ABELIAN COVERS AND ISOTRIVIAL CANONICAL FIBRATIONS

We give a pure algebraic method to construct all the infinite families of surfaces S with isotrivial canonical fibration where S is the minimal desingularization of X = Z/G and G is an Abelian group acting diagonally on the product of two smooth curves: Z = F × D. In particular we recover all the known infinite families of surfaces with isotrivial canonical fibration and we produce many new ones. Our method works in every dimension and, with minor modifications, it can be applied to construct surfaces with canonical map of degree > 1.     

GRADED MATLIS DUALITY AND APPLICATIONS TO COVERS

Abstract

We study homological properties of graded Matlis duality and apply them to get covers by Gorenstein gr-projective modules. We show that these covers are minimal graded maximal Cohen-Macaulay approximations in some cases.     

ON THE EXISTENCE OF FLAT COVERS IN R-gr

Recently, a proof of the existence of a flat cover of any module over an arbitrary associative ring with unit has been finally given (see 4-5 Bican, L., EL Bashir, R. and Enochs, E. All Modules Have Flat Covers, preprint Eklof and Trlifaj, J. How to Make Ext Vanish. J. London Math. Soc., to appear ). In this paper we prove the existence of flat covers in the category of graded modules over a graded ring. Some graded theoretical machinery is introduced to make the proof possible and new graded homological tools are developed.     

LARGE OPEN COVERS AND A POLARIZED PARTITION RELATION

Abstract

We show that a strengthened form of a property of Roth-berger implies that a certain polarized partition relation holds for the ω-covers of a space and that this partition relation implies a strengthened form of a property of Menger.     

RELAXATION OF FUNCTIONALS INVOLVING HOMOGENEOUS FUNCTIONS AND INVARIANCE OF ENVELOPES

51. IntroductionWe denote by Mm. the space of real m x n matrices. Let U' bc a function defined onM.., with values in R and n be a bounded domain in Wt. The basic problenl of the Calculusof Variations consists in minirnizing such energy functionals asI(u) = f I+'(vu(x))dx, (1.l)jt, I+'(vu(x))ax, (1.l)where u is a mapping from t1 into R"' belonging to some subset of a Sobolcv space. Inthis context, 7u designates the gradicnt of u, i.e., the m x 1l matrix witll components(7u)ij = % l where …     

ON n- WIDTHS OF PERIODIC FUNCTIONS

Let ~(r,1)_p={f:f~(r-1) is abs. cont. on I=[a, b], f is periodie with period H(=b-a),f(x_1)=0,‖f~((r))‖_p≤0}, where x_1 is any fixed point in [a, b]. The author finds the Kolmogorov, Gel'land, linear, and Berustein n-widths of ~(r,1)_p in L~p(I) for n odd, ∞>p>1. The optimal subspaces and operators are also found.     

S-TORSION FREE COVERS OF MODULES

Over Pruüfer domains every module has a torsion free cover with a flat kernel. In this paper we show that the commutative Noetherian rings that have this property are the Gorenstein rings with Krull dimension at most one. Here we use the torsion theory defined by the nonzero-divisors of the commutative ring R.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

A KY FAN MATCHING THEOREM FOR TRANSFER COMPACTLY OPEN COVERS AND THE APPLICATION TO THE FIXED POINT

In this article, a Ky Fan matching theorem for transfer compactly open covers is established. As applications, a Fan-Browder coincidence theorem, a Ky Fan best approximation theorem and a Brouwer-Schauder-Rothe type fixed point theorem are obtained.     

BOUND ON THE MAXIMUM NUMBER OF CLEAR TWO-FACTOR INTERACTIONS FOR 2n-(n-k) DESIGNS

Clear effects criterion is an important criterion for selecting fractional factorial designs [1]. Tang et al. [2] derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi's) in 2n-(n-k) designs of resolution Ⅲ and Ⅳ by constructing 2n-(n-k) designs. But the method in [2] does not perform well sometimes when the resolution is III. This article modifies the construction method for 2n-(n-k) designs of resolution Ⅲ in [2]. The modified method is a great improvement on that used in [2].     

关于AP-内射环和AGP-内射环(英文)

本文研究了AP-内射环和AGP-内射环的von Neumann正则性问题.利用P-内射环和Y J-内射环的研究方法及GW-理想的性质,得到了AP-内射环和AGP-内射环是(强)正则环的一些条件.推广了文献[7,12,14]中的相关结果.     

单形和3维立方体乘积上小覆盖的等变协边类的个数

本文研究了小覆盖的等变协边分类.利用示性函数和Stong同态确定了单形和3维立方体乘积上小覆盖的等变协边类的个数,推广了现有文献中的相关结果.     

ON CLASS PAIRS AND RADICALS

ABSTRACT

We show that, for a class of schurian algebras, which we call schurian almost triangular, the fundamental group of the algebra is isomorphic to the fundamental group of an associated simplicial complex. Moreover, we obtain a simple presentation of this group in terms of generators and relations. Finally we use it to obtain easy short proofs of some known facts on the simple connectedness of incidence algebras.     

SOME RECENT RESULTS ON CATEGORIES OF R-SPACES AND PROBABILISTIC SPACES AND ON CATEGORICAL SPECTRA

The purpose of this paper is twofold: first, to present some recent results obtained by Romanian mathematicians in the field of general and categorical topology; second, to present some current research results obtained by the author in what may be called the topological study of a category. Accordingly, the paper is divided into two parts.

The author wishes to express his gratitude to the organizing committee of this Symposium for the kind invitation to present' this paper.     

准正则环与正则环

每一个主左理想均由一个幂等元生成的环叫正则环。每一个左理想均由若干个幂等元生成的环叫准正则环。本文研究准正则环与正则环的一些性质，讨论准正则环成为正则环的一些条件，准正则环、正则环与Ｖ环之间的关系，准正则环成为Ａｂｅｌ正则环的条件。     

ON CUP-ONE AND TODA BRACKET

Abstract

The definition of the cup-one construction in various cases is recalled. A variation expressible in terms of the Toda bracket is given, enabling nontriviality of Toda brackets of a certain type to be established in a rather simple way from knowledge of the behaviour of cup-one.     

关于完全环与Noether环

（ｉ）环Ｒ是左完全环，当且仅当存在一个基数ｃ，使得任意平坦左Ｒ－模是一个拟投射模和一个ｃ－限制的ＥＳ－模的直和。（ｉｉ）Ｒ是左Ｎｏｅｔｈｅｒ环，当且仅当存在一个基数ｃ，使得任意内射左Ｒ－模的直和是一个（拟）连续模和一个ｃ－限制的ＥＳ－模的直和。