Noncommuting selfmaps and invariant approximations

Common fixed-point results are established for a new class of noncommuting selfmaps. We apply them to obtain several invariant approximation results which unify, extend, and complement well-known results.     

Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.This work was supported in part by Swiss NSF grant 20-32644.91.     

On the index of composition of integers from various sets

Given an integer n ≥ 2, let λ(n) := (log n)/(log γ(n)), where γ(n) = Π _p|n p, stand for the index of composition of n, with λ(1) = 1. We study the distribution function of (λ(n) – 1) log n as n runs through particular sets of integers, such as the shifted primes, the values of a given irreducible cubic polynomial and the shifted powerful numbers. Research supported in part by a grant from NSERC. Research supported by the Applied Number Theory Research Group of the Hungarian Academy of Science and by a grant from OTKA. Professor M.V. Subbarao passed away on February 15, 2006. Received: 3 March 2006 Revised: 28 October 2006     

Steady state analysis of an M/G/1 queue with two phase service and Bernoulli vacation schedule under multiple vacation policy

This paper examines the steady state behaviour of a batch arrival queue with two phases of heterogeneous service along and Bernoulli schedule vacation under multiple vacation policy, where after two successive phases service or first vacation the server may go for further vacations until it finds a new batch of customer in the system. We carry out an extensive stationary analysis of the system, including existence of stationary regime, queue size distribution of idle period process, embedded Markov chain steady state distribution of stationary queue size, busy period distribution along with some system characteristics.     

A topological aspect of Sobolev mappings

Let be a connected open set, . We give a sufficient condition for a mapping , , to have the property that sgn is almost everywhere of one sign. Following the work of Müller, Spector, and Tang [MST], we give an application of our results to the theory of non-linear elasticity. Received: 13 October 2000 / Accepted: 23 January 2001 / Published online: 4 May 2001     

外来的捕食物种对濒危物种的影响

In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen‘s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed.     

Enlarged symmetry groups of finite-size clusters with periodic noundary conditions

Any system that approximates an infinite lattice by a family of finite clusters (with periodic boundary conditions) passes through an intermediate region with enlarged (hidden) symmetry as the system size is increased. The hidden symmetry allows for extra degeneracies and level crossings and has application to exact-diagonalization studies, Monte Carlo simulations, lattice gauge theories, and renormalization group calculations.     

Partially finite convex programming,Part I: Quasi relative interiors and duality theory

We study convex programs that involve the minimization of a convex function over a convex subset of a topological vector space, subject to a finite number of linear inequalities. We develop the notion of the quasi relative interior of a convex set, an extension of the relative interior in finite dimensions. We use this idea in a constraint qualification for a fundamental Fenchel duality result, and then deduce duality results for these problems despite the almost invariable failure of the standard Slater condition. Part II of this work studies applications to more concrete models, whose dual problems are often finite-dimensional and computationally tractable.     

Uniform persistence for nonautonomous and random parabolic Kolmogorov systems

The purpose of this paper is to investigate uniform persistence for nonautonomous and random parabolic Kolmogorov systems via the skew-product semiflows approach. It is first shown that the uniform persistence of the skew-product semiflow associated with a nonautonomous (random) parabolic Kolmogorov system implies that of the system. Various sufficient conditions in terms of the so-called unsaturatedness and/or Lyapunov exponents for uniform persistence of the skew-product semiflows are then provided. Among others, it is shown that if the associated skew-product semiflow has a global attractor and its restriction to the boundary of the state space has a Morse decomposition which is unsaturated or whose external Lyapunov exponents are positive, then it is uniformly persistent. More specific conditions are discussed for uniform persistence in n-species, particularly 3-species, random competitive systems.     

An analytical proof of Hardy-like inequalities related to the Dirac operator

We prove some sharp Hardy-type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.