关键词： 船队加解驳   多目标规划   启发式算法   数学模型  

摘要： 文章对长江航线上推轮船队的加解驳问题进行了分析和过程抽象．建立了描述问题的数学规划模型．设计了一套启发式求解算法。

摘要： We present the results of investigations carried out at the Karpenko Physicomechanical institute of the Ukrainian Academy of Sciences and devoted to the development of the methods of nondestructive testing of multilayer dielectric objects with plane interfaces. These methods make it possible to determine the thicknesses of the layers, the depths and thicknesses of the interlayers, and their permittivities by analyzing the frequency dependence of the reflection coefficient of superhigh-frequency electromagnetic waves. The procedure of determination is based on the solution of direct and inverse problems of reflection from the tested objects. We describe and discuss some of these methods and algorithms.

关键词： computational methods for control   parallel algorithms   algebraic Riccati equations   matrix sign function  

摘要： Because of its suitability for parallel computation, the matrix sign function is a popular algorithm for solving the algebraic Riccati equation (ARE). The algorithm can be numerically unstable, however, even when combined with iterative refinement. This paper presents an enhanced algorithm which is shown to be backward stable under most circumstances. The method uses a combination of iterative refinement, scaling, and shifting, together with carefully chosen stopping criteria. An error analysis supports the algorithm modifications. Computational examples demonstrate the effectiveness of these techniques.

关键词： SU(2) theory   SU(3) theory   Lie algebras   vectors   LIE GROUPS   TENSORS   WAVE FUNCTIONS   CLEBSCH-GORDAN COEFFICIENTS   SU-3 GROUPS   COUPLING   ALGORITHMS   MULTIPLICITY   SU-2 GROUPS  

摘要： A recent paper gave an explicit construction for inducing shift tensors of a compact reductive Lie group from shift tensors of a suitably defined subgroup. The shift tensors were defined on model spaces of holomorphic vector-coherent-state wave functions. In this paper, we use these shift tensors to obtain an algorithm for computing Clebsch-Gordan coefficients. The approach reproduces the known analytical results for SU(2) and gives a simple algorithm for computing SU(3) coefficients. The algorithm is shown to yield analytical expressions for the multiplicity-free SU(3) couplings of type (lambda(2)0)x(lambda(1)0). (C) 1997 American Institute of Physics.

关键词： 数学形态学   骨架   图像细化   地图  

摘要： 在分析形态序贯同伦细化算法的基础上，针对该算法运算结果为畸变骨架的缺点，提出了一种能保持图像目标正确结构形状的加权结构元素形态序贯细化算法，并以汉字图像为例予以验证．

关键词： 算法   工步排样   冲压   级进模   数学模型  

摘要： 对多工位级进模工步排样自动优化设计问题提供了数学模型及其通用算法与应用实例。

关键词： 模型结构   自校正预报   数学模型   泰勒展开  

摘要： 从多元函数的泰勒展开出发，给出了一种描述离散系统的模型结构，并给出了基于这种模型所描述系统的自校正预报的显式算法。

关键词： 17-04   17Bxx  

摘要： We consider a certain type of algorithm designed to construct the multiplication table of algebras given by generators and relations. These computations may be performed for various classes of (not necessarily associative) algebras, such as Lie (super)algebras, Jordan algebras, associative algebras;in general, for any class of algebras axiomatised by suitable polynomial identities. The type of algorithm considered is based on straightforward computations in the free non-associative algebra on the generators, which do not depend in an essential way on the axioms of the class of algebras, in particular no concept of ''representation'' of the algebra is used. The algorithm itself is only partially specified: it proceeds by repeatedly taking steps chosen from a limited repertoire of very simple possibilities, but no fixed strategy for selecting steps is assumed. We study the question whether termination of the algorithm is guaranteed for those inputs that actually describe a finite-dimensional algebra (the question whether some arbitrary input has this property is not algorithmically decidable). We prove under certain assumptions about the strategy that termination is indeed guaranteed in this case. (C) 1997 Elsevier Science B.V.

摘要： This paper describes how computer algebra systems can be used to help students understand mathematical algorithms. Since one can write programs in these systems, one way to help the students is to show them complete programs and try to show them what the programs do. However, programs are like black boxes;you see what goes in and what comes out. To understand the program you need to show the steps that it makes because most students need to see a worked example in detail in order to see what an algorithm is doing before they understand how it works. Another problem with programs is that programs force you to be explicit about details;you must formulate the termination conditions, estimate degree bounds, specify domains of variables, etc. These details often get in the way of illustrating the basic algorithm. The premise of this article is that interactive worksheets and notebooks, which are now available in several computer algebra systems, sometimes provide a better alternative than programs as a teaching aid. In a worksheet or notebook, we can present an algorithm by following the sequence steps done. If part of the algorithm is difficult to express as a single command, or difficult to program, the results can be ''typed in'' instead. Other parts which may be difficult to formalize in a program, may be very obvious from looking at the output. To illustrate this, we have presented five algorithms as worksheets which we have used for teaching undergraduate mathematics and computer science classes. (C) 1997 Academic Press Limited.