On commutativity of near-rings with generalized derivations

In this paper we prove some theorems of commutativity for near-rings with generalized derivations. As a consequence of the results obtained, we generalize some published results. Also, we give some examples to show that some conditions in some results obtained are not redundant.     

Decomposition results for general polling systems and their applications

In this paper we derive decomposition results for the number of customers in polling systems under arbitrary (dynamic) polling order and service policies. Furthermore, we obtain sharper decomposition results for both the number of customers in the system and the waiting times under static polling policies. Our analysis, which is based on distributional laws, relaxes the Poisson assumption that characterizes the polling systems literature. In particular, we obtain exact decomposition results for systems with either Mixed Generalized Erlang (MGE) arrival processes, or asymptotically exact decomposition results for systems with general renewal arrival processes under heavy traffic conditions. The derived decomposition results can be used to obtain the performance analysis of specific systems. As an example, we evaluate the performance of gated Markovian polling systems operating under heavy traffic conditions. We also provide numerical evidence that our heavy traffic analysis is very accurate even for moderate traffic. This revised version was published online in June 2006 with corrections to the Cover Date.     

具有双线性BL(1,1,1,1)误差的非线性回归模型相关性和方差齐性的检验

在时间序列回归模型分析中,相关性和方差齐性的检验是一个很基本的问题.本文讨论了具有双线性BL(1,1,1,1)误差的非线性回归模型的相关性和方差齐性的检验问题, 用Score检验方法给出了双线性项检验、相关性检验、方差齐性检验、以及相关性和方差齐性同时检验的检验统计量.推广和发展了具有线性序列误差项回归模型的结果.本文还用数值实例说明了检验方法的实用价值.     

Global Convergence of Algorithms with Nonmonotone Line Search Strategy in Unconstrained Optimization

In this paper we state some nonmonotone line search strategies for unconstrained optimization algorithms. Abstracting from the concrete line search strategy we prove two general convergence results. Using this theory we can show the global convergence of the BFGS method with nonmonotone line search strategy. In contrast to some former results about nonmonotone line search strategies, both our convergence results and their proofs are natural generalizations of known results for the monotone case.     

On the existence of positive solution for second-order multi-points boundary value problems

Here we are concerned with the existence of positive solution for autonomous and nonautonomous second-order systems with multi-points boundary conditions. For nonautonomous systems we use the Schauder's fixed point theorem in a suitable Banach space, while for autonomous ones using fixed point theorems is usually useless because of the existence of trivial solution and for this we employed a method based on the implicit function theorem and topological degree. In order to verify the obtained results, we have considered some definite systems to verify the results numerically.     

Regularity conditions characterizing Fenchel–Lagrange duality and Farkas-type results in DC infinite programming

In this paper, we consider a DC infinite programming problem (P) with inequality constraints. By using the properties of the epigraph of the conjugate functions, we introduce some new notions of regularity conditions for (P). Under these new regularity conditions, we completely characterize the Fenchel–Lagrange duality and the stable Fenchel–Lagrange duality for (P). Similarly, we also completely characterize the Farkas-type results and the stable Farkas-type results for (P). As applications, we obtain the corresponding results for conic programming problems.     

Constraint Qualifications for Nonsmooth Mathematical Programs with Equilibrium Constraints

We study nonsmooth mathematical programs with equilibrium constraints. First we consider a general disjunctive program which embeds a large class of problems with equilibrium constraints. Then, we establish several constraint qualifications for these optimization problems. In particular, we generalize the Abadie and Guignard-type constraint qualifications. Subsequently, we specialize these results to mathematical program with equilibrium constraints. In our investigation, we show that a local minimum results in a so-called M-stationary point under a very weak constraint qualification.      

Oscillations of nonlinear hyperbolic equations with functional arguments via Riccati method

This paper is devoted to the study of the oscillatory behavior of solutions of nonlinear hyperbolic equations with functional arguments by using integral averaging method and a generalized Riccati technique. First, we establish oscillation results for nonlinear hyperbolic equations by applying oscillation criteria for Riccati inequality. Secondly, we present interval oscillation results for nonlinear hyperbolic equations. These results improve and extend oscillation results of Cui and Xu [1].     

The boundedness for solutions of a certain two-dimensional fractional differential system with delay

In this paper, we study the components-wise upper bounds for solutions of two-dimensional fractional differential system with delay. Prior to the main results, we derive some results on two-dimensional nonlinear integral inequalities, then we investigate upper bounds of solutions basing on the obtained inequalities, finally, an example is given to illustrate the theoretical results.     

Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum

We study the Cauchy problem for multi-dimensional compressible radiation hydrodynamics equations with vacuum. First, we present some sufficient conditions on the blow-up of smooth solutions in multi-dimensional space. Then, we obtain the invariance of the support of density for the smooth solutions with compactly supported initial mass density by the property of the system under the vacuum state. Based on the above-mentioned results, we prove that we cannot get a global classical solution, no matter how small the initial data are, as long as the initial mass density is of compact support. Finally, we will see that some of the results that we obtained are still valid for the isentropic flows with degenerate viscosity coefficients as well as for one-dimensional case.     

Bayesian inference for dependent elliptical measurement error models

In this article we provide a Bayesian analysis for dependent elliptical measurement error models considering nondifferential and differential errors. In both cases we compute posterior distributions for structural parameters by using squared radial prior distributions for the precision parameters. The main result is that the posterior distribution of location parameters, for specific priors, is invariant with respect to changes in the generator function, in agreement with previous results obtained in the literature under different assumptions. Finally, although the results obtained are valid for any elliptical distribution for the error term, we illustrate those results by using the student-t distribution and a real data set.     

Existence of positive periodic solutions for two kinds of neutral functional differential equations

In this work, we deal with a new existence theory for positive periodic solutions for two kinds of neutral functional differential equations by employing the Krasnoselskii fixed-point theorem. Applying our results to various mathematical models we improve some previous results.     

Fixed point theorems for multivalued non-linear $F$-contractions on quasi metric spaces with an application

In this paper, we introduce $(\alpha,\beta)$-type $F-\tau$ contraction and utilize the same to prove some fixed point results for multivalued mappings in quasi metric spaces. Furthermore, we furnish with some examples to exhibit the utility of our results. As an application, we establish the existence of a solution for a non-linear integral equation.     

Pointwise Control of the Burgers Equation and Related Nash Equilibrium Problems: Computational Approach

This article is concerned with the numerical solution of multiobjective control problems associated with nonlinear partial differential equations and more precisely the Burgers equation. For this kind of problems, we look for the Nash equilibrium, which is the solution to a noncooperative game. To compute the solution of the problem, we use a combination of finite-difference methods for the time discretization, finite-element methods for the space discretization, and a quasi-Newton BFGS algorithm for the iterative solution of the discrete control problem. Finally, we apply the above methodology to the solution of several tests problems. To be able to compare our results with existing results in the literature, we discuss first a single-objective control problem, already investigated by other authors. Finally, we discuss the multiobjective case.     

二阶共振多点边值问题正解的存在性

在不同共振条件下研究一类二阶非线性微分方程多点边值问题正解的存在性.利用范数形式的Leggett-Williams不动点定理,给出了问题正解的存在性结果,所得结论不同于已有文献.     

Semicontinuity of Approximate Solution Mappings to Parametric Set-Valued Weak Vector Equilibrium Problems

In this article, we obtain some stability results for parametric weak vector equilibrium problem with set-valued mappings. By using a scalarization method, we establish sufficient conditions for the semicontinuity of the approximate solution mappings to parametric set-valued weak vector equilibrium problem under weak assumptions. These results extend and improve some known results in the literature.     

Geometric ergodicity of affine processes on cones

For affine processes on finite-dimensional cones, we give criteria for geometric ergodicity — that is exponentially fast convergence to a unique stationary distribution. Ergodic results include both the existence of exponential moments of the limiting distribution, where we exploit the crucial affine property, and finite moments, where we invoke the polynomial property of affine semigroups. Furthermore, we elaborate sufficient conditions for aperiodicity and irreducibility. Our results are applicable to Wishart processes with jumps on the positive semidefinite matrices, continuous-time branching processes with immigration in high dimensions, and classical term-structure models for credit and interest rate risk.     

一类具有上下界的均衡问题

本文获得一类具有上、下界的抽象均衡问题解的存在性条件, 回答了Isac, Sehgal和Singh提出的一个公开问题,进一步研究了具上、下界及约束条件的抽象均 衡问题,获得了更为深刻的结果. 最后,把上述公开问题推广到两个空间的情形.     

Controllability results for the two-dimensional heat equation with mixed boundary conditions using Carleman inequalities: a linear and a semilinear case

In this paper, we prove controllability results for a two-dimensional semilinear heat equation with mixed boundary conditions. It is well-known that mixed boundary conditions can present a singular behaviour of the solution. First, we will prove global Carleman estimates then we will use these inequalities to obtain controllability results.