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1.
This note proves that, forF = ℝ, ℂ or ℍ, the bordism classes of all non-bounding Grassmannian manifoldsG
k(F
n+k), withk <n and having real dimensiond, constitute a linearly independent set in the unoriented bordism group N
d
regarded as a ℤ2-vector space. 相似文献
2.
Let G be a discrete subgroup of PU(1,n). Then G acts on ℙℂ
n
preserving the unit ball ℍℂ
n
, where it acts by isometries with respect to the Bergman metric. In this work we look at its action on all of ℙℂ
n
and determine its equicontinuity region Eq(G). This turns out to be the complement of the union of all complex projective hyperplanes in ℙℂ
n
which are tangent to ∂ℍℂ
n
at points in the Chen-Greenberg limit set Λ(G), a closed G-invariant subset of ∂ℍℂ
n
which is minimal for non-elementary groups. We also prove that the action on Eq(G) is discontinuous. Also , if the limit set is “sufficiently general” (i.e. it is not contained in any proper
k
-chain), then each connected component of Eq(G) is a holomorphy domain and it is a complete Kobayashi hyperbolic space. 相似文献
3.
New results about some sums s
n
(k, l) of products of the Lucas numbers, which are of similar type as the sums in [SEIBERT, J.—TROJOVSK Y, P.: On multiple sums of products of Lucas numbers, J. Integer Seq. 10 (2007), Article 07.4.5], and sums σ(k) = $
\sum\limits_{l = 0}^{\tfrac{{k - 1}}
{2}} {(_l^k )F_k - 2l^S n(k,l)}
$
\sum\limits_{l = 0}^{\tfrac{{k - 1}}
{2}} {(_l^k )F_k - 2l^S n(k,l)}
are derived. These sums are related to the numerator of generating function for the kth powers of the Fibonacci numbers. s
n
(k, l) and σ(k) are expressed as the sum of the binomial and the Fibonomial coefficients. Proofs of these formulas are based on a special
inverse formulas. 相似文献
4.
Yuval Z. Flicker 《Israel Journal of Mathematics》2001,122(1):61-77
The torsorP
δ=Hom⊗ (H
DR,H
σ) under the motivic Galois groupG
σ=Aut⊗
H
δ of the Tannakian category
generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP
σ→P
σ/G
σ
0
to a Gal(
)-torsor, and by its localizationsP
σ⊕k
k
ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is
an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1. 相似文献
5.
M. Kalinin 《Journal of Mathematical Sciences》2010,168(3):385-389
Let A =(x
ij
), i =1,2,... ,k, j =1,2,... ,l, 1 ≤ k ≤ l, be a matrix of independent variables, G be the set of maximal minors of A, and I = (G) be the classical determinantal ideal. We show that G is a universal Gr?bner basis of I. Also, a sufficient condition for G to be a universal comprehensive Gr?bner basis is proved. Bibliography: 12 titles. 相似文献
6.
Juan Pablo Navarrete Waldemar Barrera 《Bulletin of the Brazilian Mathematical Society》2009,40(1):99-106
In this paper, we prove following: If G ⊂ PU (2, 1) is an infinite, discrete group, acting on Pℂ2 without complex invariant lines, then the component containing ℍPℂ2 of the domain of discontinuity Ω(G) = PPℂ2∖ Λ (G), according to Kulkarni, is G-invariant complete Kobayashi hyperbolic.
The authors were supported by the Universidad Autónoma de Yucatán and the Universidad Nacional Autónoma de México. 相似文献
7.
Let X
1, X
2, ... be i.i.d. random variables. The sample range is R
n
= max {X
i
, 1 ≤ i ≤ n} − min {X
i
, 1 ≤ i ≤ n}. If for a non-degenerate distribution G and some sequences (α
k
), (β
k
) then we have
and
almost surely for any continuity point x of G and for any bounded Lipschitz function f: R → R.
相似文献
8.
S. Staněk 《Ukrainian Mathematical Journal》2008,60(2):277-298
We present existence principles for the nonlocal boundary-value problem (φ(u(p−1)))′=g(t,u,...,u(p−1), αk(u)=0, 1≤k≤p−1, where p ≥ 2, π: ℝ → ℝ is an increasing and odd homeomorphism, g is a Carathéodory function that is either regular or has singularities in its space variables, and α
k: C
p−1[0, T] → ℝ is a continuous functional. An application of the existence principles to singular Sturm-Liouville problems (−1)n(φ(u(2n−)))′=f(t,u,...,u(2n−1)), u(2k)(0)=0, αku(2k)(T)+bku(2k=1)(T)=0, 0≤k≤n−1, is given.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 240–259, February, 2008. 相似文献
9.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,133(3):1308-1313
Let {Xi, Yi}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn(j) = max0≤k≤n-j (Xk+1 + ... Xk+j)Ik,j, where Ik,k+j = I{Yk+1 < ⋯ < Yk+j} denotes the indicator function for the event in brackets, 1 ≤ j ≤ n. Let Ln be the largest index l ≤ n for which Ik,k+l = 1 for some k = 0, 1, ..., n - l. The strong law of large numbers for “the maximal gain over the longest increasing runs,”
i.e., for Mn(Ln) has been recently derived for the case where X1 has a finite moment of order 3 + ε, ε > 0. Assuming that X1 has a finite mean, we prove for any a = 0, 1, ..., that the s.l.l.n. for M(Ln - a) is equivalent to EX
1
3+a
I{X1 > 0} < ∞. We derive also some new results for the a.s. asymptotics of Ln. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 179–189. 相似文献
10.
