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1.
The q-shifted factorial defined by (a : q k)
n
= (1 – a) (1 – aq k)(1 – aq 2k)... (1 – aq (n – 1)k) appears in the terms of basic hypergeometric series. Complete asymptotic expansions as q 1 of some q-shifted factorials are given in terms of polylogarithms and Bernoulli polynomials. 相似文献
2.
A ( k – 1, k)-graph is a multi-graph satisfying e ( k – 1) v – k for every non-empty subset of e edges on v vertices, with equality when e = | E(G)|. A ( k – 1, k)-frame is a structure generalizing an ( n – 2, 2)-framework in n-space, a structure consisting of a set of ( n – 2)-dimensional bodies in n-space and a set of rigid bars each joining a pair of bodies using ball joints. We prove that a graph is the graph of a minimally rigid (with respect to edges) ( k – 1, k)-frame if and only if it is a ( k – 1, k)-graph. Rigidity here means infinitesimal rigidity or equivalently statical rigidity. 相似文献
3.
In this paper we prove that there exists an elliptic semiplane S( v, k, m) with k – m 2 if and only if there exists a group divisible design GDD
k
(( k – m)( k – 1); k – m; 0, 1) with m pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplane W(45, 7, 3) and show that W is isomorphic to the elliptic semiplane S(45, 7, 3) given by R. D. Baker. 相似文献
4.
A graph G is said to be k-critical if it has chromatic number k, but every proper subgraph of G has a ( k–1)-coloring. Gallai asked whether every large k-critical graph contains many ( k–1)-critical subgraphs. We provide some information concerning this question and some related questions. 相似文献
5.
A ( p, q)-sigraph S is an ordered pair ( G, s) where G = ( V, E) is a ( p, q)-graph and s is a function which assigns to each edge of G a positive or a negative sign. Let the sets E
+ and E
– consist of m positive and n negative edges of G, respectively, where m + n = q. Given positive integers k and d, S is said to be ( k, d)-graceful if the vertices of G can be labeled with distinct integers from the set {0, 1, ..., k + ( q – 1) d such that when each edge uv of G is assigned the product of its sign and the absolute difference of the integers assigned to u and v the edges in E
+ and E
– are labeled k, k + d, k + 2 d, ..., k + ( m – 1) d and – k, – ( k + d), – ( k + 2 d), ..., – ( k + ( n – 1) d), respectively.In this paper, we report results of our preliminary investigation on the above new notion, which indeed generalises the well-known concept of ( k, d)-graceful graphs due to B. D. Acharya and S. M. Hegde. 相似文献
6.
In this paper, we consider the bivariate Hermite interpolation introduced by Bojanov and Xu [SIAM J. Numer. Anal. 39(5) (2002) 1780–1793]. The nodes of the interpolation with Π 2k-δ, where δ=0 or 1, are the intersection points of 2 k+1 distinct rays from the origin with a multiset of k+1- δ concentric circles. Parameters are the values and successive radial derivatives, whenever the corresponding circle is multiple. The poisedness of this interpolation was proved only for the set of equidistant rays [Bojanov and Xu, 2002] and its counterparts with other conic sections [Hakopian and Ismail, East J. Approx. 9 (2003) 251–267]. We show that the poisedness of this ( k+1- δ)(2 k+1) dimensional Hermite interpolation problem is equivalent to the poisedness of certain 2 k+1 dimensional Lagrange interpolation problems. Then the poisedness of Bojanov–Xu interpolation for a wide family of sets of rays satisfying some simple conditions is established. Our results hold also with above circles replaced by ellipses, hyperbolas, and pairs of parallel lines.Next a conjecture [Hakopian and Ismail, J. Approx. Theory 116 (2002) 76–99] concerning a poisedness relation between the Bojanov–Xu interpolation, with set of rays symmetric about x-axis, and certain univariate lacunary interpolations is established. At the end the poisedness for a wide class of lacunary interpolations is obtained. 相似文献
7.
