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PostPosted: Nov.27.03 7:28 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
Эзэрхийлэн Эзлэгч Гишvvн
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Quote:
n oroitoi buren chiglelt graph dahi 3 urttai cycle iin too hamgiin ihdee hed baih ve?

Quote:
G ni zereg ni 4 baih togsgolog buleg.teguul G g Abeliin buleg bolohiig bas,Z4 ba Z2xZ2 toi izomorphic bolohiig batal gej.(end Z2 gej Z iin 2moduliarh uldegdliin angi.Z4 mon adilhan)

ene 2 iig bodchih hun alga uu :(

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PostPosted: Nov.28.03 3:18 pm 
EGO-WRAPPIN' wrote:
Quote:
n oroitoi buren chiglelt graph dahi 3 urttai cycle iin too hamgiin ihdee hed baih ve?

Quote:
G ni zereg ni 4 baih togsgolog buleg.teguul G g Abeliin buleg bolohiig bas,Z4 ba Z2xZ2 toi izomorphic bolohiig batal gej.(end Z2 gej Z iin 2moduliarh uldegdliin angi.Z4 mon adilhan)

ene 2 iig bodchih hun alga uu :(

1dehiig bodoj bolmoor ch yum shig...
2dahiin todorhoilolt ni yu bilee?? :razz:


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PostPosted: Nov.28.03 7:30 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
Эзэрхийлэн Эзлэгч Гишvvн
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1rh ni uul ni amarhan .tegej baigaad bichnee
harin 2 dahi ni...got no slightest fuckin idea :(

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 Post subject: -----------------
PostPosted: Nov.29.03 5:20 pm 
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Эрхэм Гишvvн
Эрхэм Гишvvн

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Posts: 32
EGO-WRAPPIN' wrote:
Quote:
n oroitoi buren chiglelt graph dahi 3 urttai cycle iin too hamgiin ihdee hed baih ve?

Quote:
G ni zereg ni 4 baih togsgolog buleg.teguul G g Abeliin buleg bolohiig bas,Z4 ba Z2xZ2 toi izomorphic bolohiig batal gej.(end Z2 gej Z iin 2moduliarh uldegdliin angi.Z4 mon adilhan)

ene 2 iig bodchih hun alga uu :(



heterhii amarhan yumdaa.

buleg gedeg todorhoilolt, mun 2 buleg isomorphic baih nuhtsluudiig bi heleed ugiye.

G yamar neg olonlog baig. mun * yamar neg binary uildel (GxG deer).
Daraah nuhtsluud bielj baival G -g * uildleer buleg bolno geed (G, *) gej temdegledeg.
1. forall g,h in G, g*h in G, uuruur helbel * uildleer G bituu
2. forall x,y,z in G, (x*y)*z=x*(y*z) (associative)
3. exists e in G such that x*e=e*x=x forall x in G
4. exists b in G such that b*a=a*b=e forall a in G

herev forall x,y in G, x*y=y*x bol G-g commutative buyu abelian group gene.

(G1, *), G2(#) bulguud baig.

herev exists f:G1->G2 such that

f bijective and forall x,y in G1, f(x*y)=f(x)#f(y) bol f -g isomorphism between G1 and G2 geed G1, G2 -g isomorphic groups gene.

za teheer Z2 bol (Z2, +) uund + uildel 2 moduliarh + uildel, Z4 mun adil (Z4,+) bulguud yum. Z2xZ2 direct product buyu (x1,y1)+(x2,y2)=(x1+x2, y1+y2) gej todorhoilogdoh uildleer buleg bolno.

amjilt husiye :D


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 Post subject: Re: -----------------
PostPosted: Dec.17.03 11:14 pm 
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Хvндэт Гишvvн
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heterhii amarhan yumdaa.

buleg gedeg todorhoilolt, mun 2 buleg isomorphic baih nuhtsluudiig bi heleed ugiye.

