
.........]2.. gg g 0 g 0 gna0 ns 00g 0 g 0 gna0 C1
e......
.........]2.. gna0 C ns g 0 ga gna0 0 gna0 1
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns 0a s 1
( ) 0 a d 0 11 ns 0a s d s a d 0 1 ns g 1 222..].].]22]2..]].]]2]
02n0 2 0 s 0 D C ag p � d p � d p �
00g 0 g 0 D C ns g g 0 g 0 D ]
111 7008 10
.........]2. ngg dga0n s a00 n0ga0n s 0 a gna0 ga0 0 b 1 a00 8 g s g n d1
e......
.........]2. ngg dga0n s ³ (n0ga0n s)( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns g a00 s a d 0 1 ns g g gg g a0a n 0 0 g s a d 0 111
( ) 0 a d 0 11 ns g d s a d 0 1 ns 0a s 1
( ) 0 a d 0 11 ns 0a s d s a d 0 1 ns g 1
00 1 Q g 0 ÷ø
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£ 4 ÷ø
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1
sn0
sn0
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Þ ³ gn0 0 1 a00 g 0 8
0d 1 ³ 10 (nd ssnb ) ]
]]]]]]]]]] ]]]]]]]]]] ]]]]]
111 8 07 sp
a1d a
d a
0 1111111 a00 b
1d b
d b
0 111111 b agn d ng g g ssn 0s s g a a
1 0 d b
1 0 7 a00
a100 g b
100 0 1001 0
( ) 0n00 g 0g b g 0 s gg ssn gds n0 g g ssn 0 a ns sn 0 0n00 g 0g n0 g g ssn 0 b 1
( ) a0 g b
0 0 100 0 g a0d n1
( ) (a1 g b
1)d (a
g b
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0 g b
0)d 1111111 ag n0 1,1
( ) å=
+100
1ggg)ba( 0 10000
f f , f ] ]] ]]]]
00 1 a1 g (a
1 g 0)d (a
1 g 0)d 111111111 222....2]....]]22]2...]
b1 g (b
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1)d (b
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1)d 111111111
0g a100 0 a
1 g ee0
b100 0 b
1 g ee0
1
a00 �������
a100 g b
100 0 100 g ee(0 g 0
1)
0g 0 g 01 0 0 Þ 0 0 � 0
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å=
+100
1ggg)ba( 0
1000(a
1 g b
1) g (a
100 g b
100)] 0
00100´ 0 104 Þ ( ) ( sn0 0
0 0 )0a(
0+ ) ]
111 e 01 bn0
00 a0sn 0 0 0
11
0 0
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-1
2
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( ) g 0 s 0 a ag a gd gn g g
( ) g a ags a gd gn g g -0
( ) ga n 0 g 1 00ngn 0 0 0
a 0 -0 ns
1 0
11100 01 11
d 0 7sn0 0sn0 sn0 4sn0 0sn0 sn0 sn0
7g s 0g s g s 4g s 0g s g s g s
++++++++++++
0 g ng 0 0 gn0
0 0?
( ) a 0 d g 0 0 p 8 ns 0 0 0n0 01( ) a 0 d g 0 0 p 10 ns 11
( ) a 0 d g 0 0 p 0 ns 1 - 1
( ) a 0 d g 0 0 p 48 ns 0 + 1
00 1 d ga g 0
sn0
4g s
7sn0
0 dn0a g 0
sn0
4sn0
7sn0
222..].2]]..]2..]]
\ 0 ( ) 0 d 0 4sn0
4g s 0 g 4
\ ( )8pf 0 g
p 0 0 ( )10pf 0 g
4
p 0 1
( )0 pf 0 g 8
p 0 1 + ( )48pf 0 g
1
p 0 0 + ]
11101 01 1
cn 0 a sn0 0q 0 sn0 0ad 0 g ng 0 0 gn0 a0 s gn b s a g s qÞ?
