pixelive в Москве

Это обман.
Продают  китайские проекторы стоимостью 8000 под видом немецких за 40000.
После получения денег перестают общаться.

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Это обман.
Продают  китайские проекторы стоимостью 8000 под видом немецких за 40000.
После получения денег перестают общаться.

Yoa aeiioaca auea i?iaa?aia aey ~s0 n aanii 6 16.
Aeiioaca 2. Ana cia?aiey ?(~s), ~s ? B e 1 eeiaeii iacaaeneiu iaa Q.
Anee aeiioaca 2 aa?ia, oi i?aanoaaeaiea a aeaa eeiaeiie oi?iu ec
aeiioacu 1 aaeinoaaiii. Ec yoeo aaoo aeiioac neaaoao, ?oi ?acia?iinou
eeiaeiiai i?ino?ainoaa, ii?i?aaiiiai e?aoiuie acaoa-cia?aieyie aana
w ?aaia dw, aaa ?enea dw ii?aaaey?ony i?iecaiayuae ooieoeae
X
?
w=0
dwx
w =
1
1 ? w2 ? w3
.
Oae eae ?({2}k) = ?
2k(2k + 1)!, oi yoe cia?aiey e??aoeiiaeuiu (e
aa?a eeiaeii iacaaeneiu iaa Q ia?ao niaie e 1). Oae?a, ii oai?aia
Aia?e, e??aoeiiaeuii ?enei ?(3). Ioiineoaeuii a?eoiaoe?aneeo naienoa
?(~s) i?e a?oaeo ~s ? B ieeaeie ii?aaaeaiinoe iiea iao.
Ionou eaeia-oi ?(~s0) ? Q, w(~s0) ia?aoii. Anee ?(~s0)?(2k) i?aanoaa-
eyaony a aeaa eeiaeiie eiiaeiaoee n ?aoeiiaeuiuie eiyooeoeaioaie
?enae ?(~s), ~s ? Bw( ~s0)+2k (a oae e aie?ii auou ii aeiioaca 1), oi neaai-
aaoaeuii n?aae yoeo ?enae anou oioy au iaii e??aoeiiaeuiia. Iai?eia?,
anee ?(2, 3) ? Q eee ?(3, 2) ? Q, oi iaii ec ?enae ?(3, 2, 2), ?(2, 3, 2) e
?(2, 2, 3) e??aoeiiaeuii. Aiaeiae?ii, anee eaeia-oi ?(~s0) ? Q, w(~s0)
?aoiia e ?(~s0)?(3) i?aanoaaeyaony a aeaa eeiaeiie eiiaeiaoee n ?aoei-
iaeuiuie eiyooeoeaioaie ?enae ?(~s), ~s ? Bw( ~s0)+3, oi n?aae ieo anou oioy
au iaii e??aoeiiaeuiia.
Aaeaa iu aiea?ai iaeioi?ue ?acoeuoao i eeiaeiie iacaaeneiinoe
e?aoiuo acaoa-cia?aiee.
Eaiia 2.9 Ionou x ? Q, ?enea yi
, i = 1, . . . , k oaeea, ?oi 1, y1, .. . ,
yk eeiaeii iacaaeneiu iaa Q. Oiaaa nouanoao?o k ?1 ?enae ec xyi
, ?oi
1, x e iie eeiaeii iacaaeneiu iaa Q.
2.5 A?eoiaoe?aneea naienoaa e?aoiuo acaoa-cia?aiee 37
Aieacaoaeunoai. Aoaai aieacuaaou io i?ioeaiiai. Ionou ?enea 1, x, xyi
,
i = 1, . . . , k ?1 eeiaeii caaeneiu iaa Q. O.a. nouanoao?o oaeea oaeua A1,
B1 e C1i
, ia ?aaiua iaiia?aiaiii ioe?, ?oi
A1 + B1x +
X
k?1
i=1
C1ixyi = 0.
Anee A1 = 0, oi iiaaeea yoi ?aaainoai ia x, iieo?ei, ?oi 1 e ?enea yi
, i =
1, . . . , k ?1 eeiaeii caaeneiu, ?oi ii oneiae? ia oae. Anee au ana C1i = 0,
oi x auei au ?aoeiiaeuiui. Neaaiaaoaeuii, nouanoaoao p ? [1, k ?1], ?oi
C1p 6= 0. Ionou oaeua A2, B2 e C2i
, ia ?aaiua iaiia?aiaiii ioe? oaeiau,
?oi
A2 + B2x +
X
16i6k,i6=p
C2ixyi = 0.
Aiaeiae?ii, A2 6= 0. Oiii?ei ia?aia ?aaainoai ia A2 e au?oai aoi?ia
?aaainoai, oiii?aiiia ia A1. Iieo?ei (iieaaay C1k = 0, C2p = 0)
(B1A2 ? B2A1)x +
X
k
i=1
(C1iA2 ? C2iA1)xyi = 0.
Iiaaeei yoi ?aaainoai ia x. Oiaaa iieo?ei eeiaeio? oi?io io 1, yi
, i?e-
?ai eiyooeoeaio i?e yp aoaao ?aaai C1pA2 6= 0, i?ioeai?a?ea n eeiaeiie
iacaaeneiinou? 1 e ?enae yi
. Eaiia aieacaia.
Neaanoaea 2.5 I?e e?aii iaoo?aeuiii l ?enea 1, ?(3) e eaeea-oi l
?enae ec ?(3)?(2k), k = 1, . . . , l + 1 eeiaeii iacaaeneiu iaa Q.
