Homology of algebras of families of pseudodifferential operators

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology degenerates at E² and converges to Hochschild homology. As a byproduct, we identify the space of residue traces on fibrations by manifolds with corners. In the process, we prove some structural results about algebras of complete symbols on manifolds with corners.     

Ultimate boundedness with respect to part of the variables of solutions of systems of differential equations with partly controlled initial conditions

We introduce the notions of equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables for solutions with partly controlled initial conditions. We obtain sufficient conditions for the equiultimate boundedness and uniform ultimate boundedness with respect to part of the variables of solutions with partly controlled initial conditions. We introduce the notions of equiboundedness and uniform boundedness with respect to part of the variables for solutions of systems with partly controlled initial conditions. We obtain sufficient conditions for the equiboundedness and uniform boundedness with respect to part of the variables of solutions with partly controlled initial conditions.     

Enumeration of the doubles of the projective plane of order 4

A classification of the doubles of the projective plane of order 4 with respect to the order of the automorphism group is presented and it is established that, up to isomorphism, there are 1 746 461 307 doubles. We start with the designs possessing non-trivial automorphisms. Since the designs with automorphisms of odd prime orders have been constructed previously, we are left with the construction of the designs with automorphisms of order 2. Moreover, we establish that a 2-(21,5,2) design cannot be reducible in two inequivalent ways. This makes it possible to calculate the number of designs with only the trivial automorphism, and consequently the number of all double designs. Most of the computer results are obtained by two different approaches and implementations.     

Investigation of velocity dependence of rolling frictions as a means of studying adhesion

Investigation of the rolling of two cylinders on the device described in this paper has shown that a study of the rolling friction of bodies coated with polymer films offers a means of investigating adhesion processes. It has been found that the resistance to rolling of bodies coated with nonadhesive polymers has a tendency to increase with increase in velocity, in accordance with the electrical theory of adhesion. The resistance to rolling of bodies coated with adhesive polymers passes through a maximum as the velocity increases and then decreases, in accordance with the diffusion theory of adhesion.Mekhanika Polimerov, Vol. 1, No. 4 pp. 117–122, 1965     

Application of the method of direct cutting-out to the solution of the problem of longitudinal shear of a wedge with thin heterogeneities of arbitrary orientation

The method of direct cutting-out consists of modeling of a finite body, in particular, with thin heterogeneities, using a much simpler problem for a bounded or a partially bounded body with thin heterogeneities located in the same manner and the presence of additional cracks or absolutely rigid inclusions of fairy large length, which are modeled by the boundary conditions of a bounded body. The method is tested on the problems of antiplane deformation of a symmetrically loaded crack in a wedge with free faces and an absolutely rigid inclusion placed with some tension in a wedge with restrained faces. For an elastic inclusion, we construct generalized conditions of interaction, which enable us to unify the procedure of giving different boundary conditions in the case of using the method of direct cutting-out.     

素数幂阶子群的s-半置换性对有限群结构的影响

设G为有限群,G的一个子群H称为半置换的,若对任意的K≤G,只要(|K|,|H|)=1,就有KH=HK;H称为s-半置换的,若对任意的p||C|,只要(p,|H|)=1,就有PH=HP,其中P∈Sylp(G).本文考察了素数幂阶子群的s-半置换性对有限群的超可解性的影响.     

Order of isolated singularities of solutions of elliptic systems

For second-order elliptic systems with the natural energy space W₂ ¹ solutions with an isolated singularity are considered. If the speed of growth of the solution is less than the limiting speed determined by the modulus of the elliptic system, it is proved that either the singularity is removable or its order coincides with the order of the singularity of the fundamental solution of Laplace's equation. Systems are also considered with positive nonlinear lowest terms, for which a complete classification is obtained of the possible orders of isolated singularities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 10, pp. 1349–1358, October, 1992.     

On Applications of Associativity of Dual Compositions in the Algebra of Boolean Matrices

We consider matrices of arbitrary size with elements from an arbitrary Boolean algebra with two partial multiplications that are defined in a dual way and are not associative with respect to each other in the general case. We show the connection of solvability of the simplest matrix equations, the matrix regularity, and the belonging to one-sided principal ideals with associativity of some dual compositions.     

Partial uniform boundedness of solutions of systems of differential equations with partly controlled initial conditions

We introduce the notion of partial uniform boundedness of solutions with partially controlled initial conditions in the general case, that is, the case in which the part of variables with respect to which the boundedness of solutions is studied is a subset of the part of variables with respect to which the initial conditions are controlled. We obtain a criterion for the partial uniform boundedness of solutions with partly controlled initial conditions. We introduce the notion of partial total boundedness of solutions with partly controlled initial conditions. We obtain a sufficient condition for the partial total boundedness of solutions with partly controlled initial conditions.     

