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911.
We study an elliptic transmission problem in Banach spaces. The problem is considered on the juxtaposition of two intervals, one of which of small length δ, and models physical phenomena in media constituted by two parts with different physical characteristics. We obtain results of existence, uniqueness, maximal regularity and optimal dependence on the parameter δ for Lp solutions of the problem. The main tools of our approach are impedance and admittance operators (i.e. Dirichlet-to-Neumann and Neumann-to-Dirichlet operators) and H∞ functional calculus for sectorial operators in Banach spaces. 相似文献
912.
J. Banasiak 《Journal of Mathematical Analysis and Applications》2011,378(1):89-97
We provide general criteria for existence of chaotic dynamics in Kolmogorov systems with proliferation. As applications, we provide a new proof of chaoticity of a class of constant coefficient birth-and-death systems and also show that a finite difference discretization of a class of drift diffusion equations generates chaotic dynamics. We also present a general method of constructing chaotic Kolmogorov systems. 相似文献
913.
Robert Hazlewood 《Journal of Mathematical Analysis and Applications》2011,383(1):1-24
Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let {xn} be a sequence in the unit space G(0) of G. We show that the notions of strength of convergence of {xn} in the orbit space G(0)/G and measure-theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid C?-algebra. 相似文献
914.
We consider the following problem: Given a set of m×n real (or complex) matrices A1,…,AN, find an m×m orthogonal (or unitary) matrix P and an n×n orthogonal (or unitary) matrix Q such that P*A1Q,…,P*ANQ are in a common block-diagonal form with possibly rectangular diagonal blocks. We call this the simultaneous singular value decomposition (simultaneous SVD). The name is motivated by the fact that the special case with N=1, where a single matrix is given, reduces to the ordinary SVD. With the aid of the theory of *-algebra and bimodule it is shown that a finest simultaneous SVD is uniquely determined. An algorithm is proposed for finding the finest simultaneous SVD on the basis of recent algorithms of Murota-Kanno-Kojima-Kojima and Maehara-Murota for simultaneous block-diagonalization of square matrices under orthogonal (or unitary) similarity. 相似文献
915.
Predrag S. Stanimirovi? Dragana S. Cvetkovi?-Ili? Sladjana Miljkovi? Marko Miladinovi? 《Applied mathematics and computation》2011,217(22):9358-9367
We present the full-rank representations of {2, 4} and {2, 3}-inverses (with given rank as well as with prescribed range and null space) as particular cases of the full-rank representation of outer inverses. As a consequence, two applications of the successive matrix squaring (SMS) algorithm from [P.S. Stanimirovi?, D.S. Cvetkovi?-Ili?, Successive matrix squaring algorithm for computing outer inverses, Appl. Math. Comput. 203 (2008) 19-29] are defined using the full-rank representations of {2, 4} and {2, 3}-inverses. The first application is used to approximate {2, 4}-inverses. The second application, after appropriate modifications of the SMS iterative procedure, computes {2, 3}-inverses of a given matrix. Presented numerical examples clarify the purpose of the introduced methods. 相似文献
916.
We study the L∞ path partition problem: given a path of n weighted vertices and an integer k, remove k−1 edges from the path so that the maximum absolute deviation of the weights of the resulting k sub-paths from their mean is minimized. Previously, the best algorithm solves this problem in O(nklogk) time. We present an O(nk) time algorithm. We also give improved solutions for two related problems: the Ld path partition problem and the web proxies placement problem. 相似文献
917.
Given a space M, a family of sets A of a space X is ordered by M if A={AK:K is a compact subset of M} and K⊂L implies AK⊂AL. We study the class M of spaces which have compact covers ordered by a second countable space. We prove that a space Cp(X) belongs to M if and only if it is a Lindelöf Σ-space. Under MA(ω1), if X is compact and (X×X)\Δ has a compact cover ordered by a Polish space then X is metrizable; here Δ={(x,x):x∈X} is the diagonal of the space X. Besides, if X is a compact space of countable tightness and X2\Δ belongs to M then X is metrizable in ZFC.We also consider the class M? of spaces X which have a compact cover F ordered by a second countable space with the additional property that, for every compact set P⊂X there exists F∈F with P⊂F. It is a ZFC result that if X is a compact space and (X×X)\Δ belongs to M? then X is metrizable. We also establish that, under CH, if X is compact and Cp(X) belongs to M? then X is countable. 相似文献
918.
G.H. Fath-Tabar B. Vaez-ZadehA.R. Ashrafi A. Graovac 《Discrete Applied Mathematics》2011,159(13):1323-1330
The atom-bond connectivity index is a useful topological index in studying the stability of alkanes and the strain energy of cycloalkanes. In this paper some inequalities for the atom-bond connectivity index of a series of graph operations are presented. We also prove our bounds are tight. As an application, the ABC indices of C4 nanotubes and nanotori are computed. 相似文献
919.
A key result underlying the theory of MCMC is that any η-irreducible Markov chain having a transition density with respect to η and possessing a stationary distribution π is automatically positive Harris recurrent. This paper provides a short self-contained proof of this fact using the ergodic theorem in its standard form as the most advanced tool. 相似文献
920.
Relying on the stochastic analysis tools developed in Bayraktar and Yao (2011) [1], we solve the optimal stopping problems for non-linear expectations. 相似文献