On Solvability of Lie Rings with an Automorphism of Finite Order

A new criterion for a Lie ring with a semisimple automorphism of finite order to be solvable is proved. It generalizes the effective version of Winter's criterion obtained earlier by Khukhro and Shumyatsky and by Bergen and Grzeszczuk in replacing the ideal generated by a certain set by the subring generated by this set. The proof is inspired by the original theorem of Kreknin on solvability of Lie rings with regular automorphisms of finite order and is conducted mostly in terms of Lie rings graded by a finite cyclic group.     

Numerical implementation of iteration processes applied in the study of nonlinear boundary value problems of the theory of elasticity and filtration

Nonlinear elastic problems for hardening media are solved by applying the universal iteration process proposed by A.I. Koshelev in his works on the regularity of solutions to quasilinear elliptic and parabolic systems. This requires numerically solving a linear elliptic system at each step of the iteration procedure. The method is numerically implemented in the MATLAB environment by using its PDE Toolbox. A modification of the finite-element procedure is suggested in order to solve a linear algebraic system at each iteration step. The computer model is tested on simple examples. The same nonlinear problems are also solved by the method of elastic solutions, which consists in replacing the Laplace operator in the universal iteration process by the Lamé operator of linear elasticity. As is known, this iteration process converges to a weak solution of the nonlinear problem, provided that the displacements are fixed on the boundary. The method is tested on examples with stresses on the boundary. The third part of the paper is devoted to the nonlinear filtration problem. General properties of the iteration process for nonlinear parabolic systems have been studied by A.I. Koshelev and V.M. Chistyakov. The numerical implementation is based on slightly modified PDE Toolbox procedures. The program is tested on simple examples.     

快速分析松脂澄清脂液中松节油含量的新方法

本文用统计方法研究思茅松松脂澄清脂液中松节油含量与酸值的相关关系，建立了不同于通常所用蒸馏法的新分析方法──酸值法。新方法快速、简捷、准确、经济、缩短分析时间５０分钟（７１％）；重复试验的极差的均值为０．１％，降低分析成本７０％；已用于云南省地方标准。     

A graph-theoretic proof of the non-existence of self-orthogonal Latin squares of order 6

The non-existence of a pair of mutually orthogonal Latin squares of order six is a well-known result in the theory of combinatorial designs. It was conjectured by Euler in 1782 and was first proved by Tarry in 1900 by means of an exhaustive enumeration of equivalence classes of Latin squares of order six. Various further proofs have since been given, but these proofs generally require extensive prior subject knowledge in order to follow them, or are ‘blind’ proofs in the sense that most of the work is done by computer or by exhaustive enumeration. In this paper we present a graph-theoretic proof of a somewhat weaker result, namely the non-existence of self-orthogonal Latin squares of order six, by introducing the concept of a self-orthogonal Latin square graph. The advantage of this proof is that it is easily verifiable and accessible to discrete mathematicians not intimately familiar with the theory of combinatorial designs. The proof also does not require any significant prior knowledge of graph theory.     

Numerical stability of DQ solutions of wave problems

In this paper, the solution of one-dimensional (1D) wave problems, by means of the Iterative Differential Quadrature method is discussed in terms of stability and accuracy. The 1D-wave equation with different boundary and initial conditions is considered. The time advancing scheme is here presented in a form, particularly suitable to support the discussion about stability both by the matrix method and by the energy method. The stability analysis, performed by means of these two methods, confirms the conditionally stable nature of the method. The accuracy of the solutions is discussed too.     

Stability of the periodic motions of the vibro-impact systems

In many other papers a new direct method is developed for the study of vibro-impact system stability, a case in which the stability conditions are directly and rapidly obtained. This new method is stated and applied for systems with one or several degrees of freedom whose motion is analysed by Lagrange's equations. Thus, the equations in variations determined from the differential equations are considered, which by applying the boundary conditions lead by integration to the linearized equation in perturbations necessary to write the stability conditions. As example, is analysed in detail a particular case with one degree of freedom realised by the rod-crank mechanism. Also, a general system with two degrees of freedom is completely studied.     

Solution of boundary-value problems in the theory of analytic functions of several variables in Vladimirov algebras

A solution is given for the Riemann problem for tubular domains in Vladimirov algebras in closed form by means of an integral representation of Bochner-Vladimirov type which is constructed here. In particular, the Schwartz problem is solved. The statement of the Hilbert problem in Vladimirov algebras is examined and its solution is given by a reduction to the Riemann problem, and in one case by a reduction to the Schwartz problem.Translated from Matematicheskie Zametki, Vol. 22, No. 1, pp. 51–60, July, 1977.     

Permeability of Clustered Fiber Networks: Modeling of the Unit Cell

The paper is focused on estimating the permeability of a clustered fiber network by variational methods. First, a laminar flow in ducts is considered by using polynomial trial functions. Then, a longitudinal flow through a square array is described by expanding the flow-rate field in trigonometric and Laurent series. Finally, a formal scheme for estimating the longitudinal permeability in a cluster with an irregular distribution of fibers is given. The irregular distribution is modeled by setting an individual effective radius for each fiber and then letting this fiber reach its minimum gravitational energy. The results obtained here form a basis for future predictions of the permeability of fibrous reinforcements.     

