Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

Invariant properties of systems of equations of the mechanics of inhomogeneous fluids

The invariant properties of the fundamental system of equations of the mechanics of inhomogeneous fluids and its widely used approximations are analysed by the methods of continuous group theory. Simplifying assumptions significantly alter the invariant properties of the systems of equations. Both extending and contracting the admissible symmetry group can occur and provide evidence of the violation of the conditions of equivalence between the original and derived systems. For example, the use of the incompressibility and Boussinesq approximations leads to extension of the concept of an inertial reference frame to all frames moving relative to one another with arbitrary linear acceleration.     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Proofs of definability of some varieties and sets of varieties of semigroups

We show that many important varieties and sets of varieties of semigroups may be defined by relatively simple and transparent first-order formulas in the lattice of all semigroup varieties.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Stability estimates of solutions of systems of functional-differential equations of neutral type

A system of linear functional-differential equations of neutral type is considered. Investigation of stability is carried out by the method of Lyapunov functions of quadratic form. Sufficient conditions for the asymptotic stability and estimates of the exponential decay of solutions for an arbitrary and a small deviation of the argument are obtained.Candidate of the Physicomathematical Sciences.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43. No. 9, pp. 1123–1135, September, 1991.     

Optimal control of the process of electroplating of parts of axisymmetric shape

We state the problem of optimal control of the process of electroplating of parts as a problem of coupled optimization. Problems of optimal control of electroheating and subsequent deformation of a metal billet are studied as a coupled problem. In solving the problems the gradient method and Pontryagin's principle are used.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 59–64.     

Quadratic error of unbiased estimator of density of joint distribution of sufficient statistics of multidimensional normal distribution

Quadratic errors or unbiased density estimators are obtained for a number of distributions and the cases of normal distribution and Wishart distribution are considered.Translated from Staticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 4–10, 1988.     

一类缺项算子矩阵的谱扰动

有界线性算子的点谱和剩余谱分别可进-步细分为两类:σ_(p1),σ_(p2)和σ_(r1),σ_(r2).设H,K为无穷维可分的Hilbert空间,本文将对于给定的A ∈B (H),B ∈B(K),给出了缺项算子M_C=(AC/OB)关于分类后所得四种谱的扰动结果.     

Approximation of classes of smooth functions of several variables

The paper deals with imbedding theorems and harmonic approximation for classes of periodic functions of several variables. Necessary and sufficient conditions for imbedding are found for various classes of smooth functions. The paper contains asymptotic estimates for fractional order derivatives of multidimensional Dirichlet and Favard kernels, for Fourier best approximation and for the Kolmogorov diameter of smooth function classes.Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 10, pp. 207–226, 1984.     

Computer approximation of families of curves of physically nonlinear creep of polymer materials

The determination of confidence intervals of deformations was studied for an individual measurement and arithmetical mean common for all points of an experimental family of curves. From the experimental data on the creep of polyamide resin and five different analytical equations of physically nonlinear creep, the problems of the computer approximation of families of creep curves and the determination of the material parameters are discussed. A method is proposed for a quantitative evaluation of the degree of correspondence of the initial data to the similarity of isochronous creep curves and the similarity of the creep curves.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 2, pp. 220–229, March–April, 1976.     

Extreme values of the sum of squares of degrees of bipartite graphs

In this paper we determine the minimum and maximum values of the sum of squares of degrees of bipartite graphs with a given number of vertices and edges.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

Estimate of the rate of convergence of the method of moments for the solution of singular integral equations

A foundation is given for the numerical evaluation of a fully singular integral equation with constant coefficients and Cauchy kernel by the method of moments. Uniform convergence is proven, and mean-square and uniform error estimates are established.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 29, 80–85, 1989.     

Completeness of the system of Floquet solutions of equations of the neutral type

The necessary and sufficient conditions for the completeness of the system of Floquet solutions, the eigenfunctions and associated functions of the displacement operator, over a period of the coefficient in metrics C₁ and C in the space of all solutions of the equationy (t)=q(t) y (t– n)+ay (t–m), are obtained. Here q(t) is a continuous function of the period.Translated from Matematicheskie Zametki, Vol. 3, No. 3, pp. 297–306, March, 1968.In conclusion we wish to express our deep gratitude to B. Ya. Levin and A. D. Myshkis for discussion and help with the work.     

Estimates of the number of relative minima of lattices

We prove an estimate of the number of relative minima of an arbitrary lattice (which can be noninteger and incomplete) located in a given cube. This estimate is correct up to a constant depending on the dimension and rank.