Charakterisierung semisimplizialer Mengen durch Unterteilung und Graphen

We define a subdivision functor G for semisimplicial sets such that GXGY implies XY for all pairs of semisimplicial sets X, Y and (GX)¹(GY)¹ implies XY, too, but only, as far as we know, for pairs of weakly degenerate semisimplicial sets X, Y. These results are analogous to theorems on simplicial complexes which have been proved by Finney [1] and Segal [6].

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In der Literatur werden semisimpliziale Mengen auch oft als complete semisimplicial complexes, abgekürzt css complexes bezeichnet. Wir halten uns hier im wesentlichen an die Terminologie von K. Lamotke [5].     

On the solution existence of implicit quasivariational inequalities with discontinuous multifunctions

In this article, we established some solution existence theorems for implicit quasivariational inequalities. We first established some results in finite-dimensional spaces and then a solution existence result in infinite-dimensional spaces was derived. Our theorems are proved for discontinuous mappings and sets which may be unbounded. The results presented in this article are improvements of results in Cubiotti, and Yao (Cubiotti, P. and Yao, J.C., 1997, Discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings. Mathematical Methods of Operations Research, 46, 213–328; Cubiotti, P. and Yao, J.C., 2007, Discontinuous implicit generalized quasi-variational inequalities in Banach spaces. Journal of Global Optimization (To appear))     

On nonparametric tests for symmetry inRm

This paper considers the problem for testing symmetry of a distribution inR ^m based on the empirical distribution function. Limit theorems which play important roles for investigating asymptotic behavior of such tests are obtained. The limit processes of the theorems are multiparameter Wiener process. Based on the limit theorems, nonparametric tests are proposed whose asymptotic distributions are functionals of a multiparameter standard Wiener process. The tests are compared asymptotically with each other in the sense of Bahadur.     

Countable Random Sets: Uniqueness in Law and Constructiveness

The first part of this article deals with theorems on uniqueness in law for σ-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two approaches on uniqueness theorems: first, the study of generators for σ-fields used in this context and, secondly, the analysis of hitting functions. The last section of this paper deals with the notion of constructiveness. We prove a measurable selection theorem and a decomposition theorem for constructive countable random sets, and study constructive countable random sets with independent increments.     

The core of a class of non-atomic games which arise in economic applications

We study the core of a non-atomic game v which is uniformly continuous with respect to the DNA-topology and continuous at the grand coalition. Such a game has a unique DNA-continuous extension on the space B ₁ of ideal sets. We show that if the extension is concave then the core of the game v is non-empty iff is homogeneous of degree one along the diagonal of B ₁. We use this result to obtain representation theorems for the core of a non-atomic game of the form v=f^μ where μ is a finite dimensional vector of measures and f is a concave function. We also apply our results to some non-atomic games which occur in economic applications. Received May 1998/Revised version September 1998     

Singular integrals and commutators on homogeneous groups

Let G be a homogeneous group. In this paper, the authors establish several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and BMO(G)functions on the weighted Lebesgue space on G. The conditions of these theorems are satisfied by many important operators in analysis and these operators satisfy only some weak conditions on the size of operators and are known to be bounded in the unweighted case. Some of these theorems are best possible even when G is the Euclidean space. The authors also give some applications of their theorems to the boundedness on weighted spaces of rough singular integrals, oscillatory integrals, parabolic singular integrals, their commutators and the maximal operators associated with them.     

Weighted Approximation of Functions on the Unit Sphere

The direct and inverse theorems are established for the best approximation in the weighted L^p space on the unit sphere of R^d+1, in which the weight functions are invariant under finite reflection groups. The theorems are stated using a modulus of smoothness of higher order, which is proved to be equivalent to a K-functional defined using the power of the spherical h-Laplacian. Furthermore, similar results are also established for weighted approximation on the unit ball and on the simplex of R^d.     

On some properties of sets with positive measures

Summary Steinhaus (2) gave eleven theorems on distance sets of sets with positive measure. The author of this paper has shown here that all these theorems hold good if ratio sets are considered for sets with positive measure instead of their distance sets.

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Riassunto Steinhaus (2) dà vari teoremi sugli insiemi delle distanze relative agli insiemi con misura positiva. In questa Nota l'autore dimostra che tutti i sudetti teoremi valgono ancora se per gli insiemi con misura positiva si considerano, invece degli insiemi delle distanze, gli insemi dei rapporti.

