MARKOV DECISION PROGRAMMING WITH CONSTRAINTS

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Renormalized Energy with Vortices Pinning Effect

This paper is a continuation of the previous paper in the Journal of Partial Differential Equations [1]. We derive in this paper the renormalized energy to further determine the locations of vortices in some case for the variational problem related to the superconducting thin films having variable thickness.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

Hyperbolic boundary value problem with equivalued surface on a domain with thin layer

This paper deals with a kind of hyperbolic boundary value problems with equivalued surface on a domain with thin layer. Existence and uniqueness of solutions are given, and the limit behavior of solutions is studied in this paper. Project partially supported by NSFC (No:10401009) and NCET of China (No:060275).     

Differential games with noise-corrupted measurements

In this paper, readily computable strategies for zero-sum, linear-quadratic differential games with noise-corrupted measurements are developed. Of particular significance is the fact that the governing differential equations no longer require the solution of an often difficult nonlinear, two-point boundary-value problem, but again satisfy the separation principle of linear-quadratic optimal control. The implications of the payoff relationships are considered.In a subsequent paper, we will apply the theory developed in this paper to a detailed example of a pursuit-evasion game. We discuss a missile and an airplane system where the missile supported by its launch platform has perfect state measurements and the airplane has noise-corrupted measurements.     

System of coincidence theorems with applications

In this paper, we establish systems of coincidence theorems from which solution of system of inequalities and system of minimax theorems was established in this paper.     

双向替代产品库存模型研究

运用最优控制理论和数理经济学方法研究了供应链管理时代下广泛存在的双向替代产品的最优库存问题,建立了利润最大化前提下的双向替代品的库存模型,证明了该问题解的存在性,并给出了求解最优订货量的方法步骤,可为实施有效的库存管理、降低企业的物流成本提供借鉴.     

Semiparametric quantile regression with random censoring

This paper considers estimation and inference in semiparametric quantile regression models when the response variable is subject to random censoring. The paper considers both the cases of independent and dependent censoring and proposes three iterative estimators based on inverse probability weighting, where the weights are estimated from the censoring distribution using the Kaplan–Meier, a fully parametric and the conditional Kaplan–Meier estimators. The paper proposes a computationally simple resampling technique that can be used to approximate the finite sample distribution of the parametric estimator. The paper also considers inference for both the parametric and nonparametric components of the quantile regression model. Monte Carlo simulations show that the proposed estimators and test statistics have good finite sample properties. Finally, the paper contains a real data application, which illustrates the usefulness of the proposed methods.

     

Two-player bargaining problems with unilateral pre-donation

This paper characterizes conditions for two-player bargaining problems and bargaining rules under which unilateral pre-donation always yields Pareto utility gains. The paper also computes the optimal pre-donation of each player under the class of proportional bargaining rules.     

Homotopy groups with coefficients

This paper has two goals. It is an expository paper on homotopy groups with coefficients in an abelian group and it contains new results which correct old errors and omissions in low dimensions. The homotopy groups with coefficients are functors on the homotopy category of pointed spaces. They satisfy a universal coefficient theorem, give long exact sequences when applied to fibrations, and have Hurewicz maps into homology groups with coefficients.     

Nonlinear elliptic boundary value problem with equivalued surface in a domain with thin layer

This paper deals with certain kinds of boundary value problems with equivalued surface of nonlinear elliptic equations on a domain with thin layer. We introduce the concept of renormalized solution to this problem. Existence and uniqueness of renormalized solutions are given, and the limit behaviour of solutions is studied in this paper.     

仅有局部单位元环上的范畴对偶

［１］讨论了在无单位元环上的范畴等价，本文讨论无单位无环上的范畴对偶。     

隐含的和多重相互作用的非局部微极连续统的本构理论

本文把A.C.Eringen建立的非局部微极连续统的本构理论推广到包括具有隐含的和多重相互作用的非局部性的微极连续统的情形.这里以隐含的和多重相互作用的非局部微极热弹性固体为例说明建立各自本构理论的过程并给出两个相应的有关本构理论的定理.     

Solving a two-dimensional trim-loss problem with MILP

In this paper a two-dimensional trim-loss problem connected to the paper-converting industry is considered. The problem is to produce a set of product paper rolls from larger raw paper rolls such that the cost for waste and the cutting time is minimized. The problem is generally non-convex due to a bilinear objective function and some bilinear constraints, which give rise to difficulties in finding efficient numerical procedures for the solution. The problem can, however, be solved as a two-step procedure, where the latter step is a mixed integer linear programming (MILP) problem. In the present formulation, both the width and length of the raw paper rolls as well as the lengths of the product paper rolls are considered variables. All feasible cutting patterns are included in the problem and global optimal cutting patterns are obtained as the solution from the corresponding MILP problem. A numerical example is included to illustrate the proposed procedure.     

Vector optimization problems with nonconvex preferences

In this paper, some vector optimization problems are considered where pseudo-ordering relations are determined by nonconvex cones in Banach spaces. We give some characterizations of solution sets for vector complementarity problems and vector variational inequalities. When the nonconvex cone is the union of some convex cones, it is shown that the solution set of these problems is either an intersection or an union of the solution sets of all subproblems corresponding to each of these convex cones depending on whether these problems are defined by the nonconvex cone itself or its complement. Moreover, some relations of vector complementarity problems, vector variational inequalities, and minimal element problems are also given. While this paper was being revised in September 2006, Professor Alex Rubinov (the second author of the paper) left us due to the illness. This is a very sad news to us. We dedicate this paper to the memory of Professor Rubinov as a mathematician and truly friend.     

Controllable Systems with Impacts

Control problems in dynamic systems allowing pulse forces due to the presence of unilateral active constraints are considered. This paper gives an analysis of controls used during impact interactions. A new kind of pulse controls arising at the time of impact is introduced. These problems are typical for the so-called vibroimpact systems with numerous applications, whose number is constantly increasing in recent years. The goal of the paper is to describe the phase of a controllable impact and to determine the constraint reactions.     

On Some Groups with Finite Involution Saturated with Finite Simple Groups

In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4].     

Kinematic spaces with dilatations

In this paper we show that kinematic spaces with nontrivial dilatations are commutative.     

Mathematics lessons with DERIVE

Since 1993 a group of Dutch mathematics teachers has been working on the development of teaching materials that use Derive. The group, called CAVO, published its first mathematics courseware collection in 1995. This paper reviews the content and the structure of this collection, gives the full text of one laboratory and delivers a report on the experience with these materials in the classroom. Besides providing this information, the paper also gives insight into the way CAVO works and into the process that led to this style of working.     

Fuzzy带算子环和Fuzzy带算理想

提出Fuzzy带算子环、Fuzzy带算理想和Fuzzy带算商环的定义,讨论它们的一些初等性质。