线性方程组的正解

讨论了线性方程组正解的若干性质,给出了线性方程组有正解的一个充要条件,以及由此得到的求正解的一般方法,还介绍了正解问题的若干应用.     

一类奇异次线性边值问题正解存在的充分必要条件

本文研究一类奇异次线性边值问题正解的存在性，得到Ｃ［０，１］正解和Ｃ１［０，１］正解存在的充分必要条件，也得到正解的唯一性．     

算子方程AX-XA*=B的正解与实正解

利用算子矩阵分块技巧和算子的广义逆,在A是幂等算子的情况下,给出了算子方程AX-XA＊=B有正解和有实正解的充要条件,并给出了正解和实正解的通式。     

一类边界条件中带有扰动参数的积分边值问题正解的存在性

本文研究边界条件中带有扰动参数的积分边值问题正解的存在性与不存在性及扰动参数对正解存在性的影响.利用不动点指数理论,得出边值问题至少有一个正解、两个正解以及无解的充分条件.     

一类中立型时滞差分方程的正解

研究一类中立型时滞差分方程面　　　　的正解,获得了方程存在最终正解以及非增正解的充要条件,建立了比较定理．     

非齐次线性方程组的半正解

线性方程组的不带负分量的非零解向量称为半正解.本文给出非齐次线性方程组AX= b (b≠0)的半正解结构,进而得到该类线性方程组有半正解的充分条件和必要条件以及唯一半正解的充要条件.     

一类四阶两点边值问题正解的存在性

本文应用锥上的不动点指数理论,研究四阶两点边值问题—个正解及多个正解的存在性,给出了此类问题有一个正解及多个正解存在的与其相应线性问题的第一个特征值有关的充分条件,该条件中所涉及的值是最优的.     

半线性椭圆方程正解的存在性和唯一性

本文致力于研究半线性椭圆方程正解的存在性,唯一性和非退化性;给出了保证我们所考虑的问题存在正解的一个充要条件;证明了如果某类半线性椭圆问题的正解是唯一的和非退化的,则对问题中的微分算子做小扰动后其正解也是唯一的和非退化的．作为推论,证明了正解的唯一性在区域的小扰动下是不变的．     

二阶非线性中立型时滞差分方程的正解

本文研究了一类二阶非线性中立型时滞差分方程的正解,得到了最终正解的存在性判据及存在正解的必要条件,建立了一些正解不存在性定理,所得结论推广并改进了已知的一些结果。     

非齐次线性方程组的半正解

线性方程组的不带负分量的非零解向量称为半正解本给出非齐次线性方程组Ax=B (B≠0)的半正解结构,进而得到该类线性方程组有半正解的充分条件和必要条件以及唯一半正解的充要条件。     

Realizability of words in mosaic labyrinths

In this paper we study mosaic labyrinths with the help of words generated by them in the alphabet of labels attached to arcs and vertices of a labyrinth. We consider the problem of the characterization of words generated by a labyrinth. We propose a constructive recognition criterion, it defines whether a word is generated by a labyrinth or not. We establish conditions under which a word can be generated by a unique labyrinth, by a finite number of labyrinths, or by infinitely many labyrinths.     

Well-posedness by perturbations of mixed variational inequalities in Banach spaces

In this paper, we consider an extension of the notion of well-posedness by perturbations, introduced by Zolezzi for a minimization problem, to a mixed variational inequality problem in a Banach space. We establish some metric characterizations of the well-posedness by perturbations. We also show that under suitable conditions, the well-posedness by perturbations of a mixed variational inequality problem is equivalent to the well-posedness by perturbations of a corresponding inclusion problem and a corresponding fixed point problem. Also, we derive some conditions under which the well-posedness by perturbations of a mixed variational inequality is equivalent to the existence and uniqueness of its solution.     

Proof of the Branner-Hubbard conjecture on Cantor Julia sets

By means of a nested sequence of some critical pieces constructed by Kozlovski, Shen, and van Strien, and by using a covering lemma recently proved by Kahn and Lyubich, we prove that a component of the filled-in Julia set of any polynomial is a point if and only if its forward orbit contains no periodic critical components. It follows immediately that the Julia set of a polynomial is a Cantor set if and only if each critical component of the filled-in Julia set is aperiodic. This result was a conjecture raised by Branner and Hubbard in 1992. This work was supported by the National Natural Science Foundation of China     

A NOTE ON RECURRENT SETS

ＡＮＯＴＥＯＮＲＥＣＵＲＲＥＮＴＳＥＴＳ￥ＷＥＮＺＨＩＹＩＮＧ；ＷＵＬＩＭＩＮＧ；ＺＨＯＮＧＨＯＮＧＬＩＵ（ＤｅｐａｒｔｍｅＤｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｓＷｕｈａｎ４３００７２，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅ...     