Aieacaoaeunoai. A eaiia 2.9 aicuiai x = ?(3), yk = ?(2k).
Ec yoiai neaanoaey auoaeaao a?oaia
Neaanoaea 2.6 Anee Mw - iii?anoai aaeoi?ia aana w oaeeo, ?oi ana
e?aoiua acaoa-ooieoee aana w au?a?a?ony ?aoeiiaeuiui ia?acii ?a-
?ac ?(~s), ~s ? Mw, oi nouanoao?o l oaeeo aaeoi?ia ~ti ?aciiai aana,
i ? {5, 7, . . . , 2l + 5}, ~ti ? Mi
, ?oi 1, ?(3) e ?enea ?(~ti) eeiaeii iacaaene-
iu iaa Q.
2.5 A?eoiaoe?aneea naienoaa e?aoiuo acaoa-cia?aiee 38
Ii aeiioaca 1 a ea?anoaa Mw ii?ii acyou Bw. Anee oae, oi
dimQ(Q ?
M
~s?B3?···?B2l+5
Q?(~s)) l + 2.
Oae?a, i?aaeaii,
dimQ(Q ?
M
~s?B2?···?B2l
Q?(~s)) l + 1.
Neaanoaea 2.7 Nouanoaoao oaeia
~s0 ? {(2, 3),(3, 2),(2, 2, 3),(2, 3, 2),(3, 2, 2)},
?oi ?enea 1, ?(3) e ?(~s0) eeiaeii iacaaeneiu iaa Q.
Aieacaoaeunoai. I?eiaiei neaanoaea 2.6 i?e l = 1, auae?ay M5 =
{(2, 3),(3, 2)} e M7 = {(2, 2, 3),(2, 3, 2),(3, 2, 2)}.
Aeaaa 3 ?acei?aiey e?aoiuo eioaa?aeia a eeiaeiua oi?iu 39
Aeaaa 3
?acei?aiey e?aoiuo
eioaa?aeia a eeiaeiua
oi?iu
O?a eeanne?aneei ?acoeuoaoii yaeyaony i?aanoaaeaiea aeia?aaiiao-
?e?aneiai eioaa?aea
Z
[0,1]m
Qm
i=1 x
ai?1
i
(1 ? xi)
bi?ai?1
(1 ? zx1x2 . . . xm)
a0
dx1dx2 . . . dxm
i?e iaoo?aeuiuo ai
, bi a aeaa Pm
s=0 Ps(z
?1
) Lis(z) (ni., iai?eia?, [16, Proposition
1, Lemma 1, Lemma 2]). Caanu e aaeaa eiyooeoeaiou i?e (iaia-
uaiiuo) iieeeiaa?eoiao a ?acei?aiee eioaa?aeia iiiai?eaiu n ?a-
oeiiaeuiuie eiyooeoeaioaie.
A ?aaioao [20], [21] A.I. Ni?ieei ii nouanoao aieacae oi?aanoaa
Z
[0,1]3
x
n
1
(1 ? x1)
nx
n
2
(1 ? x2)
nx
n
3
(1 ? x3)
n
(1 ? zx1x2)
n+1(1 ? zx1x2x3)
n+1 dx1dx2dx3 (3.1)
= P2,1(z
?1
) Le2,1(z) + P1,1(z
?1
) Le1,1(z) + P1(z
?1
) Le1(z) + P?(z
?1
)
e
Z
[0,1]2l
Q2l
i=1 x
ai?1
i
(1 ? xi)
n
Ql
j=1(1 ? zx1x2 . . . x2j )
n+1
dx1dx2 . . . dx2l (3.2)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 40
=
X
l
k=0
Pk(z
?1
) Li{2}k
(z) +X
l?1
k=0
Tk(z
?1
) Li1,{2}k
(z),
aaa a2j?1 = a2j = (l + 1 ? j)(n + 1) ? ?, 0 6 ? 6 l 6 n. Nouanoaiaaiea
oaeiai ?acei?aiey auei iieacaii n iiiiuu? aii?ieneiaoee Iaaa.
A aaiiie aeaaa iu eco?ei iaiauaiea yoeo oaeoia, a eiaiii ?acei?a-
iea eioaa?aea
S(z) = Z
[0,1]m
Qm
i=1 x
ai?1
i
(1 ? xi)
bi?ai?1
Ql
j=1(1 ? zx1x2 . . . xrj
)
cj
dx1dx2 . . . dxm,
0 = r0 r1 r2 · · · rl = m.
a eeiaeiua oi?iu io iaiauaiiuo iieeeiaa?eoiia. Aoaoo eniieuciaaou-
ny neaao?uea iaicia?aiey. Aoaai ienaou, ?oi ~u 6 ~v, anee aeeiu yoeo
aaeoi?ia ?aaiu e ui 6 vi i?e e?aii i = 1, . . . , l(~u) = l(~v). Iaciaai aaeoi?
~u iia?eiaiiui aaeoi?o ~v, anee ~u 6 ~v eee ~u 6 v~0 aey iaeioi?iai aaeoi?a
v~0
, iieo?aiiiai ec aaeoi?a ~v au?a?eeaaieai ianeieueeo eiiiiiaio a i?i-
ecaieuiuo ianoao. Aunioie iiiai?eaia iaciaai iaeneioi iiaoeae aai
eiyooeoeaioia.
