Finitely additive integration and local integration with respect to upper integrals

Summary We study the integration theory for general integral metrics when restricted to upper integrals q, finding improvements in the relation between the classes of the q-integrable and the q_l-integrable functions. We give new results and notions which lead to the desirable characterizations of q-integrable functions as q_l-integrable f with q(|f|) < ∞, and of q_l-integrable functions via the integrability of their upper truncations, under natural conditions which are fulfilled in most finitely additive integration theories.     

A note on worst-case performance of heuristics for maintenance scheduling problems

We study a machine scheduling model in which job scheduling and machine maintenance activities have to be considered simultaneously. We develop the worst-case bounds for some heuristic algorithms, including a sharper worst-case bound of the SPT schedule than the results in the literature, and another bound of the EDD schedule.     

Lower bound for the convergence rate of nonstationary Jacobi-like iteration

Stationary and nonstationary Jacobi-like iterative processes for solving systems of linear algebraic equations are examined. For a system whose coefficient matrix A is an H-matrix, it is shown that the convergence rate of any Jacobi-like process is at least as high as that of the point Jacobi method as applied to a system with 〈A〉 as the coefficient matrix, where 〈A〉 is a comparison matrix of A.     

An improved max-flow-based lower bound for minimizing maximum lateness on identical parallel machines

In this paper, we introduce a new concept of semi-preemptive scheduling and we show how it can be used to derive a maximum-flow-based lower bound for the P|r_j|L_max which dominates the well-known preemptive lower bound. We show that, in some cases, the proposed bound strictly dominates the preemptive one while having the same complexity.     

Positive solutions of singular boundary value problem of negative exponent Emden—Fowler equation

This paper investigates the existence of positive solutions of a singular boundary value problem with negative exponent similar to standard Emden-Fowler equation. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C¹[0, 1] positive solutions is given by means of the method of lower and upper solutions with the Schauder fixed point theorem.     

A lower bound on the performance of the quadratic discriminant function

The quadratic discriminant function is often used to separate two classes of points in a multidimensional space. When the two classes are normally distributed, this results in the optimum separation. In some cases however, the assumption of normality is a poor one and the classification error is increased. The current paper derives an upper bound for the classification error due to a quadratic decision surface. The bound is strict when the class means and covariances and the quadratic discriminant surface satisfy certain specified symmetry conditions.     

Banach空间二阶周期边值问题解的存在性

利用一些比较结果，讨论了Banach空间中二阶周期边值问题解的存在性，获得了若干解的存在性与唯一性结果。     

Periodic solutions of nonlinear impulsive differential inclusions with constraints

In this paper we obtain the existence of periodic solutions for nonlinear ``invariance' problems monitored by impulsive differential inclusions subject to impulse effects.

     

A two-stage parallel branch and bound algorithm for mixed integer programs

Mixed integer programming (MIP) models are extensively usedto aid strategic and tactical decision making in many businesssectors. Solving MIP models is a computationally intensive processand there is a need to develop solution approaches that enablelarger models to be solved within acceptable timeframes. Inthis paper, we describe the implementation of a two-stage parallelbranch and bound (PB & B) algorithm for MIP. In stage 1of the algorithm, a multiple heuristic search is implementedin which a number of alternative search trees are investigatedusing a forest search in the hope of finding a good solutionquickly. In stage 2, the search is reorganized so that the branchesof a chosen tree are investigated in parallel. A new heuristicis introduced, based on a best projection criterion, which evaluatesalternative B & B trees in order to choose one for investigationin stage 2 of the algorithm. The heuristic also serves as away of implementing a quality load balancing scheme for stage2 of the algorithm. The results of experimental investigationsare reported for a range of models taken from the MIPLIB libraryof benchmark problems.     

带有单模糊映射的一般变分不等式解的存在性

众所周知，在各种变分不等式问题中，解的存在性是最基础也是最重要的问题之一．本文的目的是在Hilbert空间中研究带有单模糊映射的一般变分不等式解的存在性．此外，还讨论了几种特殊情况．