Solution of three-dimensional problems of gas dynamics on multiprocessor computers

We give the results of solving a number of three-dimensional nonstationary problems of gas dynamics, whose programmatic implementation on multiprocessor computers is carried out using the NORMA language. We compare the effectiveness of different computing systems. Nine figures. Bibliography: 9 titles. Translated fromMetody Matematicheskoi Fiziki, 1998, pp. 172–183.     

Riemannian Geometry of Grassmann Manifolds with a View on Algorithmic Computation

We give simple formulas for the canonical metric, gradient, Lie derivative, Riemannian connection, parallel translation, geodesics and distance on the Grassmann manifold of p-planes in R ⁿ . In these formulas, p-planes are represented as the column space of n×p matrices. The Newton method on abstract Riemannian manifolds proposed by Smith is made explicit on the Grassmann manifold. Two applications – computing an invariant subspace of a matrix and the mean of subspaces – are worked out.     

Rank of maximum matchings in a graph

The matching polytope is the convex hull of the incidence vectors of all (not necessarily perfect) matchings of a graphG. We consider here the problem of computing the dimension of the face of this polytope which contains the maximum cardinality matchings ofG and give a good characterization of this quantity, in terms of the cyclomatic number of the graph and families of odd subsets of the nodes which are always nearly perfectly matched by every maximum matching.This is equivalent to finding a maximum number of linearly independent representative vectors of maximum matchings ofG; the size of such a set is called thematching rank ofG. We also give in the last section a way of computing that rank independently of those parameters.Note that this gives us a good lower bound on the number of those matchings.     

On a method of solving two-dimensional problems of the linear theory of viscoelasticity

We describe the basic propositions of the linear theory of viscoelasticity. We give transformation formulas for the resolvent integral operators of viscoelasticity with an arbitrary analytic kernel of difference type. The method of computing the irrational operator functions is illustrated by determining the real parameters of the two-dimensional stressed state of an orthotropic plate. Three figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 86–96.     

A numerical study of the dynamics of elastic articulated systems in a fluid

We propose a method and an algorithm for computing the dynamics of elastic structures of articulated form in a fluid flow taking account of the weakening in certain structural elements. In describing the motion we use two sets of radius-vectors, which are approximated in the computations by parametric local splines of first degree. The possibilities of the proposed method are illustrated using the example of the study of the dynamics of transition processes in an articulated anchor-buoy structure, which arise when there is an abrupt change in the direction of the fluid flow velocity. We determine the kinematic and force characteristics of the structure under various changes in the direction of the flow velocity. We determine the structural elements in which the weakening occurs. Three figures. Bibliography: 7 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 128–134.     

Pruning method for optimal solutions of int–int decision making scheme

This paper aims to find a faster method for optimal solutions of Feng et al.’s int^m–intⁿ decision making scheme. We first give theoretical characterizations of optimal decision sets. Then we develop a pruning method which filters out those objects that cannot be elements of any optimal decision sets in the beginning. Experimental results have shown that our method has higher efficiency in computing the optimal solutions of this scheme, particularly when we are processing soft sets with a great quantity of data.     

On dimensional properties of graphs

A dimensional property of graphs is a propertyP such that every graphG is the intersection of graphs having propertyP. IfP is a dimensional property, we describe a general method for computing the least integerk so thatG is the intersection ofk graphs having propertyP. We give simple applications of the method to computing the boxicity, the cubicity, the circular dimension, the rigid circuit dimension, and the overlap dimension, and mention connections to other concepts such as the threshold dimension.     

Finding the Medial Axis of a Simple Polygon in Linear Time

We give a linear-time algorithm for computing the medial axis of a simple polygon P . This answers a long-standing open question—previously, the best deterministic algorithm ran in O(n log n) time. We decompose P into pseudonormal histograms, then influence histograms, then xy monotone histograms. We can compute the medial axes for xy monotone histograms and merge to obtain the medial axis for P . Received May 16, 1997, and in revised form October 30, 1997.     

On global warming: Flow-based soft global constraints

In case a CSP is over-constrained, it is natural to allow some constraints, called soft constraints, to be violated. We propose a generic method to soften global constraints that can be represented by a flow in a graph. Such constraints are softened by adding violation arcs to the graph and then computing a minimum-weight flow in the extended graph to measure the violation. We present efficient propagation algorithms, based on different violation measures, achieving domain consistency for the alldifferent constraint, the global cardinality constraint, the regular constraint and the same constraint. This work was for a large part carried out while the author was at the Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands     

Computation of certain continuous integrals in the space of continuous functions defined on a compact set

We give formulas for computing integrals of functionals that are functions of linear and quadratic functionals with respect to generalized Wiener measure in the sense of J. Kuelbs in the space of continuous functions defined on a compact set.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 34, 1991, pp. 35–39.     

