ǯǽǤ͡
®ϥۥ®
ܿĻԡ 18ڡ 0:05:43 HomePage:33574
ߥƥ
ܼȤϴطʤΤǤեΥ륢
ǥեȤǡ??????@hogehoge.ne.jpȤΤϻͤʤǤ礦
18ڡ 0:06:02 33575
ڤפɡ
äȤ6̤ä
㤨УοϣܤǤȹͤ029ͳ¤ؤΤǡ
ư̤¤ˤʤΤϣ򣱡ȤäȤ
Ĥޤ
62^5+6c32^3+62=364
18ڡ 0:08:41 33576
cocolo
ޤƤǤȤޤǯꤤޤ
ǯ᡹ֳư̤¤פȴ㤤ơ305ġפäƤޤޤġ˸ơġ
ʼˡ 18ڡ 0:08:48 33577
Taro
0ޤ᤿6ͤ
625202362364
ԤΤϤ졡 18ڡ 0:08:51 33578
Ϥʤ
ޤƤǤȤޤ
μߤơ㤽ȡ
ǰƽ񤭽ФȤ̵̤ʼ硦
18ڡ 0:11:20 33579

#33578TaroƱǤ
ĤΤϼʤΤǡĤΤȤĤΤȤĤΤȤ
ʬޤ
ǽ̣ˣΤȤĴ٤Ƥɡž
̤ο᤹ͤʬäƤȤϰŻǤ礦
ޡ 18ڡ 0:11:31 33580
ߡ
˳ߤȴꤦ⡣
³㳲äơorz

̯Ǥ
18ڡ 0:11:50 33581
ߡ
ޤ˲ˡȡ
728Ĥޤ

ƬȾǣʤΤǡȾʤΤ餫Ǥ

֤֤ȼ夤ϰ褬
18ڡ 0:13:35 33582
㡼ߡ
#33576, #33578 ƱǤ3^6 ΤۤȾʬʤǤ͡
ǯꤤޤ
Ȥ礦Ȥ䤯 18ڡ 0:13:36 MAIL:kakuromaster@star.cims.jp 33583
CRYING DOLPHIN
ǯǯϤ򶴤ǡϢ³2009ߤǤ

ǯ⵹ꤤޤ
ï⤤ʤԳϡ 18ڡ 0:14:26 HomePage:ȤƻȤ33584
㡼ߡ
ۤȾʬʤΤǡĤȤͤʤƤ
#33582 Τ褦˹ͤǤ͡ʤۤɡ

#33580
6 x 2^5 = 192, 20 x 2^3 = 160, 6 x 2 = 12
Ȥ׻ѻ˽񤫤Ƥޤ
Ȥ礦Ȥ䤯 18ڡ 0:16:59 MAIL:kakuromaster@star.cims.jp 33585
ڤפɡ
ʤۤɡ(3^6-1)/2ȤΤ⤢Ǥ͡
18ڡ 0:18:47 33586
Taro
#33580
ΤȤǤ#33582Τ㡼ߡȤۤȤƱȤ񤫤Ƥޤ
㤤ϺǸ12ʤ餤Ǥ(^^;

ǯɤꤤޤ
ԤΤϤ졡 18ڡ 0:20:12 33587
ߡ
Σ729ġ000290290ȹͤ000000Ȥʤ룱Ĥ
ƤȾʬûǤ礦

728Ĥ(2438127ܣܣܣ)ߣȤƤޤ٤ޤ
18ڡ 0:20:41 33588
Die neue Frau
Ϥ⤿Ĥ̿Ǥ͡
ˡϡƷιפȤȤ顢Ǥ91ġ3ġ5ĤξͤФ褤
1Ĥξ6C12^5=192
3Ĥξ6C32^3=160
5Ĥξ6C12=12
ʾ夫19216012=364
4ʬϳݤꤹǤ
˳ھڡ 18ڡ 0:20:55 MAIL:jjyhr530@yahoo.co.jp 33589
Ѥ
0,2,90,1,9ȴ㤤Ƥޤޤå
֡ 18ڡ 0:21:06 HomePage:33590
Die neue Frau
#33576,#33578,#33580,#33583,#33585,#33587#33589ƱǤ
#33582#33588ϹȻפޤ
˳ھڡ 18ڡ 0:29:24 MAIL:jjyhr530@yahoo.co.jp 33591
⡼ޥ
0,1,2 3ˡǹͤƤƱʤΤǡ
٤Ƥοϡ3^6-1
Ʒ¤ϡоȴξƱȹͤơʢø ^^;(3^6-1)/2=364 ǡӥ󥴢
18ڡ 0:30:21 33592
Die neue Frau
#33591Ϥʤ󤫡uchinyanνˤʤäƤޤޤ
˳ھڡ 18ڡ 0:31:06 MAIL:jjyhr530@yahoo.co.jp 33593
Ѥ
K_n+2=4K_n+1 - 3K_nƲ򤭤ޤ
̲nΤȤ(3^n-1)/2
㤦ޤꤽȻפä餢ߡ#33582Ǥ
֡ 18ڡ 0:33:11 HomePage:33594
Mr.ǥ
¿γƱˡǤʤߡȯۤϽФƤʤäǤ͡