G yamar neg olonlog baig. mun * yamar neg binary uildel (GxG deer).
Daraah nuhtsluud bielj baival G -g * uildleer buleg bolno geed (G, *) gej temdegledeg.
1. forall g,h in G, g*h in G, uuruur helbel * uildleer G bituu
2. forall x,y,z in G, (x*y)*z=x*(y*z) (associative)
3. exists e in G such that x*e=e*x=x forall x in G
4. exists b in G such that b*a=a*b=e forall a in G

herev forall x,y in G, x*y=y*x bol G-g commutative buyu abelian group gene.

(G1, *), G2(#) bulguud baig.

herev exists f:G1->G2 such that

f bijective and forall x,y in G1, f(x*y)=f(x)#f(y) bol f -g isomorphism between G1 and G2 geed G1, G2 -g isomorphic groups gene.

za teheer Z2 bol (Z2, +) uund + uildel 2 moduliarh + uildel, Z4 mun adil (Z4,+) bulguud yum. Z2xZ2 direct product buyu (x1,y1)+(x2,y2)=(x1+x2, y1+y2) gej todorhoilogdoh uildleer buleg bolno.

amjilt husiye :D[/quote]thanks.bi math sain medkuildee.Minii halit oilgosnoor functional tegshitgel iig bodohod bulgiin onol nileen ahiglagdah bololtoi yum.gants bodlogo.
alivaa natural m,n buriin huvid f(m+f(n))=n+f(m+95) baih f:R-R funtkts gants baina gej batal.


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PostPosted: Dec.18.03 12:52 am 
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Эзэрхийлэн Эзлэгч Гишvvн
Эзэрхийлэн Эзлэгч Гишvvн
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kusta wrote:
G ni zereg ni 4 baih togsgolog buleg.teguul G g Abeliin buleg bolohiig bas,Z4 ba Z2xZ2 toi izomorphic bolohiig batal gej.(end Z2 gej Z iin 2moduliarh uldegdliin angi.Z4 mon adilhan)


G = {e, a, b, c} geye. end e ni G iin negj.

x gesen G-iin elementiin huvid <x> = {e, x, x^2, x^3} gesen olonlogiig avch uzye. (uuniig x-eer turugdsun ded buleg gene)

<e> = {e} boloh ni ilerhii. herev x<>e bol |<x>| > 1 baina. end |X| ni X-iin elementiin too.

herev yamar neg x<>e -iin huvid |<x>| = 4 bol G = <x> is isomorphic to Z4. in particular, abelian.

mun yamar ch x<>e in G-iin huvid |<x>| = 3 baih bolomjgui. esregees ni |<x>| = 3 geye. ene uyed x^3=e baih yostoi.

{y} = G \ <x>, uuruur helbel G = {e, x, x^2, y} gevel G = Gy = {y, xy, x^2y, y^2} gedgees
y=e or xy=e or x^2y=e or y^2=e baih yostoi.

i) y=e baih bolomjgui.
ii) xy=e => y=x^3y=x^2
iii) x^2y=e => y=x^3y=x
iv) y^2=e bol {x, x^2}={xy, x2^y} => x=xy or x=x^2y
iva) x=xy => y=e
ivb) x=x^2y => y=x^3y=x^2

ali ch tohioldold y ni <x>-t haryalagdah bolj zurchil garna.

iimees |<a>|=|<b>|=|<c>|=2 gej uzej bolno.
ene tohioldold ab=c=ba baihaas uur argagui. mun adilaar bc=a=cb, ca=b=ac baina. => abelian. ene uyed
f: G -> Z2xZ2 given by f(e) = (0,0), f(a)=(1,0), f(b)=(0,1), f(c)=(1,1) ni isomorphism boloh ni ilerhii.

Dasgal: G ni tugsgulug buleg, H ni G-iin ded buleg bol |G| ni |H|d huvaagdah bolhohiig batal.

uuniig ashiglaval |<x>|=3 baih gishuun oldohgui ni ilerhii yum. mun ene dasgalaas Fermatiin baga theorem murduj garahiig batal. :D

Nemelt (Dec.19.03 2:44pm)
G=Gx bolohiig ashiglval |<x>|=3 baidag x oldohgui bolohiig bur hyalbarhan harj bolno


Last edited by leuffi on Dec.19.03 2:45 pm, edited 3 times in total.