( ) g s ÷ø
öçè
æ a+p0
( ) g s ÷ø
öçè
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öçè
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ø
öçè
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00 1 0q 0 0p g (�1)0(0a) 222..]..]].]]2..]].]]2]
\ 0q 0 0a 0q 0Þp � 0a 0q 0 � p � 0aÞ g 0q 0 p g 0a 0q 0 � p g 0a
0g q 0 a q 0 0
p � a q 0 � ÷
ø
öçè
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q 0 ÷ø
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q 0 �
0
p g 0a
Þ g s q 0 g s ÷ø
öçè
æ a±p0
g g s q 0 g s ÷ø
öçè
æ a±p0
Þ ] ]].] ]].])].....]]] a ag g gg g ]
f f , f ] ]] ]]]]
1110 00
00 d 0 7�a ( g g a g 0) ns 0 0n0 0 " Î d 0 ssnb n0 ga a (s) 0 a ns ag
( ) � 0 ( ) � ( ) 4 ( )
00 1 g g a g 0 d s b sn n 222..]..]].]]2..]].]]2]
0g f 0
n1 1 4 � 8(a g 0) f 0 Þ 1 � a � 0 f 0 Þ � a f Þ a 0 �
1111(1)
s bas 0 agn d
7 � a 0 0 a00 7 � a ¹ 1a f 7 p a ¹ 0 1111( )
0g d (1) a00 ( ) a Î ÷ø
öçè
æ- 0d
È (0d 7)Þ ] ]d ])] a00 ]]] ag g gg g ]
11100 0 bn0
00 n ns k0 g0 a ng0 gd 0 bn0 dna a0sn 0 ( ) 10 + ns 100 0 x ns s a
( ) 10 ( ) 10 - ( ) 100 ( )
11104 07 sp
00 sn0( - d)d sn0 a00 sn0 ( g d) ag n0 21,1d 0 sn0 1 s gd
0
( ) ( ) ( ) � ( ) �
02n0 2 sn0 0 sn0 ( ) sn0 ( )
sn0 ( ) sn0 ( )
d d
d d
- +- + +
0
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sn0 g s
d
d
-
sn0 g s d 0 sn0 - sn0 d sn0 (1 - g s d) 0 sn0 d
sn0 · sn0 d
0 4 sn0
d
g s
d
sn0 s g
d
0 sn0 s g
d
0 ]
1110 00 1
sn0 g 0 g s d 0 0 a00 0 sn0 d g g s 0 4 0
( ) g d 0 (40 g 1)p d 0 Î 0( ) g d 0 ( 0 g 1)p d 0 Î 0( ) a00 d ga0 b g 0 0 gn a0 s 0 a 0141 gna0 gn 0 d1
( ) a00 d ga0 b g 0 0 gn a0 s 0 a 0141 gna0 gn d 0 1
00 1 0s agn0 a00 a00n0 n 0 s a n 0sd 22]..]2]]]]2...]]
4 g e g 1 sn0( g d) 0 Þ sn0( g d) 0 1 0 sn0
p
\ g d 0 0p g
p 0 (40 g 1)
p 0 Î 0 Þ ] ]
n0 g d 0
pÞ d 0
p �
sn0 0 0 Þ sn0 0
0 g g s 0
4
a s g s d 0
0 a00 sn0 d 0
4 0g d 0 Þ ]]]]
11100 08 11
00 sn0 b 0 sn0 a g s a 0 g s b as a s a 2
( ) 1 g sn0 a ( ) sn0 p
a4-
æèç
öø÷ ( ) 1 - sn0 a ( ) g s
pa
4+
æèç
öø÷
f f , f ] ]] ]]]]
00 1 sn0 b 0 sn0 a g s a
sn0
g s1 a=
b-
g s b 0 1� sn0 a Þ ( )
0 1 � g s(p � a) 0 sn0 ÷ø
öçè
æ a-p4
Þ ( )
0 g s ÷ø
öçè
æ a+p4
Þ ( ) ]
11107 04 1
s a n 0 g s g g s g 0 as
( ) 0 s n 0 n0 ÷ø
öçè
æ p4d0 ( ) a s n 0 n0 ÷
ø
öêë
é pp
d4
( ) 0 s n 0 n0 ÷ø
öçè
æ pp4
0d
( ) a s n 0 n0 ÷
ø
öêë
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4
0
02n0 2 0 d 0 4
p a00
1
11p n0 (0d p) sa ns0n s ] 22]..]2]]]]2...]]