᤯ǤפȻפȤˤϡɬʤ֤Dz򤤤ƤͤǤ͡51á
ʤɤǤǣʬ̤äƤ褦ʵޤ
18ڡ 0:34:03 33595
Taro
ʿѤĴ٤Ƥߤ409035Ǥ
11111111/3407407ȾƤޤ͡
ԤΤϤ졡 18ڡ 0:42:37 33596
ߡ
ͤϤ᳧͡ǯꤤޤ
˺ޤ
18ڡ 0:57:03 33597
tomh
͡ǯꤤޤ m(__)m
ԡ 18ڡ 1:34:39 MAIL:tomh@yahoo.co.jp HomePage:H to M33598
ϥ饮㡼ƥ
Ϥ褦ޤ

ץǤ

ǯ줬˴ʤäΤǯΤĤʤǤ
ǯꤤޤ
18ڡ 5:54:24 HomePage:湩ؤ˥33599
BossF
6C1x2^5+6C3x2^3+6C5x2
root of isle 18ڡ 6:14:47 HomePage:fv2f-ftk@asahi-net.or.jp33600
BossF
äȡ
root of isle 18ڡ 6:15:22 HomePage:fv2f-ftk@asahi-net.or.jp33601
abcba@jugglermoka
Happy new year!!ǯꤤޤ
dzƷοࡢʳΰۤʤnϣʲ
Τ줫ǤꡢƷ¤xοϦ_k=1^k=y (xCk-n+^(x-k+))Ĥ롣
_k=1^k=y ϦϰϤɽxCk-ɽ
-ϣʲκδȤ롣
18ڡ 8:41:16 33602

裱Ǥ͡
󡢺ǯꤤޤ
18ڡ 9:25:10 33603
uchinyan
Ϥˤϡǯ⵹ꤤפޤơϡ
ϤäƻŻ򤪵٤ߤޤǻ֤äΤǡȸƤƤߤޤ (^^;
Ĺʤޤۤ

(ˡ1)
ǽ˻פĤˡǤ
0, 2 ϶9 ϴʤΤǡư̤ο¤ˤʤϡ9 1 ġ3 ġ5 ĤȤʤǤ
9 1 Ĥξ硧9 η֤Τ 6C1 = 6 ̤ꡤĤ 5 0 2 ʤΤ 2^5 = 32 ̤ꡤǡ6 * 32 = 192 ġ
9 3 Ĥξ硧9 η֤Τ 6C3 = 20 ̤ꡤĤ 3 0 2 ʤΤ 2^3 = 8 ̤ꡤǡ20 * 8 = 160 ġ
9 5 Ĥξ硧9 η֤Τ 6C5 = 6 ̤ꡤĤ 1 0 2 ʤΤ 2^1 = 2 ̤ꡤǡ6 * 2 = 12 ġ
ʾǤ٤ƤʤΤǡ192 + 160 + 12 = 364 ġ

(ˡ1) n ؤγĥ
n äɤʤΤȡѤ˻פޤ
餫˼˳ĥǤơA = [k1ʾnʲδ]{nCk * 2^(n-k)} Ǥ͡
ơ¤ɤäƵ뤫Ǥ
ǡư̤ο¤ξ B = [k0ʾnʲζ]{nCk * 2^(n-k)} ͤȡ
A + B = [k=0,n]{nCk * 2^(n-k)} = (1 + 2)^n = 3^n
B - A = [k=0,n]{nCk * (-1)^k * 2^(n-k)} = ((-1) + 2)^n = 1
ǡA = (3^n - 1)/2b = (3^n + 1)/2 ˤʤޤ
Τˡn = 6 A = (3^6 - 1)/2 = 728/2 = 364 ˤʤޤ
Τ줤ʷ̤ϲʡȻפäΤǡθ塤ƤƤߤޤ
ޤ̲ʤȤΤ(ˡ2)Ǥ

(ˡ2)
n ʲοǤäơư̤ο¤ȤʤθĿ a(n) ġȤʤĿ b(n) ġȤȡ
(n+1) ʲξϡ(n+1) ܤ 02 9 ʤΤ(n ʲξޤǤΤ)
a(n+1) = ((n+1) ܤ 0 2 n ʲ¤) + ((n+1) ܤ 9 n ʲ¤) = 2 * a(n) + b(n)
b(n+1) = ((n+1) ܤ 9 n ʲ¤) + ((n+1) ܤ 0 2 n ʲ¤) = a(n) + 2 * b(n)
a(1) = 1, b(1) = 2
a(2) = 2 * a(1) + b(1) = 2 * 1 + 2 = 4, b(2) = a(1) + 2 * b(1) = 1 + 2 * 2 = 1 + 4 = 5
a(3) = 2 * a(2) + b(2) = 2 * 4 + 5 = 13, b(3) = a(2) + 2 * b(2) = 4 + 2 * 5 = 4 + 10 = 14
a(4) = 2 * a(3) + b(3) = 2 * 13 + 14 = 40, b(4) = a(3) + 2 * b(3) = 13 + 2 * 14 = 13 + 28 = 41
a(5) = 2 * a(4) + b(4) = 2 * 40 + 41 = 121, b(5) = a(4) + 2 * b(4) = 40 + 2 * 41 = 40 + 82 = 122
a(6) = 2 * a(5) + b(5) = 2 * 121 + 122 = 364, b(6) = a(5) + 2 * b(5) = 121 + 2 * 122 = 121 + 244 = 365
ǡ 364 ġǤ

