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1.
The properties of (q1, q2)-quasimetric spaces are examined. Multivalued covering mappings between (q1, q2)-quasimetric spaces are investigated. Given two multivalued mappings between (q1, q2)-quasimetric spaces such that one of them is covering and the other satisfies the Lipschitz condition, sufficient conditions for these mappings to have a coincidence point are obtained. A theorem on the stability of coincidence points with respect to small perturbations in the considered mappings is proved. 相似文献
2.
E. S. Zhukovskiy 《Siberian Mathematical Journal》2018,59(6):1063-1072
The recent articles of Arutyunov and Greshnov extend the Banach and Hadler Fixed-Point Theorems and the Arutyunov Coincidence-Point Theorem to the mappings of (q1, q2)-quasimetric spaces. This article addresses similar questions for f-quasimetric spaces.Given a function f: R +2 → R+ with f(r1, r2) → 0 as (r1, r2) → (0, 0), an f-quasimetric space is a nonempty set X with a possibly asymmetric distance function ρ: X2 → R+ satisfying the f-triangle inequality: ρ(x, z) ≤ f(ρ(x, y), ρ(y, z)) for x, y, z ∈ X. We extend the Banach Contraction Mapping Principle, as well as Krasnoselskii’s and Browder’s Theorems on generalized contractions, to mappings of f-quasimetric spaces. 相似文献
3.
A. V. Greshnov 《Siberian Advances in Mathematics》2017,27(4):253-262
We prove that the conditions of (q1, 1)- and (1, q2)-quasimertricity of a distance function ρ are sufficient for the existence of a quasimetric bi-Lipschitz equivalent to ρ. It follows that the Box-quasimetric defined with the use of basis vector fields of class C1 whose commutators at most sum their degrees is bi-Lipschitz equivalent to some metric. On the other hand, we show that these conditions are not necessary. We prove the existence of (q1, q2)-quasimetrics for which there are no Lipschitz equivalent 1-quasimetrics, which in particular implies another proof of a result by V. Schröder. 相似文献
4.
Let λK m,n be a complete bipartite multigraph with two partite sets having m and n vertices, respectively. A K p,q -factorization of λK m,n is a set of edge-disjoint K p,q -factors of λK m,n which partition the set of edges of λK m,n . When p = 1 and q is a prime number, Wang, in his paper [On K 1,q -factorization of complete bipartite graph, Discrete Math., 126: (1994), 359-364], investigated the K 1,q -factorization of K m,n and gave a sufficient condition for such a factorization to exist. In papers [K 1,k -factorization of complete bipartite graphs, Discrete Math., 259: 301-306 (2002),; K p,q -factorization of complete bipartite graphs, Sci. China Ser. A-Math., 47: (2004), 473-479], Du and Wang extended Wang’s result to the case that p and q are any positive integers. In this paper, we give a sufficient condition for λK m,n to have a K p,q -factorization. As a special case, it is shown that the necessary condition for the K p,q -factorization of λK m,n is always sufficient when p : q = k : (k + 1) for any positive integer k. 相似文献
5.
We show that if a finite simple group G, isomorphic to PSLn(q) or PSUn(q) where either n ≠ 4 or q is prime or even, acts on a vector space over a field of the defining characteristic of G; then the corresponding semidirect product contains an element whose order is distinct from every element order of G. We infer that the group PSLn(q), n ≠ 4 or q prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka Notebook. 相似文献
6.
We start a new characterization of the geometric 2-design AG d (n,q) among all simple 2-designs with the same parameters by handling the cases d ∈ {1,2,3,n — 2}. For d ≠ 1, our characterization is in terms of line sizes, and for d = 1 in terms of the number of affine hyperplanes. We also show that the number of non-isomorphic resolvable designs with the parameters of AG1(n,q) grows exponentially with linear growth of n. 相似文献
7.
Let G be a finite group. The main result of this paper is as follows: If G is a finite group, such that Γ(G) = Γ(2G2(q)), where q = 32n+1 for some n ≥ 1, then G has a (unique) nonabelian composition factor isomorphic to 2 G 2(q). We infer that if G is a finite group satisfying |G| = |2 G 2(q)| and Γ(G) = Γ (2 G 2(q)) then G ? = 2 G 2(q). This enables us to give new proofs for some theorems; e.g., a conjecture of W. Shi and J. Bi. Some applications of this result are also considered to the problem of recognition by element orders of finite groups. 相似文献
8.
Let G be a nonabelian group, and associate the noncommuting graph ?(G) with G as follows: the vertex set of ?(G) is G\Z(G) with two vertices x and y joined by an edge whenever the commutator of x and y is not the identity. Let S 4(q) be the projective symplectic simple group, where q is a prime power. We prove that if G is a group with ?(G) ? ?(S 4(q)) then G ? S 4(q). 相似文献
9.
Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q ? E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from Lp to Lq is found. There exists a strictly singular but not superstrictly singular operator on Lp, provided that p ≠ 2. 相似文献
10.
11.
