Heterogeneous Coupling: A Comparison of two Approaches for the Modeling of thin Structures

Two different approaches for the modeling of a heterogeneous model consisting of, e.g., bone and ligaments, are presented and compared along a simple model problem. We describe both methods and briefly discuss their advantages and disadvantages. Furthermore, we present first numerical results in 3D. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Kronecker's and Newton's Approaches to Solving: A First Comparison

These pages are a first attempt to compare the efficiency of symbolic and numerical analysis procedures that solve systems of multivariate polynomial equations. In particular, we compare Kronecker's solution (from the symbolic approach) with approximate zero theory (introduced by S. Smale as a foundation of numerical analysis). For this purpose we show upper and lower bounds of the bit length of approximate zeros. We also introduce efficient procedures that transform local Kronecker solutions into approximate zeros and conversely. As an application of our study we exhibit an efficient procedure to compute splitting field and Lagrange resolvent of univariate polynomial equations. We remark that this procedure is obtained by a convenient combination of both approaches (numeric and symbolic) to multivariate polynomial solving.     

A Modeling Perspective on Interpreting Rates of Change in Context

Functions provide powerful tools for describing change, but research has shown that students find difficulty in using functions to create and interpret models of changing phenomena. In this study, we drew on a models and modeling perspective to design an instructional approach to develop students’ abilities to describe and interpret rates of change in the context of exponential decay. In this article, we elaborate the characteristics of the model development sequence and we examine how students interpreted and described non-constant rates of change in context. We provide evidence for how a focus on the context made visible students’ reasoning about rates of change, including difficulties related to the use of language when describing changes in the negative direction. We argue that context and the use of language, forefronted in a modeling approach, should play an important role in supporting the development of students’ reasoning about changing phenomena.     

A Combined Data-Base and Algorithmic Approach to the Pallet-Loading Problem

The current trend in pallet-loading software is for fast, interactive microcomputer packages. Because of the complexity of the problem, it is unlikely that any exact algorithm will guarantee to solve all typical pallet-loading problems within the sort of time range desirable for interactive use. Therefore, the packages tend to be based on heuristic solution methods. This paper describes a way of dealing with those problems which fail to solve within the given time limit. The discussion is in terms of a recent exact algorithm for the pallet-loading problem, but the methodology can be applied in conjunction with any algorithm for which the proportion of problems exceeding the time limit is small. The result is a piece of software which guarantees to solve any typical pallet-loading problem within a few minutes on an IBM-PC.     

Algorithmic Approach to the Extinction Probability of Branching Processes

The extinction probability of a branching process is characterized as the solution of a fixed-point equation which, for a fairly general class of Markovian branching processes, is vector quadratic. We address the question of solving that equation, using a mixture of algorithmic and probabilistic arguments. We compare the relative efficiency of three iterative methods based on functional iteration, on the basis of the probabilistic interpretation of the successive iterations as well as on the basis of traditional rate of convergence analysis. We illustrate our findings through a few numerical examples and conclude by showing how they extend to more complex systems.     

Algorithmic Improvements to the Method of Martel and Aouni

This note presents some suggestions for technical improvement of the method given by Martel and Aouni for decision maker preference modelling within goal programming.     

Optimal Design of Plane Frames under Uncertainty: A Comparison of Two Approaches

Using the first collapse theorem, the necessary and sufficient survival conditions of an elasto-plastic structure consist of the yield condition and the equilibrium condition. In practical applications several random model parameters have to be taken into account. This leads to a stochastic optimization problem which cannot be solved using the traditional methods. Instead of that, appropriate (deterministic) substitute problems must be formulated. Here, the design of plane frames is considered, where the applied load is supposed to be stochastic. In the first approach the recourse problem will be formulated in the standard form of stochastic linear programming (SLP). In order to apply efficient numerical solution procedures (LP-solvers), approximate recourse problems based on discretization (RPD) and the expected value problem (EVP) are introduced. In the second approach – based on the yield condition – a quadratic cost function will be introduced. After the formulation of the stochastic optimization problem, the expected cost based optimization problem (ECBOP) and the minimum expected cost problem (MECP) are formulated as representatives of appropriate substitute problems. Subsequently, comparative numerical results using these methods are presented. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Algorithmic problems in varieties of semigroups

Translated from Algebra i Logika, Vol. 27, No. 4, pp. 440–463, July–August, 1988.     

关于Quotient Context of Morita Context的讨论

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Algorithmic testing for the deformability of suspensions

An algorithm is proposed by means of which the deformability or nondeformability of polyhedra can be tested. The algorithm is tested against the example of the so-called suspensions — polyhedra of bipyramid type. Two tables. Two figures.Translated from Ukrainskií Geometricheskií Sbornik, No. 30, 1987, pp. 109–112.     

Comparison of Parametric and Bootstrap Approaches to Obtaining Confidence Intervals for Logspline Density Estimation

In earlier articles, we developed an automated methodology for using cubic splines with tail linear constraints to model the logarithm of a univariate density function. This methodology was subsequently modified so that the knots were determined by stepwise addition-deletion and the remaining coefficients were determined by maximum likelihood estimation. An alternative approach, referred to as the free knot spline procedure, is to use the maximum likelihood method to estimate the knot locations as well as the remaining coefficients. This article compares various approaches to constructing confidence intervals for logspline density estimates, for both the stepwise procedure and the free knot procedure. It is concluded that a variation of the bootstrap, in which only a limited number of bootstrap simulations are used to estimate standard errors that are combined with standard normal quantiles, seems to perform the best, especially when coverages and computing time are both taken into account.     

Alternative Approaches to the Two-Scale Convergence

Two-scale convergence is a special weak convergence used in homogenization theory. Besides the original definition by Nguetseng and Allaire two alternative definitions are introduced and compared. They enable us to weaken requirements on the admissibility of test functions (x, y). Properties and examples are added.