线性规划模型建立的一个原则

本以运输问题,下料问题和人员班次安排为例,论述了建立线性规划数学模型的一个原则,即尽量使用不等式约束来建立模型的原则。     

线性等式约束连续型minimax问题的区间算法

研究线性等式约束连续型minimax问题,其中目标函数为Lipschitz连续函数,基于线性约束函数的区间迭代运算、区域二分原则和无解区域删除原则,建立了求解线性等式约束连续型minimax问题的区间算法,证明了算法的相关定理,给出了数值算例,该算法保证求出问题的整体解,且是可靠和有效的.     

成对需求占线服务器问题及公平原则策略

针对在对称度量空间上多服务需求的k-服务器占线问题,研究问题空间为k＋2（度量空间上有k＋2个顶点,但只有k个服务器）时的一个特例：即在任意时刻都同时有两个服务需求提出。建立了该问题的数学模型,给出了公平原则策略,该策略能使得任意两个服务器完成服务后花费费用之差不大于某个固定常数;进行了相应的策略分析和竞争比的证明,并同工作函数策略进行了比较。     

一类min-max-min问题的区间算法

讨论了一类由一阶连续可微函数构成的无约束min-max-min问题．通过构造目标函数的区间扩张、无解区域删除原则，建立了求解min-max-min问题的区间算法，证明了算法的收敛性，给出了数值算例．理论证明和数值结果表明方法是可靠和有效的．     

回载可分的闭环供应链配送中的多车辆运输策略

本文从车辆路径的角度研究了具有一个配送中心、多台车辆结合前向物流配送和逆向物流回载的闭环供应链运输策略,考虑回收产品的不同形态和可分批运输的特点,引入库存限制和成本惩罚,建立并分析了问题的数学模型．通过引入参数2σ原则构造了先分组后组内运用基于TSP的插入算法进行优化调整的启发式求解方法．算例分析表明该策略是合理有效的．     

一类约束不可微优化问题的区间极大熵方法

本文研究求解不等式约束离散ｍｉｎｉｍａｘ问题的区间算法,其中目标函数和约束函数是 Ｃ~１类函数．利用罚函数法和极大熵函数思想将问题转化为无约束可微优化问题,讨论了极大熵函数的区间扩张,证明了收敛性等性质,提出了无解区域删除原则,建立了区间极大熵算法,并给出了数值算例．该算法是收敛、可靠和有效的．     

实用下料优化问题模型建立及解法

“下料问题(cuttingstockproblem)”是把相同形状的一些原材料分割加工成若干个不同规格大小的零件的问题,此类问题在工程技术和工业生产中有着重要和广泛的应用.本文首先以材料最省为原则建立模型,采用分层基因算法模型求解出模型的解,若此结果不符合时间限制条件,则通过以客户时间需求为第一目标的分组抽样模型处理后,再借助分层基因算法给出该模型的最优解.     

科学设置“问题”促进高中数学高效教学

随着新课程的进一步开展,"问题"成为了课堂组织的重要形式,为此"问题"的布设直接关系到教学效果的高低,本文就问题的设置原则和实践谈几点笔者的想法.     

单时期需求为"离散随机型存储问题"的研究

作者通过举例以及理论证明指出目前单时期需求为"离散随机型存储问题"的处理方法所存在的错误,在此基础上引入排队论,并在对单时期需求为"离散随机型存储问题"的盈利数学期望进行研究后,根据盈利期望最大化原则,推导并建立了最佳订购量公式.     

例谈"数形结合"应用的四个误区

当我们将一个数学问题转化为一特定的图形之后，便可创造性地分析问题的解法，代数演算的确切性可以帮助我们定量地来探讨几何图形的位置及关系；当我们将一个几何问题代数化以后，便可抽象性地探索解决问题的途径．然而，在数形转换的过程中，必须遵循“数与形对应，形与数相通”的原则，如果违反了这一原则，常常会步人数形结合的误区．本文结合具体题目，从以下四个方面作以阐述．     

Physicomechanical characteristics of a disperse-filled polytetrafluoroethylene

Composite polymer materials based on PTFE containing ultradisperse -sialon (1–10 wt.%) as the cross-linking agent are studied. It is shown that the injection of small amounts of fillers (1–2 wt.%) increases the degree of composite crystallinity. A correlation between the structure, element distribution on the surface layers of samples, and tribotechnical characteristics of composites is found. The change in the physicomechanical characteristics is associated with the effect of the interstructural plasticization.Ammosov Yakutsk State University, Yakutsk, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 797–806, November–December, 1999.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

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.     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

Superapproximation and Commutator Properties of Discrete Orthogonal Projections for Continuous Splines

