Another Construction of Cartesian Authentication Codes from Geometry of Classical Groups

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The use of splitting of the equations of motion in the numerical solution of problems of the dynamics of elastic systems

Linear elastic systems with a finite number of degrees of freedom, the initial equations of motion of which are constructed using the finite element method or other discretization methods, are considered. Since, in applied dynamics problems, the motions are usually investigated in a frequency range with an upper bound, the degrees of freedom of the initial system of equations are split into dynamic and quasi-dynamic degrees. Finally, the initial system of equations is split into a small number of differential equations for the dynamic degrees of freedom and into a system of algebraic equations for determining the quasi-static displacements, represented in the form of a matrix series. The number of terms of the series taken into account depends on the accuracy required.     

Controllability and stabilization of the programmed motions of a transport robot

A non-linear mathematical model for the motion of a transport robot (TR) with a caterpillar chassis and with drives based on DC motors, which is a non-holonomic electromechanical system, is considered. Non-linear canonical transformations of the coordinates of the state and control space are constructed, which reduce the initial equations of motion of the TR to a simpler canonical form, which is convenient for analysing and synthesizing control systems for the TR. The conditions for the TR to be controllable as a controlled object are found. Algorithms are given for constructing programmed motions (PMs) of the TR. Stabilizing control laws are synthesized under which the PMs of the TR are asymptotically stable and transients of a specified nature are ensured.     

Boundedness of adjoint bases of approximate spectral subspaces and of associated block reduced Resolvents

Block reduced resolvents are often employed in iterative schemes for refining crude approximations of the arithmetic mean of a cluster of eigenvalues and of a basis of the corresponding spectral subspace. We prove that if the bases of approximate spectral subspaces are chosen in such a way that they are bounded and each element of the basis is bounded away from the span of the previously chosen elements, then the corresponding adjoint bases are also bounded. We give an integral representation of the associated block reduced resolvent and show that under such a choice of the bases, the approximate block reduced resolvents are bounded as well. This is crucial in obtaining error estimates for the iterates of several refinement schemes. In the framework of a canonical discretization procedure for finite rank operators, appropriate choices of ises are given for various finite rank approximation methods such as Projection, Sloan, Galerkin, Nyström, Fredholm, Degenerate kernel. If the bases are not chosen appropriately, the error estimates may no longer hold and the iteration scheme may not be numerically stable. Examples are given to illustrate these phenomena     

一类Kaplan-Meier估计泛函的一些大样本性质

设F,G分别表示某寿命随机变量与删失随机变量的分布函数,在不假定F、G连续的情况下该文使用点过程鞅方法证明了Kaplan－Meier估计的一类泛函的渐近正态性,并建立了一个均方误差不等式和一个概率不等式．     

Matrix of moments of the Legendre polynomials and its application to problems of electrostatics

In this work, properties of the matrix of moments of the Legendre polynomials are presented and proven. In particular, the explicit form of the elements of the matrix inverse to the matrix of moments is found and theorems of the linear combination and orthogonality are proven. On the basis of these properties, the total charge and the dipole moment of a conducting ball in a nonuniform electric field, the charge distribution over the surface of the conducting ball, its multipole moments, and the force acting on a conducting ball situated on the axis of a nonuniform axisymmetric electric field are determined. All assertions are formulated in theorems, the proofs of which are based on the properties of the matrix of moments of the Legendre polynomials.     

Enumeration of weak isomorphism classes of signed graphs

A signed graph is a graph in which each line has a plus or minus sign. Two signed graphs are said to be weakly isomorphic if their underlying graphs are isomorphic through a mapping under which signs of cycles are preserved, the sign of a cycle being the product of the signs of its lines. Some enumeration problems implied by such a definition, including the problem of self-dual configurations, are solved here for complete signed graphs by methods of linear algebra over the two-element field. It is also shown that weak isomorphism classes of complete signed graphs are equal in number to other configurations: unlabeled even graphs, two-graphs and switching classes.     

Approximation of discontinuity lines of a noisy function of two variables

In the paper, the methods are constructed and investigated of localization (determination of the location) of the line in a neighborhood of which a measured function of two variables is smooth, whereas it has a discontinuity of the first kind on this line. Instead of the exact function, there is available some of its approximations in L ₂ and the perturbation level. The problem under consideration belongs to the class of nonlinear ill-posed problems, and to solve it some regularization algorithms are needed. A simplified theoretical approach is suggested to the problem of localization of the discontinuity line of a noisy function, when the conditions on the exact function are imposed on an arbitrary small strip intersecting the discontinuity line. Some averaging methods are constructed, and estimates for the precision of the line localization are obtained.     

Verification of a class of link-level protocols

This paper describes a model of a link-level communication line, and defines a set of operations meant to form the basis of data transfer protocols. Some problems concerning verification of protocols are discussed, and it is shown that all protocols using the given operations as a basis are partially correct. Conditions are given for total correctness.     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

Characterizations of solution sets of convex vector minimization problems

Complete dual characterizations of the weak and proper optimal solution sets of an infinite dimensional convex vector minimization problem are given. The results are expressed in terms of subgradients, Lagrange multipliers and epigraphs of conjugate functions. A dual condition characterizing the containment of a closed convex set, defined by a cone-convex inequality, in a reverse-convex set, plays a key role in deriving the results. Simple Lagrange multiplier characterizations of the solution sets are also derived under a regularity condition. Numerical examples are given to illustrate the significance of the results.     

