The generalized solution of ill-posed boundary problem

In this paper, we define a kind of new Sobolev spaces, the relative Sobolev spaces Wk,p0(Ω,∑). Then an elliptic partial differential equation of the second order with an ill-posed boundary is discussed. By utilizing the ideal of the generalized inverse of an operator, we introduce the generalized solution of the ill-posed boundary problem. Eventually, the connection between the generalized inverse and the generalized solution is studied. In this way, the non-instability of the minimal normal least square solution of the ill-posed boundary problem is avoided.     

Verified Computation of Eigenpairs in the Generalized Eigenvalue Problem for Nonsquare Matrix Pencils

Consider an optimization problem arising from the generalized eigenvalue problem Ax=λBx,where A,B∈Cm×n and m>n.Ito et al.showed that the optimization problem can be solved by utilizing right singular vectors of C:=[B,A].In this paper,we focus on computing intervals containing the solution.When some singular values of C are multiple or nearly multiple,we can enclose bases of corresponding invariant subspaces of CHC,where CH denotes the conjugate transpose of C,but cannot enclose the corresponding right singular vectors.The purpose of this paper is to prove that the solution can be obtained even when we utilize the bases instead of the right singular vectors.Based on the proved result,we propose an algorithm for computing the intervals.Numerical results show property of the algorithm.     

Least-Squares Solutions of the Equation AX=B Over Anti-Hermitian Generalized Hamiltonian Matrices

Upon using the denotative theorem of anti-Hermitian generalized Hamiltonian matrices,we solve effectively the least-squares problem min‖AX-B‖over anti-Hermitian generalized Hamiltonian matrices.We derive some necessary and sufficient conditions for solvability of the problem and an expression for general solution of the matrix equation AX=B.In addition,we also obtain the expression for the solution of a relevant optimal approximate problem.     

DEGENERATE ELLIPTIC SYSTEMS OF CLASS Ⅰ

In this paper, we considered the first class (class Ⅰ) of elliptic systems of partial differential equations with a special kind of lower-order terms which are one-order singular. For the classical well-posedness of Dirichlet problem and skew derivative problem in the unit circle, we gave a discussion in full detail, and obtained complete results.     

ON GENERALIZED BUFFON NEEDLE PROBLEM FOR LATTICES

Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article , using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l < a.     

Growth and Approximation of Generalized Bi-Axially Symmetric Potentials

The paper deals with growth estimates and approximation (not necessarily entire) of solutions of certain elliptic partial differential equations. These solutions are called generalized bi-axially symmetric potentials (GBASP's). To obtain more refined measure of growth, we have defined $q$-proximate order and obtained the characterization of generalized $q$-type and generalized lower $q$-type with respect to $q$-proximate order of a GBASP in terms of approximation errors and ratio of these errors in sup norm.     

关于Wrpp半群上的Lawson偏序(英文)

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.     

一类非线性双曲型方程解的不存在性

In this paper,we prove the existence and uniqueness of the local generalized solution of the Cauchy problem for a class of nonlinear hyperbolic equation of higher order are proved.Moreover,we give the sufficient conditions for blow-up of the solution of the problem in finite time will be given.     

The Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains

The present paper deals with Tricomi and Frankl problems for generalized Chaplygin equations in multiply connected domains. We first give the representation of solutions of the Tricomi problem for the equations, and then prove the uniqueness and existence of solutions for the problem by a new method, i.e. the complex functions in the elliptic domain and the hyperbolic complex functions in hyperbolic domain are used. Finally we discuss the Frankl problem for generalized Chaplygin equations in multiply connected domains.     

Optimality Conditions for Minimax Optimization Problems with an Infinite Number of Constraints and Related Applications

This paper is concerned with the study of optimality conditions for minimax optimization problems with an infinite number of constraints,denoted by(MMOP).More precisely,we first establish necessary conditions for optimal solutions to the problem(MMOP)by means of employing some advanced tools of variational analysis and generalized differentiation.Then,sufficient conditions for the existence of such solutions to the problem(MMOP)are investigated with the help of generalized convexity functions defined in terms of the limiting subdifferential of locally Lipschitz functions.Finally,some of the obtained results are applied to formulating optimality conditions for weakly efficient solutions to a related multiobjective optimization problem with an infinite number of constraints,and a necessary optimality condition for a quasiε-solution to problem(MMOP).     

