三次系统的一类三曲线分界线环

本文证明了三次系统不可能同时存在三个三曲线x^3-3xy^2-1=0分界线环,但是可以同时存在两个三曲线分界线环,给出了同时存在两个三曲线分界线环的充要条件。     

三阶三点边值问题的三个解的存在性

研究了一类三阶三点边值问题的三个解的存在性,应用Leray-Schauder度理论得到了该问题的三个解存在的充分条件.     

标准三点转移函数

一般的三点转移函数(TTF),不便用转移矩阵来表示.对于标准三点转移函数(STTF),引入了3类联络矩阵,研究了它们的一般特性和基本关系,给出了常值型标准三点转移函数的生成方法和状态对称型标准三点转移函数的一般表达形式.     

四阶微分方程三点边值问题三个正解的存在性

在四阶微分方程非线性项f中含有未知函数“的二阶导数u”的情况下,运用Avery-Peterson不动点定理,研究了一类四阶微分方程三点边值问题三个正解的存在性,得到了该类边值问题存在三个正解的充分条件．     

关于三商映射

三商映射是完备映射和开映射的共同推广。本文综述三商映射的理论，论术这三商映射，开映射，紧覆盖映射，诱导完备映之间的一些转换关系，提出了几个供进一步研究的问题。     

基于三层粒结构的三支邻域熵

邻域粗糙集在实际应用中具有灵活性,相关的邻域信息度量在不确定性分析和知识发现中具有重要作用.经典的条件邻域熵具有相交不完备性和非层次性.对条件邻域熵进行扩展改进,建立了基于三层粒结构的三支邻域熵.首先,提出三支概率,研究三支概率的系统性和单调性;然后,利用三支概率函数及层次构建思想,提出基于三层粒结构的三支邻域熵,并获得系统性、单调性/非单调性;最后,利用实例和实验对以上相关度量的关系、性质进行验证.结果表明提出的三支邻域熵扩展和丰富了条件邻域熵.     

三度边正则图的三个无限族

图X称为边正则图，若X的自同构群Aut(X)在X的边集上的作用是正则的．本文考察了三度边正则图与四度Cayley图的关系，给出了一个由四度Cayley图构造三度边正则图的方法，并且构造了边正则图的三个无限族．     

θp型三I算法与反向三I算法支持度分析

研究了基于蕴涵算子以θp模糊推理的三Ⅰ算法与反向三Ⅰ算法的支持度理论，分析了支持度的性质，得到了α-三Ⅰ算法的FMP（FMT）计算公式与α-反向三Ⅰ算法的FMP（FMT）计算公式。     

具有三轨输出的三值触发器及其在三值时序电路中的应用

本文指出三值触发器(tri-flop)应具有三轨输出、三态预置能力、合理的逻辑功能与激励表等。以此要求为前提,本文提出了与二值触发器对应的各种三值触发器的设计,其中包括三值基本触发器(Latch)及各种类型的三值主从触发器,如置态型、D型、JKL型与T型等。这些触发器的结构及逻辑功能与以前提出的各种触发器的设计都不同。在本文中还通过实例表明,由于它们具有合理的激励表,因此能方便地应用于各种三值时序电路的设计。     

三重积分计算浅析

本文首先讨论了不同坐标系中一例三重积分的计算,然后研究了变量置换在三重积分计算中的应用,指出它是三重积分在柱(球)坐标系中计算的本质,最后讨论了例题若干变形的处理,这些都有助于丰富和完善相关的教学内容与细节.     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Asymptotics of families of solutions of nonlinear difference equations

One method to determine the asymptotics of particular solutions of a difference equation is by solving an associated asymptotic functional equation. Here we study the behaviour of the solutions in an asymptotic neighbourhood of such individual solutions. We identify several types of attraction and repulsion, which range from almost orthogonality to almost parallelness. Necessary and sufficient conditions for these types of behaviour are given.     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Radius of convexity of certain classes of analytic functions

We consider the classes of analytic functions introduced recently by K.I. Noor which are defined by conditions joining ideas of close-to-convex and of bounded boundary rotation functions. We investigate coefficients estimates and radii of convexity.