维吾尔史诗《福乐智慧》及其数学思想解读

《福乐智慧》是一部反映古代维吾尔人社会生活的百科全书,广泛地涉及到哲学、政治、法律、军事、伦理、宗教、天文学、数学等领域,其中的数学与数学教育思想尤为丰富。《福乐智慧》探讨了诸如什么是数学,为什么要学习数学,学习什么内容,如何学习数学,以及学习数学对人的一生有什么影响等问题。《福乐智慧》所涉及的数学内容包括算术、几何学、三角、代数,尤其是特别提到了欧几里得的《几何原本》。总结发掘《福乐智慧》的数学教育思想,对于批判继承中华民族的优秀文化成果,让国内其他兄弟民族乃至世界各国客观全面地了解新疆古代维吾尔数学发展史,填补我国数学发展史和中亚数学发展史上的空白等有重要意义。     

Simple paths with exact and forbidden lengths

We study new decision and optimization problems of finding a simple path between two given vertices in an arc weighted directed multigraph such that the path length is equal to a given number or it does not fall into the given forbidden intervals (gaps). A fairly complete computational complexity classification is provided and exact and approximation algorithms are suggested.     

雷达引信地杂波建模与仿真

介绍了一种用零记忆非线性变换(ZMNL)模拟具高斯谱特性的相参相关Weibull分布地杂波的方法,详细阐述了Weibull分布杂波随机序列产生的流程.仿真结果表明,该法形成的地杂波信号与理论值吻合较好,适合雷达引信的实际应用.     

求取鱼雷转角射击转角的实用算法

较为详细地推导了鱼雷转角射击公式,根据分鱼雷转向的不同总结出两类求解公式（各种态好都能用两类公式之一来解算）．最后还讨论了所导出的非线性方程的数值解算方法,该算法具有工程应用价值。     

On estimating the scale parameter of the exponential distribution with a known linear relation between the location and the scale parameter

In this article we study the estimation of the average excess life θ in a two-parameter exponential distribution with a known linear relationship between α (the minimum life) and θ of the form α = aθ, where a is known and positive. A comparison of the efficiencies of estimators which are linear combinations of the smallest sample value and the sample sum of deviations from the smallest sample value and the maximum likelihood estimators is made for various sample sizes and different values of a. It is shown that these estimators are dominated in the risk by the minimum-risk scale equivariant estimator based on sufficient statistics. A class of Bayes estimators for inverted gamma priors is constructed and shown to include a minimum-risk scale equivariant estimator in it. All the members of this class can be computed easily.     

A note on scheduling parallel machines subject to breakdown and repair

In this paper we consider n jobs and a number of machines in parallel. The machines are identical and subject to breakdown and repair. The number may therefore vary over time and is at time t equal to m(t). Preemptions are allowed. We consider three objectives, namely, the total completion time, ∑ C_j, the makespan C_max, and the maximum lateness L_max. We study the conditions on m(t) under which various rules minimize the objective functions under consideration. We analyze cases when the jobs have deadlines to meet and when the jobs are subject to precedence constraints. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

An FPTAS for scheduling a two‐machine flowshop with one unavailability interval

We study a deterministic two‐machine flowshop scheduling problem with an assumption that one of the two machines is not available in a specified time period. This period can be due to a breakdown, preventive maintenance, or processing unfinished jobs from a previous planning horizon. The problem is known to be NP‐hard. Pseudopolynomial dynamic programming algorithms and heuristics with worst case error bounds are given in the literature to solve the problem. They are different for the cases when the unavailability interval is for the first or second machine. The existence of a fully polynomial time approximation scheme (FPTAS) was formulated as an open conjecture in the literature. In this paper, we show that the two cases of the problem under study are equivalent to similar partition type problems. Then we derive a generic FPTAS for the latter problems with O(n⁵/ε⁴) time complexity. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A generalization of the weighted set covering problem

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b‐matching problem. In general, we may use a polynomial‐time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256–278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383–390], and V. Chvatal [A greedy heuristic for the set‐covering problem, Math Oper Res 4(3) (1979), 233–235] to get an approximate solution for the problem. We find a worst‐case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

提升大学生学习力之浅见

二十一世纪是终身学习、终身教育的社会。当代大学生要跟上社会发展的步伐,必须确立较强的学习力,储备良好的核心竞争力。本文在调查的基础上,经过分析总结,从学习力的内涵、现状分析、提升的途径和策略、采取相应措施等方面进行了初步的解析和阐述。     

Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999