Optimal steady-state versus periodic operation in discrete systems

The problem of improving the optimal steady state of a discrete system by means of a suitable cyclic operation is discussed. Two sufficient conditions are found by negating a necessary condition and by following a frequency-domain approach, respectively. The connection between the two conditions is also shown.This work has been supported by the Consiglio Nazionale delle Ricerche, Rome, Italy.     

Stress-driven local-solution approach to quasistatic brittle delamination

A unilateral contact problem between elastic bodies at small strains glued by a brittle adhesive is addressed in the quasistatic rate-independent setting. The delamination process is modeled as governed by stresses rather than by energies. This leads to a specific scaling of an approximating elastic adhesive contact problem, discretized by a semi-implicit scheme and regularized by a BV-type gradient term. An analytical zero-dimensional example motivates the model and a specific local-solution concept. Two-dimensional numerical simulations performed on an engineering benchmark problem of debonding a fiber in an elastic matrix further illustrate the validity of the model, convergence, and algorithmical efficiency even for very rigid adhesives with high elastic moduli.     

Automation and group structures in certain economic adjustment mechanisms

It is shown that the economic adjustment mechanism developed by Hurwicz and his associates has the structure of automata. It is then shown that certain price adjustment mechanisms, having an acceptability condition, impose a group structure upon the automaton. This condition is a bilinear invariance implied by a budget constraint. Then the automaton is defined by a subgroup, depending on agents' tastes, technologies and strategies, and by the representations of the subgroup imposed by the automaton.     

The tensor Golub–Kahan–Tikhonov method applied to the solution of ill-posed problems with a t-product structure

This paper discusses an application of partial tensor Golub–Kahan bidiagonalization to the solution of large-scale linear discrete ill-posed problems based on the t-product formalism for third-order tensors proposed by Kilmer and Martin (M. E. Kilmer and C. D. Martin, Factorization strategies for third order tensors, Linear Algebra Appl., 435 (2011), pp. 641-658). The solution methods presented first reduce a given (large-scale) problem to a problem of small size by application of a few steps of tensor Golub–Kahan bidiagonalization and then regularize the reduced problem by Tikhonov's method. The regularization operator is a third-order tensor, and the data may be represented by a matrix, that is, a tensor slice, or by a general third-order tensor. A regularization parameter is determined by the discrepancy principle. This results in fully automatic solution methods that neither require a user to choose the number of bidiagonalization steps nor the regularization parameter. The methods presented extend available methods for the solution for linear discrete ill-posed problems defined by a matrix operator to linear discrete ill-posed problems defined by a third-order tensor operator. An interlacing property of singular tubes for third-order tensors is shown and applied. Several algorithms are presented. Computed examples illustrate the advantage of the tensor t-product approach, in comparison with solution methods that are based on matricization of the tensor equation.     

An Ansatz for the asymptotics of hypergeometric multisums

Sequences that are defined by multisums of hypergeometric terms with compact support occur frequently in enumeration problems of combinatorics, algebraic geometry and perturbative quantum field theory. The standard recipe to study the asymptotic expansion of such sequences is to find a recurrence satisfied by them, convert it into a differential equation satisfied by their generating series, and analyze the singularities in the complex plane. We propose a shortcut by constructing directly from the structure of the hypergeometric term a finite set, for which we conjecture (and in some cases prove) that it contains all the singularities of the generating series. Our construction of this finite set is given by the solution set of a balanced system of polynomial equations of a rather special form, reminiscent of the Bethe ansatz. The finite set can also be identified with the set of critical values of a potential function, as well as with the evaluation of elements of an additive K-theory group by a regulator function. We give a proof of our conjecture in some special cases, and we illustrate our results with numerous examples.     

A kinetic decomposition for singular limits of non-local conservation laws

We consider a non-local regularization of nonlinear hyperbolic conservation laws in several space variables. The regularization is motivated by the theory of phase dynamics and is based on a convolution operator. We formulate the initial value problem and begin by deriving a priori estimates which are independent of the regularization parameter. Following Hwang and Tzavaras we establish a kinetic decomposition associated with the problem under consideration, and we conclude that the sequence of solutions generated by the non-local model converges to a weak solution of the corresponding hyperbolic problem. Depending on the scaling introduced in the non-local dispersive term, this weak limit is either a classical Kruzkov solution satisfying all entropy inequalities or, more interestingly, a nonclassical entropy solution in the sense defined by LeFloch, that is, a weak solution satisfying a single entropy inequality and containing undercompressive shock waves possibly selected by a kinetic relation. Finally, we illustrate our analytical conclusions with numerical experiments in one spatial variable.