共查询到20条相似文献,搜索用时 15 毫秒
1.
M. R. Gabdullin 《Proceedings of the Steklov Institute of Mathematics》2017,297(1):81-87
We show the unimprovability of a theorem on sufficient convergence conditions for the trigonometric Fourier series of a function in classes ?(L) in the case when the class ?(L) is “close” to L. 相似文献
2.
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler’s totient function and σ is the sum-of-divisors function. 相似文献
3.
Sheng Gao 《Archiv der Mathematik》2011,96(6):507-512
Let G be a finite group, and suppose that B is a p-block of G with defect group D. Let k(B) denote the number of ordinary irreducible characters in B. It was conjectured by Brauer that k(B) ≤ |D|. In this paper, we will prove Brauer’s inequality in the case that D is metacyclic and p is odd. 相似文献
4.
Sh. M. Nasibov 《Mathematical Notes》2017,101(1-2):123-131
Sufficient conditions for the blow-up of nontrivial generalized solutions of the interior Dirichlet problem with homogeneous boundary condition for the homogeneous elliptic-type equation Δu + q(x)u = 0, where either q(x) ≠ const or q(x) = const= λ > 0, are obtained. A priori upper bounds (Theorem 4 and Remark 6) for the exact constants in the well-known Sobolev and Steklov inequalities are established. 相似文献
5.
We investigate the relation between analytic Campanato spaces \(\mathcal {AL}_{p,s}\) and the spaces F(p, q, s), characterize the bounded and compact Riemann–Stieltjes operators from \(\mathcal {AL}_{p,s}\) to \(F(p,p-s-1,s)\). We also describe the corona theorem and the interpolating sequences for the class \(F(p,p-2,s)\), which is the Möbius invariant subspace of the analytic Besov type spaces \(B_p(s)\). 相似文献
6.
Iwo Labuda 《Positivity》2010,14(4):801-813
Let μ be a measure from a σ-algebra of subsets of a set T into a sequentially complete Hausdorff topological vector space X. Assume that μ is convexly bounded, i.e., the convex hull of its range is bounded in X, and denote by L
1(μ) the space of scalar valued functions on T which are integrable with respect to the vector measure μ. We study the inheritance of some properties from X to L
1(μ). We show that the bounded multiplier property passes from X to L
1(μ). Answering a 1972 problem of Erik Thomas, we show that for a rather large class of F-spaces X the non-containment of c
0 passes from X to L
1(μ). 相似文献
7.
This paper presents an approach using a recursive algorithm for packing (?, w)-rectangles into larger rectangular and L-shaped pieces. Such a problem has actual applications for non-guillotine cutting and pallet/container loading. Our motivation for developing the L-approach is based on the fact that it can solve difficult pallet loading instances. Indeed, it is able to solve all testing problems (more than 20 000 representatives of infinite equivalence classes of the literature), including the 18 hard instances unresolved by other heuristics. We conjecture that the L-approach always finds optimum packings of (?, w)-rectangles into rectangular pieces. Moreover, the approach may also be useful when dealing with cutting and packing problems involving L-shaped pieces. 相似文献
8.
V. V. Rane 《Proceedings Mathematical Sciences》2010,120(1):7-9
In the famous work of Dirichlet on class number formula, L(s, χ) at s = 1 has been expressed as a finite sum, where L(s, χ) is the Dirichlet L-series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive
Dirichlet character χ. 相似文献
9.
Junlei Zhu Yuehua Bu Miltiades P. Pardalos Hongwei Du Huijuan Wang Bin Liu 《Journal of Global Optimization》2018,72(3):539-552
The optimal channel assignment is an important optimization problem with applications in optical networks. This problem was formulated to the L(p, 1)-labeling of graphs by Griggs and Yeh (SIAM J Discrete Math 5:586–595, 1992). A k-L(p, 1)-labeling of a graph G is a function \(f:V(G)\rightarrow \{0,1,2,\ldots ,k\}\) such that \(|f(u)-f(v)|\ge p\) if \(d(u,v)=1\) and \(|f(u)-f(v)|\ge 1\) if \(d(u,v)=2\), where d(u, v) is the distance between the two vertices u and v in the graph. Denote \(\lambda _{p,1}^l(G)= \min \{k \mid G\) has a list k-L(p, 1)-labeling\(\}\). In this paper we show upper bounds \(\lambda _{1,1}^l(G)\le \Delta +9\) and \(\lambda _{2,1}^l(G)\le \max \{\Delta +15,29\}\) for planar graphs G without 4- and 6-cycles, where \(\Delta \) is the maximum vertex degree of G. Our proofs are constructive, which can be turned to a labeling (channel assignment) method to reach the upper bounds. 相似文献
10.
Gunter Malle 《Israel Journal of Mathematics》2018,228(2):527-556
We study Brauer’s long-standing k(B)-conjecture on the number of characters in p-blocks for finite quasi-simple groups and show that their blocks do not occur as a minimal counterexample for p ≥ 5 nor in the case of abelian defect. For p = 3 we obtain that the principal 3-blocks do not provide minimal counterexamples. We also determine the precise number of irreducible characters in unipotent blocks of classical groups for odd primes. 相似文献
11.
