Boundary control in critical time by elastic forces applied at two ends of an inhomogeneous rod for the case in which the wave propagation time over each of the inhomogeneity parts is the same

We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the boundary control by elastic forces bringing the originally quiescent stick into a given terminal state specified by a given terminal displacement and a given terminal velocity in a given critical time.     

On an asymptotic evaluation of the cycle index of the symmetric group

We give a short derivation of an extension of a result of Schwenk on the limiting behaviour of the cycle index of the symmetric group when it is evaluated for a given power series at a given point.     

Boundedness of the solution of the third problem for the Laplace equation

A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.Supported by GACR, Grant No. 201/00/1515.     

On the computational complexity of the Riemann mapping

In this paper we consider the computational complexity of uniformizing a domain with a given computable boundary. We give nontrivial upper and lower bounds in two settings: when the approximation of the boundary is given either as a list of pixels, or by a Turing machine.     

Choosing joint distributions so that the variance of the sum is small

The paper considers how to choose the joint distribution of several random variables each with a given marginal distribution so that their sum has a variance as small as possible. A theorem is given that allows the solution of this and of related problems for normal random variables. Several specific applications are given. Additional results are provided for radially symmetric joint distributions of three random variables when the sum is identically zero.     

On the uniqueness of the foliation of spheres of constant mean curvature in asymptotically flat 3-manifolds

In this note we study constant mean curvature surfaces in asymptotically flat 3-manifolds. We prove that, outside a given compact subset in an asymptotically flat 3-manifold with positive mass, stable spheres of given constant mean curvature are unique. Therefore we are able to conclude that the foliation of stable spheres of constant mean curvature in an asymptotically flat 3-manifold with positive mass outside a given compact subset is unique.

     

Facets of the knapsack polytope

A necessary and sufficient condition is given for an inequality with coefficients 0 or 1 to define a facet of the knapsack polytope, i.e., of the convex hull of 0–1 points satisfying a given linear inequality. A sufficient condition is also established for a larger class of inequalities (with coefficients not restricted to 0 and 1) to define a facet for the same polytope, and a procedure is given for generating all facets in the above two classes. The procedure can be viewed as a way of generating cutting planes for 0–1 programs.     

微分方程零解的弱渐近稳定与不稳定的判定定理

给出了平凡解弱渐近稳定定义及在已知导函数 d Vdt负定的情况下 ,通过 V( t,x)函数的符号性质来判定微分方程平凡解的弱渐近稳定性与不稳定性 ,并举例说明定理的应用 .     

Control of the optimum synthesis process of a four-bar linkage whose point on the working member generates the given path

This paper presents the optimum synthesis of a four-bar linkage in which the coupler point performs a path composed of rectilinear segments and a circular arc. The Grashof four-bar linkage whose geometry provides minimum deviations from the given problem for certain parts of the crank cycle is chosen. The motion of the coupler point of the four-bar linkage is controlled within the given values of allowed deviations so that it is always in the prescribed environment of the given point on the observed segment. The synthesis process tends to bring only those path segments that are beyond the boundaries within the prescribed boundary deviations. During the synthesis, allowed deviations change from the initial maximum values to the given minimum ones. Groups of mechanisms realising satisfactory approximation to the desired motion can be obtained by the method of controlled decrease of allowed deviations with the application of the Differential Evolution (DE) algorithm.     

Termination of the iterative proportional fitting procedure

The iterative proportional fitting procedure (IPF procedure) alternately fits a given nonnegative matrix to given positive row marginals and given positive column marginals. This paper proves that if the IPF procedure terminates, then this has to be within the first two steps.     

二次曲面理论的一个应用

本文使用二次曲面的化简理论 ,对于给定的三根螺旋 ,求出由它们确定的单叶双曲面     

Solution of the Neumann problem for the Laplace equation

For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single layer potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the double layer potential with a density given by a similar series.     

On the calculation of the spectra of directionally perturbed operators

A class of operators with special spectral properties is defined. An operator in this class is fairly simple, acts in a separable Hilbert space, and can be perturbed so that an a priori given function from its domain is an eigenfunction of the perturbed operator. This fact is shown to be useful for constructing operators in mathematical physics. Specific examples are given.     

On metrizability of the free monoids

A complete solution is given of the problem of S. Marcus concerning the construction of a “better” distance in the free monoids from the viewpoint of measuring the difference of contextual behaviour with respect to a given language.     

On two expressions of the MLE for a special case of the extended growth curve models

An algebraic proof is given on the equivalence between two solutions of MLEs for a special case of the extended growth curve models called the Banken model. One solution given by Verbyla and Venables is an iterative solution in the general case but reduces to a non-iterative one in the case of the Banken model. The other solution given by von Rosen is a closed-form solution specifically targeted at the Banken model. The proof has turned out to be quite challenging yet intriguing as it touches on many aspects of intricate matrix theory involving projection matrices.     

函数空间不变余度量性质的一个推广

本文对函数空间在集开拓扑下的不变余度量性质进行了推广,给出了函数空间在紧开拓扑和点收敛拓扑下不变余度量化的充要条件．     

On the BMO boundedness of the Cauchy integral on a chord-arc curve

Archiv der Mathematik - A detailed proof is given for the boundedness of the Cauchy integral acting on BMO on a chord-arc curve. Some applications are given to the Faber operator on BMOA and to the...     

On the existence of generalized inverses

Conditions are given for the existence of a generalized inverse of a ring morphism, and the results are related to the theory of semi-simple Artinian rings. Necessary and sufficient conditions are also given for the existence of a generalized inverse of a morphism on real inner product spaces.     

A Simple Proof of an Estimate for the Approximation of the Euclidean Ball and the Delone Triangulation Numbers

We give a simple proof of an estimate for the approximation of the Euclidean ball by a polytope with a given number of vertices with respect to the volume of the symmetric difference metric and relatively precise estimate for the Delone triangulation numbers. We also study the same problem for a given number of n−1-dimensional faces.