NONRADIAL POSITIVE SOLUTIONS TO SINGULAR QUASILINEAR ELLIPTIC EQUATIONS IN THE PLANE

This paper investigates 2-dimensional singular,quasilinear elliptic equations and gives some suffcient conditions ensuring the equations have infinitely many positive entire solutions. The super-subsolution method is used to prove the existence of such solutions.     

多分子生化反应模型在正平衡点的二阶近似摄动解

对一类多分子生化反应系统进行定性研究,运用摄动方法求出该模型在正平衡点当(A/C)pq+Cq(CA)q-q1=B(p-1)的二阶近似摄动解.     

Scheduling of corrugated paper production

Corrugated paper is produced by gluing three types of papers of the same breadth. Given a set of orders, we first assign each order to one of the standard breadths, and then sequence those assigned to each standard breadth so that they are continuously manufactured from the three rolls of the specified standard breadth equipped in the machine called corrugator. Here we are asked to achieve multi-goals of minimizing total length of roll papers, total loss of papers caused by the differences between standard breadths and real breadths of the orders, and the number of machine stops needed during production. We use integer programming to assign orders to standard breadths, and then develop a special purpose algorithm to sequence the orders assigned to each standard breadth. This is a first attempt to handle scheduling problems of the corrugator machine.     

Opportunistic timing and manipulation in Australian Federal Elections

In many parliamentary systems, election timing is an important decision made by governments in order to maximize their expected remaining life in power. Governments can also introduce policy or economic actions to enhance their popular standing and thus their chance of being re-elected. On the other hand, an oppositions’ natural objective is to gain power, and they will also apply controls through their own policies to reduce the governments’ chance of being re-elected. In this paper we employ a dynamic programming approach to determine the optimal timing for governments and oppositions to best utilize their limited resources. At each decision branch, the optimal control is interpreted as a Nash–Cournot equilibrium of a zero-sum political game which, in certain states, admits mixed strategy solutions. We perform a case study on the Australian Federal Election for House of Representatives.     

Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

二次概周期系数微分方程的概周期解

利用指数二分性,Schauder不动点定理和Grownwall不等式证明了一类概周期系数微分方程的概周期解、有界解的存在唯一性及概周期解的全局吸引性.     

Semilinear fractional integro-differential equations with compact semigroup

In this paper, we study the local and global existence of mild solutions to a class of fractional integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space.     

The Averaged Robbins – Monro Method for Linear Problems in a Banach Space

We consider a recursive method of Robbins–Monro type to solve the linear problem Ax=V in a Banach space. The bounded linear operator A and the vector V are assumed to be observable with some noise only. According to Polyak and Ruppert we use gains converging to zero slower than 1/n and take the average of the iterates as an estimator for the solution of the linear problem. Under weak conditions on the noise processes almost sure and distributional invariance principles are shown.     

Massera type theorem for almost automorphic solutions of functional differential equations of neutral type

In this work, we study the existence of almost automorphic solutions for functional differential equations of neutral type. We prove that the existence of a bounded solution on R⁺ implies the existence of an almost automorphic solution.     

Existence theorems for a class of nonlocal differential equations

A class of nonlocal second-order ordinary differential equations of the form

y^″(x)=f(x,y(x),(y○λ)(x),y^′(x))