The Existence of Solutions of Elliptic Equations with Neumann Boundary Condition for Superlinear Problems

In this paper, we study and discuss the existence of multiple solutions of a class of non-linear elliptic equations with Neumann boundary condition, and obtain at least seven non-trivial solutions in which two are positive, two are negative and three are sign-changing. The study of problem (1.1):{-△u αu=f(u),x∈Ω, x∈Ω,δu/δr=0,x∈δΩ,is based on the variational methods and critical point theory. We form our conclusion by using the sub-sup solution method, Mountain Pass Theorem in order intervals, Leray-Schauder degree theory and the invariance of decreasing flow.     

一类非锥映射减算子的不动点定理及应用

对一类非锥映射减算子进行了研究,得到了此类减算子不动点存在性定理,并将结果应用到具有关于u单调递减非线性项的奇异微分边值问题,此非线性项可以关于t=0,t=1和u=0奇异.     

Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System

In this paper for the M(n)/M(n)/s+GI system, i.e. for a s-server queueing system where the calls in the queue may leave the system due to impatience, we present new asymptotic results for the intensities of calls leaving the system due to impatience and a Markovian system approximation where these results are applied. Furthermore, we present a new proof for the formulae of the conditional density of the virtual waiting time distributions, recently given by Movaghar for the less general M(n)/M/s+GI system. Also we obtain new explicit expressions for refined virtual waiting time characteristics as a byproduct.     

Nonparametric Estimation of Hazard Rate Under the Constraint of Monotonicity

This article shows how to smoothly “monotonize” standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of forms, depending on choice of kernel estimator and on the distance function used to define a certain constrained optimization problem. We confine attention to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce “quadratic” inequality constraints to “linear” equality constraints, and so our method may be implemented using little more than conventional Newton–Raphson iteration. Thus, the necessary computational techniques are very familiar to statisticians. We show both numerically and theoretically that monotonicity, in either direction, can generally be imposed on a kernel hazard rate estimator regardless of the monotonicity or otherwise of the true hazard rate. The case of censored data is easily accommodated. Our methods have straightforward extension to the problem of testing for monotonicity of hazard rate, where the distance function plays the role of a test statistic.     

Necessary and sufficient condition for the existence of positive solutions of a coupled system for elastic beam equations

In this work, by using fixed point theorem and monotone iterative technique, the author establishes a necessary and sufficient condition of the existence of positive solutions for a class of nonlinear singular elastic beam differential system under reasonable conditions. Moreover, some uniqueness results of positive solution and the estimate of convergent rate of the iterative sequence of solution are obtained.     

Analysis of the adaptive MMAP[K]/PH[K]/1 queue: A multi-type queue with adaptive arrivals and general impatience

In this paper we introduce the adaptive MMAP[K] arrival process and analyze the adaptive MMAP[K]/PH[K]/1 queue. In such a queueing system, customers of K different types with Markovian inter-arrival times and possibly correlated customer types, are fed to a single server queue that makes use of r thresholds. Service times are phase-type and depend on the type of customer in service. Type k customers are accepted with some probability a_i,k if the current workload is between threshold i − 1 and i. The manner in which the arrival process changes its state after generating a type k customer also depends on whether the customer is accepted or rejected.     

Some estimates in spaces

We consider a class of rearrangement invariant Banach Function Spaces recently appeared in a paper by the same authors, containing at the same time some Lorentz spaces Γ(ν), classical Lebesgue spaces and small Lebesgue spaces. We discuss the main properties coming directly from the norm, and, for certain values of the involved parameters, we prove some estimates of the norm of the associate space.     

An example of an almost greedy uniformly bounded orthonormal basis for

We construct a uniformly bounded orthonormal almost greedy basis for L_p(0,1), 1<p<∞. The example shows that it is not possible to extend Orlicz's theorem, stating that there are no uniformly bounded orthonormal unconditional bases for L_p(0,1), p≠2, to the class of almost greedy bases.     

Convergence of Markov Chains in Information Divergence

Information theoretic methods are used to prove convergence in information divergence of reversible Markov chains. Also some ergodic theorems for information divergence are proved.      

A zero entropy endomorphism is nonstandard

We present an example of an ergodic transformation , a variant of a zero entropy non-loosely Bernoulli map of Feldman, such that the sequence of random variables generated by the [,Id] endomorphism is nonstandard.