This paper builds upon the L_p-stability results for discrete orthogonal projections on the spaces S_h of continuous splines of order r obtained by R. D. Grigorieff and I. H. Sloan in (1998, Bull. Austral. Math. Soc.58, 307–332). Properties of such projections were proved with a minimum of assumptions on the mesh and on the quadrature rule defining the discrete inner product. The present results, which include superapproximation and commutator properties, are similar to those derived by I. H. Sloan and W. Wendland (1999, J. Approx. Theory97, 254–281) for smoothest splines on uniform meshes. They are expected to have applications (as in I. H. Sloan and W. Wendland, Numer. Math. (1999, 83, 497–533)) to qualocation methods for non-constant-coefficient boundary integral equations, as well as to the wide range of other numerical methods in which quadrature is used to evaluate L₂-inner products. As a first application, we consider the most basic variable-coefficient boundary integral equation, in which the constant-coefficient operator is the identity. The results are also extended to the case of periodic boundary conditions, in order to allow appplication to boundary integral equations on closed curves.     

Coordinate and subspace optimization methods for linear least squares with non-quadratic regularization

This work addresses the problem of regularized linear least squares (RLS) with non-quadratic separable regularization. Despite being frequently deployed in many applications, the RLS problem is often hard to solve using standard iterative methods. In a recent work [M. Elad, Why simple shrinkage is still relevant for redundant representations? IEEE Trans. Inform. Theory 52 (12) (2006) 5559–5569], a new iterative method called parallel coordinate descent (PCD) was devised. We provide herein a convergence analysis of the PCD algorithm, and also introduce a form of the regularization function, which permits analytical solution to the coordinate optimization. Several other recent works [I. Daubechies, M. Defrise, C. De-Mol, An iterative thresholding algorithm for linear inverse problems with a sparsity constraint, Comm. Pure Appl. Math. LVII (2004) 1413–1457; M.A. Figueiredo, R.D. Nowak, An EM algorithm for wavelet-based image restoration, IEEE Trans. Image Process. 12 (8) (2003) 906–916; M.A. Figueiredo, R.D. Nowak, A bound optimization approach to wavelet-based image deconvolution, in: IEEE International Conference on Image Processing, 2005], which considered the deblurring problem in a Bayesian methodology, also obtained element-wise optimization algorithms. We show that the last three methods are essentially equivalent, and the unified method is termed separable surrogate functionals (SSF). We also provide a convergence analysis for SSF. To further accelerate PCD and SSF, we merge them into a recently developed sequential subspace optimization technique (SESOP), with almost no additional complexity. A thorough numerical comparison of the denoising application is presented, using the basis pursuit denoising (BPDN) objective function, which leads all of the above algorithms to an iterated shrinkage format. Both with synthetic data and with real images, the advantage of the combined PCD-SESOP method is demonstrated.     

Effect of the adhesion interaction and the degree of filling on the internal stresses in finely divided crystalline fillers of epoxy composites

Two kinds of model composite materials with finely divided (1) crystal fillers—LiF or polyethylene-filled epoxy resin cured by polyethylenepolyamine — are investigated by X-ray diffractometry. It is found that tensile stresses arise in LiF crystals, which show a strong adhesion interaction with the binder, for all degrees of filling (from =2.2 to =74 vol.%) examined. Their values remain constant up to a degree of filling at which the boundary layers come into contact with one another. Then, the inner stresses decrease with increasing . In the crystalline regions of polyethylene, where the adhesion between the binder and crystals is weak, the inner stresses are compressive. It is shown that the thickness of the boundary layer of the matrix on the surface of filler particles can be evaluated by the method used.Institute of Polymer Mechanics, Latvian University, Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 807–820, November–December, 1999.     

Rigid isotopy classification of real algebraic curves of bidegree (3,3) on quadrics

A rigid isotopy of nonsingular real algebraic curves on a quadric is a path in the space of such curves of a given bidegree. We obtain the rigid isotopy classification of nonsingular real algebraic curves of bidegree (3, 3) on a hyperboloid and on an ellipsoid. We also study of the space of real algebraic curves of bidegree (3, 3) with a single node or cusp. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 810–815, December, 1999.     

Embeddings of the classesH ω

In this paper we study functions belonging to the classesV _ε and ΛBV, which are encountered in the theory of Fourier trigonometric series. Necessary and sufficient conditions for the embedding of the classesH _ω in the classesV _ϕ and ABV are obtained. Translated fromMatematicheskie Zametki, Vol. 64, No. 5, pp. 713–719, November, 1998. This research was supported by the program “Leading Scientific Schools” under grant No. 96/97-15-96073.