Hong Lin Xiao-feng Guo 《应用数学学报(英文版)》2007,23(1):155-160
Let φ(G),κ(G),α(G),χ(G),cl(G),diam(G)denote the number of perfect matchings,connectivity,independence number,chromatic number,clique number and diameter of a graph G,respectively.In this note,by constructing some extremal graphs,the following extremal problems are solved:1.max{φ(G):|V(G)|=2n,κ(G)≤k}=k[(2n-3)!!],2.max{φ(G):|V(G)|=2n,α(G)≥k}=[multiply from i=0 to k-1(2n-k-i)[(2n-2k-1)!!],3.max{φ(G):|V(G)|=2n,χ(G)≤k}=φ(T_(k,2n))T_(k,2n)is the Turán graph,that is a complete k-partite graphon 2n vertices in which all parts are as equal in size as possible,4.max{φ(G):|V(G)|=2n,cl(G)=2}=n1,5.max{φ(G):|V(G)|=2n,diam(G)≥2}=(2n-2)(2n-3)[(2n-5)!!],max{φ(G):|V(G)|=2n,diam(G)≥3}=(n-1)~2[(2n-5)!!]. 相似文献
11.
Given a graph G, a (k;a,b,c)-star in G is a subgraph isomorphic to a star K1,3 with a central vertex of degree k and three leaves of degrees a, b and c in G. The main result of the paper is:
Every planar graph G of minimum degree at least 3 contains a (k;a,b,c)-star with a≤ b≤ c and (i) k = 3, a≤ 10, or (ii) k = 4, a = 4, 4≤ b≤ 10, or (iii) k = 4, a = 5, 5≤ b≤ 9, or (iv) k = 4, 6≤ a≤ 7, 6≤ b≤ 8, or (v) k = 5, 4≤ a≤ 5, 5≤ b≤ 6 and 5≤ c≤ 7, or (vi) k = 5 and a = b = c = 6. 相似文献
12.
Let X ⊂ ℂn be a smooth affine variety of dimension n – r and let f = (f1,..., fm): X → ℂm be a polynomial dominant mapping. We prove that the set K(f) of generalized critical values of f (which always contains
the bifurcation set B(f) of f) is a proper algebraic subset of ℂm. We give an explicit upper bound for the degree of a hypersurface containing K(f). If I(X)—the ideal of X—is generated by
polynomials of degree at most D and deg fi ≤ d, then K(f) is contained in an algebraic hypersurface of degree at most (d + (m – 1)(d – 1)+(D – 1)r)n-rDr. In particular if X is a hypersurface of degree D and f: X → ℂ is a polynomial of degree d, then f has at most (d + D –
1)n-1D generalized critical values. This bound is asymptotically optimal for f linear. We give an algorithm to compute the set
K(f) effectively. Moreover, we obtain similar results in the real case. 相似文献
13.
A connected, finite two-dimensional CW-complex with fundamental group isomorphic toG is called a [G, 2]
f
-complex. LetL⊲G be a normal subgroup ofG. L has weightk if and only ifk is the smallest integer such that there exists {l
1,…,l
k}⊆L such thatL is the normal closure inG of {l
1,…,l
k}. We prove that a [G, 2]
f
-complexX may be embedded as a subcomplex of an aspherical complexY=X∪{e
1
2
,…,e
k
2
} if and only ifG has a normal subgroupL of weightk such thatH=G/L is at most two-dimensional and defG=defH+k. Also, ifX is anon-aspherical [G, 2]
f
-subcomplex of an aspherical 2-complex, then there exists a non-trivial superperfect normal subgroupP such thatG/P has cohomological dimension ≤2. In this case, any torsion inG must be inP. 相似文献
14.