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo
eioaa?aeia
Eaiia 3.1 Iaiauaiiua iieeeiaa?eoiu Les1,s2,...,sn
(z) n ?acee?iuie ia-
ai?aie eiaaenia eeiaeii iacaaeneiu iaa C(z).
Aieacaoaeunoai. Ecaanoii, ?oi iaiauaiiua iieeeiaa?eoiu Lis1,s2,...,sn
(z)
n ?acee?iuie iaai?aie eiaaenia eeiaeii iacaaeneiu iaa C(z) (ni. [37],
[23]). Iaai?u ooieoee {Le~s(z)} e {Li~s(z)} n w(~s), ia i?aainoiayuei iaei-
oi?iai oeene?iaaiiiai ?enea e oii?yai?aiiuo ii aic?anoaie? aeeiu
~s, naycaiu i?aia?aciaaieai c aa?oiao?aoaieuiie iao?eoae n iaioeaauie
aeaaiiaeuiuie yeaiaioaie (ni. [23, ioieo 3])
Le~s(z) = Li~s(z) +X
~t
Li~t
(z),
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 41
aaa aaeoi?a ~t a noiia eia?o oio ?a aan, ?oi e ~s, ii iaiuoo? aeeio. Ioeoaa
e neaaoao eeiaeiay iacaaeneiinou Le~s(z) iaa C(z).
Neaanoaea 3.1 Anee ooieoey f(z) eiaao i?aanoaaeaiea a aeaa eiia?-
iie noiiu P
~s P~s(z
?1
) Le~s(z), P~s(x) iiiai?eaiu, oi yoi i?aanoaaeaiea
aaeinoaaiii.
Ii?aaaeei eiaaen ?aoeiiaeuiie ooieoee R(x) = P(x)
Q(x)
eae I(R) =
deg P ? deg Q. Ooieoee R(?1, ?2, . . . , ?l) = R1(?1)· · · Rl(?l) io ianeieueeo
ia?aiaiiuo niiinoaaei aaeoi? ec eiaaenia (I(R1), . . . , I(Rl)).
Oai?aia 3.1 Ionou aey ooieoee R(?1, ?2, . . . , ?l) = R1(?1). . . Rl(?l) au-
iieiyaony ia?aaainoai I(R1) + I(R2) + · · · + I(Rj ) + j 6 0 aey e?aiai
j = 1, . . . , l e ana iie?na Rj ea?ao a iii?anoaa {0, ?1, ?2, . . . }. I?e
yoii iaicia?ei mj iaeneiaeuiue ec ii?yaeia yoeo iie?nia, p e P
niioaaonoaaiii ieieiaeuiia e iaeneiaeuiia cia?aiey aanie?oiuo
aaee?ei iie?nia anao ooieoee Rj
.
Oiaaa i?e z ? C, z 1 noiia
X
n1n2...nl1
R(n1, n2, . . . , nl)z
n1?1
(3.3)
i?aanoaaeyaony a aeaa
X
~s
P~s(z
?1
) Le~s(z), (3.4)
aaa noiie?iaaiea aaaaony ii aaeoi?ai ~s, oaiaeaoai?y?uei oneiae?
~s 6 (m1 ? m2 ? · · · ? ml), aaa '' icia?aao eeai caiyoo?, eeai ie?n i?e
eaeii-eeai eo ?ani?aaaeaiee (a ?anoiinoe, aoaoo auiieiyouny ia?a-
aainoaa l(~s) 6 l e w(~s) 6 m1 + m2 + · · · + ml), a P~s(x) iiiai?eaiu n
?aoeiiaeuiuie eiyooeoeaioaie oaeea, ?oi
ord
z=0
P?(z) 1, ord
z=0
P~s(z) p + 1 i?e ~s 6= ?, deg P~s(x) 6 P + 1.
Aiiieieoaeuii, anee auiieiy?ony ia?aaainoaa
I(R1) + I(R2) + · · · + I(Rj ) + j 6 ?1, j = 1, . . . , l, (3.5)
oi P~s(1) = 0, aey aaeoi?ia ~s n s1 = 1.
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 42
Aiea?ai aia?aea neaao?uo? eaiio.
Eaiia 3.2 Ionou l iaoo?aeuiia ?enei e oai?aia 3.1 aa?ia aey ooie-
oee R(?1, ?2, . . . , ?r) = R1(?1)· · · Rr(?r) i?e r l (a neo?aa l = 1 ieeaeeo
i?aaiiei?aiee ia o?aaoaony). Oiaaa oai?aia aa?ia aey R(?1, ?2, . . . , ?l) =
R1(?1)R2(?2). . . Rl(?l), Rj (x) = 1
(x+pj )
uj
. Oneiaea (3.5) a yoii neo?aa ?aa-
iineeuii u1 2. Auniou iiiai?eaiia P~s ia i?aainoiayo
max(l! · (w(~u)2w(~u)
)
l?1P
l
, 1) (3.6)
e D
w(~u)?w(~s)
P P~s(z) ? Z[z].
Aieacaoaeunoai. O?aaoaony aieacaou oai?aio 3.1 aey noiiu
X
n1n2...nl1
z
n1?1Y
l
j=1
1
(nj + pj )
uj
, (3.7)
i?e?ai min
16j6l
pj = p, max
16j6l
pj = P. Oaeea noiiu aoaai aaeaa iacuaaou
yeaiaioa?iuie. Ionou r0 = 0, rj = u1 + u2 + · · · + uj
, m = rl = w(~u).
