Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1)

7,220 views

Published on

.

Published in: Education
  • Be the first to comment

  • Be the first to like this

ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1)

  1. 1. 30 1: 1.2: ! "! #$ %! "! #$ % & % ' ( % ! " # $ % & ' ( # # $ # # )*+,-./0 + ! " # $# %& % & ' ( # # $ # # )*+,-./0 + 1 2 3 2 & 2 $ 4$ 5# " $ $ " 6 $ $ ( 2 2 # 4$ 5# 7 8 9 $ 2: 8 . # "$% % ) $ ) % ): " " * ( $! % )% )*)$ % ! + * ! + , % " % " ( ) ( )% " ! "! #$ %. ! " # $# %& )% " ! "! #$ %. " " * - (-) " " * (-) -. 1. + ) ) 1. ) $% + '! " # $# %& ! " # $%& $ # $ ' # $# $ ( $# $ # ) # *# $%& $ # $ ' log x bx a b aανν= = logb a ) # *# $%& $ # $ ' * + : 3 2 4 3 3 5 2 2 1/4 2 log 8 3 2 8 log 81 4 3 81 log 125 3 5 125 1 1 1 log 1/16 2 4 4 16 αϕο αϕο αϕο αϕο = = = = = = = = =
  2. 2. -. 1. + ) ) 2. & *)# + ) ) (! " # $# %& 30, * # . ) / ! + , ) $ ) / ) 2, 0 $ * *)# (% ! + ) % 1 ) 2 % ): % * ( % * *)# (% ! + ) % # " ) 0 )#3 ) 3 : ; ./0; 2log logx x= ; ./0;; ./0; 1 log1=0 2 log2=1 4 log4=2 8 log8=3 16 log16=4 32 log32=5 64 log64=6 … 1024 log1024=10 ; ./0; 2048 log2048=11 4096 log4096=12 8192 log8192=13 … 220 log220=20 230 log230=30 240 log240=40 … -. 1. + ) ) 3. *)$ % + (& )% + ) %) )! " # $# %& 4* "$ " + ( *) 0 ) ) 0,% $ ) ) ( ): & ! * # , % ) ( «",0 )» " "$ ! + ) . ,2 $ ) *, ) ! + ) % ) 5 , % # " ) *( : log logK b ba K a= ,2 $ ) *, ) ! + ) % ) 5 , % # " ) *( : $ $ " ) ( # ) % 2 %: 6 ) " $ ) # , % $% & «",0 )». 5 . %: # ) )*)# +) * *)# (% ! + ) %: (log )X b a logX b a log log log (log ) K b b X X b b a K a a a = = log log log (log ) K X X a K a a a = = -. 1. + ) ) 3. *)$ % + ( !! + - %) *! " # $# %& ) )# )*)$ , ) $ , " ! + # " ) ! + ) «" + » / , ) #$! : log log log c b c a a b = )*)$ ) " !( ) $ / # ) *) % ) $% ) *( 2. * + : 2 8 2 64 3 9 3 log 32 5 log 32 1.66 log 8 3 log 2048 11 log 2048 1.83 log64 6 log 27 3 log 27 1.5 log 9 2 = = = = = = = = = -. 1. + ) ) 3. *)$ % + ( + ) % ) , # ) 6! %) +! " # $# %& ( # ) ) 2 % *( )*)$ %: log ( ) log log log log log b b b b b b xy x y x x y y = + = − 6 ) )*)# +) * *)# (% ! + ) %: + ! " " " . ! + ) % , ) " * 0 + %: " " ) , )% " , )% "$ ) * " " , )% ! )"$ : log( ) log log log log log xy x y x x y y = + = − log (log )b bxy x y= ⋅ log log ( )b bxy xy≠
  3. 3. -. 1. + ) ) 3. *)$ % + ( #0 % *( ) ,! " # $# %& 1 # ) 2 % (" !( )# ) )*)$ 0 +,%: logb x b x= 2 5 10 log 2 log ( ) 5 10 n n n n n n+ = = + )*)$ % 0 )*) ) $ ) )% " ! "! #$ %, $" #0 . )% )% % # )#,% / 2. * + : 2 2 log log4 log4 2 2 4 2 2 2 n n n n n n = = = = 10log ( ) 10 n n n n+ = + -. 1. + ) ) 4. 0)# % f(x)=log x ! " # $# %& 30 ! " )0 " )# ( " ) ) % 2 ) ) + 0)# " % f(x)=log x: ( $ ): f(x) 2 ) " !( + ( ) )# $ "$ " ) * " " ! )# ). $ " )# " ," ) + . $ ) ) " ) . -. 1. + ) ) 5. &)"!$% # ) )"!$% + ) % ! " # $# %& # ) )% 2 % )%: % + 0 % ) : 1 2 ( ) loglog ( ) logloglog f n n f n n = = % + 0 % ) : 1 ) ". . , : ) )% " % " ," ) + . : !! # ) $ ) " )# " % " ) 1 2 ( ) log(log ) ( ) log(log(log )) f n n f n n = = log(log 256) log(8) 3 log(log(log16)) log(log 4) log(2) 1 = = = = = logloglog loglog logn n n< < . * ! + # 1. 5 *) + ! " # $# %& < # = < # - .! & / . 0. 1 log x bx a b aανν= = log 2x x a aανν= = log ( ) log logb b bxy x y= + log( ) log logxy x y= + x x / . 2# ! 3## / 4 ! ! . & ! # / . 5%6 ! " log log logb b b x x y y = − log log log x x y y = − log log log c b c a a b = log log log 2 c c a a = log logK b ba K a= log logK a K a= log (log )X X b ba a= log (log )X X a a= logb x b x= log 2 x x=
