Oriented Cohomology Theories of Algebraic Varieties

This article contains proofs of the results announced by Panin and Smirnov (http://www. math.uiuc.edu/k-theory/0459/2000) in the part concerning general properties of oriented cohomology theories of algebraic varieties. It is constructed one-to-one correspondences between orientations, Chern structures and Thom structures on a given ring cohomology theory. The theory is illustrated by motivic cohomology, algebraic K-theory, algebraic cobordism theory and by other examples.     

Regularity of Continuous Linear Operators on Banach Function Spaces

In this paper we present some characterizations of Banach function spaces on which every continuous linear operator is regular.     

On Algebraic Curves whose Osculating Planes Belong to the Maximal Number of Independent Linear Complexes

We extend to higher Gaussian maps two classical theorems by Giuseppe Gherardelli and Beniamino Segre which give a sharp lower bound on the rank and characterize the borderline case.     

一类幂级数求和函数的代数方程方法

建立幂级数和函数相关的代数方程,给出形如sum from n=o to ∞ anxn(其中an为以n为变元的多项式)的幂级数求和函数的一种方法.     

Algebraic K-Theory In Low Degree and The Novikov Assembly Map

We prove that the Novikov assembly map for a group factorizes,in ‘low homological degree’, through the algebraicK-theory of its integral group ring. In homological degree 2,this answers a question posed by N. Higson and P. Julg. As adirect application, we prove that if is torsion-free and satisfiesthe Baum-Connes conjecture, then the homology group H₁(; Z)injects in and in , for any ring A such that . If moreover B is of dimension lessthan or equal to 4, then we show that H₂(; Z) injects in and in , where A is as before, and ₂ is generated by the Steinberg symbols{,}, for . 2000 Mathematical Subject Classification: primary 19D55, 19Kxx,58J22; secondary: 19Cxx, 19D45, 43A20, 46L85.     

Algebraic Shifting and Basic Constructions on Simplicial Complexes

We try to understand the behavior of algebraic shifting with respect to some basic constructions on simplicial complexes, such as union, coning, and (more generally) join. In particular, for the disjoint union of simplicial complexes we prove Δ(K ˙∪ L) = Δ(Δ(K) ˙∪ Δ(L)) (conjectured by Kalai [6]), and for the join we give an example of simplicial complexes K and L for which Δ(K*L)≠Δ(Δ(K)*Δ(L)) (disproving a conjecture by Kalai [6]), where Δ denotes the (exterior) algebraic shifting operator. We develop a ‘homological’ point of view on algebraic shifting which is used throughout this work.     

The Existence and Local Behavior of Multivariate Algebraic Function Approximations

The existing scheme of rational polynomial approximants, defined by multivariate power series, is extended to define approximants with branch points. The existence theorem is obtained. The basic properties used to define the rational approximants can be preserved almost intactly. Especially, the local behavior of the     

Tate''s Conjecture, Algebraic Cycles and Rational K-Theory in Characteristic p

The purpose of this article is to discuss conjectures on motives, algebraic cycles and K-theory of smooth projective varieties over finite fields. We give a characterization of Tate's conjecture in terms of motives and their Frobenius endomorphism. This is used to prove that if Tate's conjecture holds and rational and numerical equivalence over finite fields agree, then higher rational K-groups of smooth projective varieties over finite fields vanish (Parshin's conjecture). Parshin's conjecture in turn implies a conjecture of Beilinson and Kahn giving bounds on rational K-groups of fields in finite characteristic. We derive further consequences from this result.     

Boolean Metric Spaces and Boolean Algebraic Varieties

Abstract

The concepts of Boolean metric space and convex combination are used to characterize polynomial maps A ⁿ ?→?A ^m in a class of commutative Von Neumann regular rings including p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e., sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.     

零维代数簇的分解及其应用

本文利用Groebner基，给出了一种分解零维代数簇的方法，并且讨论了这种方法在理想的准素分解以及几何定理机器证明中的应用．     

连续凸函数的判据及几何特征

从凸函数定义出发研究了连续函数与凸函数的关系,给出了连续凸函数的几个判定条件,并刻划它们的几何特征.     

代数函数域的一些Artin-Schreier型扩张相伴的Riemann-Roch空间

阐明给定代数函数域上一些除子的Riemann-Roch空间是代数几何码构造的基础.给出代数函数域的一些Artin-Schreier型扩张的Riemann-Roch空间的一组基,并应用于编码理论,得到F_(16)上参数分别是[54,43,5],[54,41,7],[54,40,8]的代数几何码.     

拓扑向量空间中实齐性连续函数的延拓定理

得到如下结果,在有限维具To公理的拓扑向量空间中,其内任意不含原点的有界闭集上定义的齐性连续函数均可延拓为全空间上的齐性连续函数。     

On Generalized Algebraic Cone Metric Spaces and Fixed Point Theorems

In this paper, the author first introduces the concept of generalized algebraic cone metric spaces and some elementary results concerning generalized algebraic cone metric spaces. Next, by using these results, some new fixed point theorems on generalized (complete) algebraic cone metric spaces are proved and an example is given. As a consequence, the main results generalize the corresponding results in complete algebraic cone metric spaces and generalized complete metric spaces.     

On Homotopy Groups of Real Algebraic Varieties and their Complexifications

Let X ₀ be a topological component of a nonsingular real algebraic variety and i:X → X _C is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i:X ₀ → X _C and obtain several results using rational homotopy theory and other standard tools of homotopy theory.     

Nonstandard Point Counting for Algebraic Varieties

For varieties over a field k, we define motivic measures with values in ordered fields, using point counting over finite fields and taking the limits with respect to ultrafilters. Some properties and problems related to such measures are discussed. We define similar measures for algebraic dynamical systems by counting periodic points, and explain how they can be used to prove certain statements, such as the non-rationality of a motivic zeta function.     

线性空间上凸函数的可微性与次可微性

讨论了定义在线性空间上的广义实值凸函数的可做性和次可微性．     

分片代数曲线交点的结式求法

本文对确定分片代数曲线的二元样条函数的整体表达式中的截断引入参数表示,给出了分片代数曲线交点的结式求法．理论与实例表明,这种算法是有效的．     

函数一致连续的几个充分条件

得到了函数一致连续的几个充分条件.     

Musielak-Orlicz-Sobolev空间中的序连续性质和最佳逼近算子的连续性质

借鉴Orlicz-Sobolev空间中的受控最佳逼近算子问题的研究结果,抓住Musielak-Orlicz-Sobolev空间的构成特点,利用△_2条件及其否定,给出了MusielakOrlicz-Sobolev空间具有序连续性的充要条件,同时研究了该空间中最佳逼近算子的连续性.