PERIODIC SOLUTIONS AND ALMOST PERIODIC SOLUTIONS OF NONLINEAR INTEGRAL EQUATIONS

ＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳＡＮＤＡＬＭＯＳＴＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＳ　ＯＦ　ＮＯＮＬＩＮＥＡＲ　ＩＮＴＥＧＲＡＬＥＱＵＡＴＩＯＮＳＭｕｈａｍｍａｄＮ．Ｉｓｌａｍ＆ＹａｗｖｉＡ．Ｆｉａｇｂｅｄｚｉ（ＫｉｎｇＦａｈｄＵｎｉｖｅｒｓｉｔｙ...     

SOME TOPOLOGICAL PROPERTIES ABOUT ALMOST PERIODIC DIFFERENTIAL EQUATIONS AND ALMOST PERIODIC SOLUTIONS

ＳＯＭＥ　ＴＯＰＯＬＯＧＩＣＡＬ　ＰＲＯＰＥＲＴＩＥＳ　ＡＢＯＵＴ　ＡＬＭＯＳＴ　ＰＥＲＩＯＤＩＣ　ＤＩＦＦＥＲＥＮＴＩＡＬ　ＥＱＵＡＴＩＯＮＳ　ＡＮＤ　ＡＬＭＯＳＴ　ＰＥＲＩＯＤＩＣ　ＳＯＬＵＴＩＯＮＳＺｈａｎｇＪｉａｎｆｅｎｇ（张剑峰）（Ｆｕｚｈ...     

UNIQUENESS AND ITERATIVE METHOD OF POSITIVE RADIALLY SYMMETRIC SOLUTIONS FOR SINGULAR ELLIPTIC EQUATIONS

ＵＮＩＱＵＥＮＥＳＳＡＮＤＩＴＥＲＡＴＩＶＥＭＥＴＨＯＤＯＦＰＯＳＩＴＩＶＥＲＡＤＩＡＬＬＹＳＹＭＭＥＴＲＩＣＳＯＬＵＴＩＯＮＳＦＯＲＳＩＮＧＵＬＡＲＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＺｈａｏＺｅｎｇｑｉｎ（赵增勤）（ＱｕｆｕＮｏｒｍａｌＵｎｉｖｅ...     

A NOTE ON REGULARITY AND EXISTENCE OF SOLUTIONS FOR A CLASS OF NON－UNIFORMLY DEGENERATE ELLIPTIC EQUATIONS

ＡＮＯＴＥＯＮＲＥＧＵＬＡＲＩＴＹＡＮＤＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＮＯＮ－ＵＮＩＦＯＲＭＬＹＤＥＧＥＮＥＲＡＴＥＥＬＬＩＰＴＩＣＥＱＵＡＴＩＯＮＳ￥ＬＩＪＵＮＪＩＥ（Ｄｅｐｔ．ｏｆＭａｔｈ．，ＺｈｅｊｉａｎｇＵｎｉ...     

MAJOR－EFFICIENT SOLUTIONS AND WEAKLY MAJOR－EFFICIENT SOLUTIONS OF MULTIOBJECTIVE PROGRAMMING

ＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＡＮＤＷＥＡＫＬＹＭＡＪＯＲ－ＥＦＦＩＣＩＥＮＴＳＯＬＵＴＩＯＮＳＯＦＭＵＬＴＩＯＢＪＥＣＴＩＶＥＰＲＯＧＲＡＭＭＩＮＧ￥ＨＵＹＵＤＡ（Ｄｅｐｔ．ｏｆＡｐｐｌ．Ｍａｔｈ．，ＳｈａｎｇｈａｉＪｉａｏＴｏｎ...     

A NECESSARY AND SUFFICIENT CONDITION OF EXISTENCE OF GLOBAL SOLUTIONS FOR SOME NONLINEAR HYPERBOLIC EQUATIONS

ＡＮＥＣＥＳＳＡＲＹＡＮＤＳＵＦＦＩＣＩＥＮＴＣＯＮＤＩＴＩＯＮＯＦＥＸＩＳＴＥＮＣＥＯＦＧＬＯＢＡＬＳＯＬＵＴＩＯＮＳＦＯＲＳＯＭＥＮＯＮＬＩＮＥＡＲＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳ￥ＺＨＡＮＧＱＵＡＮＤＥ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅ...     

