On the use of Boltzmann's transformation to solve diffusion problems

The use of Boltzmann's transformation to numerically solve diffusion problems using CALPHAD databases is discussed and illustrated with examples. It is shown how it can be applied to problems involving multicomponent, multiphase systems with composition dependent molar volumes. The formation of Kirkendall porosity is also discussed.     

On the use of genetic algorithms to solve location problems

This paper seeks to evaluate the performance of genetic algorithms (GA) as an alternative procedure for generating optimal or near-optimal solutions for location problems. The specific problems considered are the uncapacitated and capacitated fixed charge problems, the maximum covering problem, and competitive location models. We compare the performance of the GA-based heuristics developed against well-known heuristics from the literature, using a test base of publicly available data sets.Scope and purposeGenetic algorithms are a potentially powerful tool for solving large-scale combinatorial optimization problems. This paper explores the use of this category of algorithms for solving a wide class of location problems. The purpose is not to “prove” that these algorithms are superior to procedures currently utilized to solve location problems, but rather to identify circumstances where such methods can be useful and viable as an alternative/superior heuristic solution method.     

求解最长循环公共子序列问题的两个算法

最长循环公共子序列（LCCS）是两个字符串在所有可能的循环移位操作下能得到的最长公共子序列（LCS）。针对穷举移位量求解LCCS效率过低的问题,设法对候选移位量进行筛选。通过证明循环移位操作对两字符串间LCS长度增量影响的上下限,得到最优移位量的必要条件,从而减小了求解LCCS的枚举量;在此基础上,建立了求解LCCS的迭代方法,只经过少数几次迭代便可消除绝大部分无效候选移位量;此外,还提出一个可在◢O（mn）◣时间复杂度下快速估算LCCS长度的近似算法。大量随机模拟表明,当两字符串间的相似度明显高于随机字符串的相似度时,提出的两种算法表现良好。     

A suboptimal control algorithm for constrained problems using cubic splines

A suboptimal control algorithm for linear-quadratic regulator problems with state variable inequality constraints (SVIC) is developed. The state and control variables are approximated by cubic splines on an uniform mesh. Through collocation at the knots, the dynamic equations and SVIC are reduced to a set of linear algebraic equations and the suboptimal control is constructed from the solution of a quadratic programming problem with sparse matrices. The number of non-zero storage elements required for these matrices varies linearly with the number of mesh points.Computational experience for specific examples is presented and compared with other approaches described in the literature. Good to excellent accuracy is obtained with modest computational requirements. Memory considerations and on-line implementation are discussed. From both the computational and storage aspects, the approach offers an effective alternative for SVIC problems. Extensions of the algorithm to more general control problems are suggested.     

三次样条构造的伪逆解法

为了提高三次样条构造的可行性, 基于矩阵的伪逆方法, 提出一种不依赖额外约束条件的三次样条构造的伪逆解法。该解法通过求解出三次样条二阶导数的最小范数解, 从而较好地构造出三次样条函数。理论分析及数值实验结果表明该三次样条构造的伪逆解法具有简单、有效等特点。综合分析各种构造解法的性质, 对各种三次样条构造解法进行归类比较, 为在实际工程计算应用中选择合适的三次样条构造解法提供了指导方向。     

On some approaches to solve CFD problems

This paper presents two efficient methods for spatial flows calculations. In order to simulate of incompressible viscous flows, a second-order accurate scheme with an incomplete LU decomposed implicit operator is developed. The scheme is based on the method of artificial compressibility and Roe flux-difference splitting technique for the convective terms. The numerical algorithm can be used to compute both steady-state and time-dependent flow problems. The second method is developed for modeling of stationary compressible inviscid flows. This numerical algorithm is based on a simple flux-difference splitting into physical processes method and combines a multi level grid technology with a convergence acceleration procedure for internal iterations. The capabilities of the methods are illustrated by computations of steady-state flow in a rotary pump, unsteady flow over a circular cylinder and stationary subsonic flow over an ellipsoid.     

