On solving systems of ordinary differential equations on MIMD-computers

The error of solution of Cauchy problems for systems of ordinary differential equations is estimated in the case where the input data are approximate. It is shown how to prepare a program for computing the right-hand sides of the system automatically and simultaneously. Diagrams are presented to illustrate the efficiency of parallelization. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 175–182, March–April 2007.     

Breaking the search space symmetry in partitioning problems: An application to the graph coloring problem

Many problems consist in splitting a set of objects into different groups so that each group verifies some properties. In practice, a partitioning is often encoded by an array mapping each object to its group numbering. In fact, the group number of an object does not really matter, and one can simply rename each group to obtain a new encoding. That is what we call the symmetry of the search space in a partitioning problem. This property may be prejudicial for optimization methods such as evolutionary algorithms (EA) which require some diversity during the search.     

Age Differences in Everyday Problem-Solving and Decision-Making Effectiveness: A Meta-Analytic Review.

The authors report a meta-analysis of age differences in everyday problem-solving/decision-making effectiveness (EPSE). Effect sizes were calculated to reflect 3 age group comparisons: old versus young, young versus middle-aged, and middle-aged versus old. Findings from the meta-analysis of 28 separate studies with an aggregate of 4,482 participants do not support theories of preserved EPSE in late adulthood. Although significant age differences of moderate magnitude persisted across methodological and theoretical domains, rating criteria (experimenter vs. participant) emerged as a significant moderator of the effect magnitude and direction. In addition, EPSE in older adults was bolstered when problem content was interpersonal and when samples were highly educated. Finally, the current results support the conceptual integration of findings from the everyday problem-solving and everyday decision-making literatures. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A classification of tournaments having an acyclic tournament as a minimum feedback arc set

Given a tournament with an acyclic tournament as a feedback arc set we give necessary and sufficient conditions for this feedback arc set to have minimum size.     

Application of piece‐wise linear weight functions for 2D 8‐node quadrilateral element in contact problems

The present study is a continuation of our previous work with the aim to reduce problems caused by standard higher order elements in contact problems. The difficulties can be attributed to the inherent property of the Galerkin method which gives uneven distributions of nodal forces resulting in oscillating contact pressures. The proposed remedy is use of piece‐wise linear weight functions. The methods to establish stiffness and/or mass matrix for 8‐node quadrilateral element in 2D are presented, i.e. the condensing and direct procedures. The energy and nodal displacement error norms are also checked to establish the convergence ratio. Interpretation of calculated contact pressures is discussed. Two new 2D 8‐node quadrilateral elements, QUAD8C and QUAD8D, are derived and tested in many examples, which show their good performance in contact problems. Copyright © 2004 John Wiley & Sons, Ltd.     

On a three-dimensional axisymmetric boundary-value problem of nonlinear elastic deformation: Asymptotic solution and exponentially small error

In this paper, we study a three-dimensional axisymmetric boundary-value problem of a slender cylinder composed of a nonlinearly elastic material subjected to an axial force. Starting from the field equations, after a transformation and proper scalings, we identify a small variable and two small parameters, which characterize the present problem. Then, by an approach involving compound series-asymptotic expansions, a nonlinear ODE is derived, which governs the axial strain (the first-term in the series expansion). By imposing the zero radial displacement conditions at two ends, we manage to get the analytical solution of the axial strain, from which all other physical quantities can be deduced and thus the three-dimensional displacement field can be determined. Graphical results are presented, which show that there are two boundary layers near the two ends while the middle part is in a state of almost uniform extension. The asymptotic structure of the analytical solution is derived, which offers clear explanations to the structure of the deformed configuration and shows that the thickness of both boundary layers is of the order of the radius. We also point out the relevance of the present results to the St. Venant’s problem. In particular, we obtain the explicit uniformly-valid exponentially small error term, when the obtained deformed configuration is compared to the configuration of a uniform extension.     

Singular Trajectories in Multi-Input Time-Optimal Problems: Application to Controlled Mechanical Systems

This paper deals with the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems have certain special properties. These properties are explored and used in conjunction with the Pontryagin maximum principle to determine the structure of singular extremals and, in particular, time-optimal trajectories. The theory is illustrated by an application to a time-optimal problem for a class of underwater vehicles.     

Frequency domain solution to delay-type Nehari problem

This paper generalizes the frequency-domain results on the delay-type Nehari problem in the stable case to the unstable case. The solvability condition of the delay-type Nehari problem is formulated in terms of the nonsingularity of three matrices. The optimal value γ_opt is the maximal γ∈(0,∞) such that one of the three matrices becomes singular. All sub-optimal compensators are parameterized in a transparent structure incorporating a modified Smith predictor.     

非透视3点问题的解析解

由于在机器人导航等领域新的图像装置不符合透视规则,无法运用传统的透视位置估计方法,采用吴氏零点分解方法,给出非透视3点问题的解析解.利用新图像装置的几何条件,建立了非透视3点方程系统.