ON THE UPPER ESTIMATES OF FUNDAMENTAL SOLUTIONS OF PARABOLIC EQUATIONS ON RIEMANNIAN MANIFOLDS

ＯＮＴＨＥＵＰＰＥＲＥＳＴＩＭＡＴＥＳＯＦＦＵＮＤＡＭＥＮＴＡＬＳＯＬＵＴＩＯＮＳＯＦＰＡＲＡＢＯＬＩＣＥＱＵＡＴＩＯＮＳＯＮＲＩＥＭＡＮＮＩＡＮＭＡＮＩＦＯＬＤＳ￥ＬＩＪＩＡＹＵ；ＳＨＡＯＸＩＮ（ＤｅｐａｒｔｍｅｌｌｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ａ...     

SOME DYNAMICAL PROPERTIESOF QUADRATIC RATIONAL MAPS

ＳＯＭＥ　ＤＹＮＡＭＩＣＡＬ　ＰＲＯＰＥＲＴＩＥＳ　ＯＦ　ＱＵＡＤＲＡＴＩＣ　ＲＡＴＩＯＮＡＬ　ＭＡＰＳＳＯＭＥＤＹＮＡＭＩＣＡＬＰＲＯＰＥＲＴＩＥＳＯＦＱＵＡＤＲＡＴＩＣＲＡＴＩＯＮＡＬＭＡＰＳ￥ＹＩＮＹＯＮＧＣＨＥＮＧ（ＣｅｌｌｔｒｅｆｏｒＭａｔ...     

A CHARACTERIZATION OF THE SOLUTIONS OF p－ORDER FEIGENBAUM＇S FUNCTIONAL EQUATION WITH TOPOLOGICAL ENTROPY 0

ＡＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦｐ－ＯＲＤＥＲＦＥＩＧＥＮＢＡＵＭ＇ＳＦＵＮＣＴＩＯＮＡＬＥＱＵＡＴＩＯＮＷＩＴＨＴＯＰＯＬＯＧＩＣＡＬＥＮＴＲＯＰＹ０（廖公夫）￥ＬｉａｏＧｏｎｇｆｕ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｊｉ...     

LARGE－TIME BEHMIOR OF SOLUTIONS FOR THE SYSTEM OF COMPRESSIBLE ADIABATIC FLOW THROUGHPOROUS MEDIA

ＬＡＲＧＥ－ＴＩＭＥＢＥＨＭＩＯＲＯＦＳＯＬＵＴＩＯＮＳＦＯＲＴＨＥＳＹＳＴＥＭＯＦＣＯＭＰＲＥＳＳＩＢＬＥＡＤＩＡＢＡＴＩＣＦＬＯＷＴＨＲＯＵＧＨＰＯＲＯＵＳＭＥＤＩＡ￥ＸＩＡＯＬＩＮＧ（Ｌ．ＨＳＩＡＯ）Ｄ．ＳＥＲＲＥ（ＩｎｓｔｉｔｕｔｅｏｆＭａｔ...     

The best Euclidian fit to a given distance matrix in prescribed dimensions

In this paper we determine the Euclidean distance matrix which is closest to a given (not necessarily Euclidian) one. We admit a wide class of appropriate matrix norms as measures of closeness. Majorization results on sums of eigenvalues of symmetric matrices serve as basic tools.     

On the least squares fit by radial functions to multidimensional scattered data

Summary This paper investigates some aspects of discrete least squares approximation by translates of certain classes of radial functions. Its specific aims are (i) to provide conditions under which the associated least squares matrix is invertible and (ii) to give upper bounds for the Euclidean norms of the inverses of these matrices (when they exist).The second named author was supported by the National Science Foundation under grant number DMS-8901345     

Block scaling with optimal Euclidean condition

Let $\text{M}$ denote the set of all complex n×n matrices whose columns span certain given linear subspaces. The minimal Euclidean condition number of matrices in $\text{M}$ is given in terms of the canonical angles between the linear subspaces, and optimal matrices in $\text{M}$ are described. The result is also stated in terms of norms of certain projections.     