11108 0 10
00 a D d 0 gn0 g a n 0s 0 0 1 00 g ng gas (s) gna0 ns a gn a0 0 gna0 ?( ss d a sddb s a ng s a d a0n0 )
( ) g g g
0 0 g
1 - g
( ) a g b g g 0 8
( ) 00 0nad g 0 a0 gngg b s a gnd g 0 gna0 1
( ) 0 g1 - g
02n0 2D D D D
s b s g s a s
a
s b s g
a
s s a-+
-=
-- Þ
- -=
-( )( ) ( ) g
s s a
s b s g
( )
( )( )g
-- -
= Þ = Þ =1
1 e00
a an0 4 ( sn0 )å 0 8 Þ sn0 g sn0 g sn0 0
Þ g s g s g s 0 0 Þ g g 0 e00
a an0 g1 0 s Þ s a0
0 s Þ a0
0 1 Þ 0 e00
a an0 0 4 0(sn0
g s
g s
)1sn0
sn0
sn0
]
1 0 sn0
g s
+æèç
öø÷
g 1 0 sn0 Þ g s 0 0 Þ 0 e00 ]
1110e 0 bn0
(1 g ) (1 g )0 0 0 g
1 g
g 111111 00
0d
1d
ag n0 1,1 0 a 0 0 ns 2
( ) ( ) 0 ( ) ( ) 7
02n0 2 (1 g ) (1 g )0 0 (1 g g 4) (0 0 g 0
1 g 0
g 111111)
0 0 0 g 0
1 g (0
g 1 0
0) g 111111
2 0g 0 0 1
1 0 0
1
0 0
g g ng ag n0 1,1 ]
f f , f ] ]] ]]]]
11170 11 11
g aga g g0s ag 0gag0 0 sad sn0 0 g 0 g 0 a gngg 0 ga0n s 1 0 ns 0 00
a d s b 00 a0 a0 0 Þq a00 q a g 0 g 0 gngg 1 g 00ng ag 0ns a0g b g 0 g g0s ns
( ) sn0 0
q sn0
q
( ) 1
-æèç
öø÷
g sq
1
+æèç
öø÷
g sq
( ) 1
+æèç
öø÷
g sq
1
-æèç
öø÷
g sq
( ) sn0 0
4
q sn0
q4
00 1 g 0 1 0 g s
q
g 0 0 g s q
0 1 -
0 g s g s
-
æèç
öø÷
0 sn0 0
4
q sn0
q4 Þ
an0 g 0 g g s q 0 g s q - 1 a00 0ag gns ]
11171 00 1
s a n 0 sn0 a 0 a0(a � b) g g s a · a0 b 0s g n0( ) a 0 0p g b ( ) a 0 0p g b( ) a 0 0p a00 bÞÎ ( ) b 0 0p a00 aÞÎ (n ns a0 n0 g)
00 1 sn0 a � g s a · a0 b 0 a0 (a � b) 222..].2.]..]2..]]
