On generalized inverse transversals

Let S be a regular semigroup, S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S, if V（x）∩S°≠Ф. In this paper, some properties of this kind of semigroups are discussed. In particular, a construction theorem is obtained which contains some recent results in the literature as its special cases.     

The weak asymptotic equivalence and the generalized inverse

In this paper, we discuss the relationship between the weak asymptotic equivalence relation and the generalized inverse in the class \({\mathcal{A}} \) of all nondecreasing and unbounded functions, defined and positive on a half-axis [a,+∞) (a > 0). In the main theorem, we prove a proper characterization of the functional class \({{ORV} \cap \mathcal{A}} \), where ORV is the class of all \({\mathcal{O}} \)-regularly varying functions (in the sense of Karamata).     

A generalized inverse method for asymptotic linear programming

Consider a linear program in which the entries of the coefficient matrix vary linearly with time. To study the behavior of optimal solutions as time goes to infinity, it is convenient to express the inverse of the basis matrix as a series expansion of powers of the time parameter. We show that an algorithm of Wilkinson (1982) for solving singular differential equations can be used to obtain such an expansion efficiently. The resolvent expansions of dynamic programming are a special case of this method.     

Some asymptotic relations for the generalized inverse

In this paper we investigate the connection between the asymptotic relations of subordination and the negligence with the generalized inverse function in the class of all nondecreasing and unbounded functions, which are defined on a half-axis [a,+∞)(a>0). In the main theorems we prove a characterization of all nondecreasing, unbounded slowly varying functions.     

具有广义分解态射的加权Moore-Penrose逆

研究范畴中态射的加权Moore-Penrose逆,利用态射广义分解的性质给出了态射加权Moore-Penrose逆存在的一些充要条件,导出了态射的加权Moore-Penrose逆的表达式,推广了态射Moore-Penrose逆的相应结果.     

Proper asymptotic unitary equivalence in KK-theory and projection lifting from the corona algebra

In this paper we generalize the notion of essential codimension of Brown, Douglas, and Fillmore using KK-theory and prove a result which asserts that there is a unitary of the form ‘identity + compact’ which gives the unitary equivalence of two projections if the ‘essential codimension’ of two projections vanishes for certain C^∗-algebras employing the proper asymptotic unitary equivalence of KK-theory found by M. Dadarlat and S. Eilers. We also apply our result to study the projections in the corona algebra of C(X)⊗B where X is [0,1], (−∞,∞), [0,∞), and [0,1]/{0,1}.     

On sparse reflexive generalized inverse

We study sparse generalized inverses $H$ of a rank-$r$ real matrix $A$. We give a construction for reflexive generalized inverses having at most $r^2$ nonzeros. For $r=1$ and for $r=2$ with $A$ nonnegative, we demonstrate how to minimize the (vector) 1-norm over reflexive generalized inverses. For general $r$, we efficiently find reflexive generalized inverses with 1-norm within approximately a factor of $r^2$ of the minimum 1-norm generalized inverse.     

Co-elementary equivalence, co-elementary maps, and generalized arcs

By a generalized arc we mean a continuum with exactly two non-separating points; an arc is a metrizable generalized arc. It is well known that any two arcs are homeomorphic (to the real closed unit interval); we show that any two generalized arcs are co-elementarily equivalent, and that co-elementary images of generalized arcs are generalized arcs. We also show that if is a function between compacta and if is an arc, then is a co-elementary map if and only if is an arc and is a monotone continuous surjection.

     

关于正则态射的广义Moore-Penrose逆

通过态射的正则性,讨论加法范畴中态射的广义Moore-Penrose逆.给出了正则态射的广义Moore-Penrose逆存在的几个充要条件以及广义Moore-Penrose逆的表达式.     

矩阵广义逆新的扰动上界

利用矩阵的奇异值分解方法,研究了矩阵广义逆的扰动上界,得到了在F-范数下矩阵广义逆的扰动上界定理,所得定理推广并彻底改进了近期的相关结果.相应的数值算例验证了定理的有效性.     

关于周期对称三对角矩阵的广义特征值反问题

在给定部分特征值、部分特征向量及附加条件下提出了一类反问题,并给出了此问题解存在性的证明及求解的算法.     

On asymptotic equivalence of perturbed linear systems of differential and difference equations

Standard results on asymptotic integration of systems of linear differential equations give sufficient conditions which imply that a system is strongly asymptotically equivalent to its principal diagonal part. These involve certain dichotomy conditions on the diagonal part as well as growth conditions on the off-diagonal perturbation terms. Here, we study perturbations with a triangularly-induced structure and see that growth conditions can be substantially weakened. In addition, we give results for not necessarily triangular perturbations which in some sense “interpolate” between the classical theorems of Levinson and Hartman-Wintner. Some analogous results for systems of linear difference equations are also given.     

Note on the iterative methods for computing the generalized inverse over Banach spaces

In this paper, we construct iterative methods for computing the generalized inverse A over Banach spaces, and also for computing the generalized Drazin inverses a^d of Banach algebra element a. Moreover, we estimate the error bounds of the iterative methods for approximating A or a^d. Copyright © 2011 John Wiley & Sons, Ltd.     

The weak and strong asymptotic equivalence relations and the generalized inverse<Superscript>*</Superscript>

We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class A \mathcal {A} of all nondecreasing unbounded positive functions on a half-axis [a,+∞) (a > 0). As a main result, we prove a proper characterization of the functional class R _∞ ∩ A \mathcal {A} , where R _∞ is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI ^* ∩ A \mathcal {A} .     

Blowup and decay behavior of solutions to the generalized Boussinesq‐type equation with strong damping

In this paper, we study the Cauchy problem for the generalized Boussinesq‐type equation with strong damping. By defining a suitable solution space with time‐weighted norms and under smallness condition on the initial data, we establish the global existence and decay property of the solutions. Under certain conditions on the initial data, we also provide blowup of the solutions.     

A topological equivalence result for a family of nonlinear difference systems having generalized exponential dichotomy

We obtain sufficient conditions ensuring the topological and strong topological equivalence of two perturbed difference systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a strongly and Hölder topological equivalence.     

求鳞状因子循环矩阵的逆阵及广义逆阵的快速付氏变换法

借助快速付立叶变换(FFT),本文给出一种求n阶鳞状因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法,该算法的计算复杂性为O(nlog2n),最后给出的两个数值算例表明了该算法的有效性.