高维有限元空间中的谱基

高维有限元空间中的谱基施锡泉（大连理工大学数学科学研究所）ＡＣＯＮＳＴＲＵＣＴＩＶＥＭＥＴＨＯＤＯＦＨＩＧＨ－ＤＩＭＥＮＳＩＯＮＡＬＨＩＥＲＡＲＣＨＩＣＡＬＢＡＳＩＳ￥ＳｈｉＸｉ－ｑｕａｎ（Ｉｎｓｔ．ｏｆＭａｔｈ．，ＤａｌｉａｎＵｎｉｖｅｒｓｉｔｙｏ...     

An estimate of the weak invariance defect of sets with piecewise smooth boundary

Many applied problems reduce to the general geometric problem of finding a point of a linear manifold in a finite-dimensional space that is closest to the origin. There are many specific formulations of this problem, including the search for octahedral and Euclidean projections, i.e., vectors of a linear manifold with smallest octahedral and Euclidean norms. We consider the properties of solutions to the problem of finding points of linear manifolds that are closest to the origin and relations between these solutions under various specifications of the problem. In particular, we study the properties of octahedral and Euclidean projections and analyze the influence on these projections of variation of weight coefficients in the norms.     

塑性极限分析的不可微模型及其光滑化算法

藉助于凸规划的Lagrange对偶理论,建立了Mises屈服条件下理想刚塑性材料Hill最大塑性功原理的对偶问题,并据此建立了极限分析的一个不可微凸规划模型．该模型不仅避免了对屈服条件的线性化,而且其离散化形式为线性约束下Euclid模之和的极小化问题．针对Euclid模的不可微性,提出理想刚塑性体极限分析的一种光滑化算法．通过计算平面应力和平面应变问题的极限荷载因子和相应的坍塌机构,验证了算法的有效性．     

Strict double diagonal dominance in Euclidean Jordan algebras

In the first part of the paper, we deal with Euclidean Jordan algebraic generalizations of some results of Brualdi on inclusion regions for the eigenvalues of complex matrices using directed graphs. As a consequence, the theorems of Brauer–Ostrowski and Brauer on the location of eigenvalues are extended to the setting of Euclidean Jordan algebras. In the second part, motivated by the work of Li and Tsatsomeros on the class of doubly diagonally dominant matrices with complex entries and its subclasses, we present some inter-relations between the H-property, generalized strict diagonal dominance, invertibility, and strict double diagonal dominance in Euclidean Jordan algebras. In addition, we show that in a Euclidean Jordan algebra, the Schur complements of a strictly doubly diagonally dominant element inherit this property.     

Products of idempotent matrices over integral domains

We say that a ring R has the idempotent matrices property if every square singular matrix over R is a product of idempotent matrices. It is known that every field, and more generally, every Euclidean domain has the idempotent matrices property. In this paper we show that not every integral domain has the idempotent matrices property and that if a projective free ring has the idempotent matrices property then it must be a Bezout domain. We also show that a principal ideal domain has the idempotent matrices property if and only if every fraction a/b with b≠0 has a finite continued fraction expansion. New proofs are also provided for the results that every field and every Euclidean domain have the idempotent matrices property.     

Theoretical justification of interior point algorithms for solving optimization problems with nonlinear constraints

A family of interior point algorithms is considered. These algorithms can be used for solving mathematical programming problems with nonlinear inequality constraints. Some weighted Euclidean norms are applied to finding a descent direction for improving the solution. These norms vary with iterations. A theoretical justification of the algorithms with some assumptions (including the nonsingularity of the problem) is presented.     

The euclidean distance degree of orthogonally invariant matrix varieties

The Euclidean distance degree of a real variety is an important invariant arising in distance minimization problems. We show that the Euclidean distance degree of an orthogonally invariant matrix variety equals the Euclidean distance degree of its restriction to diagonal matrices. We illustrate how this result can greatly simplify calculations in concrete circumstances.