Eniieucoy eaiio 2.1, au?a?aiea (3.7) ii?ii caienaou a aeaa eioaa?aea
I(p1, p2, . . . , pl) = Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj
Ql
j=1(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm.
I?iaaaai eiaoeoe? ii aaee?eia p1 + p2 + · · · + pj
. I?e yoii iiea?ai
oieuei, ?oi noiia (3.7) i?aanoaaeia a aeaa (3.4), oae eae a ea?aii ec
?acae?aaiuo neo?aaa iao?oaii i?ineaaeou ca noaiaiyie iiiai?eaiia, a
oae?a ca ia?aie?aieai ia aaeoi?a iieo?a?ueony iaiauaiiuo iieeeiaa-
?eoiia.
Aaca eiaoeoee (p1 = p2 = · · · = pl = 0) neaaoao ec eaiiu 2.2 I(0, 0, . . . ,
0) = z
?1 Leu1,u2,...,ul
(z).
?anniio?ei neo?ae pj 0 aey e?aiai j = 1, . . . , l. Ec ?aaainoaa
x1x2 . . . xrl =
1 ? (1 ? zx1x2 . . . xrl
)
z
neaaoao, ?oi
I(p1, p2, . . . , pl) = z
?1
I(p1 ? 1, p2 ? 1, . . . , pl ? 1)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 43
?z
?1
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj?1
Ql?1
j=1(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm.
A iineaaiai eioaa?aea i?ieioaa?e?oai ii ia?aiaiiui xrl?1+1, xrl?1+2, . . . ,
xrl e iieo?aiiue eioaa?ae ?acei?ei a noiio ii eaiia 2.1
I(p1, p2, . . . , pl) = z
?1
I(p1 ? 1, p2 ? 1, . . . , pl ? 1)
? z
?1
·
1
p
ul
l
·
X
n1n2...nl?11
z
n1?1Y
l?1
j=1
1
(nj + pj ? 1)uj
.
Eioaa?ae I(p1 ? 1, p2 ? 1, . . . , pl ? 1) i?aanoaaeyaony a aeaa (3.4) ii i?aa-
iiei?aie? eiaoeoee, a au?eoaaiay noiia i?aanoaaeyaony a aeaa (3.4) ii
oneiae? eaiiu (iia caaeneo io l ? 1 ia?aiaiiie). Oaeei ia?acii ii?ii
n?eoaou p = min
16j6l
pj = 0.
Ionou oaia?u ph 0 i?e iaeioi?ii h 1. Caieoai ?aaainoai
(xrh?1+1xrh?1+2 . . . xrh
)
ph = (xrh?1+1xrh?1+2 . . . xrh
)
ph?1
+(xrh?1+1xrh?1+2 . . . xrh
)
ph
(1 ? zx1x2 . . . xrh?1
)
?(xrh?1+1xrh?1+2 . . . xrh
)
ph?1
(1 ? zx1x2 . . . xrh
),
ec eioi?iai neaaoao
I(p1, p2, . . . , ph, . . . , pl) = I(p1, p2, . . . , ph ? 1, . . . , pl)
+
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj
Ql
j=1
j6=h?1
(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm
?
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
p
0
j
Ql
j=1
j6=h
(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm,
aaa p
0
j = pj i?e j 6= h e p
0
h = ph ? 1. Eniieucoy eaiio 2.1, ia?aieoai yoi
?aaainoai eae
I(p1, p2, . . . , ph, . . . , pl)
= I(p1, p2, . . . , ph ? 1, . . . , pl) (3.8)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 44
+
X
n1n2...nl?11
z
n1?1
h
Y?2
j=1
1
(nj + pj )
uj
?
1
(nh?1 + ph?1)
uh?1 (nh?1 + ph)
uh
·
Y
l?1
j=h
1
(nj + pj+1)
uj+1
(3.9)
?
X
n1n2...nl?11
z
n1?1
h
Y?1
j=1
1
(nj + pj )
uj
?
1
(nh + ph ? 1)uh(nh + ph+1)
uh+1
·
Y
l?1
j=h+1
1
(nj + pj+1)
uj+1
(3.10)
A neo?aa h = l au?eoaaiay noiia auaeyaeo eae
1
p
ul
l
X
n1n2...nl?11
z
n1?1Y
l?1
j=1
1
(nj + pj )
uj
E I(p1, p2, . . . , ph ? 1, . . . , pl) i?eiaieii i?aaiiei?aiea eiaoeoee, a aaa
a?oaea noiiu ii oneiae? eaiiu i?aanoaaey?ony a aeaa (3.4).
Inoaaony aieacaou ooaa??aaiea eaiiu aey eioaa?aea
I(p1, 0, . . . , 0) = Z
[0,1]m
(x1x2 . . . xr1
)
Yoa aeiioaca auea i?iaa?aia aey ~s0 n aanii 6 16.
Aeiioaca 2. Ana cia?aiey ?(~s), ~s ? B e 1 eeiaeii iacaaeneiu iaa Q.
Anee aeiioaca 2 aa?ia, oi i?aanoaaeaiea a aeaa eeiaeiie oi?iu ec
aeiioacu 1 aaeinoaaiii. Ec yoeo aaoo aeiioac neaaoao, ?oi ?acia?iinou
eeiaeiiai i?ino?ainoaa, ii?i?aaiiiai e?aoiuie acaoa-cia?aieyie aana
w ?aaia dw, aaa ?enea dw ii?aaaey?ony i?iecaiayuae ooieoeae
X
?
w=0
dwx
w =
1
1 ? w2 ? w3
.
