Unconditionally Cauchy series and Cesàro summability

In this paper we obtain new characterizations of weakly unconditionally Cauchy series and unconditionally convergent series through Cesàro summability. We study new spaces associated to a series in a Banach space; as a consequence, new characterizations of complete and barrelled normed spaces are proved.     

Implicit multifunction theorems in complete metric spaces

In this paper, we establish some new characterizations of metric regularity of implicit multifunctions in complete metric spaces by using lower semicontinuous envelopes of the distance functions to set-valued mappings. Through these new characterizations it is possible to investigate implicit multifunction theorems based on coderivatives and on contingent derivatives as well as the perturbation stability of implicit multifunctions.     

Factorizations of EP operators

In this paper we characterize EP operators through the existence of different types of factorizations. Our results extend to EP operators existing characterizations for EP matrices and give new characterizations both for EP matrices and EP operators.     

Total nonpositivity of nonsingular matrices

In this paper, nonsingular totally nonpositive matrices are studied and new characterizations are provided in terms of the signs of minors with consecutive initial rows or consecutive initial columns. These characterizations extend an existing characterization that uses some restrictive hypotheses.     

Nonsingularity Conditions for Multifunctions

We discuss three different characterizations of continuity properties for general multifunctions S : R^d Rⁿ. Each of these characterizations is given by the same simple nonsingularity condition, but stated in terms of three different generalized derivatives. Two of these characterizations are known, but the third is new to this paper. We discuss how all three have immediate analogues as generalized inverse mapping theorems, and we apply our new characterization to develop a fundamental and very broad sensitivity theorem for solutions to parameterized optimization problems.     

L-Fuzzy映射的刻画

在文献 [6]中 ,史福贵借助于 L -fuzzy关系定义了 L -fuzzy集间的 L -fuzzy映射并借助于它们的水平截集给出了其若干刻画。在这篇文章中 ,我们将借助于另外的截集给出 L -fuzzy映射的一种新刻画。从而我们也得到了 L -fuzzy单射和 L -fuzzy满射的新刻画。     

Poisson过程作为更新过程的若干新的特征刻画

本文将给出Poisson过程作为更新过程的一系列新的特征刻画．这些刻画是借助于更新过程中所有关键量的条件概率分布或条件期望来表述的．所给的条件是至任一指定时刻发生的抵达敷为已知．     

Exponential distributions on semigroups

Three fundamental characterizations of the standard exponential distribution on [0, ) are the remaining life, memoryless and constant failure properties. Analogs of these properties are studied for distributions on a class of semigroups in which the semigroup operation replaces addition, a compatible partial order replaces the ordinary order, and a left-invariant measure replaces Lebesgue measure. Partial characterizations of exponential distributions on such semigroups are obtained and the semigroup formulation provides new characterizations of certain aging properties studied in reliability-increasing failure rate, new better than used, and increasing failure rate average.     

Characterizations of EP matrices and weighted-EP matrices

A square complex matrix A is said to be EP if A and its conjugate transpose A^∗ have the same range. In this paper, we first collect a group of known characterizations of EP matrix, and give some new characterizations of EP matrices. Then, we define weighted-EP matrix, and present a wealth of characterizations for weighted-EP matrix through various rank formulas for matrices and their generalized inverses.     

Halving circular arcs in normed planes

Studying the relation between the length of a chord of the unit circle and the length of the arc corresponding to it, some new characterizations of the Euclidean plane among all normed planes are obtained. All these results yield characterizations of inner product spaces in higher dimensions. Supported by the National Natural Science Foundation of China, grant number 10671048.     

Characterizations of totally balanced matrices

A (0,1)-matrix is totally balanced if it does not contain as a submatrix the incidence matrix of any cycle of length at least 3. Several alternative characterizations of these matrices are presented. These characterizations follow from properties of strongly chordal graphs, studied by Farber, and maximal totally balanced matrices, studied by Anstee. Using these characterizations, efficient recognition algorithms for totally balanced matrices are presented. In addition, a new completion algorithm for building a maximal totally balanced matrix from an arbitrary totally balanced matrix follows from these results.     

Necessary versus equal players in axiomatic studies

This note introduces three variants of existing axioms in which equal players are replaced by necessary players. We highlight that necessary players can replace equal players in many well-known axiomatic characterizations, but not in all. In addition, we provide new characterizations of the Shapley value, the class of positively weighted Shapley values, the Solidarity value and the Equal Division value. This sheds a new light on the real role of equal treatment of equals in the axiomatic literature.     

On some characterizations of greedy-type bases

In 1999, S. V. Konyagin and V. N. Temlyakov introduced the so-called Thresholding Greedy Algorithm. Since then, there have been many interesting and useful characterizations of greedy-type bases in Banach spaces. In this article, we study and extend several characterizations of greedy and almost greedy bases in the literature. Along the way, we give various examples to complement our main results. Furthermore, we propose a new version of the so-called Weak Thresholding Greedy Algorithm (WTGA) and show that the convergence of this new algorithm is equivalent to the convergence of the WTGA.     

半度量空间的刻画

We use the notions of weak base g-functions and pair networks to give some new characterizations of semi-metric spaces.     

Characterizations of classical orthogonal polynomials on quadratic lattices

This paper is devoted to characterizations of classical orthogonal polynomials on quadratic lattices by using a matrix approach. In this form we recover the Hahn, Geronimus, Tricomi and Bochner type characterizations of classical orthogonal polynomials on quadratic lattices. Moreover a new matrix characterization of classical ortho-gonal polynomials in quadratic lattices is presented. From the Bochner type characterization we derive the three-term recurrence relation coefficients for these polynomials.     

Two new properties of ideals of polynomials and applications

In this paper we introduce two properties for ideals of polynomials between Banach spaces and showhow useful they are to deal with several a priori different problems. By investigating these properties we obtain, among other results, new polynomial characterizations of L_∞ spaces and characterizations of Banach spaces whose duals are isomorphic to f 1 (Λ).     

弱投射维数

引入了弱投射模及弱投射维数的概念,说明弱投射模是FP-投射模的真子类.给出了环的整体弱投射维数的刻画,并得到了凝聚环和Noether的一些新的同调刻画.     

Commutators of maximal functions on spaces of homogeneous type and their weighted,local versions

We obtain the characterizations of commutators of several versions of maximal functions on spaces of homogeneous type. In addition, with the aid of interpolation theory, we provide weighted version of the commutator theorems by establishing new characterizations of the weighted BMO space. Finally, a concrete example shows that the local version of commutators also has an independent interest.     

The Owen and Banzhaf–Owen values revisited

In this work, we consider games with coalitional structure. We afford two new parallel axiomatic characterizations for the well-known Owen and Banzhaf–Owen coalitional values. Two properties are common to both characterizations: a property of balanced contributions and a property of neutrality. The results prove that the main difference between these two coalitional values is that the former is efficient, while the latter verifies a property of 2-efficiency.     

Characterizations of normal, hyponormal and EP operators

In this paper normal and hyponormal operators with closed ranges, as well as EP operators, are characterized in arbitrary Hilbert spaces. All characterizations involve generalized inverses. Thus, recent results of S. Cheng and Y. Tian [S. Cheng, Y. Tian, Two sets of new characterizations for normal and EP matrices, Linear Algebra Appl. 375 (2003) 181-195] are extended to infinite-dimensional settings.