The spaces X in which every prime z°-ideal of C(X) is either minimal or maximal are characterized. By this characterization, it turns out that for a large class of topological spaces X, such as metric spaces, basically disconnected spaces and one-point compactifications of discrete spaces, every prime z°-ideal in C(X) is either minimal or maximal. We will also answer the following questions: When is every nonregular prime ideal in C(X) a z°-ideal? When is every nonregular (prime) z-ideal in C(X) a z°-ideal? For instance, we show that every nonregular prime ideal of C(X) is a z°-ideal if and only if X is a ?-space (a space in which the boundary of any zeroset is contained in a zeroset with empty interior). 相似文献
12.
The notion of derivatives for smooth representations of GL(n, ? p ) was defined in [BZ77]. In the archimedean case, an analog of the highest derivative was defined for irreducible unitary representations in [Sah89] and called the “adduced” representation. In this paper we define derivatives of all orders for smooth admissible Fréchet representations of moderate growth. The real case is more problematic than the p-adic case; for example, arbitrary derivatives need not be admissible. However, the highest derivative continues being admissible, and for irreducible unitarizable representations coincides with the space of smooth vectors of the adduced representation.In the companion paper [AGS] we prove exactness of the highest derivative functor, and compute highest derivatives of all monomial representations.We apply those results to finish the computation of adduced representations for all irreducible unitary representations and to prove uniqueness of degenerate Whittaker models for unitary representations, thus completing the results of [Sah89, Sah90, SaSt90, GS13a]. 相似文献
13.
In this paper we use the spine decomposition and martingale change of measure to establish a Kesten–Stigum Llog L theorem for branching Hunt processes. This result is a generalization of the results in Asmussen and Hering (Z. Wahrscheinlichkeitstheor.
Verw. Geb. 36:195–212, 1976) and Hering (Branching Processes, pp. 177–217, 1978) for branching diffusions. 相似文献
14.
Crossing numbers of graphs are in general very difficult to compute. There are several known exact results on the crossing
number of the Cartesian products of paths, cycles or stars with small graphs. In this paper we study cr(Km □ Pn), the crossing number of the Cartesian product Km □ Pn. We prove that
for m ≥ 3,n ≥ 1 and cr(Km □ Pn)≥ (n − 1)cr(Km+2 − e) + 2cr(Km+1). For m≤ 5, according to Klešč, Jendrol and Ščerbová, the equality holds. In this paper, we also prove that the equality holds for
m = 6, i.e., cr(K6 □ Pn) = 15n + 3.
Research supported by NFSC (60373096, 60573022). 相似文献
15.
A. A. Yukhimenko 《Moscow University Mathematics Bulletin》2010,65(2):69-71
The system of exponents $
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
$
\left\{ {e^{i\lambda _n t} } \right\}_{n \in \mathbb{Z}}
is considered. A sufficient condition for a Riesz-property basis in the weighted space L
p
(−π, π) is obtained. 相似文献
16.
M. R. Gabdullin 《Mathematical Notes》2016,99(5-6):861-869
The paper deals with the question of the divergence of Fourier series in function spaces wider than L = L[?π, π], but narrower than Lp = Lp[?π, π] for all p ∈ (0, 1). It is proved that the recent results of Filippov on the generalization to the space ?(L) of Kolmogorov’s theorem on the convergence of Fourier series in Lp, p ∈ (0, 1), cannot be improved. 相似文献
17.
Let K be a Hausdorff space and C
b
(K) be the Banach algebra of all complex bounded continuous functions on K. We study the Gateaux and Fréchet differentiability of subspaces of C
b
(K). Using this, we show that the set of all strong peak functions in a nontrivial separating separable subspace H of C
b
(K) is a dense G
δ subset of H, if K is compact. This gives a generalized Bishop’s theorem, which says that the closure of the set of all strong peak points for
H is the smallest closed norming subset of H. The classical Bishop’s theorem was proved for a separating subalgebra H and a metrizable compact space K. 相似文献
18.
Monia Giandomenico Adam N. Letchford Fabrizio Rossi Stefano Smriglio 《Mathematical Programming》2009,120(2):381-401
Although the lift-and-project operators of Lovász and Schrijver have been the subject of intense study, their M(K, K) operator has received little attention. We consider an application of this operator to the stable set problem. We begin
with an initial linear programming (LP) relaxation consisting of clique and non-negativity inequalities, and then apply the
operator to obtain a stronger extended LP relaxation. We discuss theoretical properties of the resulting relaxation, describe
the issues that must be overcome to obtain an effective practical implementation, and give extensive computational results.
Remarkably, the upper bounds obtained are sometimes stronger than those obtained with semidefinite programming techniques.
相似文献
19.
For a commutative ring A with identity, and for infinite cardinals α as well as the symbol ∞, which indicates the situation in which there are no cardinal restrictions, one defines A to be α-regular if for each subset D of A, with |D| < α and de = 0, for any two distinct d, e ∈ D, there is an s ∈ A such that d
2
s = d, for each d ∈ D, and if xd = 0, for each d ∈ D, then xs = 0 相似文献
20.
Jiri Rohn 《Optimization Letters》2012,6(3):585-591
A theorem of the alternatives for the equation \({|Ax|-|B||x|=b\ (A,B\in{\mathbb{R}}^{n\times n},\, b\in{\mathbb{R}}^n)}\) is proved and several consequences are drawn. In particular, a class of matrices A, B is identified for which the equation has exactly 2 n solutions for each positive right-hand side b. 相似文献