数学教学改革与大学生创新能力培养

培养大学生的创新意识,提高大学生的创新能力是高等教育的日标。本文主要从课程设置改革、课堂教学改革以及数学建模三个方面对学生创新能力的培养进行探讨。     

计算机在酸碱溶液pH值计算中的应用

设计了一种计算强酸(碱)及三元以内弱酸(碱)pH 值的通用程序。该程序解决了多元酸(碱)二级电离不可忽略的计算问题,其计算结果与实验值相一致。     

An integrated approach for water resources decision making under interactive and compound uncertainties

In recent years, the issue of water allocation among competing users has been of great concern for many countries due to increasing water demand from population growth and economic development. In water management systems, the inherent uncertainties and their potential interactions pose a significant challenge for water managers to identify optimal water-allocation schemes in a complex and uncertain environment. This paper thus proposes a methodology that incorporates optimization techniques and statistical experimental designs within a general framework to address the issues of uncertainty and risk as well as their correlations in a systematic manner. A water resources management problem is used to demonstrate the applicability of the proposed methodology. The results indicate that interval solutions can be generated for the objective function and decision variables, and a number of decision alternatives can be obtained under different policy scenarios. The solutions with different risk levels of constraint violation can help quantify the relationship between the economic objective and the system risk, which is meaningful for supporting risk management. The experimental data obtained from the Taguchi's orthogonal array design are useful for identifying the significant factors affecting the means of total net benefits. Then the findings from the mixed-level factorial experiment can help reveal the latent interactions between those significant factors at different levels and their effects on the modeling response.     

Extension of the pool-adjacent-violators algorithm

The pool-adjacent-violators algorithm (PAVA) is an efficient algorithm which converges in a finite number of steps. However, it has been applicable so far only in isotonic regression with the simple order. This report extends its applicability to other quadratic programming problems, including certain one-sided multivariate testing problems and concave regression problems.     

Selective Maintenance in System Reliability with Random Costs of Repairing and Replacing the Components

In this paper we consider the problem of determining the optimum number of repairable and replaceable components to maximize a system's reliability when both, the cost of repairing the components and the cost of replacement of components by new ones, are random. We formulate it as a problem of non-linear stochastic programming. The solution is obtained through Chance Constrained programming. We also consider the problem of finding the optimal maintenance cost for a given reliability requirement of the system. The solution is then obtained by using Modified E-model. A numerical example is solved for both the formulations.     

建构数理辩证逻辑系统必须澄清的一些理论问题

为了建构数理辩证逻辑系统,必须首先正确理解如下几个理论问题:1.关于数理辩证逻辑的名称问题;2.辩证逻辑的研究对象和学科性质问题;3.辩证逻辑能够不能够和应该不应该形式化问题;4.非形式化辩证逻辑与数理辩证逻辑的关系问题;5.正确区分逻辑矛盾与辩证矛盾问题;6.数理辩证逻辑与数理普通逻辑的关系问题.     

A hybrid genetic algorithm/mathematical programming approach to the multi-family flowshop scheduling problem with lot streaming

This paper presents a hybrid genetic algorithm/mathematical programming heuristic for the n-job, m-machine flowshop problems with lot streaming. The number of sublots for each job and the size of sublots are directly addressed by the heuristic and setups may be sequence-dependent. A new aspect of the problem, the interleaving of sublots from different jobs in the processing sequence, is developed and addressed. Computational results from 12 randomly generated test sets of 24 problems each are presented.     

Duality of the improved algebraic method (DIAM)

In this note we present a variant of the improved algebraic method (IAM) using a duality analysis to solve linear programming (LP) problems where more insights to the method are presented. When the coordinates of all vertices are computed, any feasible point can be expressed as a linear combination of the vertices. The objective function is expressed as a weighted sum of its evaluation at the feasible vertices and the optimal point is associated with the highest/lowest coefficient of the weighted sum.     

Selection of cost-optimal 2k−p fractional factorials

Selecting an optimal 2^k?pfractional factorial is structured as a mathematical programming problem. An algorithm is defined for the solution, and the case of additive costs is shown to have a known solution for resolution III designs.     

An integrated approach for the electronic contract manufacturer selection problem

In the global competitive environment, lead companies have to outsource their manufacturing to electronic contract manufacturers (ECM) in order to reduce operational cost and capture higher profit. Thus, the process of selecting contract manufacturers to be strategic partners is important for these companies. For this reason, this paper proposes an integrated approach for the electronic contract manufacturer selection problem, combining the voting method and the goal programming (GP) model to take into account quantitative factors involved in the selection process, which is applied to a real-world ECM selection problem encountered by a leading provider of complete broadband access solutions. Results of the case study indicate that the voting method can acquire the rating information quickly from manufacturing managers based on suitable evaluating criteria. The rating information simultaneously incorporates ECMs' performance scores as a weight for each ECM. A production planner can easily employ the GP model and ECMs’ weight information to effectively assign demand quantities to ECMs. Therefore, the integrated approach is a practical and useful tool for solving the contract manufacturer selection problem.