(ˡ2)ΰ̲
a(n+1) = 2 * a(n) + b(n)
b(n+1) = a(n) + 2 * b(n)
a(1) = 1, b(1) = 2
򤭤ޤ
a(n+1) + b(n+1) = 3 * (a(n) + b(n)) = ... = 3^n * (a(1) + b(1)) = 3^n * (1 + 2) = 3^(n+1)
a(n+1) - b(n+1) = a(n) - b(n) = ... = a(1) - b(1) = 1 - 2 = -1
a(n+1) = (3^(n+1) - 1)/2, b(n+1) = (3^(n+1) + 1)/2
a(n) = (3^n - 1)/2, b(n) = (3^n + 1)/2
Τˡ(ˡ1) n ξȰפޤ

(ˡ3)
(ˡ2)ҥȤˤʤäƤޤѤƹͤƤߤޤ
̤ˡn ʲǤϤʤ礦 n ξ硤n 2 ʾʤСΤȤޤ
n ܤ 2 9 ʤΤǡ
(礦 n γư̤ο¤ȤʤθĿ)
= (n ܤ 2 (n-1) ʲο¤ȤʤθĿ) + (n ܤ 9 (n-1) ʲο¤ȤʤθĿ)
= ((n-1) ʲο¤ȤʤθĿ) + ((n-1) ʲο¤ȤʤθĿ)
= ((n-1) ʲοθĿ) = 3^(n-1)
(礦 n γư̤ο¤ȤʤθĿ)
= (n ܤ 2 (n-1) ʲο¤ȤʤθĿ) + (n ܤ 9 (n-1) ʲο¤ȤʤθĿ)
= ((n-1) ʲο¤ȤʤθĿ) + ((n-1) ʲο¤ȤʤθĿ)
= ((n-1) ʲοθĿ) = 3^(n-1)
ʤΤǡɡ
(礦 n γư̤ο¤ȤʤθĿ) = (礦 n γư̤ο¤ȤʤθĿ) = 3^(n-1)
ϡ2 ʾξǤ
1 塤n = 1ξ 0 Τ̤ǡξ礬 1 ġξ礬 2 Ĥǡξ礬 1 ¿ʤޤ
ǡn ʲΤ 3^n ġ줫̤ 0 θơ
(n ʲγư̤ο¤ȤʤθĿ) = (3^n - 1)/2
(n ʲγư̤ο¤ȤʤθĿ) = (n ʲγư̤ο¤ȤʤθĿ) + 1 = (3^n + 1)/2
Ǥϡn = 6 Ȥơ(3^6 - 1)/2 = 728/2 = 364 ġˤʤޤ

ʤ¿꤯ɤǤ
(n ʲγư̤ο¤ȤʤθĿ)
= [k=1,n](礦 k γư̤ο¤ȤʤθĿ)
= [k=1,n]{3^(k-1)}
= (3^n - 1)/(3 - 1)
= (3^n - 1)/2
ȤƤ⤤Ǥ͡
ͥνȡ 18ڡ 12:07:47 MAIL:uchi@sco.bekkoame.ne.jp 33604

ηΤȤΡݣ3^(N-1)ĤοƬˣޤϣդ
ȹͤơܣܣܣܣܣᣳȤޤ
ܿĻԡ 18ڡ 12:18:28 HomePage:33605

ʤۤɡѤʤͤϤҤ񤭽ФƤޤ
18ڡ 12:23:47 33606
o
ġġġĤξ
˧󡤿޷Ǥ,ߤιΤΤꤷƤϤɤǤ
18ڡ 12:29:00 33607

Ǥ顣
18ڡ 12:29:47 33608
ϺĹܲ
֤ޤäޤ
627󤬲򤱤Ϣ³ڤƤޤޤޤĤĴĥޤɸΨ80ǤβϤƱǤ
18ڡ 12:30:10 33609
uchinyan
ǼĤɤߤޤ

#33576#33578#33580#33583#33589#33595(¿ʬ)#33600#33602(¿ʬ)#33604(ˡ1)
9 1 ġ3 ġ5 ĤȾʬˡ
#33602
亣dzƷοࡢʳΰۤʤnϣʲ
Τ줫ǤꡢƷ¤xοϦ_k=1^k=y (xCk-n+^(x-k+))Ĥ롣
䤿_k=1^k=y ϦϰϤɽxCk-ɽ
䣲-ϣʲκδȤ롣
äơ{(n+2)^x - n^x}/2 ˤʤΤǤϤʤΤʡ

#33607
䣹ġġġĤξ
Ȥˡ#33576ʤɤ΢֤Ǥ̤ʬषޤ

#33579
ǰƽ񤭽ФȤ̵̤ʼ硦
#33606
Ҥ񤭽ФƤޤ
񤭽Фˡ

#33582#33588#33592#33604(ˡ3)Ⱦ
0 ¤ʤΤȶʤΤƱĤȤȤȤˡ

#33594#33604(ˡ2)


#33599
ץࡣ

#33605#33609#33604(ˡ3)θȾ
ηΤȤΡݣ3^(N-1)ĤοƬˣޤϣդ
Ȥˡ#33582ʤɤȻƤޤ̤ʬषޤ
ͥνȡ 18ڡ 13:01:47 MAIL:uchi@sco.bekkoame.ne.jp 33610