Oae eae ?({2}k) = ?
2k(2k + 1)!, oi yoe cia?aiey e??aoeiiaeuiu (e
aa?a eeiaeii iacaaeneiu iaa Q ia?ao niaie e 1). Oae?a, ii oai?aia
Aia?e, e??aoeiiaeuii ?enei ?(3). Ioiineoaeuii a?eoiaoe?aneeo naienoa
?(~s) i?e a?oaeo ~s ? B ieeaeie ii?aaaeaiinoe iiea iao.
Ionou eaeia-oi ?(~s0) ? Q, w(~s0) ia?aoii. Anee ?(~s0)?(2k) i?aanoaa-
eyaony a aeaa eeiaeiie eiiaeiaoee n ?aoeiiaeuiuie eiyooeoeaioaie
?enae ?(~s), ~s ? Bw( ~s0)+2k (a oae e aie?ii auou ii aeiioaca 1), oi neaai-
aaoaeuii n?aae yoeo ?enae anou oioy au iaii e??aoeiiaeuiia. Iai?eia?,
anee ?(2, 3) ? Q eee ?(3, 2) ? Q, oi iaii ec ?enae ?(3, 2, 2), ?(2, 3, 2) e
?(2, 2, 3) e??aoeiiaeuii. Aiaeiae?ii, anee eaeia-oi ?(~s0) ? Q, w(~s0)
?aoiia e ?(~s0)?(3) i?aanoaaeyaony a aeaa eeiaeiie eiiaeiaoee n ?aoei-
iaeuiuie eiyooeoeaioaie ?enae ?(~s), ~s ? Bw( ~s0)+3, oi n?aae ieo anou oioy
au iaii e??aoeiiaeuiia.
Aaeaa iu aiea?ai iaeioi?ue ?acoeuoao i eeiaeiie iacaaeneiinoe
e?aoiuo acaoa-cia?aiee.
Eaiia 2.9 Ionou x ? Q, ?enea yi
, i = 1, . . . , k oaeea, ?oi 1, y1, .. . ,
yk eeiaeii iacaaeneiu iaa Q. Oiaaa nouanoao?o k ?1 ?enae ec xyi
, ?oi
1, x e iie eeiaeii iacaaeneiu iaa Q.
2.5 A?eoiaoe?aneea naienoaa e?aoiuo acaoa-cia?aiee 37
Aieacaoaeunoai. Aoaai aieacuaaou io i?ioeaiiai. Ionou ?enea 1, x, xyi
,
i = 1, . . . , k ?1 eeiaeii caaeneiu iaa Q. O.a. nouanoao?o oaeea oaeua A1,
B1 e C1i
, ia ?aaiua iaiia?aiaiii ioe?, ?oi
A1 + B1x +
X
k?1
i=1
C1ixyi = 0.
Anee A1 = 0, oi iiaaeea yoi ?aaainoai ia x, iieo?ei, ?oi 1 e ?enea yi
, i =
1, . . . , k ?1 eeiaeii caaeneiu, ?oi ii oneiae? ia oae. Anee au ana C1i = 0,
oi x auei au ?aoeiiaeuiui. Neaaiaaoaeuii, nouanoaoao p ? [1, k ?1], ?oi
C1p 6= 0. Ionou oaeua A2, B2 e C2i
, ia ?aaiua iaiia?aiaiii ioe? oaeiau,
?oi
A2 + B2x +
X
16i6k,i6=p
C2ixyi = 0.
Aiaeiae?ii, A2 6= 0. Oiii?ei ia?aia ?aaainoai ia A2 e au?oai aoi?ia
?aaainoai, oiii?aiiia ia A1. Iieo?ei (iieaaay C1k = 0, C2p = 0)
(B1A2 ? B2A1)x +
X
k
i=1
(C1iA2 ? C2iA1)xyi = 0.
Iiaaeei yoi ?aaainoai ia x. Oiaaa iieo?ei eeiaeio? oi?io io 1, yi
, i?e-
?ai eiyooeoeaio i?e yp aoaao ?aaai C1pA2 6= 0, i?ioeai?a?ea n eeiaeiie
iacaaeneiinou? 1 e ?enae yi
. Eaiia aieacaia.
Neaanoaea 2.5 I?e e?aii iaoo?aeuiii l ?enea 1, ?(3) e eaeea-oi l
?enae ec ?(3)?(2k), k = 1, . . . , l + 1 eeiaeii iacaaeneiu iaa Q.
Aieacaoaeunoai. A eaiia 2.9 aicuiai x = ?(3), yk = ?(2k).
Ec yoiai neaanoaey auoaeaao a?oaia
Neaanoaea 2.6 Anee Mw - iii?anoai aaeoi?ia aana w oaeeo, ?oi ana
e?aoiua acaoa-ooieoee aana w au?a?a?ony ?aoeiiaeuiui ia?acii ?a-
?ac ?(~s), ~s ? Mw, oi nouanoao?o l oaeeo aaeoi?ia ~ti ?aciiai aana,
i ? {5, 7, . . . , 2l + 5}, ~ti ? Mi
, ?oi 1, ?(3) e ?enea ?(~ti) eeiaeii iacaaene-
iu iaa Q.
2.5 A?eoiaoe?aneea naienoaa e?aoiuo acaoa-cia?aiee 38
Ii aeiioaca 1 a ea?anoaa Mw ii?ii acyou Bw. Anee oae, oi
dimQ(Q ?
