Reflexive solution to a system of matrix equations

We derive necessary and sufficient conditions for the existence and an expression of the （anti）reflexive solution with respect to the nontrivial generalized reflection matrix P to the system of complex matrix equations AX = B and XC = D. The explicit solutions of the approximation problem min x∈Ф ｜｜X - E｜｜F was given, where E is a given complex matrix and Ф is the set of all reflexive （or antireflexive） solutions of the system mentioned above, and ｜｜·｜｜ is the Frobenius norm. Furthermore, it was pointed that some results in a recent paper are special cases of this paper.

On Edge Irregular Reflexive Labeling of Categorical Product of Two Paths

Among the huge diversity of ideas that show up while studying graph theory,one that has obtained a lot of popularity is the concept of labelings of graphs.Graph labelings give valuable mathematical models for a wide scope of applications in high technologies(cryptography,astronomy,data security,various coding theory problems,communication networks,etc.).A labeling or a valuation of a graph is any mapping that sends a certain set of graph elements to a certain set of numbers subject to certain conditions.Graph labeling is a mapping of elements of the graph,i.e.,vertex and for edges to a set of numbers(usually positive integers),called labels.If the domain is the vertex-set or the edge-set,the labelings are called vertex labelings or edge labelings respectively.Similarly,if the domain is V(G)[E(G)],then the labeling is called total labeling.A reflexive edge irregular k-labeling of graph introduced by Tanna et al.:A total labeling of graph such that for any two different edges ab and a'b'of the graph their weights has wt_(x)(ab)=x(a)+x(ab)+x(b) and wt_(x)(a'b')=x(a')+x(a'b')+x(b') are distinct.The smallest value of k for which such labeling exist is called the reflexive edge strength of the graph and is denoted by res(G).In this paper we have found the exact value of the reflexive edge irregularity strength of the categorical product of two paths (P_(a)×P_(b))for any choice of a≥3 and b≥3.

用Reflexive ACL实现网络单向访问

通过建立路由器访问控制列表,可以控制任何IP地址对网络的访问,但要实现网络的单向访问,一般的访问列表是无法做到的。本文从实际应用的角度出发,利用一种特殊的ACL-ReflexiveACL,即自反访问控制列表,来实现网络的单向访问,并分析、阐述了它的配置过程。

Nilpotent Elements and Nil-Reflexive Property of Generalized Power Series Rings

Let R be a ring and (S,≤) a strictly ordered monoid. In this paper, we deal with a new approach to reflexive property for rings by using nilpotent elements, in this direction we introduce the notions of generalized power series reflexive and nil generalized power series reflexive, respectively. We obtain various necessary or sufficient conditions for a ring to be generalized power series reflexive and nil generalized power series reflexive. Examples are given to show that, nil generalized power series reflexive need not be generalized power series reflexive and vice versa, and nil generalized power series reflexive but not semicommutative are presented. We proved that, if R is a left APP-ring, then R is generalized power series reflexive, and R is nil generalized power series reflexive if and only if R/I is nil generalized power series reflexive. Moreover, we investigate ring extensions which have roles in ring theory.

THE GENERALIZED REFLEXIVE SOLUTION FOR A CLASS OF MATRIX EQUATIONS (AX-B,XC=D)

In this article, the generalized reflexive solution of matrix equations （AX = B, XC = D） is considered. With special properties of generalized reflexive matrices, the necessary and sufficient conditions for the solvability and the general expression of the solution are obtained. Moreover, the related optimal approximation problem to a given matrix over the solution set is solved.

“反思社会学”,还是“反身社会学”--Reflexive Sociology汉译探析

对布迪厄思想关键词reflexive sociology,现至少有"反思社会学""反思性社会学""反观社会学""反身社会学""反身性社会学"等五种译法。鉴于"反思社会学"之"反思"混淆了reflexive和reflective,前者尚可译为"反身",后者除了"反思"再无词可译。使用"反思社会学"无异于让reflexive抢了reflective的地盘,而reflective在布迪厄著作中同样常见。reflexive本义即为"反身",且布迪厄赋予实践突出的意义,而实践仰仗行动者的身体。在汉语中,"身"有"我自己""你自己""他自己"之意,如"反求诸身";又有实践的意蕴,如"身体力行"。故建议使用"反身社会学"翻译reflexive sociology。

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

Approximate controllability of infinite dimensional linear systems in nonreflexive state spaces

This paper deals with the problem of approximate controllability of infinite dimensional linear systems in nonreflexive state spaces. A necessary and sufficient condition for approximate controllability via L^p（[0, T], U）, 1≤p〈∞ is obtained,where L^p（ [0, T], U） is the control function space.

Bilevel generalized mixed equilibrium problems involving generalized mixed variational-like inequality problems in reflexive Banach spaces

A new bilevel generalized mixed equilibrium problem （BGMEP） involving generalized mixed variational-like inequality problems （GMVLIPs） is introduced and studied in the reflexive Banach spaces. First, an auxiliary generalized mixed equilibrium problem （AGMEP） is introduced to compute the approximate solutions of the BGMEP involving the GMVLIPs. By using a minimax inequality, the existence and the unique- ness of solutions of the AGMEP are proved under mild conditions without any coercive assumptions. By using an auxiliary principle technique, the new iterative algorithms are proposed and analyzed, with which the approximate solutions of the BGMEP are computed. The strong convergence of the iterative sequence generated by the algorithms is shown under mild conditions without any coercive assumptions. These new results can generalize some recent results in this field.

Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces

A new system of generalized mixed equilibrium problems （SGMEPs） involving generalized mixed variational-like inequality problems is introduced and studied in reflexive Banach spaces. A system of auxiliary generalized mixed equilibrium problems （SAGMEPs） for solving the SGMEPs is first introduced. Existence and uniqueness of the solutions to the SAGMEPs is proved under quite mild assumptions without any coercive conditions in reflexive Banach spaces. Using the auxiliary principle technique, a new iterative algorithm for solving the SGMEPs is proposed and analyzed. Strong convergence of the iterative sequences generated by the algorithm is also proved under quite mild assumptions without any coercive conditions. These results improve, unify, and generalize some recent results in this field.

Note on Reflexive Algebras with Non-distribut iveInvariant Lattices

In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.

The Reflexive Solutions of the Matrix Equations (AX,XB^H )= (C,D^H )

The matrix equations (AX, XBH)=(C, DH) have been widely used in structural design, parameter identification, linear optimal control, and so on. But few researches studied the reflexive solutions. A new approach for the reflexive solutions to the matrix equations was proposed. By applying the canonical correlation decomposition (CCD) of matrix pairs, the necessary and sufficient conditions for the existence and the general expression for the reflexive solutions of the matrix equations (AX, XBH)=(C, DH) were established. In addition, by using the methods of space decomposition, the expression of the optimal approximation solution to a given matrix was derived.

Block Decompositions and Applications of Generalized Reflexive Matrices

Generalize reflexive matrices are a special class of matrices ?that have the relation where? and ?are some generalized reflection matrices. The nontrivial cases ( or ) of this class of matrices occur very often in many scientific and engineering applications. They are also a generalization of centrosymmetric matrices and reflexive matrices. The main purpose of this paper is to present block decomposition schemes for generalized reflexive matrices of various types and to obtain their decomposed explicit block-diagonal structures. The decompositions make use of unitary equivalence transformations and, therefore, preserve the singular values of the matrices. They lead to more efficient sequential computations and at the same time induce large-grain parallelism as a by-product, making themselves computationally attractive for large-scale applications. A numerical example is employed to show the usefulness of the developed explicit decompositions for decoupling linear least-square problems whose coefficient matrices are of this class into smaller and independent subproblems.

Feedback Systems on a Reflexive Banach Space—Linearization

The aim of our work is to formulate and demonstrate the results of the normality, the Lipschitz continuity, of a nonlinear feedback system described by the monotone maximal operators and hemicontinuous, defined on real reflexive Banach spaces, as well as the approximation in a neighborhood of zero, of solutions of a feedback system [A,B] assumed to be non-linear, by solutions of another linear, This approximation allows us to obtain appropriate estimates of the solutions. These estimates have a significant effect on the study of the robust stability and sensitivity of such a system see [1] [2] [3]. We then consider a linear FS , and prove that, if ; , with the respective solutions of FS’s [A,B] and corresponding to the given (u,v) in . There exists,, positive real constants such that, . These results are the subject of theorems 3.1, ... , 3.3. The proofs of these theorems are based on our lemmas 3.2, ... , 3.5, devoted according to the hypotheses on A and B, to the existence of the inverse of the operator I+BA and . The results obtained and demonstrated along this document, present an extension in general Banach space of those in [4] on a Hilbert space H and those in [5] on a extended Hilbert space .

Applicationof Transferin Chinese Students' Learningon Reflexive Pronouns

The thesis is designed to investigate what the Chinese reflexive transfer is and how it works on the basis of behaviorism.Through the analysis of binding theory, mismatches between Chinese reflexive and English reflexive would be discussed in two main aspects, namely, long-distance binding and subject orientation. To test and support the argument, more sufficient teaching data would be processed from questionnaire. At the end of the analysis, it is supposed to put forward suggestions for teaching English reflexive to Chinese students.

The Short Local Algebras of Dimension 6 with Non-projective Reflexive Modules

Let A be a finite-dimensional local algebra over an algebraically closed field,let J be the radical of A.The modules we are interested in are the finitely generated left A-modules.Projectivemodules are always reflexive,and an algebra is self-injective iff allmodules are reflexive.We discuss the existence of non-projective reflexive modules in case A is not self-injective.We assume that A is short(this means that J^(3)=0).In a joint paper with Zhang Pu,it has been shown that 6 is the smallest possible dimension of A that can occur and that in this case the following conditions have to be satisfied:J^(2)is both the left socle and the right socle of A and there is no uniform ideal of length 3.The present paper is devoted to showing the converse.

Least-Squares Solution of Inverse Problem for Hermitian Anti-reflexive Matrices and Its Appoximation

In this paper, we first consider the least-squares solution of the matrix inverse problem as follows： Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X, B we have minA ｜｜AX - B｜｜. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by SE. Then the matrix nearness problem for the matrix inverse problem is discussed. That is： Given an arbitrary A^＊, find a matrix A E SE which is nearest to A^＊ in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.

Some Equivalent Conditions for Block Independence of Reflexive Inner Inverse of Block Matrix

The definition of block independence in generalized inverse of block matrix was introduced in [1]. In this paper, we give some equivalent conditions for two m × n matrices being block independent in reflexive inner inverse .

Least-Squares Solutions of Matrix Equations(AX = B,XC = D) for Hermitian Reflexive (Anti-Hermitian Reflexive) Matrices and Its Approximation

In this paper,the Hermitian reflexive（Anti-Hermitian reflexive）least-squares so-lutions of matrix equations（AX = B,XC = D）are considered.With special properties of partitioned matrices and Hermitian reflexive（Anti-Hermitian reflexive）matrices,the general expression of the solution is obtained.Moreover,the related optimal approximation problem to a given matrix over the solution set is considered.