Some fundamental problems of the theory of thermoviscoelasticity

Methods of solving quasistatic problems of the linear theory of thermoviscoelasticity are discussed. Special attention is given to the method of approximations. Modern methods of solving contact problems with a variable boundary and problems with a time-dependent boundary are briefly reviewed. Methods of solving problems with a nonuniform temperature field are outlined. The basic relations of the nonlinear theory of thermoviscoelasticity are given. Its various modifications and simplifications associated with the introduction of fairly general assumptions are examined. Methods of solving problems in certain nonlinear theories are noted. Nonisothermal (coupled) problems of thermoviscoelasticity and questions relating to the general theory with physical and geometric nonlinearity are discussed.Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 1, pp. 41–58, January–February, 1971.     

Exact and asymptotic solutions of the equation of internal gravity waves in a wedge-shaped region

The field of internal gravity waves in a wedge-shaped region of a stratified medium is considered. Using a Kantorovich–Lebedev transformation, exact solutions are obtained which describe an individual mode and the complete wave field. The asymptotics of an individual wave mode are constructed by the WKB method, and are expressed in terms of a hypergeometric function, as well as the asymptotics of the complete wave field, which are expressed in terms of a semilogarithmic function. The results of numerical calculations of the wave field using the exact and asymptotic formulae are presented for the parameters of a stratified medium, characteristic for the dynamics of the ocean. The limits of their applicability are estimated.     

On the equivalence of two conditions for the existence of transversals

There are two conditions which are known to be necessary for the existence of a transversal in any family of sets, but both are sufficient only if the family is countable. This paper proves that these conditions are always equivalent to each other. The families which are compatible with these conditions are characterised, in the sense that each of their subfamilies possesses a transversal if it satisfies the conditions. Using this, a conjecture of Podewski and Steffens is proved.     

Semiconjugates of One-dimensional Maps

R -semiconjugate maps are defined as a natural means of relating a map F of R m to a mapping { of the interval via a link map H . Invariants are seen to be special types of semiconjugate links where { is the identity. Basic relationships between the dynamical behaviors of { and F are established, and conditions under which a link map H is a Liapunov function are obtained. Examples and applications involving concepts from stability to chaos are discussed.     

Applications of Parameterizations of Oblique Duals of a Frame Sequence

Two parameterizations of oblique duals of a given frame sequence are applied to show that the sum of a frame sequence and one of its oblique duals may not be a frame sequence, and that type II dual is locally (and globally) optimal in some sense and that the excesses of the frame sequence and its oblique duals are the same. Other observations on the duals of a frame sequence are included also.     

Simulation of nonlinear properties of ferroelectric and piezoceramicmaterials

Ferroelectric and piezoelectric materials are becoming a very significant part of smart materials that are used widely as actuators, sensors and most common applications such as vibration control, precision positioning, precision cutting and microelectromechanical systems (MEMS). Piezoceramic materials show nonlinear characteristics when they are under high electromechanical loading. In this study, nonlinear behaviour of tetragonal perovskite type piezoceramic materials is simulated using micromechanical model. In the simulations uni‐axial loading is applied. The calculations which are based on a linear constitutive model, nonlinear domain switching model and a model of probability to switch are performed at each grain. The different domain switching effects (900 or 1800 domain switching for tetragonal perovskite structure) due to energy differences, different probability functions, different statistical random generators and material parameters are analyzed. Finally, simulation results are compared with the data of experiments are giving in literature. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adhesivity of polymatroids

Two polymatroids are adhesive if a polymatroid extends both in such a way that two ground sets become a modular pair. Motivated by entropy functions, the class of polymatroids with adhesive restrictions and a class of selfadhesive polymatroids are introduced and studied. Adhesivity is described by polyhedral cones of rank functions and defining inequalities of the cones are identified, among them known and new non-Shannon type information inequalities for entropy functions. The selfadhesive polymatroids on a four-element set are characterized by Zhang-Yeung inequalities.     

BCH-代数的原子与分支

在BCH—代数中引入了原子与分支的概念，给出了一个元素为BCH-代数原子的一系列等价条件，证明了一个BCH—代数的所有原子作成的集合是一个广义结合BCI—代数，最后对BCH—代数分支的性质进行了讨论。     

非自治动力系统的原像熵

本文对紧致度量空间上的连续自映射序列应用生成集和分离集引入了点原像熵、原像分枝熵以及原像关系熵等几类原像熵的定义并进行了研究.主要结果是:(1) 证明了这些熵都是等度拓扑共轭不变量.(2)讨论了这些原像熵之间及它们与拓扑熵之间的关系,得到了联系这些熵的不等式.(3)证明了对正向可扩的连续自映射序列而言, 两类点原像熵相等,原像分枝熵与原像关系熵也相等.(4)证明了对(a).由闭Riemann 流形上的一个扩张映射经充分小的C1-扰动生成的自映射序列,以及(b).有限图上等度连续的自映射序列,有零原像分枝熵.