We study certain subcomplexes Δ′ of an arbitrary simplicial complex Δ such that H mi( k[Δ])-H mi( k[Δ′]) for any 0 i<dim( k[Δ′]). Here, H mi( k[Δ]) is the ith local cohomology module of the Stanley-Reisner ring k[Δ] of Δ over a field k. Our technique is an elegant approach to one of the most generalized versions of the rank selection theorems of J. Munkres (1984, Michigan Math. J.31, 113–128, Theorem 6.4) and R. Stanley (1979, Trans. Amer. Math. Soc.249, 139–157, Theorem 4.3). 相似文献
8.
In this paper, we achieve the general solution and the generalized Hyers–Ulam–Rassias stability of the following functional equation f(x+ky)+f(x−ky)=k2f(x+y)+k2f(x−y)+2(1−k2)f(x) | for fixed integers k with k≠0,±1 in the quasi-Banach spaces. 相似文献
9.
Let
denote the subspace arrangement formed by all linear subspaces in
given by equations of the form
where 1
i1<<
ikn and (
1,…,
k){+1,−1}
k.Some important topological properties of such a subspace arrangement depend on the topology of its intersection lattice. In a previous work on a larger class of subspace arrangements by Björner and Sagan (J. Algebraic Combin. 5 (1996) 291–314) the topology of the intersection lattice
turned out to be a particularly interesting and difficult case.We prove in this paper that Pure(Π
n,k±) is shellable, hence that Π
n,k± is shellable for
k>
n/2. Moreover, we prove that
unless
i≡
n−2 (mod
k−2) or
i≡
n−3 (mod
k−2), and that
is free abelian for
i≡
n−2 (mod
k−2). In the special case of Π
2k,k± we determine homology completely. Our tools are generalized lexicographic shellability, as introduced in Kozlov (Ann. Combin. 1 (1997) 67–90), and a spectral sequence method for the computation of poset homology first used in Hanlon (Trans. Amer. Math. Soc. 325 (1991) 1–37).We state implications of our results on the cohomology of the complements of the considered arrangements.
相似文献
10.
We study the problem of sampling uniformly at random from the set of
k-colorings of a graph with maximum degree Δ. We focus attention on the Markov chain Monte Carlo method, particularly on a popular Markov chain for this problem, the Wang–Swendsen–Kotecký (WSK) algorithm. The second author recently proved that the WSK algorithm quickly converges to the desired distribution when
k11Δ/6. We study how far these positive results can be extended in general. In this note we prove the first non-trivial results on when the WSK algorithm takes exponentially long to reach the stationary distribution and is thus called
torpidly mixing. In particular, we show that the WSK algorithm is torpidly mixing on a family of bipartite graphs when 3
k<Δ/(20logΔ), and on a family of planar graphs for any number of colors. We also give a family of graphs for which, despite their small chromatic number, the WSK algorithm is not ergodic when
kΔ/2, provided
k is larger than some absolute constant
k0.
相似文献
11.
Suppose
Ax =
b is a system of linear equations where the matrix
A is symmetric positive definite and consistently ordered. A bound for the norm of the errors
k
=
x–
x
k of the AOR method in terms of the norms of
k
=
x
k–
x
k–1 and
k+1 =
x
k+1–
x
k and their inner product is derived.
相似文献
12.
Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal
k–Toeplitz matrix
A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of
A which enables us to state some conditions for the existence of
A–1. Our results also extend known results for the case when the residue mod
k of the order of
A is equal to 0 or
k–1 (
Numer. Math., 10 (1967), pp. 153–161.).The work was supported by
CMUC (Centro de Matemática da Universidade de Coimbra) and by
Acção Integrada Luso-Espanhola E-6/03 相似文献
13.
We study the (
k + 1)-Lie structures,
k-left commutative and homotopy (
k + 1)-Lie structures with multiplication generated by Wronskians and prove that the nontrivial structures of
n-Lie algebras appear only in the case of small characteristic.Original Russian Text Copyright © 2005 Dzhumadil’daev A. S.__________Translated from
Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 4, pp. 759–773, July–August, 2005.