١ߤޤ󡣤ˤؤꡣ


log2ʣݣˡlog1/2ʣݣˡ声
ʤưȤ

4^62^10

κͤȺǾͤ衣
18ڡ 13:38:19 33611
ޥ
󤹤ͤʤ󤫽񤭽Фơ֤1뤴ȤˣܤˤʤäƤΤǤϡפȻפäƣܣܣܣܣܣᣳˤޤʹͤǤƱˤʤäƤޤ˿ʤȤʤȤ
18ڡ 16:42:16 33612
???
Option Explicit
Dim a(6) As Integer
Sub Macro1()
Sheets("Sheet1").Select
Cells(1, 1).Value = 0
Call saiki(1)
Range("A1").Select
End Sub
Sub saiki(ByVal n As Integer)
a(n) = 1
While a(n) <= 3
If n < 6 Then
Call saiki(n + 1)
Else
Call check(0)
End If
a(n) = a(n) + 1
Wend
End Sub
Sub check(ByVal x As Integer)
Dim wa As Integer
Dim nn As Long
Dim j As Integer
wa = 0
For j = 1 To 6
wa = (wa + m(a(j))) Mod 2
Next j
If wa Then
Cells(1, 1).Value = Cells(1, 1).Value + 1
nn = 0
For j = 1 To 6
nn = nn * 10 + m(a(j))
Next j
Cells(Cells(1, 1).Value, 2).Value = nn
Range("B" & Cells(1, 1).Value).Select
End If
End Sub
Private Function m(ByVal n As Integer) As Integer
Select Case n
Case 1
m = 0
Case 2
m = 2
Case Else
m = 9
End Select
End Function
18ڡ 17:19:11 33613
ߤ
򸫤ƤˤΩäΤǣʬƤȤϻפǤ
ǰʤϻŻǼ˵餺ġ

ɤĥäƤ⣱ʬDzϻˤԲǽǤ
18ڡ 19:13:00 33614
̵
1ξ硢2ξĤȾʬƹͤޤ褯ͤ0ΰ֤򵤤ˤ6ǹͤСƤηοʹޤޤ뤳ȤˤʤǤ͡㡧0090209020
19ʶ 11:54:30 33615
⡼ޥ
#33605

أηΤȤΡݣ3^(N-1)ĤοƬˣޤϣդ
ȹͤơ١ϡ

ɡΤǤ뤫顢#33582 ΤߡιͤƱǤ͢

äꤷޤ ^^v
19ʶ 12:18:05 33616

#33616
áʤۤɡ
(3^6-1)/2!!
ܿĻԡ 19ʶ 14:47:35 HomePage:33617
ϥ饮㡼ƥ
#33611

Mathemaiticaǥץ

Maximize[4^x - 6*2^x + 10, Log[2*(x - 1)] + Log[1/2*(3 - x)] <= 0, x]

Minimize[4^x - 6*2^x + 10, Log[2*(x - 1)] + Log[1/2*(3 - x)] <=0, x]

ˤƺͣǾ-8+4^(log3/log2)

19ʶ 17:31:47 HomePage:湩ؤ˥33618
Mr.ǥ
#33611
ꡡ13(1)
Ϳѷơlog[2](x-1)log[2](3-x)0
äơlog[2]{(x-1)/(3-x)}0ꡡ(x-1)/(3-x)1
򤤤ơ(1)Ȥ碌ơ12
ء2^x Ȥȡ2ء4(2)
^26ء10(ء3)^21
(2)ꡡء3x=log[2]3ˤΤȤǾͣء4ʣ2ˤΤȤͣ Ȥ롣
ϥ饮㡼ƥȰ㤦̤Ǥޤ
19ʶ 21:56:32 33619
ΩعĹ
ޤ1ǹͤޤ
1塡3̤
2塡236̤
3塡23318̤
4塡233354̤
5塡23333162̤
6塡233333486̤

ˡ2ͤޤ
ܶ
ܴ
ܶʤߤ˾0϶Ǥ롣

02Ͷ2̤ꡡ9ʹ1̤

1塡1̤ꡡ2̤϶
2塡122̤ꡡ
111̤ꡡ3̤ꡡ3̤϶ˡ0Ƭˤʤ
3塡326̤
3139̤ꡡ9̤϶
4塡9218
91927̤ꡡ27̤϶
5塡27254
2712781̤ꡡ81̤϶
6塡812162
81181243̤

1392781243364̤
110ڡ 3:57:44 33620

#33619
Mr.ǥǤϲƱˡǤ

#33618ϥ饮㡼ƥ
㤤ƤΤǤϡ
110ڡ 9:53:58 33621
ϥ饮㡼ƥ
#33619

MATHEMATICAΤְۤäƤߤǤ
Ǿͤ
-8+4^(log3/log2)
Ϸ׻ȤʤǤ
ץx<3Τޤ޲򤤤Ƥ褦Ǥ
ٹϽФƤޤ̵򤷤Ƥޤ
110ڡ 9:58:46 HomePage:湩ؤ˥33622
uchinyan
ȡ#33611ǤλȻפޤ
21/2 пʤΤΰʤΤȽȤޤ
ɤΤ褦Ǥϥ饮㡼ƥϡΰȤƲ򤫤Ƥޤ
(äȤ⡤βˤ̤ꤢꤽǤ)
ʤϥ饮㡼ƥήϡ̾ϡͤϤʤǾͤ 1 Ȥ٤ʤΤǤ礦
MATHEMATICAη̤ˤޤ
äˡ- 8 + 4^(log3/log2) = 1 ɮǤñˤǤޤ
γǧϡޤʽʤäؤνˤƤޤ礦 (^^;
ͥνȡ 110ڡ 12:16:02 MAIL:uchi@sco.bekkoame.ne.jp 33623

