On the Structure of the Complements of Chebyshev Sets

A set is called a Chebyshev set if it contains a unique best approximation element. We study the structure of the complements of Chebyshev sets, in particular considering the following question: How many connected components can the complement of a Chebyshev set in a finite-dimensional normed or nonsymmetrically normed linear space have? We extend some results from [A. R. Alimov, East J. Approx, 2, No. 2, 215--232 (1996)]. A. L. Brown's characterization of four-dimensional normed linear spaces in which every Chebyshev set is convex is extended to the nonsymmetric setting. A characterization of finite-dimensional spaces that contain a strict sun whose complement has a given number of connected components is established.     

Representation theory of the system quiver

Let A be a three-point algebra with Gabriel quiver the system quiver Q, Then, up to isomorphism and duality, A is tame if and only if A is or degenerates to a factor of a tame algebra in the tame Table T if and only if A/rad5 A is tame, and A is wild if and only if A has a wild algebra in the wild Table W as a factor if and only if A is controlled wild.     

幺半群的强半格上的Rees矩阵半群的平移壳

设含幺元的半群A是幺半群A~_e的半格,其中A的幺元为1_A,A~_e的幺元为e,所有幺元e的集合为E(A),则对于幺半群A上的Rees矩阵半群S和幺半群A~_e上的Rees矩阵半群S~_e,以下五个条件是等价的:(1)任意的e∈E(A),a∈A,有ae=ea;(2)A是幺半群A~_e的强半格;(3)S是S~_e的强半格;(4)A的平移壳和A~_e的平移壳的强半格同构;(5)S的平移壳和S~_e的平移壳的强半格同构.     

On the Passage to the Limit in the Construction of Geometric Solutions of the Riemann Problem

Mathematical Notes - A method for constructing geometric solutions of the Riemann problem for an impulsively perturbed conservation law is described. A complete classification of the possible...     

Application of the coefficient of ergodicity in the estimation of the spectral radius of real matrices

It is shown that every real matrix A can be put in correspondence with a certain stochastic matrix P in such a way that the coefficient of ergodicity(P) of the matrix P enables us to give an estimate of the spectral radius of the matrix A. This estimate takes into account the signs of the elements of A, which makes it in many cases more accurate than the generally known estimates. In the case where one of the characteristic values of the matrix A and the characteristic vector corresponding to it are known, an estimate of the localization of the remaining characteristic values of the matrix A is obtained.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 137–142, January, 1978.     

Optimisation of the structure of the clinical laboratory

In many clinical laboratories span of control problems make it necessary to divide the clinical laboratory into sections (departments, job shops). A section is in fact a set of workstations where tests are performed on samples. A mathematical programming model is described which clusters workstations in such way that the maximum idle time of staff in staff assignment periods is minimized. An example demonstrates the usefulness of the approach.     

非奇异阵特征极值和条件数的近似计算

本文从共轭梯度法的公式推导出对称正定阵A与三对角阵B的相似关系,B的元素由共轭梯度法的迭代参数确定.因此,对称正定阵的条件数计算可以化成三对角阵条件数的计算,并且可以在共轭梯度法的计算中顺带完成.它只需增加O(s)次的计算量,s为迭代次数.这与共轭梯度法的计算量相比是可以忽略的.当A为非对称正定阵时,只要A非奇异,即可用共轭梯度法计算ATA的特征极值和条件数,从而得出A的条件数.对不同算例的计算表明,这是一种快速有效的简便方法.     

An estimate of the gradient of the propagation speed of elastic waves on the basis of the interference refracted wave

A method is proposed for estimating the gradient of the propagation speed of elastic waves on the basis of the interference structure of the refracted wave. Testing is carried out with numerical and experimental materials.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 99, pp. 123–26, 1980.     

Approximative compactness of the algebraic sum of sets

Let X be a group with an invariant metric, A and B nonempty subsets of X with B compact. It is proved that if A is an existence set [1] (approximatively compact [2]) then A + B and B + A are existence sets (approximatively compact). An example is given of a one-dimensional linear metric space (with an invariant metric) in which there exist an approximatively compact set A and an element v such that A + v is not an existence set.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 55–60, January, 1978.     