Partial linearization for generalized fractional programming

An algorithm based on partial linearization is proposed to deal with generalized fractional programs. This algorithm is shown to be equivalent to the so called generalized Dinkelbach's algorithm applying to this problem. Hence we have another setting for this last algorithm.This research was supported by NSERC (grant A8312) and FCAR (grant 0899).     

Generalized PP and Zip Subrings of Matrix Rings

Let R be an abelian ring. We consider a special subring An, relative to α2,…, αn∈ REnd（R）, of the matrix ring Mn（R） over a ring R. It is shown that the ring An is a generalized right PP-ring （right zip ring） if and only if the ring R is a generalized right PP-ring （right zip ring）. Our results yield more examples of generalized right PP-rings and right ziu rings.     

Generic automorphisms of the universal partial order

We show that the countable universal-homogeneous partial order has a generic automorphism as defined by the second author, namely that it lies in a comeagre conjugacy class of Aut. For this purpose, we work with `determined' partial finite automorphisms that need not be automorphisms of finite substructures (as in the proofs of similar results for other countable homogeneous structures) but are nevertheless sufficient to characterize the isomorphism type of the union of their orbits.

     

Left and right generalized Drazin invertible operators

In this paper, we define and study the left and the right generalized Drazin inverse of bounded operators in a Banach space. We show that the left (resp. the right) generalized Drazin inverse is a sum of a left invertible (resp. a right invertible) operator and a quasi-nilpotent one. In particular, we define the left and the right generalized Drazin spectra of a bounded operator and also show that these sets are compact in the complex plane and invariant under additive commuting quasi-nilpotent perturbations. Furthermore, we prove that a bounded operator is left generalized Drazin invertible if and only if its adjoint is right generalized Drazin invertible. An equivalent definition of the pseudo-Fredholm operators in terms of the left generalized Drazin invertible operators is also given. Our obtained results are used to investigate some relationships between the left and right generalized Drazin spectra and other spectra founded in Fredholm theory.     

Isomorphism problems and groups of automorphisms for generalized Weyl algebras

We present solutions to isomorphism problems for various generalized Weyl algebras, including deformations of type-A Kleinian singularities and the algebras similar to introduced by S. P. Smith. For the former, we generalize results of Dixmier on the first Weyl algebra and the minimal primitive factors of by finding sets of generators for the group of automorphisms.

     

Slender partial quadrangles and their automorphisms

The partial quadrangle PQ(s, t, μ) is an incidence system consisting of points and lines in which every line contains s + 1 points, every point sits on t + 1 lines (two lines meet in at most one point), and the meet of the neighborhoods of any two non-adjacent points in the collinearity graph is a μ-coclique. We provide a classification for partial quadrangles PQ(s, t, μ) with t ⩽ 6, and study into their automorphisms. Supported by RFBR grant No. 05-01-00046 and by RFBR-NSFC grant No. 05-01-39000. __________ Translated from Algebra i Logika, Vol. 45, No. 5, pp. 603–619, September–October, 2006.     

三角矩阵代数的自同构

本文研究了三角代数的自同构.利用三角代数的基本概念及自同构定义,得到三角代数的自同构形式,并刻画了其内自同构的具体形式.     

On a Generalized Finite Intersection Property

We continue the study of the right finite intersection property under a weaker condition on annihilators, introducing the concept of generalized right finite intersection property (simply, generalized right FIP). We observe the structure of rings with the generalized right FIP and examine the generalized right FIP for various kinds of basic extensions of rings with the property. We show that the generalized right FIP does not go up to polynomial rings, and that the 2-by-2 full matrix ring over a domain has the generalized right FIP. In the process, we also obtain an equivalent condition for which a nonzero polynomial, over the ring of integers modulo n ≥ 2, is a non-zero-divisor.     

X-Inner Automorphisms,Automorphisms, and Isomorphisms of Skew Polynomial Rings

Abstract

In this paper, we examine the X-inner automorphisms, automorphisms, and isomorphisms of skew polynomial rings of the form K[x][y;δ], where K is a field of characteristic 0 and δ is a derivation of K [x] such that x ^δ is a polynomial of degree ≥ 1. We 1.  determine the group of X-inner automorphisms of K [x][ y;δ],

2.  analyze the structure of the group of automorphisms of K [x][ y;δ], and

3.  examine the isomorphism classes of skew polynomial rings of the form K [x][ y;δ].

We also provide several examples which indicate the importance of the base field in computing the X-inner automorphisms, automorphisms, and isomorphism classes of K [x][ y;δ].