Smoothing of cubic parametric splines

The most common curve representation in CADCAM systems of today is the cubic parametric spline. Unfortunately this curve will sometimes oscillate and cause unwanted inflexions which are difficult to deal with. This paper has developed from the need to eliminate oscillations and remove inflexions from such splines, a need which may occur for example when interpolating data measured from a model. A method for interactive smoothing is outlined and a smoothing algorithm is described which is mathematically comparable to manual smoothing with a physical spline.     

Multiwavelets of the third-degree Hermitian splines orthogonal to cubic polynomials

A new type of multiwavelets with reduced support is proposed for the case of the third-degree Hermitian splines. Their advantage is proved for the numerical data compression over the well-known type of cubic multiwavelets. The results of the numerical experiments are presented.     

Calculations of curvature continuous cubic splines

The connection between the recursion formula for B-splines and the de Boor algorithm is well-known. This connection can be transferred to the curvature continuous cubic case where the use of results of Goodman & Unsworth (for a recursion formula) and Boehm (for a de Boor-like algorithm) yields two different pairs of recursion formulas and de Boor-like algorithms. Some properties are discussed.     

Uniform convergence of interpolation by cubic splines

For a sequence of meshes on [0, 1] sufficient conditions are given to obtain uniform convergence of cubic spline interpolants for continous functions respectively for the third derivatives of cubic spline interpolants for functions fromC ³ [0, 1].     

薄板样条函数在空间数据插值中的应用

薄板样条函数是空间数据插值中一种重要的方法,介绍了该方法的基本原理,并以珠江河道地形数据为例,借助地理信息系统的二次开发功能,将薄板样条函数应用于空间插值,通过与测试样本点以及克里金插值在最大值、标准误等方面的比较分析,证明薄板样条函数是一种有效的空间数据插值方法。     

On certain problems of the structure of ultrafilters related to extensions of abstract control problems

We study the procedures for constructing ultrafilters in measurable spaces that are in a general sense based on Cartesian products. Our constructions intend to use ultrafilters as generalized elements in extension constructions for abstract reachability problems with asymptotic constraints. Constrains of this kind may arise, for instance, with sequential relaxation of boundary and intermediate conditions in control problems. In this case, families of sets of admissible regular controls in practically interesting cases represent filter bases, which makes it natural to use ultrafilters (maximal filters) that are admissible, in a certain sense, with respect to these families. We assume that counterparts of reachability sets considered in this work are sets in a topological space; the latter may be non-metrizable which occurs, for instance, in typical applications of the pointwise convergence topology. Such a topology may also be useful in impulse control problems, where one studies sheafs of motions as counterparts of reachability sets for exact and approximate satisfaction of trajectory constraints.     

Iterative MC-algorithm to solve the global optimization problems

A new method was proposed to solve the global minimization problems of the Hölder functions on compact sets obeying continuous functions. The method relies on the Monte Carlo batch processing intended for constructing the sequences of values of the “quasi-global” minima and their decrements. A numerical procedure was proposed to generate a probabilistic stopping rule whose operability was corroborated by numerous tests and benchmarks with algorithmically defined functions.     

Family of cubic splines with one degree of freedom

A plane cubic spline segment can be specified in many ways. In this paper a specification method that can be divided into two phases is presented. The first phase relates the segment to the geometry of a deining triangle, but leaves one degree of freedom. This degree of freedom is in the polynomial coefficients as a linear parameter and the variation of the geometric relationship of the segment to the defining triangle as this parameter varies is explored. The second phase of the specification requires a choice of value for this parameter in accordance with a criterion of fairness that is specified. To support the method of this phase the variation of the curvature of the segment with changes in the parameter value is demonstrated.To show how the specification method can be used, the paper shows that the interpolation problem for general points in the plane can give rise to a set of defining triangles. An algorithm for generating such triangles for an open or closed curve problem for a given set of points is described. Results of using an implementation of this algorithm together with the specification method are presented.     

Numerical integration of partial differential equations using cubic splines

This paper presents techniques for the numerical solution of partial differential equations using cubic spline collocation.

The main spline relations are presented and incorporated into solution procedures for partial differential equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. Truncation errors and stability are briefly discussed. Finally, some examples of their application to parabolic and hyperbolic systems with mixed boundary conditions are presented.

The results obtained are encouraging and justify further research in this field.