货运列车的编组调度问题的研究

对于货运列车的编组调度问题,建立了以压缩中时和增加运量为双目标、多约束的0-1规划模型,采用逐步紧缩中时约束的方法得到了问题一的调度方案.在此基础上对装载特别物资的车辆施加更强的中时约束得到了问题二的调度方案.提出了列车匹配系数的概念并建立了列车最优配对原则,根据该原则对列车进行优化编组得到了问题三的调度方案.基于问题二的数据转换处理得到了问题四的调度方案.     

Verification of a class of self-timed computational networks

A mathematical model for systolic networks is generalized and applied to a class of VLSI cellular networks which is defined to include both systolic and self-timed networks. The general model is kept simple by assuming that a computation does not deadlock, that is by separating the verification of liveness from the the verification of the results. The main contribution of this paper concerns the study of deadlock in self-timed computational networks. More specifically, an algebra of events is developed and used to prove that the liveness of any self-timed network is determined uniquely by its initial state. Moreover, a method is presented for the verification of liveness in networks preset to given initial states.This work was supported in part under ONR contract N00014-80-C-0455.     

城市可持续发展综合评价的一种方法

用层次分析法设计城市可持续发展评价模型.采用熵技术支持下的层次分析法确定系统指标权重,用加权平均法对可持续发展状态进行综合评价.并对鞍山市进行实例分析,指出鞍山市可持续发展能力总体呈上升趋势,但表现一定的波动性,与鞍山市的发展现状相符.     

组合预测方法在黑龙江垦区大豆产量预测中的应用

首先建立了黑龙江垦区九三地区的大豆单产的Logistic模型,通过梯度法得出模型的参数估计值,并对模型进行了分析.其次,再利用逐步回归方法建立了大豆产量与气象因子的逐步回归模型,确定了影响九三地区大豆产量的主要气象因子,最后运用组合预测和最优权数计算的方法,建立了九三地区大豆产量的组合预测模型,进一步提高了模型的精度,这对指导大豆生产具有重要意义.     

Measurement of the emitter field in the presence of an external source

A two-layer array antenna is used to measure the field of an emitter in the presence of an external field. The measurement problem is posed as an inverse scattering problem. Specifically, in the course of measurement, the array antenna separates the total field into the external field and the outgoing fields scattered by the emitter and the antenna plus the field radiated by the emitter. The external field is used to calculate the scattered field at the emitter. The field radiated by the emitter is determined by subtracting the scattered field at the emitter from the total field radiated and scattered by the emitter and the antenna.     

Sensitivity analysis of hyperbolic optimal control problems

The aim of this paper is to perform sensitivity analysis of optimal control problems defined for the wave equation. The small parameter describes the size of an imperfection in the form of a small hole or cavity in the geometrical domain of integration. The initial state equation in the singularly perturbed domain is replaced by the equation in a smooth domain. The imperfection is replaced by its approximation defined by a suitable Steklov??s type differential operator. For approximate optimal control problems the well-posedness is shown. One term asymptotics of optimal control are derived and justified for the approximate model. The key role in the arguments is played by the so called ??hidden regularity?? of boundary traces generated by hyperbolic solutions.     

Continuity of solutions of a quasilinear hyperbolic equation with hysteresis

This paper is devoted to the investigation of quasilinear hyperbolic equations of first order with convex and nonconvex hysteresis operator. It is shown that in the nonconvex case the equation, whose nonlinearity is caused by the hysteresis term, has properties analogous to the quasilinear hyperbolic equation of first order. Hysteresis is represented by a functional describing adsorption and desorption on the particles of the substance. An existence result is achieved by using an approximation of implicit time discretization scheme, a priori estimates and passage to the limit; in the convex case it implies the existence of a continuous solution.     

Numerical analysis of nonlinear model of excited carrier decay

This paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.     

Games of timing with resources of mixed type

The paper considers a game of timing which is closely related to the so-called duels. This is a game connected with the distribution of resources by two players. Each of the players is in possession of some amount of resource to be distributed by him in the time interval [0, 1]. In his behavior, Player 1 is restricted by the necessity of taking all of his resources at a single point, while Player 2 has no restrictions. For the payoff function, defined as for duels, the game is solved; explicit formulas on the value of the game and the optimal strategies for the players are found.     

Mathematical modeling and study of the process of solidification in metal casting

The process of melting and solidification in metal casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. The mathematical formulation of the problem and its finite-difference approximation are given. A numerical algorithm is presented for solving the direct problem. The results are described and analyzed in detail. Primary attention is given to the evolution of the solidification front and to how it is affected by the parameters of the problem. Some of the results are illustrated by plots.     

Optimization of periodic systems

The problem of designing a regulator, optimal by a quadratic performance criterion, on an infinite time interval is examined for a linear periodic system. It is assumed that the control plant's motion is described by a system of linear periodic finite-difference equations. Controllable plants whose motion is described by differential and by finite-difference equations on different parts of the period are analyzed as well. The optimal regulator design problem is reduced to the determination of a periodic solution of an appropriate Riccati equation. An algorithm for constructing such a solution is derived. It is noted that this result can be used in periodic optimization problems /1/ and in the design of a stabilization system for a pacing apparatus.