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.     

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.     

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.     

解析函数与Lipschitz条件

研究了解析函数与Lipschitz条件,得到了如下两个结果:(i)设D是一平面区域,f(z)在D中解析,00,对任意z∈D有|f′(z)|≤md(z,D)k-1,则f∈Lipk(D)且‖f‖k≤cmk,其中c=c(D)是仅与D有关的常数.     

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.     

Analytic and asymptotic properties of non-symmetric Linnik's probability densities

The function

含有解析函数与亚纯函数的一些不等式

指出文献 [2 ]和文献 [4]中的错误 ,并且得到含有单位圆盘内接解析函数与亚纯函数的几个不等式 .     

Modulus of Continuity of Piecewise Analytic Functions

We obtain conditions under which the modulus of continuity of a piecewise analytic function given on a closed interval of the real axis is an analytic function in a neighborhood of zero.     

Right Spread序的若干封闭性质

§1Introductionandmotivation Itisalwaysofinteresttocomparethevariabilityoftworandomvariablesinreliability theoryandeconomics.Thecomparisonsbasedonmomentssuchasvarianceandstandard deviationarenotveryinformativealthoughsuchmeasuresaresimpletouse.Meanwhile,sincethesecomparisonsarestaticones,andhencetheirapplicationsinsomefields,e.g.,reliabilityandfinance,arerestricted.Inthesefields,however,somedynamicalcomparisons areneeded.Asaresult,severalstochasticordersthataremorerefinedhavebeen establishedi…     

两类解析函数族的一些性质

研究两类解析函数族的性质，推广了Chichra[4]、Mocanu[5]和Obradovic[6]的一些结果。另外，也指出了S.Owa[8]的一个错误。     

复指数Dirichlet级数表示的解析函数

本文对一个在角形区域由复指数Dirichlet级数表示且在一固定水平带形有界解析不恒为零的函数的存在性,给出了充分必要条件.     

解析函数的又一等价定理

将Morera定理中的条件∫γf(z)dz=0改为∫f-gds=0,证明其结论仍然成立,并由此得出一个单值复变函数f(z)在G中解析的充要条件,即解析函数的又一等价定理.     

On Conversion of the L'Hopital Rule for Analytic Functions

We consider the question about the possibility of conversion of the L'Hopital rule for the limits of ratios of analytic functions at a boundary point of the analyticity domain in a Stolz angle.     

Probabilistic asymptotic properties of some combinatorial optimization problems

A class of combinatorial optimization problems with sum- and bottleneck objective function is described, having the following probabilistic asymptotic behaviour: With probability tending to one the ratio between worst and optimal objective function value approaches one as the size of the problem tends to infinity.Problems belonging to this class are among others quadratic assignment problems, as well as certain combinatorial and graph theoretical optimization problems.The obtained results suggest that even very simple heuristic algorithms incline to yield good solutions for high dimensional problems of this class.     

关于解析函数的一个易想象的不等式及其应用

本文关于解析函数给出了一个可作几何理解的不等式,由此易得出一个有关解析函数零点的命题,而代数学基本定理成为它的直接推论．     

可变幅角复系数的解析函数族

研究了在单位开圆盘内单叶解析且规范化的复系数函数族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）的一些性质,给出了其子族gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）在内闭一致收敛拓扑下的极值点和支撑点,并讨论解决了gφ1,φ2,φ3,φ4（m1,m2,m3,m4;λ）与凸函数相关的一些半径问题,推广了近来的一些研究结果．