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 Post subject: Re: -----------------
PostPosted: Dec.18.03 1:36 am 
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Эзэрхийлэн Эзлэгч Гишvvн
Эзэрхийлэн Эзлэгч Гишvvн
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kusta wrote:
thanks.bi math sain medkuildee.Minii halit oilgosnoor functional tegshitgel iig bodohod bulgiin onol nileen ahiglagdah bololtoi yum.gants bodlogo.
alivaa natural m,n buriin huvid f(m+f(n))=n+f(m+95) baih f:R-R funtkts gants baina gej batal.


f:R->R bish N->N biz dee te?

N->N gevel ingej bodoj bolno.

f(m - 95 + f(n + f(k)) = n + f(k) + f(m). nuguu talaas f(m - 95 + f(n + f(k)) = f(m - 95 + k + f(n + 95)) = n + 95 + f(m + k) uchraas

f(m + k) + 95 = f(m) + f(k) bolno.
endees f(m) = m*(f(1) - 95) + 95 bolohiig hyalbarhan batalj bolno.

f(f(n)) = f(n)*(f(1)-95) + 95
n + f(95) = n + 95*(f(1)-95) + 95

=> n = 1 gevel (f(1)-95)^2 = 1 => f(1) = 96 or f(1) = 94.

f(1) = 96 bol f(n) = n + 95 buguud ene ni bodlogiin nuhtsuliig hangahniilerhii.
f(1) = 94 bol f(96) = 95 - 96 =-1 bolj N->N gedegt zurchilnu. iimees f(n) = n + 95.


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 Post subject: Re: -----------------
PostPosted: Dec.18.03 2:27 am 
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Хvндэт Гишvvн
Хvндэт Гишvvн
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leuffi wrote:
kusta wrote:
thanks.bi math sain medkuildee.Minii halit oilgosnoor functional tegshitgel iig bodohod bulgiin onol nileen ahiglagdah bololtoi yum.gants bodlogo.
alivaa natural m,n buriin huvid f(m+f(n))=n+f(m+95) baih f:R-R funtkts gants baina gej batal.


f:R->R bish N->N biz dee te?

N->N gevel ingej bodoj bolno.

f(m - 95 + f(n + f(k)) = n + f(k) + f(m). nuguu talaas f(m - 95 + f(n + f(k)) = f(m - 95 + k + f(n + 95)) = n + 95 + f(m + k) uchraas

f(m + k) + 95 = f(m) + f(k) bolno.
endees f(m) = m*(f(1) - 95) + 95 bolohiig hyalbarhan batalj bolno.

f(f(n)) = f(n)*(f(1)-95) + 95
n + f(95) = n + 95*(f(1)-95) + 95

=> n = 1 gevel (f(1)-95)^2 = 1 => f(1) = 96 or f(1) = 94.

f(1) = 96 bol f(n) = n + 95 buguud ene ni bodlogiin nuhtsuliig hangahniilerhii.
f(1) = 94 bol f(96) = 95 - 96 =-1 bolj N->N gedegt zurchilnu. iimees f(n) = n + 95.
tiin N-N ug tavil ni bol.R-R bol yahnuu gej zugeer bichsiin.chi hen be.onoliin mat d surdguu?tugtsnuu?.


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 Post subject:
PostPosted: Dec.18.03 2:38 am 
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Хvндэт Гишvvн
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aa ter dasgal bodlogo gaigui baihaa.(Lagrange)


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 Post subject: Re: -----------------
PostPosted: Dec.18.03 2:38 am 
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Эзэрхийлэн Эзлэгч Гишvvн
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kusta wrote:
tiin N-N ug tavil ni bol.R-R bol yahnuu gej zugeer bichsiin.Bulgiin onoliig yamar negen baidlaar ashiglajyum boluu gej bodood .chi hen be.onoliin mat d surdguu?tugtsnuu?.


