Analytic Independence of an Ideal Relative to Certain Injective Module Over a Commutative Noetherian Ring

In this paper we will introduce the concepts of analytic independence and analytic spread for ideals relative to certain injective module over a commutative Noetherian ring.     

On the coefficients of Hilbert quasipolynomials

The Hilbert function of a module over a positively graded algebra is of quasi-polynomial type (Hilbert-Serre). We derive an upper bound for its grade, i.e. the index from which on its coefficients are constant. As an application, we give a purely algebraic proof of an old combinatorial result (due to Ehrhart, McMullen and Stanley).

     

用广义拟Hadamard卷积定义的广义积分算子的封闭性质

首先利用广义拟-Hadamard卷积引入一个广义积分算子;其次,应用两个经典不等式和系数不等式研究广义积分算子及其特殊殊算子在某些非标准化广义解析函数类上的封闭性质.     

Core of ideals of Noetherian local rings

The core of an ideal is the intersection of all its reductions. In 2005, Polini and Ulrich explicitly described the core as a colon ideal of a power of a single reduction and a power of for a broader class of ideals, where is an ideal in a local Cohen-Macaulay ring. In this paper, we show that if is an ideal of analytic spread in a Noetherian local ring with infinite residue field, then with some mild conditions on , we have for any minimal reduction of and for .

     

离散数学教材中传递闭包的两个问题

设R和F是有限集合X上的两个关系.借助关系图的概念,本文确定了分别满足t(R∪F)=t(R)∪t(F),t(s(R))=s(t(R))的R和F的充分必要条件,解决了耿素云、曲婉玲和王捍贫2002年编著的《离散数学教程》第40页和44页中的两个遗留问题.     

The Analytic Spread of Monomial Ideals

Abstract

We compute the analytic spread of a monomial ideal I of the ring ?[[x ₁,…,x _n ]] in terms of the Newton polyhedron of I.     

关于多值解析函数的教学研究

复变函数论中的多值函数教学是一个难点.钟玉泉先生的教材在这一难点的处理方面是较成功的.他通过例题,介绍多值函数分成单值分支的方法,介绍求函数值的方法,并对这些方法进行了总结,得出的结论是:当给定初值后,只有通过连续变化才能得到其它点的函数值.这一点和传统的代入法求函数值完全不同.然而该教材就在这一总结之后,又用代入法求Arcsin2.我们认为这自我否定了刚刚建立起来的求值方法,扰乱了读者的思想.本文通过对Arcsinz分成单值解析分支的讨论,对求Arcsin2提出了新的教材处理方案,以期和读者商榷.     

关于某些调和函数

用H表示形如f(z)=h(z) g(z)的调和函数族,其中h和g是单位圆盘内的解析函数.本文考虑H的三类子族函数.其中的两族为PH(α)=f∶Ref(z)z≥α和NH(α)=f∶Ref(z)θz≥θα,其中0≤α<1和θ=argz.本文得到了函数f属于其中一族的一个充分必要条件,并且获得了一些系数不等式和偏差定理.     

Computing the Ehrhart quasi-polynomial of a rational simplex

We present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms were known for integer simplices and for rational polytopes of a fixed dimension. The algorithm is based on the formula relating the th coefficient of the Ehrhart quasi-polynomial of a rational polytope to volumes of sections of the polytope by affine lattice subspaces parallel to -dimensional faces of the polytope. We discuss possible extensions and open questions.

     

拟二次多项式的迭代

本文初次探讨了更广泛的拟多项式迭代．得到几个初步的定理．希望将复动力系统的一些定理推广到拟动力系统．     

Analytic Discs and Extension of CR Functions

Let M be a manifold of X = C ⁿ , A a small analytic disc attached to M, z ^o a point of A where A is tangent to M, z ¹ another point of A where M extends to a germ of manifold M ₁ with boundary M. We prove that CR functions on M which extend to M ₁ at z ¹ also extend at z ^o to a new manifold M ₂. The directions M ₁ and M ₂ point to, are related by a sort of connection associated to A which is dual to the connection obtained by attaching 'partial analytic lifts' of A to the co-normal bundle to M in X.     

A New Approach to Analytic Multifunctions

We show how the theory of analytic multifunctions can be developed in an elementary and self-contained fashion, using the abstract notions of gauge and multigauge. This approach also yields new information about the metric properties of analytic multifunctions, leading to analogues of Schwarz's lemma and the Schwarz–Pick theorem.     

复变函数中刘维尔定理的新证明

利用截断函数的性质给出了复变函数中刘维尔定理的一种新的证明方法.     

P-叶星像函数类的一些充分条件

令Hn(p)表示形如f(z)=zp ∑ ∞k=n pakzk,且在单位圆U={z;|z|<1}内解析的函数f(z) 的全体所成的函数类.本文应用微分从属技巧得到了p-叶β级星像函数的一些充分条件,所得结果推广了一些作者的相关结果.     

Noncommutative plurisubharmonic polynomials part I: Global assumptions

We consider symmetric polynomials, p, in the noncommutative (nc) free variables {x₁,x₂,…,xg}. We define the nc complex hessian of p as the second directional derivative (replacing xT by y)

     

Maximal periods of (Ehrhart) quasi-polynomials

A quasi-polynomial is a function defined of the form q(k)=cd(k)kd+cd−1(k)kd−1+?+c₀(k), where c₀,c₁,…,cd are periodic functions in k∈Z. Prominent examples of quasi-polynomials appear in Ehrhart's theory as integer-point counting functions for rational polytopes, and McMullen gives upper bounds for the periods of the cj(k) for Ehrhart quasi-polynomials. For generic polytopes, McMullen's bounds seem to be sharp, but sometimes smaller periods exist. We prove that the second leading coefficient of an Ehrhart quasi-polynomial always has maximal expected period and present a general theorem that yields maximal periods for the coefficients of certain quasi-polynomials. We present a construction for (Ehrhart) quasi-polynomials that exhibit maximal period behavior and use it to answer a question of Zaslavsky on convolutions of quasi-polynomials.