  4. 4. . * ! + # 2. ! "! #$ % % #03 2 : 6 ) % * 5-6 )%. " " # ! ( * ! + " ) 2 % / : ! " # $# %& (2 ) " )# % " ! "! #$ % )% " # )% ) 2 % / : 1. - # (.) " ) ). 1. ) )% " ( 2) ( (* ! * * " ) # " ) " *)$ ) ) * ) %, !!)3% " / 2 2. #0 . )% )% % # )#,% / 2, ) " )3 % )*)$ 3. 6 " 2 )% % # , % ( % )*)$ % ! + ) 4. +# % # , % # ) 0, " ,! )% )#,% )% log 2 x x = . * ! + # 2. ! "! #$ % 1. ( (.) " + ( * " % " ( 2 + (.) ) % %. ) 2 + + (.) " ) ) , «# »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
  5. 5. . * ! + # 2. ! "! #$ % 3. 2 )% % # , % 1" ) " 3 % # , % # ) # )% " 2 )% ! + " , 0 ) (%. $ % # ) " !) ) , # # ) , ", ) $! % ) * )% " ) % ) (% ! + " * )+ " ! *! " # $# %& . * ! + # 2. ! "! #$ % 4. (+# ) # 3 !)# / . (2 ) % # , % , 0 ( )% " 2 )% , " "$ )% + ,% 0,%. - )#$ * +$ ) +) " 0 ( ) " # % )% + ,% 0,% " ! "! #$ %. !!! " " , ) " #(5 ) ) " "! # ( , ) $ ) , " #(5 ) +) $ /# ) , $ : +! " # $# %& , ) $ ) , " #(5 ) +) $ /# ) , $ : " . + !( $ "$ $ % ) " " " "$ )% , *) + !( $ , $ " 0 . " ) ) + !( "$ ,%: # ) 3 % , % "$ $ " ) " !! "! ) , . . : , # ) " !) ) " ! , $ # ) # ) "$ $ %. . .: / $, ) ,% , ! 9 * " ! " ) # , % "$ % $ % " , " #(5 ). 5 6 logn n n n< < 2 4 2 logn n n+ < + ) "$0 % ) % ) .$ "$ $ ) 8" , "!, ") ! )# : . * ! + # 2. ! "! #$ % 4. (+# ) # 3 ,3 # ! . 7.% ! .%8 3#/ " ( ) (1)nΤ = Θ )(log)( nn k Θ=Τ )()( k nn Θ=Τ )()( n an Θ=Τ )!()( nn Θ=Τ )()( n nn Θ=Τ 8" , "!, ") ! )# : ' $ $ 6 2 (1) 6 6>1 «# $» n 6 6 «# $» n 6 6 1<a<2, ,/: ,% «# $» n 6 6 «# $» n log log log logK n n n< < 2 3 ... K n n n n< < < < ... 2 3 ...n n n n a b< < < < < ! n n n< . * ! + # 2. ! "! #$ % 4. (+# ) # 3 1 ) #! " * )+ " ! % 2 %: ! " # $# %& ( ): 9 ," ): 2 3log log 2.32n n n< < 1 2 3f f f< <
  6. 6. . * ! + # 2. ! "! #$ % % * ( 3 " % " ," ) ) " % )% 2 )%: ! " # $# %& . # )% # 6 $ % 1 " ! + % #$! % ! + % % " ! +) . * " " ! + # )/3%, # ) 2( " ) *( 0 )#3 ) 3 # ) ! + ) % ! " # $# %& 5 4 1.log 25 2.log 644 8 3 4 9 6 2.log 64 3.log 64 4.log7 5.log 45 6.log 62 7.log 33 8.log 80 9.log 244 . # )% # 6 $ % 2 " ! + % #$! % ! + ) % # % !! + / %: ! " # $# %& 128 4 1.log 32 2.log 5124 9 4 2.log 512 3.log 27 4.log 1/ 2 . # )% 0 + 1 )% " # )% (2 ) " )# % " ! "! #$ %: '! " # $# %& log 1 log 2 ( ) 1.5 ( ) 10log ( ) 0.005log n n n f n n f n n f n n = = =3 4 ( ) 0.005log ( ) 1.15 n n f n n f n n = =
  7. 7. . # )% 0 + 2 )% " # )% (2 ) " )# % " ! "! #$ %: (! " # $# %& log 1 5 2 6 2 ( ) 8log 4 ( ) 10( ) n n f n n n n f n n n n = + = + + 2 5 7 3 4 4 ( ) ( ) log n f n n n n f n n = ⋅ + = . # )% 0 + 3 )% " # )% (2 ) " )# % " ! "! #$ %: )! " # $# %& 1 2 ( ) 3 ( ) log( ) n n f n f n n = = log 3 5 4 ( ) 2 ( ) ( ) n n f n f n n = =

×