#33623uchinyanͤ
ΤɽۣǤ͡ޤ
Ĥμɽ狼äƤȴŤ󤸤ƤޤޤǤ
ϥ饮㡼ƥ͡r.ǥ͡Ŧĺuchinyan͡Ǥ򤪤ޤޤǤ
110ڡ 12:21:28 33624
ϥ饮㡼ƥ
#33623

Τ褦Ǥ͡

Maximize[4^x - 6*2^x + 10, Log[2, (x - 1)] + Log[1/2, (3 - x)] <=0, x]

ʤx=2ΤȤͣȤʤޤ

ؤϤä˺ƤޤѤƤܼѤʤ
ΤǡʿؤμˤɬסˡºݤǤѤʤΤ
̤ȻפޤޤlogϼпȻפޤ

ǤMathematicaϼѤˤʤ褦Ǥ
110ڡ 18:08:38 HomePage:湩ؤ˥33625
ϥ饮㡼ƥ
ǤϼŪФޤ

󥯤դˤӿۤ˳ӿ夹5
֤ǥ󥯤϶ˤʤȤ롣
ޤ󥯤ξ֤ӿۤĤƵ夹ȥ
8 ֤ˤʤȤ롣
󥯤ο̤ȾʬˤƱӿۤȵ
˳硢֤Ĥȿ̤Ϥˤʤ뤫

ӿۤο̤Ͽ̤ʿ㤹롣
ޤϰ̤ο夬ήȤ롣
ޤǥ󥯤ηϱ췿Ȥ롣
110ڡ 18:55:13 HomePage:湩ؤ˥33626
ϥ饮㡼ƥ

пǻפФޤlog-1ϡiСǤ͡ؤݤʤȤ
ɤɤĥ졢ȸм¿ȸ¤ʤȤǤ礦
ءء⹻ءʰϡˤȳȤʧ졢
ܼŪʿؤˤʤäƹԤɤǤĤޤ狼ʤȤ
ݤǤ

ޤlog2/log3ηǻפФޤå۶μ
log4/log3=1.26...ͭ̾Ǥ12ʤɤ
ǤϤʤΤե饯Ǥ

饳å۶ͭµΥĤδ֤Ϣ³ʶ
Υ̵Ǥʵդ˼ºŪȻפ
Fractal, Chaos, Wavelet򤤿ؤǤ

Ρ٥ޤΤˤǤΤǸ߼Ҳ˹׸٤礭
ءʳء椬ޤޤƤޤ󡣰ƣ
θϥΡ٥ޤΤǤïкѳؾޤ
ȤޤΨʬαѤϷкѤˤȤɤޤ
ޤΤ̽ʡ򤪵ꤷޤ

111 16:21:42 HomePage:湩ؤ˥33627
λȼ
äȻ𤬤äơäȥȥ饤ޤ

ͺǯꤤפޤ
zerostar 112ʷ 7:19:18 33628
ϥ饮㡼ƥ

п褯ȤºŪǤ

ʪAȾǯBȤʪޤ
ʪBȾǯCȤʪȤʤޤ

ǽʪA礢äȤƣǯФä
A,B,CΤ줾νŤϤ餫

logϿؤǤϼп¿̤ιؤǤϾп
ʳؤǤ줬¿褦Ǥ̤Υ
ȥԡʤɤϣʤǹͤޤΤǤ

γ͡ؤŪǤϤʤºݤ
ϡ߷פˤϤΤɬפǤ뤳ȤФƤ
ʣǿʤСؼΤ¸ߤʤ
Ȥ⤢ΤäƤƤΩĤ
ȤǤ狼ȻפäƿٶƤ

112ʷ 17:04:33 HomePage:湩ؤ˥33629
Ф
ϥ饮㡼ƥ
ɤŦǤ͡湩ؤΥץǤääǤäͤλ줬пʤƼºݤ˻ȤΤϸȤޤ󡣤ʤߤʪءʲؤΰʬˤǤϾпʤʡʬ򤯤줬ˤʤ뤱̵пľ褦ʵ

ΩĤɤϤƤؤǤʢΤΤʤȤ򲡤
112ʷ 22:36:05 33630
ϥ饮㡼ƥ
#33630

ؤ餷ƱǤ
ؤǤϿʤΤǻϹؤ˹Ԥޤ

湩ؤǤϿؼԤ¿ʤꤹơTheorem ȤCollaryȤ
Difinition)ϤޤäŸƤΤ
Ť沰ȤƤϰ´Фޤ

пϤϤѤƤ褦Ǥ͡
Ф졢

113ʲС 9:50:37 HomePage:湩ؤ˥33631

ͤϿزʤܻؤƤޤ
ؤ餷
113ʲС 10:15:40 33632
uchinyan
ȡΤ褦ǯˤʤ꤫ƤǯμԤϥ饮㡼ƥ򤯤ΤϸݤȿǤ
Ǥʬʤȳ󺤤Ǥ礦顤ȥ饤Ƥߤޤ
ɤʬФ褦ʤΤǡλȤǤνϤɤʤΤʡ
ȤѤʵ⤢ޤ

ȤȤǡ괺Ǥ礦

#33626
ο̤ 1 Ȥ 25/256

#33629
򤯤ˤȾʤɤμɬפǤkg ñ̤ǡ
A = (1/2)^5 = 0.03125
B = 3 * (1/2)^(8/3) - 3 * (1/2)^6 = 0.42560(6̤ͼθ)
C = 1 - 3 * (1/2)^(8/3) + (1/2)^6 = 0.54315(6̤ͼθ)
ʤ˻ŦϤʤäΤǡˤ̷»Ϥʤ
A + B + C = 1
ˤʤäƤޤ

