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わかパタ chapter3
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Masamune Kobayashi
February 05, 2018
Science
0
65
わかパタ chapter3
研究室での勉強会に用いた資料です
Masamune Kobayashi
February 05, 2018
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Transcript
3
.- - > 2
1 [1] - . 3 9 > 3
1 [1] - . 3 4 !" #$ !% !&
… !" (#$ ) !& (#$ ) !% (#$ ) … )&$ )%$ )"$ … 1* #" , #% , ⋯, #- !. (#$ ))> ).$ ( ) ).$ > )0$ 1 ≠ 3 35 #$ ∈ 7.
1 [1] - . 3 5 3 !" ( ,
> #$" = &$ !" − )$" , *" ) :( *" +, , +. , ⋯ , +0 = , . ∑ #$" . 0 $2, = , . ∑ (&$ !" − )$" ). 0 $2, = , . ∑ (+$ 56" − )$" ). 0 $2, +7 2 6" 2
1 [1] - . 3 6 " " #$ ,
#& , ⋯ , #( = ∑ "+ (#$ , #& , ⋯ , #( ) . +/$ J 6( 4 > #1 5 2 26( "+ # = $ & (2 3+ − 5+ )& = $ & (# 67+ − 5+ )& ) 5+ 26( ) 5+ = 8 1 (3+ ∈ ;$ ) −1 (3+ ∈ ;& )
- 3 [2] 1-. 7 8 79 8 79 !
= ($% , $' , ⋯ , $) )+ ,(!) -, ( ,4 -, = /0 /! = ( /0 /12 , /0 /13 , ⋯ , /0 /14 )+ 8 79 , !' , !5 , ⋯ , !6 > 4 /0 /!7 = -8 , = 0 : = 1,2, ⋯ , = )3 /0 /!7 = ∑ /0? /!7 = @ AB' ∑ !8 +CA − E8A CA = 0 @ AB'
- 3 [2] 1-. 8 ) !×($ + 1) ()*++,-.
0! 9 /0 4 (pattern ≝ (89 , 8; , ⋯ , 8. )+ /0 ≝ /09 , /0; , ⋯ , /0. + (> = 1,2, ⋯ , A) 0 .30 ( 1 B C9 , C; , ⋯ , CD = 9 ; ∑ ‖()*++,-. C0 − /0 H ; D 0I9 JK JCL = ()*++,-. + ()*++,-. C0 − /0 = 0 0 . 0 ,3 (pattern 40>2
- 3 [2] 1-. 9 (4 !"#$$%&' $ !"#$$%&' )*
= !"#$$%&' $ ,* (. = 1,2, ⋯ , 3) 5. !"#$$%&' $ !"#$$%&') 5 ,5 )* = (!"#$$%&' $ !"#$$%&' )56!"#$$%&' $ ,* (. = 1,2, ⋯ , 3) ) 7 ,5 3 )* 5 1 > 8" ,*" ,5
1 [3] 3 -. "#$%%&'( % "#$%%&'( 2
> 2 10
11 !" # = !" − ' () (!" !"
− '*" ) (, = 1,2, ⋯ , 1) ) 1 = , 6 ' >( 1 [3] 3 -.
12 (, - ))7 1 7 >H ! " #
= !" − ' ()* (!+ = !" − ' ,"- .- (0 = 1,2, ⋯ , 5) 1 [3] 3 -. 78- 7!" = 78- 79" (.- ) : 79" (.- ) 7!" 78- 79" (.- ) = 9" .- − ;"- = ,"- 79" (.- ) 7!" = .- > (, - ))7
[1] 2. ) (( > H 1 !" ($% )
1 8 '" ( = * 1 (( > 0) 0 (( < 0) (0 = 1,2, ⋯ , 4) 1 > 1 - W > 13
[1] 2. " $ 14 & 1
#$ #% … … &' &( &) … … *$' *$( *$) ∑ , $ -. /$ (1) #3 0 #3 (&) #5 (&) #% (&) "'% 0 / 1 0 / 1 0 / 1 " ! #& 67
[1] 2. , 0> ! #$ %& > 0 (*
∈ ,$ ) #$ %& < 0 (* ∉ ,$ ) (0 = 1,2, ⋯ , 6) , 1 0 9 ) ! 7$ * = 1 78 * = 0 9 ≠ 0 (0, 9 = 1,2, ⋯ , 6) , 2 1 ( 15
[1] 2. ) (> !"# = % 1 ()# ∈
+" ) 0 ()# ∉ +" ) (/ = 1,2, ⋯ , 3) 2 !"# , )# ∈ +" +4 1 5 6" )# = 0, !"# = 1 64 )# = 1 , !4# = 0 (7 ≠ /) 16
[1] 2. 3 3 ! #$ % = #$ +
( ) *+ #, % = #, − ( ) *+ 2 - > 3 3 3 ) ((3 2H - > 3 17
23 . [2] . H > >f . H >
r 0 (, - ))> d> w W>o > > . > r > i 18
23 . [2] : > : > > > 19
> > ( - ) 20 … !" !# !$
… … > … … … … … … … … … … … … … … … … … … … … … … … 1 & ( … …
( ) (51 4 ! ( #$ 21 % &
' ℎ)$ = ∑ ,-) .-$ - .)$ = /) (ℎ)$ ) /) ℎ2$ .-$ .)$ .2$ ,-) ,)2 .-$ : >: % ℎ)$ : - >: ,-) : >: 2 ℎ)$
6 > " 2 6 #$ ) #$ = &
' ∑ (*+$ − -+$ )' + 7 6 # = ∑ #$ $ () 22
8 ! , ( 8 ( 2 ) ( 2
2> , ) 2 23 # $% & = #$% − )*%+ ,$+ -!+ -#$% = -!+ -ℎ%+ / -ℎ%+ -#$% *%+ = -!+ -ℎ%+ -ℎ%+ -#$% = ,$+
!"# 24 !$# = &'( &)*( = &'( &+*( ,
&+*( &)*( = &'( &+*( . $ /(ℎ $# ) ( ) 34# 35 $# = 5$# − 7$# ) 34# 35$# = 8 34# 3ℎ9# , 3ℎ9# 35$# 9 = 8 !9# :$9 9 34# 3ℎ 9# = !9# 3ℎ9# 35 $# = :$9
8 > "# $% & = ( 1 (& >
0) 0 (& < 0) (/ = 1,2, ⋯ , 3) 1 ) ( ) ) 25
)( 26 ! " = $ $%&'( (+,) !.(") =
!(")(1 − !("))
f "# , fHi "# % ℎ#' = )#' (1
− )#' ) .#' 3 2 .#' = ()#' − /#' ))#' (1 − )#' ) o 0 .1' 1 2#1 )#' (1 − )#' ) > d r 3 ) (( W - 3 27