基于可替代资源的稀缺资源利用问题研究

在线性规划资源利用问题模型基础上,研究了减少一种稀缺程度相对较高的资源限量,同时增加一定比例的另一种可替代该资源的稀缺程度相对较低的资源限量,而使企业原有最优生产目标值不减的问题.通过对不同情况的分类讨论,得到相应的资源改变量及其比例的取值决定和取值范围,对稀缺资源的节省利用具有一定意义.     

国民经济最优规划中的共轭问题研究

本论文针对稀缺资源提出国民经济最优化的共轭问题．由共轭定理得到了共轭问题解一致的可能性及其成立的条件，共轭定理为检验国民经济协调发展提供了理论依据和方法．论文着重讨论了以劳动资源为稀缺资源的国民经济规划共轭问题，给出其约束条件的影子价格的经济意义，证明了同一约束条件的影子价格是成比例的，劳动资源的影子价格是国民财富的影子价格的倒数．同时指出产品与资源等价替代系数与其影子价格有关，影子价格是产品与资源的短缺性、产品与资源的平衡的度量．最后讨论了影子价格与生产活动的消耗、劳动消耗与效益的关系．     

线性规划在饲料配方中的应用

本文应用线性规划方法，以计算机为工具，对哈尔滨国营红旗农场养鸡场饲料传统配方进行了优化设计，经过 ３个周期的使用，证明每年可节省饲料费 ２８万元，经济效益十分显著。     

用边际法求解一类设备的最优分配问题

本文针对一类设备的最优分配问题，将利润表转化为边际利润表，并建立了相应的寻优方程，通过实例说明，在一定情况下，用改进后的算法比常规算法节省一定的计算工作量。     

用边际法求解－类设备的最优分配问题

本文针对一类设备的最优分配问题，将利润表转化为边际利润表，并建立了相应的寻优方程，通过实例说明，在一定情况下，用改进后的算法比常规算法节省一定的计算工作量．     

东西部能源经济系统可持续发展博弈分析

引入经济可持续发展能源可承受度概念,建立中央和东西部地区兼顾经济增长及能源可持续发展的博弈模型,分析西部大开发战略中中央、东部和西部能源开发的战略选择,得到能源作为稀缺资源在地区及全国范围内最优配置的相关结论.     

弹性圆板在一侧受均载而四周固定的条件下不用Kirchhoff—Love假设的一...

本文在前文［１］所得的微分方程和有关边界条件的基础上，求得一这些方程在有关边界条件下的解析解。当然，为了节省计算工作量，我们进一步简化了一级近似理论，使它在保持合理的基础上，更加简单化了。     

正交试验设计在麦白霉素高产菌株选育中的应用

本文应用正交试验设计改进了麦白霉素的生产工艺，在四个关键环节上选出了比对照组高出７００μ／ｍｌ以上的高产稳定菌株。该法使试验次数减少，选育周期缩短，既节省了人力物力和降低了生产成本，又增加了麦白霉素药粉的产量，取得了可观的经济效益。     

基于双层规划的集群式供应链供应商激励机制研究

对存在多级供应商的集群式供应链中稀缺资源供应的激励问题进行了研究。在假设市场某种零部件稀缺,制造商的产量直接与零部件供应量链相关,而零部件供应量直接与一级供应商努力程度相关的情况下,建立了相应的单多双层规划模型,分别研究了制造商针对供应商结盟与不结盟的情况下的最优激励机制。最后进行了仿真,结果表明本文的激励机制能较好激励供应商并能有效防范其结盟。     

求最短路问题的改进算法

本对图论中含有负权的最短路问题的算法进行了讨论，给出了一个具有“可节省存储空间、提高运算速度、易编程实现”等优点的改进算法（算法三），并通过例题进一步验证了该改进算法的优越性，具有一定的现实意义。     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments

The double Laplace transform of the distribution function of the integral of the positive part of the Brownian bridge was determined by M. Perman and J.A. Wellner, as well as the moments of this distribution. The purpose of the present paper is to determine the asymptotics of this distribution for large values of the argument, and the corresponding asymptotics of the moments.     

基于偏序集的PROMETHEE方法优化研究

尽管PROMETHEE是当前最受欢迎的多准则决策方法之一,但在实践应用过程中,模型的应用范围与质量依然受制于指标权重问题。一些常用的赋权方法,不仅没有解决不确定权重问题,反而增加了决策风险。在偏序集相关定理的基础上,给出权重的定性信息即权重次序,由流出矩阵、流入矩阵和净流矩阵等定义,得到了PROMETHEE的偏序集表达形式。当流入和流出之和为常数时,证明了模型存在对偶性质。根据对偶性质,简化了PROMETHEE方法的分析步骤,删减模型冗余信息。应用偏序集表示的PROMETHEE,突破了模型没有具体权重便无法应用的思维定势,解决了模型赋权困难,增强了模型的鲁棒性,拓展了模型处理数据类型的范围。     