ϡء⹻ϡؤˤƤޤؤܤ (^^;ʪˤޤ
Ǥܤ졤ɡ󻺶Ȥ˿Ȥ򤪤Ƥޤ
log ϤȤޤͤ
ء⹻ϡޤ׻ܤμȤ⤢пơѤǼп
ػϡäѤ鼫пǤпؿʣ̤ؤγĥʤɤ򤫤äǤ
ҲͤˤʤäƤȳؤǾʤɤ򤫤ꡤ줬 2 ΥȥԡΤäˤʤޤ

ޤΤϡʪٶ˻ػ˿ؤٶȤʤäȤǤ
ؤδܤʬäƤʤǤΤʪϤ줤˺Ƥޤޤ (^^;
⤦١ؤǤοؤʪٶʤפäƤޤ

㤤󡤴ĥäƤ
Ʊǯγ͡餱˴ĥޤ礦 ^^/
ͥνȡ 113ʲС 12:41:39 MAIL:uchi@sco.bekkoame.ne.jp 33633
ϥ饮㡼ƥ
#33633

꤬ȤޤʬʬDz򤱤ΤǤ礦
ʬΰ̣ɬפȻפޤեȤ
ºݤϤμȤȤä
ΤǤߤޤ

󥿡1718Τ褦Ǥ̴
ĥäƤ󥿡ʤäȤƤ
οؤʤɤ䤵Ȼפޤ

uchinyan󡢤꤬ȤޤǤ
󥯤ή̤ή̤ʤ̤
ɤΤǷФΤǤ

Ⱦ
ȾȾʬˤʤ롩ˤA̤
ñ˵Ȼפޤ¤ϿեMathematica
Ǥ

A=1/32
B=3/64(-1+82^1/3)
CʣʼǤǤ1-A-Bǵ롣
ȵޤޤ

ʪΤȤ˲򤤤Ƥ餤ޤƴդޤ
AˤѤϰϤΤ褦ʵޤ
⤦ɤޤǤȤ˺ޤ70ФΤۤ˶᤯
ʤäƤޤ
ͤ뵤Ϥ¤껻ĥޤ
ꤤޤ
113ʲС 16:27:11 HomePage:湩ؤ˥33634
⡼ޥ
#33634,#33633 ϥ饮㡼ƥuchinyanء
ߤޤ󤬡狼פнޤ...
ΩΤΤ狼ޤΤ...^^;
ĤƤ뤫ɤ狼ޤ...ꤤޤ m(_ _)m
114ʿ 0:12:14 33635
ϥ饮㡼ƥ
#33635

ߤޤ󡢴ñʤ褦񤷤Ǥ

󥯤ο̤ΤȤޤ
ȵ̤1/8Ǥ

ӿλh̤Ȥ

dh/dt=-k*h

ǤΤǤ줫t=0ΤȤh=1t=10h=0
򤤤 k ޤ̤夯Τή̤
ή̤Ȥеޤޤ

ޤȾΰ̣ϤȤAȤʪ100ǯФĤ
Ⱦʬޤ뤳ȤѲϻؿؿŪǤ뤳Ȥ
狼A500ǯ̤Ϥ狼ޤuchinyan
줿ˤ̷»ŻҤȤФ줿
̡̤뤳ȤǤǤ̵뤷Ƥޤ

ܤuchinyanˤʹȤȤ
uchinyanꤤޤ

114ʿ 10:18:12 HomePage:湩ؤ˥33636
uchinyan
#33635#33636
ɤ鿶Ƥޤä褦ʤΤǡޤ (^^;
إѥ졼ɤʤΤǡؿΤʤϡƼϤ m(__)m

ĹʤꤽʤΤǡ줾˴ؤƤˤޤ͡
ͥνȡ 114ʿ 14:20:06 MAIL:uchi@sco.bekkoame.ne.jp 33637
uchinyan
(㴳ɲýޤ)
ޤ#33626̤ꡤ˴ؤƤǤ
#33636ǥϥ饮㡼ƥꤷƤ뵭ˡǿʤޤ
Ĥޤꡤ󥯤ηϱѤϰʤΤǡñ 1 ȤƤ򼺤ޤ
ޤο̤ 1 Ȥ̤ξ h Ȥޤ0 <= h <= 1 Ǥ
ΤȤ V = 1 * h = h Ȥʤޤt ֡ñ̤ϻ֡ˤޤ

ޤ󤫤ӿǤ
ӿ̤Ͽ̤ʿ㤹Τ k > 0 Ȥȡ
dV/dt = - k * h
ޥʥϡѤ뤳Ȥ̣ƤޤV = h ꡤ
dh/dt = - k * h
ǤͿ줿狼 k ޤʬ򤯤ȡ
1/h * dh/dt = - k
(1/h * dh/dt)dt = - kdt
(1/h)dh = - kdt
2 * h = - kt + ʬ
t = 0 V = h = 1 ʤΤǡʬ = 2 ǡ
2 * h = - kt + 2
t = 5 V = h = 0 ʤΤǡ
0 = - 5k + 2
k = 2/5
ˤʤޤ