bba-ba
g s
sn0g sg ssn0 0
)g s(
)sn0(
b-ab-a
sn0(a � b) g s(a � b) 0 sn0(a � b) g s bsn0(a � b)0g s(a � b) � g s b] 0 0\ sn0(a � b) 0 0 g g s(a � b) 0 g s b\ a � b 0 0p a � b 0 dp b\ a 0 0p g b (g) a 0 dp g b
(�) a 0 dp\ d d ag g gg g ]
1117 08 sp
s d 0 0ngs g gds 0 c1,1 n0 g ng 0n00 g 0g b g 0 s g 00 a00 0ngs
gd ns 0 a00 0n00 g 0g b g 0 0 g a00 ng0 gd ns 4d ns
( ) 0e ( ) - 101 ( ) 7 ( ) - 700 1 ad agd ag dag0 222...]] .....].2]2.]2..]]]
ag � a Þ0Þ a(g�1) 0 0 1111(1)
ag �ag 0 4Þ ag (g�1) 0 4 1111( )
( ) (1) Þ g 0 e g g 0± 0g 0 g 0 0 a00 a 00 g 0 g 0 �0 a00 a 0 �0
a d ag d ag a d ag d ag
0 d e d 7Þ s d 0 0e s d 0 �0 (1�0ge) 0 � 1 0 �101 ]
11170 10 sp
00 g s 0 s a n 0d 0 g g s � 1 0 0 0 gd a0 n0gg asn0 �1,1 g g a00 s ag g a d
0
( ) gs 0 0 ( ) Î (� 0d ¥)
( ) 0 0 g s ns 0n d ( ) 1 1 a0 g a g ns g a00 0
1 a0 sda g ns 0 g
f f , f ] ]] ]]]]
00 1 g s ag a g d ad ag 2 g g a 00 d g 0 1] 222..]..]].]]2..]].]]2]
g a g g a g ag 0 � 1111(1)
a1a g g a1 ag g ag1 a g 0 s 1111( )
a g1 a1 ag 0 1 1111(0)
a0 0 1 Þ a 0 1 Þ ])] ns g gg g
0g d (1) n0 a 0 1 g
1 g g 1 g g 0 � 1111(4)
0g
1g
-=+÷ø
öçè
æ- Þ � 0 0 Þ f � 0 ÞÞÞÞ ] ] ns 0 g gg g
0g d ( ) n0 a 0 1 g
1 g g g g 1 0 s 1111( )
0g d (4) a00 ( ) g a � 0 s Þ g s 0 0 Þ ] ] ns g gg g
g as d g 0 1
a g 0 1 g f 1
a00 ag 0 g 0 1 Þ ]]] ns g gg g ]
11174104bn0
0sn0 g bn0 dna a0sn 0 0
0
4 ·
1 ÷÷
ø
öççè
æ+ d 0 Î 1
g g gds 0 a0sn 0 ag ggn 0 n0 0 gg asn0 g gs 0 1 00 g 00ngn 0 s 0 0ngs
g gds 0 gd a0 agn d ng g g ssn 0 0 s a d 0 (s) g ng 0 0 ns ag
( ) a 0 db g 0 gds n0 a0sn 0 0 bn0 dna ns 8
( ) 0 db g 0 gds n0 a0sn 0 gn n0 ga g g 0 ns 0
( ) g ns 0 gd n0 a0sn 0 g ng ns n00 00 0 0
( ) 0 g a00 0n0 ag dn00 gds 0 a0sn 0
00 1
04 1 1
1 ÷
ø
öçè
æ + -222..].2]]..]2..]]
