Matrix extensions and eigenvalue completions, the generic case

In this paper we provide new necessary and sufficient conditions for the so-called eigenvalue completion problem.

     

闭路函子和同纬函子保持同伦正则性

证明了闭路函子和同纬函子保持同伦正则性 ,同时构造出了一系列同伦等价的空间     

群与模范畴中的积和余积

积和余积是范畴学中的一对对偶概念,作为范畴学的一对基本概念自然在其具体对象中就会有所体现,以群,模为对象来讨论它们的积和余积。     

态射的广义Moore—Penrose逆

本文定义了态射的广义Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆，给出了它存在的一些充要条件，确定了它的一些表达式，推广了关于态射的Ｍｏｏｒｅ－Ｐｅｎｒｏｓｅ逆的相应结果。     

Classification of extremal contractions from smooth fourfolds of -type

We investigate divisorial contractions of extremal rays from
smooth fourfolds. When the exceptional divisor is contracted to a curve, we prove that the divisor is a -bundle or quadric bundle over a smooth curve and the contraction is the blowing up along the curve. Furthermore we determine the local analytic structure of the contraction.

     

On Connectedness via Closure Operators

This paper describes a convenient modification of the approach presented in the paper Closure operators and connectedness by G. Castellini and D. Hajek, which is shown to give a suitable generalization of left- and right-constant subcategories, both at the object and the morphism levels. We show in particular that the framework we introduce here allows the simultaneous study of the classes of connected topological spaces, of concordant continuous maps and of monotone continuous maps.     

On classification of polarized varieties with non-integral nef values

Let be an -dimensional normal projective variety with only Gorenstein, terminal, -factorial singularities. Let be an ample line bundle on . Let denote the nef value of . The classification of via the nef value morphism is given for the situations when satisfies or .

     

The E-theoretic descent functor for groupoids

The paper establishes, for a wide class of locally compact groupoids Γ, the E-theoretic descent functor at the C^∗-algebra level, in a way parallel to that established for locally compact groups by Guentner, Higson and Trout. Section 2 shows that Γ-actions on a C₀(X)-algebra B, where X is the unit space of Γ, can be usefully formulated in terms of an action on the associated bundle B^?. Section 3 shows that the functor B→C^∗(Γ,B) is continuous and exact, and uses the disintegration theory of J. Renault. Section 4 establishes the existence of the descent functor under a very mild condition on Γ, the main technical difficulty involved being that of finding a Γ-algebra that plays the role of Cbcont(T,B) in the group case.     

范畴中态射集的加权减序

利用态射的加权广义逆,引进并讨论态射集中的加权减序和加权星序.给出了态射集中的加权减序的一些刻画和性质以及加权减序和加权星序之间的关系.加权减序和加权星序都是态射集中的新的偏序.所得结果均可应用于矩阵理论中.
关键词：态射;加权广义逆;加权减序;加权星序