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341.
Zhenhai Liu 《Journal of Differential Equations》2008,244(6):1395-1409
This paper is devoted to the periodic problem for quasilinear parabolic hemivariational inequalities at resonance as well as at nonresonance. By use of the theory of multi-valued pseudomonotone operators, the notion of generalized gradient of Clarke and the property of the first eigenfunction, we build a Landesman-Lazer theory in the nonsmooth framework of quasilinear parabolic hemivariational inequalities. 相似文献
342.
Yossi Moshe 《Journal of Number Theory》2007,123(1):224-240
Let H(x) be a monic polynomial over a finite field F=GF(q). Denote by Na(n) the number of coefficients in Hn which are equal to an element a∈F, and by G the set of elements a∈F× such that Na(n)>0 for some n. We study the relationship between the numbers (Na(n))a∈G and the patterns in the base q representation of n. This enables us to prove that for “most” n's we have Na(n)≈Nb(n), a,b∈G. Considering the case H=x+1, we provide new results on Pascal's triangle modulo a prime. We also provide analogous results for the triangle of Stirling numbers of the first kind. 相似文献
343.
In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove
that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity
for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point
theory.
Second author is Corresponding author. 相似文献
344.
Artūras Dubickas 《Journal of Number Theory》2006,117(1):222-239
We prove that for any non-zero real number ξ the sequence of fractional parts {ξ(3/2)n}, n=1,2,3,…, contains at least one limit point in the interval [0.238117…,0.761882…] of length 0.523764…. More generally, it is shown that every sequence of distances to the nearest integer ||ξ(p/q)n||, n=1,2,3,…, where p/q>1 is a rational number, has both ‘large’ and ‘small’ limit points. All obtained constants are explicitly expressed in terms of p and q. They are also expressible in terms of the Thue-Morse sequence and, for irrational ξ, are best possible for every pair p>1, q=1. Furthermore, we strengthen a classical result of Pisot and Vijayaraghavan by giving similar effective results for any sequence ||ξαn||, n=1,2,3,…, where α>1 is an algebraic number and where ξ≠0 is an arbitrary real number satisfying ξ∉Q(α) in case α is a Pisot or a Salem number. 相似文献
345.
Abstract. Let G be a simply connected domain in the complex plane bounded by a closed Jordan curve L and let P
n
, n≥ 0 , be polynomials of respective degrees n=0,1,··· that are orthonormal in G with respect to the area measure (the so-called Bergman polynomials). Let ϕ be a conformal map of G onto the unit disk. We characterize, in terms of the asymptotic behavior of the zeros of P
n
's, the case when ϕ has a singularity on L . To investigate the opposite case we consider a special class of lens-shaped domains G that are bounded by two orthogonal circular arcs. Utilizing the theory of logarithmic potentials with external fields, we
show that the limiting distribution of the zeros of the P
n
's for such lens domains is supported on a Jordan arc joining the two vertices of G . We determine this arc along with the distribution function. 相似文献
346.
《Applied Mathematics and Optimization》2008,45(3):251-267
We study a class of optimization dynamics problems related to investment under uncertainty. The general model problem is
reformulated in terms of an obstacle problem associated to a second-order elliptic operator which is not in divergence form.
The spatial domain is unbounded and no boundary conditions are a priori specified. By using the special structure of the differential
operator and the spatial domain, and some approximating arguments, we show the existence and uniqueness of a solution of the
problem. We also study the regularity of the solution and give some estimates on the location of the coincidence set. 相似文献
347.
Given N?2 positive integers a1,a2,…,aN with GCD(a1,…,aN)=1, let fN denote the largest natural number which is not a positive integer combination of a1,…,aN. This paper gives an optimal lower bound for fN in terms of the absolute inhomogeneous minimum of the standard (N−1)-simplex. 相似文献
348.
Glenn H. Hurlbert 《Discrete Applied Mathematics》2007,155(18):2594-2600
Deo and Micikevicius recently gave a new bijection for spanning trees of complete bipartite graphs. In this paper we devise a generalization of Deo and Micikevicius's method, which is also a modification of Olah's method for encoding the spanning trees of any complete multipartite graph K(n1,…,nr). We also give a bijection between the spanning trees of a planar graph and those of any of its planar duals. Finally we discuss the possibility of bijections for spanning trees of DeBriujn graphs, cubes, and regular graphs such as the Petersen graph that have integer eigenvalues. 相似文献
349.
I. Shiokawa 《Indagationes Mathematicae》2008,19(1):151-161
Let q ≥ 2 and 0 ≤ r ≤ q − 2 be integers. In this paper, we study pattern sequences for patterns in ‹q, r›-numeration systems through their generating functions. Our result implies that any nontrivial linear combination over ? of pattern sequences chosen from different ‹q, r›-numeration systems cannot be a linear recurrence sequence. In particular, pattern sequences in different ‹q, r›-numeration systems are linearly independent over ?, while within one ‹q, r›-numeration system they can be linearly dependent ?. 相似文献
350.
Akos Magyar 《Monatshefte für Mathematik》2002,136(4):287-296
Optimal lower bounds are given for the discrepancy of point distributions w.r.t. geodesic balls on spheres and hyperbolic
spaces. The mean discrepancy is estimated below by using a non-commutative version of the Fourier transform method developed
by Beck for Euclidean spaces.
Received March 2, 2000; in revised form February 28, 2002 Published online August 19, 2002 相似文献