The nonlinear and scaled growth of the ottoman and Roman empires

In this work, mathematical models for the growth of the Ottoman and Roman Empires are found. The time interval considered for both cases covers the time from the birth of the empire to the end of the fast expansion period. These empires are assumed to be nonlinearly growing and self-multiplying systems. This approach utilizes the concepts of chaos theory, and scaling. The area governed by the empire is taken as the measure of its growth. It was found that the expansion of each empire on lands, seas, and on both (i.e., lands+seas) can be expressed by power laws. In the Ottoman Empire, the nonlinear growth power of total area is approximately equal to the golden ratio, and the nonlinear growth power of the expansion on lands is approximately equal to the square root of 2. In the case of the Romans, some numbers associated with the golden ratio, or the square root of 2, appear as the power of the nonlinear growth term. The appearance of both the golden ratio and the square root of 2 show that both empires had intention on achieving stability during their growth.     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

Mario Pieri’s address at the University of Catania

The contributions made by the Italian mathematician Mario Pieri (1860-1913) are well known in the field of geometry. Pieri was a member of the School of Peano at the University of Turin. There he became engaged both by the problems of logic and by the philosophical aspects of Peano’s epistemology. This article was motivated by Pieri’s address given at the University of Catania, at the inauguration of the 1906-1907 academic year. My aim is to identify Pieri’s philosophical premises as found in his works and to present them in the general framework of the historical development of the Peano School.     

Generalized derivatives and nonsmooth optimization, a finite dimensional tour

During the early 1960’s there was a growing realization that a large number of optimization problems which appeared in applications involved minimization of non-differentiable functions. One of the important areas where such problems appeared was optimal control. The subject of nonsmooth analysis arose out of the need to develop a theory to deal with the minimization of nonsmooth functions. The first impetus in this direction came with the publication of Rockafellar’s seminal work titledConvex Analysis which was published by the Princeton University Press in 1970. It would be impossible to overstate the impact of this book on the development of the theory and methods of optimization. It is also important to note that a large part of convex analysis was already developed by Werner Fenchel nearly twenty years earlier and was circulated through his mimeographed lecture notes titledConvex Cones, Sets and Functions, Princeton University, 1951. In this article we trace the dramatic development of nonsmooth analysis and its applications to optimization in finite dimensions. Beginning with the fundamentals of convex optimization we quickly move over to the path breaking work of Clarke which extends the domain of nonsmooth analysis from convex to locally Lipschitz functions. Clarke was the second doctoral student of R.T. Rockafellar. We discuss the notions of Clarke directional derivative and the Clarke generalized gradient and also the relevant calculus rules and applications to optimization. While discussing locally Lipschitz optimization we also try to blend in the computational aspects of the theory wherever possible. This is followed by a discussion of the geometry of sets with nonsmooth boundaries. The approach to develop the notion of the normal cone to an arbitrary set is sequential in nature. This approach does not rely on the standard techniques of convex analysis. The move away from convexity was pioneered by Mordukhovich and later culminated in the monographVariational Analysis by Rockafellar and Wets. The approach of Mordukhovich relied on a nonconvex separation principle called theextremal principle while that of Rockafellar and Wets relied on various convergence notions developed to suit the needs of optimization. We then move on to a parallel development in nonsmooth optimization due to Demyanov and Rubinov called Quasidifferentiable optimization. They study the class of directionally differentiable functions whose directional derivatives can be represented as a difference of two sublinear functions. On other hand the directional derivative of a convex function and also the Clarke directional derivatives are sublinear functions of the directions. Thus it was thought that the most useful generalizations of directional derivatives must be a sublinear function of the directions. Thus Demyanov and Rubinov made a major conceptual change in nonsmooth optimization. In this section we define the notion of a quasidifferential which is a pair of convex compact sets. We study some calculus rules and their applications to optimality conditions. We also study the interesting notion of Demyanov difference between two sets and their applications to optimization. In the last section of this paper we study some second-order tools used in nonsmooth analysis and try to see their relevance in optimization. In fact it is important to note that unlike the classical case, the second-order theory of nonsmoothness is quite complicated in the sense that there are many approaches to it. However we have chosen to describe those approaches which can be developed from the first order nonsmooth tools discussed here. We shall present three different approaches, highlight the second order calculus rules and their applications to optimization.     

Formulations and valid inequalities for the node capacitated graph partitioning problem

We investigate the problem of partitioning the nodes of a graph under capacity restriction on the sum of the node weights in each subset of the partition. The objective is to minimize the sum of the costs of the edges between the subsets of the partition. This problem has a variety of applications, for instance in the design of electronic circuits and devices. We present alternative integer programming formulations for this problem and discuss the links between these formulations. Having chosen to work in the space of edges of the multicut, we investigate the convex hull of incidence vectors of feasible multicuts. In particular, several classes of inequalities are introduced, and their strength and robustness are analyzed as various problem parameters change.