M
~s?B3?···?B2l+5
Q?(~s)) l + 2.
Oae?a, i?aaeaii,
dimQ(Q ?
M
~s?B2?···?B2l
Q?(~s)) l + 1.
Neaanoaea 2.7 Nouanoaoao oaeia
~s0 ? {(2, 3),(3, 2),(2, 2, 3),(2, 3, 2),(3, 2, 2)},
?oi ?enea 1, ?(3) e ?(~s0) eeiaeii iacaaeneiu iaa Q.
Aieacaoaeunoai. I?eiaiei neaanoaea 2.6 i?e l = 1, auae?ay M5 =
{(2, 3),(3, 2)} e M7 = {(2, 2, 3),(2, 3, 2),(3, 2, 2)}.
Aeaaa 3 ?acei?aiey e?aoiuo eioaa?aeia a eeiaeiua oi?iu 39
Aeaaa 3
?acei?aiey e?aoiuo
eioaa?aeia a eeiaeiua
oi?iu
O?a eeanne?aneei ?acoeuoaoii yaeyaony i?aanoaaeaiea aeia?aaiiao-
?e?aneiai eioaa?aea
Z
[0,1]m
Qm
i=1 x
ai?1
i
(1 ? xi)
bi?ai?1
(1 ? zx1x2 . . . xm)
a0
dx1dx2 . . . dxm
i?e iaoo?aeuiuo ai
, bi a aeaa Pm
s=0 Ps(z
?1
) Lis(z) (ni., iai?eia?, [16, Proposition
1, Lemma 1, Lemma 2]). Caanu e aaeaa eiyooeoeaiou i?e (iaia-
uaiiuo) iieeeiaa?eoiao a ?acei?aiee eioaa?aeia iiiai?eaiu n ?a-
oeiiaeuiuie eiyooeoeaioaie.
A ?aaioao [20], [21] A.I. Ni?ieei ii nouanoao aieacae oi?aanoaa
Z
[0,1]3
x
n
1
(1 ? x1)
nx
n
2
(1 ? x2)
nx
n
3
(1 ? x3)
n
(1 ? zx1x2)
n+1(1 ? zx1x2x3)
n+1 dx1dx2dx3 (3.1)
= P2,1(z
?1
) Le2,1(z) + P1,1(z
?1
) Le1,1(z) + P1(z
?1
) Le1(z) + P?(z
?1
)
e
Z
[0,1]2l
Q2l
i=1 x
ai?1
i
(1 ? xi)
n
Ql
j=1(1 ? zx1x2 . . . x2j )
n+1
dx1dx2 . . . dx2l (3.2)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 40
=
X
l
k=0
Pk(z
?1
) Li{2}k
(z) +X
l?1
k=0
Tk(z
?1
) Li1,{2}k
(z),
aaa a2j?1 = a2j = (l + 1 ? j)(n + 1) ? ?, 0 6 ? 6 l 6 n. Nouanoaiaaiea
oaeiai ?acei?aiey auei iieacaii n iiiiuu? aii?ieneiaoee Iaaa.
A aaiiie aeaaa iu eco?ei iaiauaiea yoeo oaeoia, a eiaiii ?acei?a-
iea eioaa?aea
S(z) = Z
[0,1]m
Qm
i=1 x
ai?1
i
(1 ? xi)
bi?ai?1
Ql
j=1(1 ? zx1x2 . . . xrj
)
cj
dx1dx2 . . . dxm,
0 = r0 r1 r2 · · · rl = m.
a eeiaeiua oi?iu io iaiauaiiuo iieeeiaa?eoiia. Aoaoo eniieuciaaou-
ny neaao?uea iaicia?aiey. Aoaai ienaou, ?oi ~u 6 ~v, anee aeeiu yoeo
aaeoi?ia ?aaiu e ui 6 vi i?e e?aii i = 1, . . . , l(~u) = l(~v). Iaciaai aaeoi?
~u iia?eiaiiui aaeoi?o ~v, anee ~u 6 ~v eee ~u 6 v~0 aey iaeioi?iai aaeoi?a
v~0
, iieo?aiiiai ec aaeoi?a ~v au?a?eeaaieai ianeieueeo eiiiiiaio a i?i-
ecaieuiuo ianoao. Aunioie iiiai?eaia iaciaai iaeneioi iiaoeae aai
eiyooeoeaioia.
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo
eioaa?aeia
Eaiia 3.1 Iaiauaiiua iieeeiaa?eoiu Les1,s2,...,sn
(z) n ?acee?iuie ia-
ai?aie eiaaenia eeiaeii iacaaeneiu iaa C(z).
Aieacaoaeunoai. Ecaanoii, ?oi iaiauaiiua iieeeiaa?eoiu Lis1,s2,...,sn
(z)
n ?acee?iuie iaai?aie eiaaenia eeiaeii iacaaeneiu iaa C(z) (ni. [37],
[23]). Iaai?u ooieoee {Le~s(z)} e {Li~s(z)} n w(~s), ia i?aainoiayuei iaei-
oi?iai oeene?iaaiiiai ?enea e oii?yai?aiiuo ii aic?anoaie? aeeiu
~s, naycaiu i?aia?aciaaieai c aa?oiao?aoaieuiie iao?eoae n iaioeaauie
aeaaiiaeuiuie yeaiaioaie (ni. [23, ioieo 3])
Le~s(z) = Li~s(z) +X
~t
Li~t
(z),
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 41
aaa aaeoi?a ~t a noiia eia?o oio ?a aan, ?oi e ~s, ii iaiuoo? aeeio. Ioeoaa
e neaaoao eeiaeiay iacaaeneiinou Le~s(z) iaa C(z).