T-型树谱唯一性的一个简单刻画

图G称为谱唯一的,如果任何与G谱相同的图一定与G同构.一棵树称为T-型树如果其仅有一个最大度为3的顶点.本文给出了T-型树谱唯一性的一个简单刻画,从而完全解决了T-型树的谱唯一性问题.     

Application of the nonlinear theory of heredity to the description of time effects in polymeric materials

A relation is established between the heredity theory with time-invariant nonlinearity and fractional-exponential kernels and the Volterra-Fréchet theory for uniaxial tension. A constitutive equation is proposed for processes accompanied by decreasing strain. A procedure for determining the necessary material characteristics from creep and recovery data is considered.     

Finding the most probable nonnegative solutions of systems of linear algebraic equations by the maximum likelihood method

A probabilistic method of regularization is proposed. This method enables obtaining nonnegative solutions to systems of linear algebraic equations. A theorem of existence of the best possible solution is proved. A numerical example application of the method is given.     

Gaussian elimination and the ranks of the components in the Cartesian decomposition of a matrix

Let A = B + iC, where B = B*, C = C*, be the Cartesian decomposition of an n × n matrix A, and let the component B (or C) have rank r < n. It is shown that for a nonsingular A, the inverse A⁻¹ has an analogous property. This implies that all the (correctly defined) Schur complements in A have Cartesian decompositions with component B (or C) of rank ≤ r. The active submatrix at each step of the Gaussian elimination applied to A is the Schur complement of the appropriate leading principal submatrix. Bibliography: 2 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 31–35.     

On the Calculation of the Interaction Potential in Multiatomic Systems

Computational Mathematics and Mathematical Physics - A numerical method for finding the potential of a multiatomic system in the real space is proposed. A distinctive feature of this method is the...     

格矩阵半群的Euler-Fermat公式

给出并证明格矩阵半群的Euler-Fermat公式:A(n-1)2 1 = A(n-1)2 1 [n], A ∈ Mn(L)其中L是任意的分配格,Mn(L)是L上所有n阶矩阵构成的半群.这是布尔矩阵半群的Euler-Fermat公式的一种推广.     

无和数列的倒数和

设A={a1,a2,...}是一个严格递增的正整数数列,如果每一个an都不能写成它前面一些不同项的和,则称A为无和数列.令ρ(A)=∑∞k=11ak.1962年,Erds证明了,对任意无和数列A,有ρ(A)103.1977年,Levine和O’Sullivan改进为ρ(A)3.9998.最近,Chen进一步改进为ρ(A)3.0752.本文证明了,对于无和数列A={a1,a2,...}(a1a2···),当a12时,有ρ(A)2.526.     

On the dispersion matrix of variance estimators of the sample mean in the analysis of simulation output

A classical problem of stochastic simulation is how to estimate the variance of point estimators, the prototype problem being the sample mean from a steady-state autocorrelated process. A variety of estimators for the variance of the sample mean have been proposed, all designed to provide robustness to violations of assumptions, small variance, and reasonable computing requirements. Evaluation and comparison of such estimators depend on the ability to calculate their variances.A numerical approach is developed here to calculate the dispersion matrix of a set of estimators expressible as quadratic forms of the data. The approach separates the analysis of the estimator type from the analysis of the data type. The analysis for overlapping-batch-means estimators is developed, as is the analysis for steady-state first-order autoregressive and moving-average data. Closed-form expressions for overlapping-batch-means estimators and independently distributed data are obtained.     

On the application of the regularization method for the correction of improper problems of convex programming

A family of grid methods is constructed for the numerical solution of a wave equation with delay of general form; the methods are based on the idea of separating the current state and the history function. A theorem on the order of convergence of the methods is obtained by means of embedding into a general difference scheme with aftereffect. Results of calculating test examples with constant and variable delays are presented.