相似文献
14.
We consider the Sturm-Liouville operator on a convex smooth curve lying in the complex plane and connecting the points 0 and 1. We prove that if the eigenvalues λ
k with large numbers are localized near a single ray, then this ray is the positive real semiaxis. Moreover, if the eigenvalues λ
k are numbered with algebraic multiplicities taken into account, then λ
k ∼ π ·
k as
k → +∞.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 72–84.Original Russian Text Copyright © 2005 by Kh. K. Ishkin.
相似文献
15.
The topological properties of the generalized Neuwirth groups,
nk are discussed. For examp, we demonstrate that the group,
nk is the fundamental group of the Seifert fibered space
nk. Moreover, discuss some other invariants and algebraic properties of the above groups.This work was supported by Polish grant (BW-5100–5–0259–9) and the Russian Foundation for Basic Research (grant number 98–01–00699).
2000 Mathematics Subject Classification: 20F34, 57M05, 57M60
相似文献
16.
Let
G be a connected graph with least eigenvalue –2, of multiplicity
k. A
star complement for –2 in
G is an induced subgraph
H =
G –
X such that |
X| =
k and –2 is not an eigenvalue of
H. In the case that
G is a generalized line graph, a characterization of such subgraphs is used to decribe the eigenspace of –2. In some instances,
G itself can be characterized by a star complement. If
G is not a generalized line graph,
G is an
exceptional graph, and in this case it is shown how a star complement can be used to construct
G without recourse to root systems.
相似文献
17.
Summary This paper deals with quadrature formulae of Gauss type corresponding to subspaces of spline functions
S
m–1, k
of degree
m–1 with
k fixed knots. We shall show monotonicity of the quadrature formulae for functions which are contained in the so-called convexity cone of
S
m–1,k
Moreover, we apply these results to monosplines and establish comparison theorems for these splines.
相似文献
18.
In a paper with the same title [3], we proved Chvátal's conjecture that
k-tough graphs have
k-factors if they satisfy trivial necessary conditions. In this paper, we prove the following stronger result: Suppose
|V(G)| k + 1,
k |V(G)| even, and
|S| k w(G – S) – 7/8
k if
w(G – S) 2, where
w(G – S) is the number of connected components of
G – S. Then
G has a
k-factor.
相似文献
19.
A typical problem in extremal combinatorics is the following. Given a large number
n and a set
L, find the maximum cardinality of a family of subsets of a ground set of
n elements such that the intersection of any two subsets has cardinality in
L. We investigate the generalization of this problem, where intersections of more than 2 subsets are considered. In particular, we prove that when
k–1 is a power of 2, the size of the extremal
k-wise oddtown family is (
k–1)(
n– 2log
2(
k–1)). Tight bounds are also found in several other basic cases.Research supported in part by NSF grant DMS 99-70270 and by the joint Berlin/Zurich graduate program Combinatorics, Geometry, Computation, financed by the German Science Foundation (DFG) and ETH ZürichResearch supported in part by NSF grant DMS-0200357, by an NSF CAREER award and by an Alfred P. Sloan fellowship. webpage: http://www.math.ucsd.edu/vanvu/
相似文献
20.
P. Hall, [2], gave necessary and sufficient conditions for a bipartite graph to have a perfect matching. Koning, [3], proved that such a graph can be decomposed into
k edge-disjoint perfect matchings if and only if it is
k-regular. It immediately follows that in a
k-regular bipartite graph
G, the deletion of any set
S of at most
k – 1 edges leaves intact one of those perfect matchings. However, it is not known what happens if we delete more than
k – 1 edges. In this paper we give sufficient conditions so that by deleting a set
S of
k + r edges
r 0, still
G – S has a perfect matching. Furthermore we prove that our result, in some sense, is best possible.
相似文献