P. Bundschuh 《Journal of Mathematical Sciences》2012,180(5):550-555
For any rational integer q, |q|?>?1, the linear independence over \( \mathbb{Q} \) of the numbers 1, ζ q (1), and ζ ?q (1) is proved; here \( {\zeta_q}(1) = \sum\limits_{n = 1}^\infty {\frac{1}{{{q^n} - 1}}} \) is the so-called q-harmonic series or the q-zeta-value at the point 1. Besides this, a measure of linear independence of these numbers is established. 相似文献
12.
Consider the set of all proper edge-colourings of a graph G with n colours. Among all such colourings, the minimum length of a longest two-coloured cycle is denoted L(n, G). The problem of understanding L(n, G) was posed by Häggkvist in 1978 and, specifically, L(n, K n,n ) has received recent attention. Here we construct, for each prime power q ≥ 8, an edge-colouring of K n,n with n colours having all two-coloured cycles of length ≤ 2q 2, for integers n in a set of density 1 ? 3/(q ? 1). One consequence is that L(n, K n,n ) is bounded above by a polylogarithmic function of n, whereas the best known general upper bound was previously 2n ? 4. 相似文献
13.
Call a sequence of k Boolean variables or their negations a k-tuple. For a set V of n Boolean variables, let T k (V) denote the set of all 2 k n k possible k-tuples on V. Randomly generate a set C of k-tuples by including every k-tuple in T k (V) independently with probability p, and let Q be a given set of q “bad” tuple assignments. An instance I = (C,Q) is called satisfiable if there exists an assignment that does not set any of the k-tuples in C to a bad tuple assignment in Q. Suppose that θ, q > 0 are fixed and ε = ε(n) > 0 be such that εlnn/lnlnn→∞. Let k ≥ (1 + θ) log2 n and let \({p_0} = \frac{{\ln 2}}{{q{n^{k - 1}}}}\). We prove that
相似文献
$$\mathop {\lim }\limits_{n \to \infty } P\left[ {I is satisfiable} \right] = \left\{ {\begin{array}{*{20}c} {1,} & {p \leqslant (1 - \varepsilon )p_0 ,} \\ {0,} & {p \geqslant (1 + \varepsilon )p_0 .} \\ \end{array} } \right.$$
14.
V. I. Zenkov 《Siberian Mathematical Journal》2016,57(6):1002-1010
Given a finite group G with socle isomorphic to L 2(q), q ≥ 4, we describe, up to conjugacy, all pairs of nilpotent subgroups A and B of G such that A ∩ B g ≠ 1 for all g ∈ G. 相似文献
15.
We study the Möbius invariant spacesQ p andQ p, 0 of analytic functions. These scales of spaces include BMOA=Q1, VMOA=Q1, 0 and the Dirichlet space=Q0. Using the Bergman metric, we establish decomposition theorems for these spaces. We obtain also a fractional derivative characterization for bothQ p andQ p, 0 . 相似文献
16.
In this paper, we establish the preserving log-convexity of linear transformation associated with p, q-analogue of Pascal triangle, i.e., if the sequence of nonnegative numbers {xn}n is logconvex, then \({y_n} = {\sum\nolimits_{k = 0}^n {\left[ {\frac{n}{k}} \right]} _{pq}}{x_k}\) so is it for q ≠ p ≥ 1. 相似文献
17.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):6-23
Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters φ and ψ, then φ(1) = ψ(1). In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for symplectic groups Sp4(q) and PSp4(q). 相似文献
18.
M. De Boeck 《Designs, Codes and Cryptography》2012,63(2):171-182
The main theorem of this article gives a classification of the codewords in \({C^{\bot}_{n-1}(n,q)}\) , the dual code of points and hyperplanes in PG(n, q), q even, with weight smaller than \({q+\sqrt[3]{q^{2}}+1}\). In the proof, we rely on the classification of the small blocking sets in PG(2, q), q even. 相似文献
19.
Wolter Groenevelt 《The Ramanujan Journal》2018,47(2):317-337
The 6j-symbols for representations of the q-deformed algebra of polynomials on \(\mathrm {SU}(2)\) are given by Jackson’s third q-Bessel functions. This interpretation leads to several summation identities for the q-Bessel functions. Multivariate q-Bessel functions are defined, which are shown to be limit cases of multivariate Askey–Wilson polynomials. The multivariate q-Bessel functions occur as 3nj-symbols. 相似文献
20.
Let g be the finite dimensional simple Lie algebra of type An, and let U? = U q (g,Λ) and U = U q (g,Q) be the quantum groups defined over the weight lattice and over the root lattice, respectively. In this paper, we find two algebraically independent central elements in U? for all n ≥ 2 and give an explicit formula of the Casimir elements for the quantum group U? = U q (g,Λ), which corresponds to the Casimir element of the enveloping algebra U(g). Moreover, for n = 2 we give explicitly generators of the center subalgebras of the quantum groups U? = U q (g,Λ) and U = U q (g,Q). 相似文献