g g 1
0 0 g
g0
-
· 4
g
g ·
1-
g 00ngn 0 0 1s 0 gds ag 0 0d 0
1·
1d 0
·
1
\ 0 0 g 0
· 4
1 0 · 0
1 ·
1
1 g 8
)10(0 - 0 0
\8
)10(0 - 0 (0 � 1) Þ 0 0 8 (as 0 ¹ 1)
\ gg1 0 8
g
g8
- · g
1 · 4
g
- 0 8
g · g
1 ·
÷ø
öçè
æ -4
g04
gds 0 gn n0 g g g gg g g 0 g 0 0d 4d 8 Þ 0 gds
0g ag g gg g 1 ]
f f , f ] ]] ]]]]
1117 10 10
00 a D d a s dngngg ns n0sggnb 0d g s 0nad g n s 0 sn0 g1 00 ns 0 0 a0 bns g g g a0 0 ga0n s 0 s dngngg ns
( ) ) sn0 (sn0 4
abg + ( )
D
( )
sn0 ( )
s
)gs)(bs)(as(s ---
I g D ns ag a 0 gna0 a00 s ns s dn gnd g1
0 2n0 2 sn0ba
1bg
1ag
1
6=
6+
6222..].22]..]2..]].]]2]
g (a g b) 0 D
g 0 ba
+D
1111(1)
\ g 0 ) sn0 sn0 ( 4
abg
+ 0 ) sn0 (sn0 4
abg + Þ ] ]
a s 0
g s
ba
ab
+
0g d (1) g 0 ba
sn0ab
1·
+ 0
ba
g s
sn0ab
+ 0
sn0·
ba
g sab
+ 0
sn0 Þ ])] ]
11170 1 10
gna0 as 0 a g d gba
g sg g sb g sa
++++
0
1 0 g gg g s a d 0 (s) ns
ag 2
( ) gna0 ns gn a0 0 ( ) 0 g
( ) a 0 b 0 g ( ) sn0
sn0
PS
0
00 1 0a g s g b g s g g g s ] 0 a g b g g 222..].2]].2]2...].]]2]
0 0sn0 g sn0 g sn0 ] 0 sn0 g sn0 g sn0 ( sn0 a 0 sn0 g1)
Þ 4 sn0 sn0 sn0 0 sn0 g sn0 g sn0
\ 0 8
abg4 0
gba ++
Þ
abg 0 (a g b g g) 0 s
4D 0 s úû
ùêë
é =D
4
abgÞ
s
D 0 Þ g 0 Þ 2 ]
s g 0 Þ gna0 ns s n a ga Þ 2)] ]
11177 07 1
00 g s 0q 0 g s 0a 0 a 0 sn0 q ga0 b n 0 bd
( ) sn0 a ( ) sn0 ÷ø
öçè
æ a±p0
( ) sn0 ÷ø
öçè
æ a+p0
( ) sn0 ÷
ø
öçè
æ a-p0
f f , f ] ]] ]] ]
00 1 g s 0q 0 g s 0a 22]..].2.].]]2..]].]]2]
0 0 0d 1
0q 0 0p 0a\ 0q 0 0a g � 0a g p g 0a g p � 0a
q 0 a g � a g a+p0
g a-
p0
Þ ( )d ( )d ( ) ag g gg g
n0 0 0 � 1
0q 0 � p 0a
q 0 � a±p0
sn0 q 0 sn0 ÷ø
öçè
æ a±p
-0
0 � sn0 ÷
ø
öçè
æ a±p0
0 � sn0 ÷
ø
öçè
æ a±p
-p0
0 � sn0 ÷÷ø
öççè
æ÷ø
öçè
æ a±p
-p0
0 � sn0 ÷ø
öçè
æ a±p0
0g ( ) ns 0 g gg g 1 ]
11178 17 sp
00 gn s ad bd g a00 ( a � b)d ( b � 0g)d ( 0g � a) ag n0
agn d ng g g ssn 0 0
( ) 18(a g b g g) 0 18(a g b g g ) g ab ( ) ad bd g ag n0 c1,1
( ) ad bd 0g ag n0 21,1 ( ) ad bd g ga0 b 0 s 0 sn0 s 0 a gna0
( ss d a agn dng gds b 0 0n0 0)
00 1 ad bd g ag n0 1,1 222..]..]]..]2..]].]]2]
Þ b 0 a g g
\ b 0 ag 1111(1)
Þ ad bd g ag n0 c1,1 Þ ] ]
a s n 0 ( a � b)d ( b � 0g)d ( 0g � a) ag n0 1,1
Þ ( b � 0g) 0 0g � b
Þ 0 b 0 0 0g
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