J. C. Gupta 《Proceedings Mathematical Sciences》2000,110(4):415-430
Let G
n,k
be the set of all partial completely monotone multisequences of ordern and degreek, i.e., multisequencesc
n(β1,β2,…, β
k
), β1,β2,…, βk
= 0,1,2,…, β1+β2 + … +β
k
≤n,c
n(0,0,…, 0) = 1 and
whenever β0 ≤n - (β1 + β2 + … + β
k
) where Δc
n(β1,β2,…, β
k
) =c
n(β1 + 1, β2,…, β
k
)+c
n(β1,β2+1,…, β
k
)+…+c
n (β1,β2,…, β
k
+1) -c
n(β1,β2,…, β
k
). Further, let Π
n,k
be the set of all symmetric probabilities on {0,1,2,…,k}
n
. We establish a one-to-one correspondence between the sets G
n,k
and Π
n,k
and use it to formulate and answer interesting questions about both. Assigning to G
n,k
the uniform probability measure, we show that, asn→∞, any fixed section {it{cn}(β1,β2,…, β
k
), 1 ≤ Σβ
i
≤m}, properly centered and normalized, is asymptotically multivariate normal. That is,
converges weakly to MVN[0, Σ
m
]; the centering constantsc
0(β1, β2,…, β
k
) and the asymptotic covariances depend on the moments of the Dirichlet (1, 1,…, 1; 1) distribution on the standard simplex
inR
k. 相似文献
15.
R. Seibold E. Krätzel 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》1998,68(1):305-320
Zusammenfassung We consider the distribution ofk-full numbers. But we go into more detail and investigate suchk-full integers which are at the same timel-free. We give asymptotic results for the numberN
k,l (x) ofk- full andl-free integers not exceedingx in cases ofl =k + r with 2 ≤r ≤ 5. Moreover, we consider these cases and the casesk = 2, 3,l ≥k + 2 also under the assumption of Riemann’s Hypothesis.
相似文献
16.
Xian Zu Lin 《数学学报(英文版)》2011,27(5):863-870
Let G/P be a homogenous space with G a compact connected Lie group and P a connected subgroup of G of equal rank. As the rational cohomology ring of G/P is concentrated in even dimensions, for an integer k we can define the Adams map of type k to be l
k
: H*(G/P, ℚ) → H*(G/P, ℚ), l
k
(u) = k
i
u, u ∈ H
2i
(G/P, ℚ). We show that if k is prime to the order of the Weyl group of G, then l
k
can be induced by a self map of G/P. We also obtain results which imply the condition that k is prime to the order of the Weyl group of G is necessary. 相似文献
17.
18.
LetH be any complex inner product space with inner product <·,·>. We say thatf: ℂ→ℂ is Hermitian positive definite onH if the matrix
is Hermitian positive definite for all choice ofz
1,…,z
n inH for alln. It is strictly Hermitian positive definite if the matrix (*) is also non-singular for any choice of distinctz
1,…,z
n inH. In this article, we prove that if dimH≥3, thenf is Hermitian positive definite onH if and only if
whereb
k,l
≥0 for allk, l in ℤ, and the series converges for allz in ℂ. We also prove thatf of the form (**) is strictly Hermitian positive definite on anyH if and only if the setJ={(k,l):b
k,l
>0} is such that (0,0)∈J, and every arithmetic sequence in ℤ intersects the values {k−l: (k, l)∈J} an infinite number of times. 相似文献
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19.
Nir Ben David 《Israel Journal of Mathematics》2009,170(1):317-335
A finite group G is of central type (in the non-classical sense) if it admits a non-degenerate cohomology class [c] ∈ H
2(G, ℂ*) (G acts trivially on ℂ*). Groups of central type play a fundamental role in the classification of semisimple triangular complex
Hopf algebras and can be determined by their representation-theoretical properties.
Suppose that a finite group Q acts on an abelian group A so that there exists a bijective 1-cocycle π ∈ Z
1(Q,Ǎ), where Ǎ = Hom(A, ℂ*) is endowed with the diagonal Q-action. Under this assumption, Etingof and Gelaki gave an explicit formula for a non-degenerate 2-cocycle in Z
2(G, ℂ*), where G:= A × Q. Hence, the semidirect product G is of central type.
In this paper, we present a more general correspondence between bijective and non-degenerate cohomology classes. In particular,
given a bijective class [π] ∈ H
1(Q,Ǎ) as above, we construct non-degenerate classes [cπ] ∈ H
2(G,ℂ*) for certain extensions 1 → A → G → Q → 1 which are not necessarily split. We thus strictly extend the above family of
central type groups. 相似文献
20.
For two vertices u and v of a connected graph G, the set I[u,v] consists of all those vertices lying on a u−v shortest path in G, while for a set S of vertices of G, the set I[S] is the union of all sets I[u,v] for u,v∈S. A set S is convex if I[S]=S. The convexity number con(G) of G is the maximum cardinality of a proper convex set of G. The clique number ω(G) is the maximum cardinality of a clique in G. If G is a connected graph of order n that is not complete, then n≥3 and 2≤ω(G)≤con(G)≤n−1. It is shown that for every triple l,k,n of integers with n≥3 and 2≤l≤k≤n−1, there exists a noncomplete connected graph G of order n with ω(G)=l and con(G)=k. Other results on convex numbers are also presented.
Received: August 19, 1998 Final version received: May 17, 2000 相似文献