ˡ󥯤Ǥ̤ϰʤΤǡ8 ֤ꡤ = 1/8 Ǥ

ơ褤衤ȾʬӿξԤǤϡ
dV/dt = - k * h + 1/8
dh/dt = - 2/5 * h + 1/8
Ǥt = 0h = 1/2 Dz򤤤ơ֤ʬФäȤĤޤ t -> 硤 h ФǤ
x = - 2/5 * h + 1/8 Ȥȡt = 0 x0 = - 2/5 * (1/2) + 1/8 = 1/8 - (2)/5 < 0 ǡ
dx/dh = - 1/5 * 1/h
dh/dx = - 5 * h = 25/2 * (x - 1/8)
dh/dx * dx/dt = dh/dt = - 2/5 * h + 1/8 = x
25/2 * (x - 1/8) * dx/dt = x
25/2 * (1 - 1/8 * 1/x) * dx/dt = 1
{25/2 * (1 - 1/8 * 1/x) * dx/dt}dt = dt
25/2 * (1 - 1/8 * 1/x)dx = dt
25/2 * (x - 1/8 * log|x|) = t + ʬ
ǡlog ϼпǤt = 0 x = x0 ʤΤǡ
ʬ = 25/2 * (x0 - 1/8 * log|x0|)
Ĥޤꡤ
25/2 * (x - 1/8 * log|x|) = t + 25/2 * (x0 - 1/8 * log|x0|)
(x - x0) - log|x/x0|^(1/8) = 2/25 * t
log(e^(x-x0) * |x0/x|^(1/8)) = 2/25 * t
log(e^x/|x|^(1/8) * |x0|^(1/8)/e^x0) = 2/25 * t
e^x/|x|^(1/8) * |x0|^(1/8)/e^x0 = e^(2/25 * t)
|x|^(1/8)/e^x = |x0|^(1/8)/e^x0 * e^(- 2/25 * t)
ǰʤ顤 x hˤĤƲ򤯤ΤϴñǤϤޤ
֤ʬ˷Фä t -> ξĴ٤ΤϲǽǤ
ޤ|x0|^(1/8)/e^x0 0 ǤʤǤޤe^x μ¿Ǥ
ǡt -> Ǥ e^(- 2/25 * t) -> 0 ʤΤǡx -> 0 ˤʤޤ
ϡ- 2/5 * h + 1/8 -> 0h -> 5/16h -> 25/256 ̣ޤ
ǡ֤ФĤȡ̤ 25/256 ˤʤޤ

ʾǽǤʪŪʹͻ򤹤ȡäȴñ˲򤱤ޤ
֤ʬ˷ФäȤο̤ΤǤʪŪ˹ͤơ
̤ĤޤǤưȤϹͤŤ餯ͤ˰ꤹΤͽۤǤޤ
ºݡӿ 2/5 * h h h иꡤ̤ϰʤΤǡХ󥹤 h ǰꤹǤ礦
ξ硤ꤹʾ塤̤ѲΨ dh/dt 0 ˤʤȹͤޤƤޤˡ
dh/dt = - 2/5 * h + 1/8
äΤǡ
dh/dt = - 2/5 * h + 1/8 = 0
α¦򤤤ơh = 25/256 ˤʤޤ
ۤɤݤʷ׻ϡʪŪľ΢դƤ뤳Ȥˤʤޤ

ʤߤˡľʪǤϡ¿ʬؤǤ⡤ȤƤǤ
ۤɤΤ褦ʿŪ΢դɬܤǤ衣΢դʤǤϡۤǤ (^^;

ʤ줯餤ϡοؤǽꤵƤ⤪ϤʤǤ͡
ͥνȡ 114ʿ 18:36:41 MAIL:uchi@sco.bekkoame.ne.jp 33638
uchinyan
(㴳ɲýޤ)
ˡ#33629Ⱦꡤ˴ؤƤǤ
򤯤ˤϡ㴳ͽμɬפǤ
ʤ⸽пϼпǤ

ޤʪʪǤäȤƻ N ĤäȤȡ
θͻҤ N 㤹뤳ȤΤƤޤ
Ĥޤꡤ > 0 ʤɤȤޤt ֤Ȥȡ
dN/dt = - N
Ǥt = 0 N = N0 ȤƤʬ򤯤ȡ
1/N * dN/dt = -
(1/N * dN/dt)dt = (-)dt
(1/N)dN = (-)dt
log|N| = - * t + ʬ
N = * e^(-t)
N = N0 * e^(-t)
Ǥǡt -> t + T ȤʤäȤ N -> N/2 Ȥʤ T ȾȤޤ
N = N0 * e^(-t)
N/2 = N0 * e^(-(t + T))
ʤΤǡ
2 = e^(T)
= log2/TT = log2/
ˤʤޤǡ
N = N0 * e^(- log2/T * t) = N0 * e^(- log2 * t/T) = N0 * (e^log(1/2))^(t/T)
log e^(log2) = 2 ʤΤǡ
N = N0 * (1/2)^(t/T)
Ȥ񤱤ޤ

ơʾνβ˲򤤤Ƥޤ礦
ʪ ABC t ǯνŤ ABC Ȥޤñ̤ kg Ǥ
ޤAB ab ȤAB Ⱦ TaTb Ȥޤ
ǡդȤǤۤɤͽμǤϸĿǤϽŤǤ
餫˰㤦ΤʤΤǡ̩ˤϡδ֤ĤʤΡ 1 ĤνŤʤɡ
ɬפǤ礦󼨤줿Ǥä˸ڤʤΤǡ
ʪ⤳ѤʤABC θ 1 ĤνŤϤۤȤƱȲꤷޤ
ȡΤݤǡۤɤäŤˤ⤽ΤޤΩޤ
ʲǤϡββ˲򤭤ޤ