     

CONTRIBUTIONS TO ABSTRACT ANALYTIC NUMBER THEORY

Abstract

This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on abstract analytic number theory. They concern weighted inversion theorems of the Wiener type, mean-value theorems for multiplicative functions, and Ramanu-jan expansions.     

FIXED POINT THEOREMS IN A LOCALLY CONVEX SPACE

Abstract

The notion of diminishing orbital diametral sum for a pair of commuting mappings has been introduced into a Hausdorff locally convex space whose topology is generated by a family of seminorms. Subsequently, this notion is utilized to prove common fixed point theorems which generalize certain theorems of Kirk and Tan.     

Convergence theorems for adapted sequences of random sets

We consider random sets with values in a separable Banach space. We study set-valued amarts, L¹-amarts, uniform amarts and submartingales. For all these classes of random sets, we prove convergence theorems in all main modes of set convergence (weak, Wijsman, Mosco, and Hausdorff). We also prove new convergence theorems for vector-valued subpramarts and pramarts.     

Some Theorems on Meromorphic Univalent Functions

In this paper, we will show some deviation theorems and theorems of rotational angles in classes of Σ(p) and Σ(p,q) of meromorphic univalent functions.     

Comparing equivalences on precubical sets and spaces

We study equivalences of concurrent processes represented by objects of algebraic topology. We use methods of category theory and consider precubical sets (analogs of semisimplicial sets) and precubical spaces (analogs of cell complexes). In particular, we consider categories of these objects and construct subcategories of path-objects. We define open morphisms with respect to these subcategories and formulate criteria for a morphism to be open. We prove that the equivalence of precubical sets (spaces) based on open morphisms coincides with a behavioral equivalence of concurrent processes.     

The Module Decomposition of Super-Symmetric Powers of Matrices

ABSTRACT

Let M be the k  ×  m matrices over ?. The GL ( k ) ×  GL ( m ) decompositions of the symmetric and of the exterior powers of M are described by two classical theorems. We describe a theorem for Lie superalgebras, which implies both of these classical theorems as special cases. The constructions of both the exterior and the symmetric algebras are generalized to a class of algebras defined by partitions. That superalgebra theorem is further generalized to these algebras.     

Some Extension Theorems for Regular Functions of Several Quaternionic Variables

In this paper we study the extension theorems for solutions of inhomogeneous Cauchy-Fueter system. In particular cases, we obtain the extension theorems for regular functions of several quaternionic variables. At the end of the paper we give some applications of these theorems.     

A theorem of the closed graph type

The author proves a theorem about systems of sets which generalizes the closed graph theorem. To illustrate its application proofs, are given of several generalizations of the closed graph theorem, of selection theorems, a transitivity theorem for C^...-algebras and factorization theorems in Banach algebras.     

Determination of Dirac operator with eigenvalue-dependent boundary and jump conditions

Dirac operator with eigenvalue-dependent boundary and jump conditions is studied. Uniqueness theorems of the inverse problems from either Weyl function or the spectral data (the sets of eigenvalues and norming constants except for one eigenvalue and corresponding norming constant; two sets of different eigenvalues except for two eigenvalues) are proved. Finally, we investigate two applications of these theorems and obtain analogues of a theorem of Hochstadt-Lieberman and a theorem of Mochizuki-Trooshin.     

On fuzzy semi δ-<Emphasis Type="Italic">V</Emphasis> continuity in fuzzy δ-<Emphasis Type="Italic">V</Emphasis> topological space

New concepts of fuzzy semi δ-V and fuzzy semi δ-Λ sets were introduced in our work “On fuzzy semi δ-Λ sets and fuzzy semi δ-V sets V-6,” J. Trip. Math. Soc., 6, 81–88 (2004). It was shown that the family of all fuzzy semi δ-V sets forms a fuzzy supra topological space on X denoted by (X, FS ^δV ). The aim of this paper is to introduce the concept of fuzzy semi δ-V continuity in a fuzzy δ-V topological space. Finally, some properties, preservation theorems, etc., are studied. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 712–717, May, 2008.     

Applications of Extreme Points to Distortion Estimates

Sharp distortion theorems for close-to-convex functions which satisfy Re ?'(z) > γ are proved using extreme points.     

Espaces de Banach representables

We study the Banach spaces which are isomorphic to a subspace ofl ^∞(N) which is analytic inR ^N. We prove structure theorems which show that some pathological situations cannot take place in this class. We show that a non-metrizable separable compact of Rosenthal has a continuous image which is not a compact of Rosenthal.