R->R gevel jishee ni f(n) = 95 - n gej bolno sht.:D yur ni tasraltgui ch yum uu uur yamar negen nuhtsul baihgui bol ene bodlogiin nuhtsul hangah 2^R shirheg yalgaatai function baigaag batalj bolno.(songoltiin axiom hereglene l dee)

bulgiin onol ashiglasan bodolt bol yostoi chutgur buu med hehe.
bi onoliin mathid baisiin, ner leuffi :razz:


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PostPosted: Dec.18.03 2:41 am 
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Хvндэт Гишvvн
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sain medkui yum neg nom haraad shuud nohtsliig ni oorchlood bichchsiin.tsaad uchiriig ni sain oisongui. :eek: 8O


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PostPosted: Dec.18.03 2:24 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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R-iig Q deerh vector ogtorgui gej uzeed {1}-iig aguulsan basis A avya (uuniig hamel basis gedeg buguud end songoltiin axiom heregtei). uuruur helbel, duriin bodit too x-iig yag neg utgaar x = r_0 + r_1*a_1 + r_2*a_2 + .. + r_n*a_n, r_i in Q, a_i in A gej bichij bolno gesen ug.

duriin W:A->{-1, 1} function songon avaad

f(r_0 + r_1*a_1 + r_2*a_2 + .. + r_n*a_n) = W(1)*r_0 + 95 + W(a_1)*r_1*a_1 + W(a_2)*r_2*a_2 + .. + W(a_n)*r_n*a_n gej todorhoilyo.

ene f ni bodlogiin nuhtsul hangahiig amarhan harj bolno.

Dasgal: 1. end bid 2^R shirheg yalgaatiai function baiguullaa. bodlogiin nuhtsul hangah R^R shirheg yalgaatai function orshin baihiig batal. (2^R < R^R)
2. herev f-iig tasraltgui gevel ene bodlogo yag 2 shiidtei bolohiig batal.
3. f:R->R, f(x+y)=f(x)+f(y) function tegshitgel hyazgaargui olon shiidtei bolohiig batal.


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 Post subject: Re: -----------------
PostPosted: Dec.18.03 2:40 pm 
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Халих Хvслийн Жигvvр Гишvvн
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leuffi wrote:
kusta wrote:
tiin N-N ug tavil ni bol.R-R bol yahnuu gej zugeer bichsiin.Bulgiin onoliig yamar negen baidlaar ashiglajyum boluu gej bodood .chi hen be.onoliin mat d surdguu?tugtsnuu?.


R->R gevel jishee ni f(n) = 95 - n gej bolno sht.:D yur ni tasraltgui ch yum uu uur yamar negen nuhtsul baihgui bol ene bodlogiin nuhtsul hangah 2^R shirheg yalgaatai function baigaag batalj bolno.(songoltiin axiom hereglene l dee)

bulgiin onol ashiglasan bodolt bol yostoi chutgur buu med hehe.
bi onoliin mathid baisiin, ner leuffi :razz:

leiffi-s asuult
Songoltiin axiom-g unen bolohiig batal :razz:

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 Post subject: Re: -----------------
PostPosted: Dec.18.03 10:15 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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Aibo wrote:
leiffi-s asuult
Songoltiin axiom-g unen bolohiig batal :razz:


hahaha, Aibo uduud baigaarai. naadhaa chi Cohen-oos asuu. dalimand ni Hilbertiin 1r bodlogiin shiideliig ch gesen asuuchihgui yuu, adilhan argaar bodogddog gesen. hervee hyalbarhan batalchihval heleerei, 2uulaa Fieldsiin shagnaliig chine ugaaj saihan uuya.:D


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 Post subject: Re: -----------------
PostPosted: Dec.18.03 11:20 pm 
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Халих Хvслийн Жигvvр Гишvvн
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leuffi wrote:
Aibo wrote:
leiffi-s asuult
Songoltiin axiom-g unen bolohiig batal :razz:


hahaha, Aibo uduud baigaarai. naadhaa chi Cohen-oos asuu. dalimand ni Hilbertiin 1r bodlogiin shiideliig ch gesen asuuchihgui yuu, adilhan argaar bodogddog gesen. hervee hyalbarhan batalchihval heleerei, 2uulaa Fieldsiin shagnaliig chine ugaaj saihan uuya.:D

Cohen-g olood ir. Tegvel asuulaa. :razz:
Za za bi fields bish, Turing shagnal l avii. chamd fields-n shagnal-g uldeeye. :hihi:

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PostPosted: Dec.19.03 12:41 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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hehe Cohen-oos buur sain guival, songoltiin axiomiig buruu ch gej batalj ugnu biz, ugaasaa olonlogiin onoltoi hamaaralgui yum chine zuv ch gej uzej bolno buruu ch gej uzej bolno. gehdee bi lav songoltiin axiomgui baisnaas gutalgui baisan ni deer :razz:


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PostPosted: Dec.19.03 5:18 pm 
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Халих Хvслийн Жигvvр Гишvvн
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leuffi wrote:
hehe Cohen-oos buur sain guival, songoltiin axiomiig buruu ch gej batalj ugnu biz, ugaasaa olonlogiin onoltoi hamaaralgui yum chine zuv ch gej uzej bolno buruu ch gej uzej bolno. gehdee bi lav songoltiin axiomgui baisnaas gutalgui baisan ni deer :razz:

Suhbaatar-n sairan holt :razz:

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PostPosted: Dec.19.03 5:36 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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aibo arhangain tank huldeg ,burheer evdd :lol: eg

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PostPosted: Dec.30.03 8:26 pm 
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Уянгат Дууч Гишvvн
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uur goy bodlog tavih uhn baina uu???


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PostPosted: Jan.04.04 11:07 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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yamarhuu yanziin bodlogo taviulmaar bna?


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 Post subject:
PostPosted: Jan.04.04 11:30 pm 
|G|=2n (n ni sondgoi too)baih togsgolog buleg G ni 2 indekstei ded bulegtei bolohiig batal. :eek:


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PostPosted: Jan.15.04 6:24 pm 
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Элэг Зvрхний Хайрыг Булаагч
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a,b,n -natural , b>1, (b^n)-1|a bol a iin b-tiin toolliin system deh bichleg n hamgiin bagadaa n shirheg 0 ees yalgaatai tsifr aguulna gej batal :)

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 Post subject: --------------
PostPosted: Jan.23.04 2:23 pm 
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Эрхэм Гишvvн
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RAGING BULL wrote:
a,b,n -natural , b>1, (b^n)-1|a bol a iin b-tiin toolliin system deh bichleg n hamgiin bagadaa n shirheg 0 ees yalgaatai tsifr aguulna gej batal :)


(b^n-1) | a ==> a >= b^n-1, B=b - 1 geye. tegvel

k natural, a = k * BB...B (n shirheg B) helbertei bn. now it's so easy by induction on k.

herev k*BB...B ni dor hayaj n shirheg non-zero tsifrtei bol k*BB...B + BB...B ni mun adil gedgiig harahad amarhan :?


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PostPosted: Jan.24.04 5:15 am 
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Тvмнээс Төгөлдөр Гишvvн
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Nogoo hun d*r*k, uher mal aar duudaad tuuh muuh haviar heruul hiideg nohor harin ene haviar yu bolood ergeldee vee? :razz:

Bodlogo nii hariu: 2^(m-1)*m
Maple deer counttrees(complete(2,m)) geed shalgaj bolno.


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PostPosted: Jan.24.04 5:17 am 
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Тvмнээс Төгөлдөр Гишvvн
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K(p,q) iin huvid: p^(q-1)*q^(p-1)


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 Post subject: Re: --------------
PostPosted: Jan.25.04 2:21 pm 
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Эзэрхийлэн Эзлэгч Гишvvн
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Ideal wrote:
RAGING BULL wrote:
a,b,n -natural , b>1, (b^n)-1|a bol a iin b-tiin toolliin system deh bichleg n hamgiin bagadaa n shirheg 0 ees yalgaatai tsifr aguulna gej batal :)


(b^n-1) | a ==> a >= b^n-1, B=b - 1 geye. tegvel

k natural, a = k * BB...B (n shirheg B) helbertei bn. now it's so easy by induction on k.

herev k*BB...B ni dor hayaj n shirheg non-zero tsifrtei bol k*BB...B + BB...B ni mun adil gedgiig harahad amarhan :?

нэг л ноотой санагдаад байхийн...яадаг лvд бэ?
ахиад бичкэн нэмж тайлбарлаад энэ хєлдvv толгойг сэнхрvvлээч :-)

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