Neaanoaea 3.1 Anee ooieoey f(z) eiaao i?aanoaaeaiea a aeaa eiia?-
iie noiiu P
~s P~s(z
?1
) Le~s(z), P~s(x) iiiai?eaiu, oi yoi i?aanoaaeaiea
aaeinoaaiii.
Ii?aaaeei eiaaen ?aoeiiaeuiie ooieoee R(x) = P(x)
Q(x)
eae I(R) =
deg P ? deg Q. Ooieoee R(?1, ?2, . . . , ?l) = R1(?1)· · · Rl(?l) io ianeieueeo
ia?aiaiiuo niiinoaaei aaeoi? ec eiaaenia (I(R1), . . . , I(Rl)).
Oai?aia 3.1 Ionou aey ooieoee R(?1, ?2, . . . , ?l) = R1(?1). . . Rl(?l) au-
iieiyaony ia?aaainoai I(R1) + I(R2) + · · · + I(Rj ) + j 6 0 aey e?aiai
j = 1, . . . , l e ana iie?na Rj ea?ao a iii?anoaa {0, ?1, ?2, . . . }. I?e
yoii iaicia?ei mj iaeneiaeuiue ec ii?yaeia yoeo iie?nia, p e P
niioaaonoaaiii ieieiaeuiia e iaeneiaeuiia cia?aiey aanie?oiuo
aaee?ei iie?nia anao ooieoee Rj
.
Oiaaa i?e z ? C, z 1 noiia
X
n1n2...nl1
R(n1, n2, . . . , nl)z
n1?1
(3.3)
i?aanoaaeyaony a aeaa
X
~s
P~s(z
?1
) Le~s(z), (3.4)
aaa noiie?iaaiea aaaaony ii aaeoi?ai ~s, oaiaeaoai?y?uei oneiae?
~s 6 (m1 ? m2 ? · · · ? ml), aaa '' icia?aao eeai caiyoo?, eeai ie?n i?e
eaeii-eeai eo ?ani?aaaeaiee (a ?anoiinoe, aoaoo auiieiyouny ia?a-
aainoaa l(~s) 6 l e w(~s) 6 m1 + m2 + · · · + ml), a P~s(x) iiiai?eaiu n
?aoeiiaeuiuie eiyooeoeaioaie oaeea, ?oi
ord
z=0
P?(z) 1, ord
z=0
P~s(z) p + 1 i?e ~s 6= ?, deg P~s(x) 6 P + 1.
Aiiieieoaeuii, anee auiieiy?ony ia?aaainoaa
I(R1) + I(R2) + · · · + I(Rj ) + j 6 ?1, j = 1, . . . , l, (3.5)
oi P~s(1) = 0, aey aaeoi?ia ~s n s1 = 1.
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 42
Aiea?ai aia?aea neaao?uo? eaiio.
Eaiia 3.2 Ionou l iaoo?aeuiia ?enei e oai?aia 3.1 aa?ia aey ooie-
oee R(?1, ?2, . . . , ?r) = R1(?1)· · · Rr(?r) i?e r l (a neo?aa l = 1 ieeaeeo
i?aaiiei?aiee ia o?aaoaony). Oiaaa oai?aia aa?ia aey R(?1, ?2, . . . , ?l) =
R1(?1)R2(?2). . . Rl(?l), Rj (x) = 1
(x+pj )
uj
. Oneiaea (3.5) a yoii neo?aa ?aa-
iineeuii u1 2. Auniou iiiai?eaiia P~s ia i?aainoiayo
max(l! · (w(~u)2w(~u)
)
l?1P
l
, 1) (3.6)
e D
w(~u)?w(~s)
P P~s(z) ? Z[z].
Aieacaoaeunoai. O?aaoaony aieacaou oai?aio 3.1 aey noiiu
X
n1n2...nl1
z
n1?1Y
l
j=1
1
(nj + pj )
uj
, (3.7)
i?e?ai min
16j6l
pj = p, max
16j6l
pj = P. Oaeea noiiu aoaai aaeaa iacuaaou
yeaiaioa?iuie. Ionou r0 = 0, rj = u1 + u2 + · · · + uj
, m = rl = w(~u).
Eniieucoy eaiio 2.1, au?a?aiea (3.7) ii?ii caienaou a aeaa eioaa?aea
I(p1, p2, . . . , pl) = Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj
Ql
j=1(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm.
I?iaaaai eiaoeoe? ii aaee?eia p1 + p2 + · · · + pj
. I?e yoii iiea?ai
oieuei, ?oi noiia (3.7) i?aanoaaeia a aeaa (3.4), oae eae a ea?aii ec
?acae?aaiuo neo?aaa iao?oaii i?ineaaeou ca noaiaiyie iiiai?eaiia, a
oae?a ca ia?aie?aieai ia aaeoi?a iieo?a?ueony iaiauaiiuo iieeeiaa-
?eoiia.
Aaca eiaoeoee (p1 = p2 = · · · = pl = 0) neaaoao ec eaiiu 2.2 I(0, 0, . . . ,
0) = z
?1 Leu1,u2,...,ul
(z).
