Multiobjective fractional programming duality theory

Results of Geoffrion for efficient and properly efficient solutions of multiobjective programming problems are extended to multiobjective fractional programming problems. Duality relationships are given for these problems where the functions are generalized convex or invex.     

Surrogate duality in a branch-and-bound procedure

Recent research has led to several surrogate multiplier search procedures for use in a primal branch-and-bound procedure. As single constrained integer programming problems, the surrogate subproblems are also solved via branch-and-bound. This paper develops the inner play between the surrogate subproblem and the primal branch-and-bound trees which can be exploited to produce a number of computational efficiencies. Most important is a restarting procedure which precludes the need to solve numerous surrogate subproblems at each node of a primal branch-and-bound tree. Empirical evidence suggests that this procedure greatly reduces total computation time.     

相对论速度与双曲几何

本文试图将非欧几何之——双曲几何引入狭义相对论.结果表明,在一定的映射关系下,双曲坐标变换对应于相对论速度变换,双曲几何空间构成伪欧速度空间的等距浸入子空间.     

轮式装甲车辆的几何通过性建模与仿真

介绍了轮式装甲车辆通过障碍物的规则,分析了几何障碍物属性和通过判断条件,针对几何障碍物属性,提出了几何障碍物的通过算法,建立了几何通过性模型。采用VC＋＋编程对模型进行了仿真,通过仿真实验验证了算法和模型的可行性。     

A note on duality in homogeneous fractional programming

For a linear fractional programming problem, Sharma and Swarup have constructed a dual problem, also a linear fractional program, in which the objective functions of both primal and dual problems are the same. Craven and Mond have extended this result to a nonlinear fractional programming problem with linear constraints, and a dual problem for which the objective function is the same as that of the primal. This theorem is now further extended from linear to differentiable convex constraints.     

A duality model for a generalized minmax program

We consider a generalized minmax programming problem, and establish, under certain weaker convexity assumptions, the Fritz John sufficient optimality conditions for such a problem. A dual program is introduced and using those optimality conditions duality theorems are proved relating the dual and the primal. Duality for the generalized fractional programming problem is considered as an application of the results proved.     

利用酉几何构作non-Cartesion认证码

利用酉几何构作了一个non-Cartesion认证码,计算了它的参数;当编码规则按等概率分布选取时,求出了模仿攻击和替换攻击成功的概率。     

Geometry of the total time on test transform

Total time on test (TTT) plots provide a useful graphical method for tentative identification of failure distribution models. Identification is based on properties of the TTT transform. New properties of the TTT transform distribution are obtained. These results are useful to the user of TTT plots. Although IFR (DFR) distributions are particularly easy to identify from TTT plots, the user must exercise caution relative to identification of IFR A (DFRA) distributions.     

利用微分几何参数研究小型阵列的布局

以微分几何为工具,分析和研究了小型阵列的阵列流形的微分几何参数与信号到达方向估计精度之间的关系,并在此基础上推导分析了小型阵列在各个方向上的测向性能与阵列几何布局之间的关系,最后给出小型阵列布局的设计思路。并以五元阵为例,对几种不同的几何布局进行仿真对比和分析,验证了设计思路的正确性。     

激光辐射方位的确定技术

介绍了确定来袭激光束方位的成像技术、时间延迟技术和屏蔽技术的基本原理和发展现状;分析了3种技术的优缺点;探讨了来袭激光方位确定技术的发展方向.     

基于复杂表面形状的端铣切削力模型

以传统的端铣切削力模型为基础,针对复杂加工表面形状,提出了一种更加符合实际加工情况的端铣切削力模型。该模型的建立涉及到复杂表面形状的几何表示、不同刀具轨迹的描述和刀齿-工件接触计算等关键技术。通过对模拟结果进行分析,验证了所建端铣切削力模型的有效性。     

论几何直观在小学数学教学中的应用

《义务教育课程标准(2011版)》提出将几何直观作为数学学习的十大核心概念之一,其是数学学习的重要内容,也是广泛使用的数学思想方法.文章对几何直观的内涵进行了简要介绍,基于数与代数、几何与图形、概率与统计以及综合与实践四大模块,对几何直观的使用进行了说明.并提出教师要有使用几何直观的意识、使用几何直观的知识基础、信息技术基础以及培养学生利用几何直观的意识.     

基于几何关系的视线指令制导律研究

针对近程车载防空系统拦截空地导弹的制导问题,设计了一种视线指令制导律.首先建立了地面站、拦截弹和空地导弹三者之间相对运动模型,然后以控制拦截弹位于地面站和空地导弹连线上为目标,根据三者在空间的几何关系设计了一种视线指令制导律,并对拦截的可行性进行了分析.仿真结果验证了所设计的制导律能够有效保证地面站的安全,与比例导引律相比,提高了制导精度,缩短了拦截时间.     

画法几何模型在计算机辅助图测、图解及图显中的应用

本文用画法几何的模型,以计算机为辅助工具,进行图测、图解和图显。试行结果既快速准确,又形象直观。使数据的计算过程及计算结果可视化,便于检查结果、修改参数及调试程序。     

基于可视图和几何逼近算法的避障路径动态规划研究

为了满足实时仿真的需求,CGF装甲车和武装直升机等的路径规划问题都可以简化成二维平面中的路径规划问题.研究了二维平面中路径规划的核心问题--避障路径规划问题.首先以可视图法所建的求解环境为基础,将避障路径规划转化为一个多阶段决策问题,对于每一个阶段的子问题,应用改进可视图法和几何逼近算法进行求解,得出各阶段的最短路径,最后对避障路径规划进行动态规划求解.     

高等几何中共点线(共线点)问题的证明

通过一题十种证法试图说明,共点线（共线点）问题的证明在高等几何中的重要作用。     

The procurement problem: An integer programming problem well suited to a solution using duality

A procurement problem, as formulated by Murty [10], is that of determining how many pieces of equipment units of each of m types are to be purchased and how this equipment is to be distributed among n stations so as to maximize profit, subject to a budget constraint. We have considered a generalization of Murty's procurement problem and developed an approach using duality to exploit the special structure of this problem. By using our dual approach on Murty's original problem, we have been able to solve large problems (1840 integer variables) with very modest computational effort. The main feature of our approach is the idea of using the current evaluation of the dual problem to produce a good feasible solution to the primal problem. In turn, the availability of good feasible solutions to the primal makes it possible to use a very simple subgradient algorithm to solve the dual effectively.