ޤA Ǥ餫ˡ
dA/dt = - a * A
ޤ t = 0A = 1 Dz򤯤ȡ
A = e^(- a * t) = (1/2)^(t/Ta)
Ǥ

ˡB ǤB ϡA ʬ a * A C ؤʬ b * B Τǡ
dB/dt = a * A - b * B
dB/dt = a * e^(- a * t) - b * B
ˤʤޤt = 0B = 0 Dz򤱤ФǤ
dB/dt + b * B = a * e^(- a * t)
e^(b * t) * dB/dt + b * e^(b * t) * B = a * e^((b - a) * t)
d(e^(b * t) * B)/dt = a * e^((b - a) * t)
e^(b * t) * B = a/(b - a) * e^((b - a) * t) + ʬ
t = 0B = 0 ꡤ
e^(b * t) * B = a/(b - a) * e^((b - a) * t) - a/(b - a)
B = a/(b - a) * (e^(- a * t) - e^(- b * t))
B = (1/Ta)/(1/Tb - 1/Ta) * ((1/2)^(t/Ta) - (1/2)^(t/Tb))
B = Tb/(Tb - Ta) * ((1/2)^(t/Tb) - (1/2)^(t/Ta))

ǸˡC ǤC B ʬ b * B ʤΤǡ
dC/dt = b * B
dC/dt = ab/(b - a) * (e^(- a * t) - e^(- b * t))
ˤʤޤt = 0C = 0 Dz򤱤ФǤ
C = ab/(b - a) * (- 1/a * (e^(- a * t) - 1) + 1/b * (e^(- b * t) - 1))
C = 1 - b/(b - a) * e^(- a * t) + a/(b - a) * e^(- b * t)
C = 1 - (1/Tb)/(1/Tb - 1/Ta) * (1/2)^(t/Ta) + (1/Ta)/(1/Tb - 1/Ta) * (1/2)^(t/Tb)
C = 1 - Tb/(Tb - Ta) * (1/2)^(t/Tb) + Ta/(Tb - Ta) * (1/2)^(t/Ta)

ʾǡABC ΰ̷ޤޤ

ơTa = 100Tb = 300 ʤΤǡ
A = (1/2)^(t/100)
B = 3/2 * (1/2)^(t/300) - 3/2 * (1/2)^(t/100)
C = 1 - 3/2 * (1/2)^(t/300) + 1/2 * (1/2)^(t/100)
t = 500 ȡ
A = (1/2)^5
B = 3/2 * (1/2)^(5/3) - 3/2 * (1/2)^5 = 3 * (1/2)^(8/3) - 3 * (1/2)^6
C = 1 - 3/2 * (1/2)^(5/3) + 1/2 * (1/2)^5 = 1 - 3 * (1/2)^(8/3) + (1/2)^6
Ȥʤޤ

ʤΩ餫Ǥ̷»ϹθʤäΤǡ
A + B + C = 1
ΩƤޤ

줰餤⡤ͽμĤǡοؤ˽ФƤ⤪Ϥʤʤ
Ȥ⡤ʪ ʬΤǡʪǤϡä̵ʡ
ͥνȡ 114ʿ 18:34:39 MAIL:uchi@sco.bekkoame.ne.jp 33639
⡼ޥ
#33636 ϥ饮㡼ƥ󡢤꤬Ȥޤ...Orz...
ޤ褯狼ʤǤ...^^;
ޤͤƤߤޤ m(_ _)m;v
114ʿ 15:04:55 33640
⡼ޥ
#33638,#33639 uchinyan󡢤꤬Ȥޤ ^^
񤭹줿üåפƤޤ...
ɴ̣Ƥޤ...
ξ̾˴ m(_ _)m
114ʿ 15:08:02 33641
uchinyan
#33641⡼ޥ󤵤
礭ʽϤޤ󤬡㴳ɲýޤ
ͥνȡ 114ʿ 18:44:27 MAIL:uchi@sco.bekkoame.ne.jp 33642
ϥ饮㡼ƥ
uchinyan󡢥⡼ޥ󤵤

ܤ˶̣⤿줿Ȥ˴դޤ
uchinyan̤ǤΤդä뤳Ȥ
ޤ󡣤ߤޤuchinyanˤݤ򤪤ޤ

̤äǤ
>ʤߤˡľʪǤϡ¿ʬؤǤ⡤ȤƤǤ
>ۤɤΤ褦ʿŪ΢դɬܤǤ衣΢դʤǤϡۤǤ (^^;

湩ؤϾؤΰθ椬ǽߤǤʬʿ
꤫Ȥϱ䡹³Ƥޤ

ʬȯࡢ³ưबʤȽꤹŪʤΤ
nκ˼¿ˤΤΤ뤫ɤȽƱǤ

򤫤ˡʣʾ¿༰κβŪʲϤʤȤͭ̾˵ͤ
ʤޤ
RouthHurwitzȤˡǤǤΤǤǰʤ˿ŪʤΤǻϾ
Ȥޤ󡣰Ūʬΰξϻǰʤޤޤ
οؼԤȥ饤Ƥޤ

㤤ԤʬؤΤäƤޤʹƿؤαѤ⤽ʤȤޤ褿
Ȼפޤ

114ʿ 20:04:23 HomePage:湩ؤ˥33643