生态系统的参数确定问题

通过不同观测数据研究捕食者—被捕食者生态系统参数确定问题.研究了四种情形1.观察数据无误差,并已知一个参数值.这种情况下,参数可由其相轨线和最小二乘法精确确定.2.观察数据无误差,但所有参数未知.此时仅靠相轨线的研究,无论给出多少组精确数据,都无法精确确定这些参数.通过原非线性模型的数值计算和网格搜索法,至少需要4组数据,同样得到了精度较高的参数值.3.当观测数据有误差时,根据解的周期性,引入标准周期的概念,在一个标准周期里讨论参数的确定问题,并利用标准周期内的捕食者与被捕食者的数量均值与系统的平衡点的关系对参数进行修正,然后使用网格法进行搜索,进一步提高了参数的精度.4.当观测时间也有误差时,先选取相对最优的随机正态数对观测时刻进行修正,然后再利用3.的方法估计参数.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

Preservation of rates of convergence under mappings

For appropriate metrics characterizing various modes of stochastic convergence, it is shown that rates of convergence are preserved by a large class of functions. For example, the extensions of a Lipschitz function on a separable metric space S to the space of all probability measures on S with the Prohorov metric and to the space of all S-valued random variables with the usual metric associated with convergence in probability inherit the Lipschitz property. Consequently, just as with the continuous mapping theorem associated with ordinary convergence, new rate of convergence theorems can sometimes be obtained from old ones by applying appropriate mappings.     

Robust counterparts of inequalities containing sums of maxima of linear functions

This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g. problems with sums of absolute values, and arise when taking the robust counterpart of a linear inequality that is affine in the decision variables, affine in a parameter with box uncertainty, and affine in a parameter with general uncertainty.     

Estimation of fractal dimension of random fields on the basis of variance analysis of increments

This paper deals with estimation of fractal dimension of realizations of random fields. Numerical methods are based on analysis of variance of increments. It is proposed to study fractal properties with the use of a specific characteristic of randomfields called a “variational dimension.” For a class of Gaussian fields with homogeneous increments the variational dimension converges to the Hausdorff dimension. Several examples are presented to illustrate that the concept of variational dimension can be used to construct effective computational methods.     

Distributions of functionals of diffusions with jumps

The paper deals with a generalization of diffusion with jumps. One of the main points is that values of jumps depend on positions of the diffusion before the jump. The next generalization concerns moments of jumps. These moments occur in accordance with the compound Poisson process or with jumping moments constructed by inverse integral functionals of the diffusion. Bibliography: 8 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 339, 2006, pp. 15–36.     

The lattice of convex subgroupoids of an ordered groupoid

Let V(A) (V_o (A)) be the lattice consisting of ϕ and all convex subgroupoids (with zero) of an o-groupoid A (with zero) with respect to the union B∨C which is the convex subgroupoid generated by B∩C and the set-theoretical intersection. In this paper, we study partially ordered groupoids (o-groupoids with zero) without proper convex subgroupoids (with zero), o-groupoids (with zero) for which V(A) (V_o (A)) is a chain, is the Cartesian product of two chains, is modular, is distributive, is complemented, or has a finite length, and also o-groupoids with zero and with associative powers (o-semigroups) in which every subgroupoid with zero (sub-semigroup) is convex. Finally, we give some results about lattice-closed classes of o-groupoids.     

Comparison of theories for stability of truss structures. Part 2: Computation of critical solution of stability

Critical solution of stability is the optimum solution of cross-sectional area with stability constraint. By applying the linear Eulerian theory of stability, the critical solution with discrete variables for general truss structures is computed in this paper. Then, in order to compare the results with the ones in previous publications and to reveal the applicability of various theories of stability, the critical solutions with continuous cross-sectional areas are computed for several examples by applying various theories of stability.     

Use of forms of high order in discussions of the stability of systems of differential equations with delay

A method of investigating forms of arbitrarily high order with respect to sign-definiteness in some cone of the space Rⁿ that coincides with a coordinate angle is given. The results obtained allowed us to use such functions as Lyapunov functions for the study of questions of stability for systems of differential equations with delayed argument.Translated from Dinamicheskie Sistemy, No. 9, pp. 15–21, 1990.     

A Model of Obsolescence of Organizational Rules

The phenomenon of obsolescence has found little attention in past research on organizational change. Most research on organizational change has instead been concerned with the opposite of obsolescence, that is, with mechanisms which render organizational structures increasingly persistent. However, everyday experience teaches that organizational structures become outdated as surrounding conditions shift. This article explores obsolescence by means of mathematical modeling and empirical analysis. Obsolescence is conceptualized as a result of flows of conditions in, out, and between two states: consistent conditions and inconsistent conditions. The model predicts that the obsoleteness curve rises with decreasing increments over time. This is tested with empirical data on organizational rule change. The results confirm the obsolescence model. This revised version was published online in August 2006 with corrections to the Cover Date.