Construction of fundamental solutions of two-dimensional problems of the nonstationary theory of elasticity

We propose a method of constructing the images of the fundamental solutions in the space of the Laplace transform with respect to time, leading to simple formulas. The method is illustrated using three dynamical problems: planar deformation for an anisotropic body; flexural vibrations of an anisotropic plate; and vibrations of a shallow isotropic shell of arbitrary Gaussian curvature. Quadrature formulas are given for computing the values of the fundamental solutions. We give a new interpretation and a new method of computing the values of the special functions used in the construction of singular solutions in problems of the static theory of shells. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 86–92.     

A note on the arithmetic of differential equations

In this note we give a method for computing the differential Galois group of some linear second-order ordinary differential equations using arithmetic information, namely the p-curvatures.     

On the operator formulation of a class of problems of linear fluid dynamics

We propose a new operator formulation of a rather large class of problems of linear fluid dynamics. We give a result on the unique solvability of an evolution problem. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 118–122.     

Optimization over the polyhedron determined by a submodular function on a co-intersecting family

A greedy algorithm solves the problem of maximizing a linear objective function over the polyhedron (called the submodular polyhedron) determined by a submodular function on a distributive lattice or a ring family. We generalize the problem by considering a submodular function on a co-intersecting family and give an algorithm for solving it. Here, simple-minded greedy augmentations do not work any more and some complicated augmentations with multiple exchanges are required. We can find an optimal solution by at most 1/2n(n – 1) augmentations, wheren is the number of the variables and we assume a certain oracle for computing multiple exchange capacities.     

Examples of Calabi–Yau Threefolds as Covers of Almost-Fano Threefolds

We give a method for producing examples of Calabi–Yau threefolds as covers of degree d ≤ 8 of almost-Fano threefolds, computing explicitely their Euler– Poincaré characteristic. Such a method generalizes the well-knownclassical construction of Calabi–Yau threefolds as double covers of the projective space branched along octic surfaces.     

Iterative methods for the computation of a few eigenvalues of a large symmetric matrix

The task of computing a few eigenvalues and associated eigenvectors of a large sparse symmetric matrix arises in many applications. We present new iterative methods designed for the determination of a few extreme or non-extreme eigenvalues and associated eigenvectors. Our methods are based on the recursion formulas of the Implicitly Restarted Lanczos method introduced by Sorensen [1992], but differ from previous applications of these formulas in the selection of accelerating polynomial. The methods of the present paper require very little computer storage. Numerical examples illustrate that the methods can give rapid convergence. Dedicated to Åke Björck on the occasion of his 60th birthday This work was supported by NSF grants F377 DMR-8920147 ALCOM, DMS-9409422 and DMS-9205531.     

An algorithm for computing the one-dimensional electromagnetic field in a conducting ferromagnetic cylinder based on the method of finite differences

We propose an algorithm for computing the electromagnetic field in a conducting ferromagnetic cylinder, characterized by the presence of only the axial component of the electric field intensity vector. The algebraization of the partial derivatives over the radius is carried out using a high-precision method of finite differences, and the numerical integration with respect to time is done on the basis of the implicit method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 145–148.     

Determination of the boundary of the plastic zone in a mineral vein weakened by a three-dimensional hole

We propose a method of computing the boundary of the plastic zone formed in a neighborhood of the hole during the mining of a mineral. The problem is studied in a three-dimensional formulation. The boundary of the plastic zone is determined from the condition of continuity of the vertical normal stresses acting on the surface of contact of an elastic half-space and an elastoplastic layer. The computation is carried out for a hole having a parallelepipedal shape. One figure. Bibliography: 2 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 6–10, 1991.     

A direct approach to Bergman kernel asymptotics for positive line bundles

We give an elementary proof of the existence of an asymptotic expansion in powers of k of the Bergman kernel associated to L ^k , where L is a positive line bundle over a compact complex manifold. We also give an algorithm for computing the coefficients in the expansion.     

求矩阵对策全部解的单纯形法

给出求矩阵对策全部解的一种单纯形法 ,并指出参考文献 [1 ]中的两个错误 .