?anniio?ei neo?ae pj 0 aey e?aiai j = 1, . . . , l. Ec ?aaainoaa
x1x2 . . . xrl =
1 ? (1 ? zx1x2 . . . xrl
)
z
neaaoao, ?oi
I(p1, p2, . . . , pl) = z
?1
I(p1 ? 1, p2 ? 1, . . . , pl ? 1)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 43
?z
?1
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj?1
Ql?1
j=1(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm.
A iineaaiai eioaa?aea i?ieioaa?e?oai ii ia?aiaiiui xrl?1+1, xrl?1+2, . . . ,
xrl e iieo?aiiue eioaa?ae ?acei?ei a noiio ii eaiia 2.1
I(p1, p2, . . . , pl) = z
?1
I(p1 ? 1, p2 ? 1, . . . , pl ? 1)
? z
?1
·
1
p
ul
l
·
X
n1n2...nl?11
z
n1?1Y
l?1
j=1
1
(nj + pj ? 1)uj
.
Eioaa?ae I(p1 ? 1, p2 ? 1, . . . , pl ? 1) i?aanoaaeyaony a aeaa (3.4) ii i?aa-
iiei?aie? eiaoeoee, a au?eoaaiay noiia i?aanoaaeyaony a aeaa (3.4) ii
oneiae? eaiiu (iia caaeneo io l ? 1 ia?aiaiiie). Oaeei ia?acii ii?ii
n?eoaou p = min
16j6l
pj = 0.
Ionou oaia?u ph 0 i?e iaeioi?ii h 1. Caieoai ?aaainoai
(xrh?1+1xrh?1+2 . . . xrh
)
ph = (xrh?1+1xrh?1+2 . . . xrh
)
ph?1
+(xrh?1+1xrh?1+2 . . . xrh
)
ph
(1 ? zx1x2 . . . xrh?1
)
?(xrh?1+1xrh?1+2 . . . xrh
)
ph?1
(1 ? zx1x2 . . . xrh
),
ec eioi?iai neaaoao
I(p1, p2, . . . , ph, . . . , pl) = I(p1, p2, . . . , ph ? 1, . . . , pl)
+
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
pj
Ql
j=1
j6=h?1
(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm
?
Z
[0,1]m
Ql
j=1(xrj?1+1xrj?1+2 . . . xrj
)
p
0
j
Ql
j=1
j6=h
(1 ? zx1x2 . . . xrj
)
dx1dx2 . . . dxm,
aaa p
0
j = pj i?e j 6= h e p
0
h = ph ? 1. Eniieucoy eaiio 2.1, ia?aieoai yoi
?aaainoai eae
I(p1, p2, . . . , ph, . . . , pl)
= I(p1, p2, . . . , ph ? 1, . . . , pl) (3.8)
3.1 Iauay oai?aia i ?acei?aiee e?aoiuo eioaa?aeia 44
+
X
n1n2...nl?11
z
n1?1
h
Y?2
j=1
1
(nj + pj )
uj
?
1
(nh?1 + ph?1)
uh?1 (nh?1 + ph)
uh
·
Y
l?1
j=h
1
(nj + pj+1)
uj+1
(3.9)
?
X
n1n2...nl?11
z
n1?1
h
Y?1
j=1
1
(nj + pj )
uj
?
1
(nh + ph ? 1)uh(nh + ph+1)
uh+1
·
Y
l?1
j=h+1
1
(nj + pj+1)
uj+1
(3.10)
A neo?aa h = l au?eoaaiay noiia auaeyaeo eae
1
p
ul
l
X
n1n2...nl?11
z
n1?1Y
l?1
j=1
1
(nj + pj )
uj
E I(p1, p2, . . . , ph ? 1, . . . , pl) i?eiaieii i?aaiiei?aiea eiaoeoee, a aaa
a?oaea noiiu ii oneiae? eaiiu i?aanoaaey?ony a aeaa (3.4).
Inoaaony aieacaou ooaa??aaiea eaiiu aey eioaa?aea
I(p1, 0, . . . , 0) = Z
[0,1]m
(x1x2 . . . xr1
)

Это обман.Моя история: хотел купить проектор Epson EH-TW5300,позвонил оператору,он начал рассказывать что лучше взять не Epson так как у них очень много их возвращают(как оказалось ,они всем так говорят) ,а другой отличный "немецкий" проектор Ledminox-фирма,мол мало известная ,но очень качественная,а этот проектор с отличными характеристиками,да и стоит всего 40000 тысяч рублей,почти как и Epson.Согласился.Привезли быстро.Но при ближайшем рассмотрении замечательный "немецкий" проектор оказался дешевым китайским,на Али Экспрессе такие же,только под другим названием стоят 11-13 тысяч рублей.Из "немецкого" в нем только надпись на коробке,да и сайт фирмы в интернете не открывается.Позвонил на в Pixelive ,если честно,не сильно надеясь,попросил оформить возврат.Сказали что передадут мое пожелание в отдел качества или еще куда-то(на ходу,видимо,придумывали) и что нужно ждать.С тех пор телефоны на сайте на мои звонки перестали отвечать,идет постоянный гудок.Подал заявление в полицию и прокуратуру.Вот и вся история.Так что если хотите купить дешевый китайский проектор по цене "немецкого" ,т.е. в три цены,то вам в Pixelive(у них есть еще идентичный сайт под другим названием). А лучше обходите их стороной.И не ведитесь на положительные отзывы,они их сами пишут,поверьте,очень смешно их читать.