随机环境中的马氏链的不变测度与遍历性

本文考虑了一类特殊的随机环境的马氏链。假设随机“Doeblin”条件成立，我们证明了随机环境的马氏链的不变测度存在，且任何初始分布以指数收敛速度到些不变测度。进一步的，存在关于绕积算子遍历的不变测度。最后，我们得到了随机马氏链的强大数定律。     

On essential sets and essential components of efficient solutions for vector optimization problems

In this paper, we first introduce the notions of an essential set and an essential component of the set of efficient solutions for continuous vector optimizations on a nonempty compact subset of a metric space. Then we show that for each of these vector optimizations, each set of all efficient solutions corresponding to the same optimal values is essential. Basing on this result, we give full characterizations of an essential point, an essential set and an essential component, respectively. As an application, we prove that for continuous quasiconvex vector optimization problems on a nonempty compact subset of a metric vector space, each component of the set of efficient solutions is essential even though the efficient solution set is not connected.     

Total absolute curvature and tightness of noncompact manifolds

In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

     

On the complexity of the word problem for automaton semigroups and automaton groups

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSpace-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently.A detailed listing of the contributions of this paper can be found at the end of this paper.     

Approximation of conformal mappings of annular regions

Summary. In this paper we examine the convergence rates in an adaptive version of an orthonormalization method for approximating the conformal mapping of an annular region onto a circular annulus. In particular, we consider the case where has an analytic extension in compl() and, for this case, we determine optimal ray sequences of approximants that give the best possible geometric rate of uniform convergence. We also estimate the rate of uniform convergence in the case where the annular region has piecewise analytic boundary without cusps. In both cases we also give the corresponding rates for the approximations to the conformal module of . Received February 2, 1996     

关于Bell多项式及其它的一些恒等式

本文引入了一个新的多项式,即Bell多项式.利用初等数论及组合方法,证明了包含该多项式的一些恒等式.作为这些恒等式的应用,给出了关于Bell数的同余式.     

Discontinuous local semiflows for Kurzweil equations leading to LaSalle's invariance principle for differential systems with impulses at variable times

In this paper, we consider an initial value problem for a class of generalized ODEs, also known as Kurzweil equations, and we prove the existence of a local semidynamical system there. Under certain perturbation conditions, we also show that this class of generalized ODEs admits a discontinuous semiflow which we shall refer to as an impulsive semidynamical system. As a consequence, we obtain LaSalle's invariance principle for such a class of generalized ODEs. Due to the importance of LaSalle's invariance principle in studying stability of differential systems, we include an application to autonomous ordinary differential systems with impulse action at variable times.     

On a constructive approximation of the efficient outcomes in bicriterion vector optimization

For bicriterion quasiconvex optimization problems, we present a constructive procedure for an approximation of the efficient outcomes. Performing this procedure we can estimate the accuracy of the approximation. Conversely, if we prescribe an accuracy for the approximation, we can calculate the number of points which have to be computed by a certain scalarization method to remain under the given accuracy. Finally, we give a numerical example.     

An exact penalty method for weak linear bilevel programming problem

In this paper, we present an exact penalty method, which is different from the existing penalty method, for solving weak linear bilevel programming problem. Then, we establish an existence result of solutions for such a problem. Finally, we propose an algorithm and give two examples to illustrate its feasibility.     

An approach for solving of a moving boundary problem

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.     

双根树上二阶非齐次马氏链的强大数定律和Shannon-McMillan定理

本文首先研究了双根树上转移矩阵为逐点转移的二阶非齐次马氏链的强极限定理,同时得到双根树上二阶非齐次马氏链的强大数定律.最后,给出了双根树上二阶非齐次马氏链几乎处处收敛意义下的Shannon-McMillan定理.     

Distributed algorithms for weighted problems in sparse graphs

We study distributed algorithms for three graph-theoretic problems in weighted trees and weighted planar graphs. For trees, we present an efficient deterministic distributed algorithm which finds an almost exact approximation of a maximum-weight matching. In addition, in the case of trees, we show how to approximately solve the minimum-weight dominating set problem. For planar graphs, we present an almost exact approximation for the maximum-weight independent set problem.     

Optimal control of a two-dimensional contact problem

We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result.     

Bigeneric initial ideals, diagonal subalgebras and bigraded Hilbert functions

In this paper we study some problems concerning bigraded ideals. By introducing the concept of bigeneric initial ideal, we answer an open question about diagonal subalgebras and we give a necessary condition for a function to be the bigraded Hilbert function of a bigraded algebra. Moreover, we give an upper bound for the regularity of a bistable ideal in terms of the degrees of its generators.     

Constructive method for solving a linear minimax problem of optimal control

In this paper, we propose a constructive method for solving a linear minimax problem of optimal control. Following the Gabasov-Kirillova approach, we introduce the concept of so-called support control. After establishing an optimality criterion for the support control, we describe a scheme for reducing the initial infinite-dimensional problem to a finite-dimensional one, which can be solved numerically by the methods of linear programming. At the end, we give an illustrative example.     

L—Fuzzy偏序集

借助L-fuzzy关系在L-fuzzy中集中引入L-fuzzy偏序,自然地有了L-fuzzy偏序集,进一步借助水平截集刻画了L-fuzzy偏序集。     

The convergence ball and error analysis of the two-step Secant method

Under the assumption that the nonlinear operator has Lipschitz continuous divided differences for the first order, we obtain an estimate of the radius of the convergence ball for the two-step secant method. Moreover, we also provide an error estimate that matches the convergence order of the two-step secant method. At last, we give an application of the proposed theorem.     

Numerical enclosure for multiple eigenvalues of an Hermitian matrix whose graph is a tree

In this paper we consider a numerical enclosure method for multiple eigenvalues of an Hermitian matrix whose graph is a tree. If an Hermitian matrix A whose graph is a tree has multiple eigenvalues, it has the property that matrices which are associated with some branches in the undirected graph of A have the same eigenvalues. By using this property and interlacing inequalities for Hermitian matrices, we show an enclosure method for multiple eigenvalues of an Hermitian matrix whose graph is a tree. Since we do not generally know whether a given matrix has exactly a multiple eigenvalue from approximate computations, we use the property of interlacing inequalities to enclose some eigenvalues including multiplicities.In this process, we only use the enclosure of simple eigenvalues to enclose a multiple eigenvalue by using a computer and interval arithmetic.