两类微分多项式的Picard例外值

设ｆ（ｚ）为平面内非常数亚纯函数，本文考虑了形如ｆ￣ｎＱ［ｆ］为正整数，Ｑ［ｆ］为ｆ的线性齐次微分多项式或ｆ′的多项式）的微分多项式的值分布。推广了Ｗ．Ｋ．Ｈａｖｍａｎ￣［１］和Ｅ．Ｍｕｅｓ￣［４］的结果。     

图的字典序积和自同态幺半群

Ｆ．Ｈａｒａｒｙ￣［１］和Ｇ．Ｓａｂｉｄｕｓｓｉ￣［２］考虑过图Ｘ和ｙ的字典序积Ｘ［Ｙ］的自同构群ＡｕｔＸ［Ｙ］与它们各自的自同构群的圈积ＡｕｔＸ［ＡｕｔＹ］的关系，并给出了两者相等的一种刻划．在本文，我们考虑更广意义上的问题，即Ｘ［Ｙ］的自同态幺半群ＥｎｄＸ［Ｙ］与各自的自同态幺半群的圈积ＥｎｄＸ［ＥｎｄＹ］的关系，也给出了两者相等的一种刻划，同时得到了下面结果：如果Ｘ和Ｙ都是不含Ｋ＿３导出子图的连通图，且其中之一图有奇数围长，那么ＥｎｄＸ［Ｙ］＝ＥｎｄＸ［ＥｎｄＹ］．     

关于Bernstein多项式导数的迭代极限

关于Ｂｅｒｎｓｔｅｉｎ多项式导数的迭代极限何甲兴（吉林工业大学数学系，长春１３００２５）设ｆ定义在［０，１］上，ｆ的Ｂｅｒｎｓｔｅｉｎ算子为其中自从Ｋｅｌｉｓｋｙ和Ｒｉｖｌｉｎ￣［１］研究了算子Ｂ＿ｎ（ｆ，ｘ）的迭代以来，一些作者￣［２－５］除给出不...     

多裂纹圆柱弯曲问题的奇异积分

本文在文［１］的基础上，利用文［２］给出的无裂纹柱体弯曲问题的通解，求得了多裂纹圆柱横力弯曲应力函数及横截面剪应力的奇异积分表达式。本文方法借助数值积分表达式￣［３］，极易在微机上实现，可以完全类似文［１］所做的那样进行数值计算．     

L─Fuzzy群的同态与同构及其性质

本文在Ｌ－ｆｕｚｚｙ群的概念￣［３］的基础上，用集合套概念￣［１］定义了Ｌ－ｆｕｚｚｙ群间的同态与同构。进而给出了它们的一些性质。最后，我们给出了Ｌ－ｆｕｚｚｙ群的同态基本定理。     

直接控制系统绝对稳定的充要性准则

本文对于几类直接控制系统，得到了绝对稳定的充分必要条件，并讨论了控制系统的两次简化形式￣［２，４］．所得结果改进了文［１７～１２］中有关结论。     

关于微分多项式的一些结果

设ｆ是平面内超越亚纯函数，满足Ｎ（ｒ，ｆ）＝Ｓ（ｒ，ｆ）．Ｐ［ｆ］是ｆ的多项式，Ｑ［ｆ］是ｆ的微分多项式。本文考虑了形如Ｐ［ｆ］ｆ＇＋Ｑ［ｆ］（特殊情形为ｆ￣ｎｆ＇＋Ｑ［ｆ］及Ｐ［ｆ］ｆ＇－Ｃ，Ｃ为常数）的微分多项式的值分布，推广并改进了Ｗ．Ｋ．Ｈａｙｍａｎ，Ｊ．Ｃｌｕｎｉｅ，Ｅ．Ｍｕｅｓ等人关于整函数的一些结果。     

A_(2n)~(1)的某些水平为2的标准模的结构

在本文中我们推广了Ｍｉｓｒａ￣［１］的结果，利用Ｌｅｐｏｗｓｋｙ和Ｗｉｌｓｏｎ引进的Ｚ－代数来研究标准模的结构，对仿射李代数Ａ我们能够确定某些水平为２的标准模的真空空间的一组基，本文的结果同Ｍｉｓｒａ￣［５］的结果完全不同。     

关于一类S~（1，1）_3（△~（2）_（mn））插值与逼近

设△￣（２）＿（ｍｘ）是矩形域Ｄ＝［ａ，ｂ］［ｃ，ｄ］的Ⅱ－型三角剖分．Ｓ￣（１，１）＿３（△￣（２）＿（ｍｘ）是带边界条件的三元三次样条空间：本文我们将讨论一类Ｓ￣（１，１）＿３（△￣（２）＿（ｍｘ））的插值问题，证明了它的存在性，唯一性及逼近阶：如果ｆ∈Ｃ￣４（Ｄ），则有｜ｆ－ｓ｜≤ｋ（ｌ）．ｍａｘ（ρ△，ρ￣（－１）＿△）．‖ｆ‖．．ｈ￣２．     

一类种内竞争模型的稳定性

一类种内竞争模型的稳定性曹贤通（郑州纺织工学院，郑州４５０００７）在本文中，我们研究一种按生殖能力不同而分类的种内竞争模型￣［１］这里，Ｊ（ｔ）和Ａ＿ｉ（ｔ）分别表示幼虫和第ｉ成虫群体的数量；ｎ＞０为固有净增长率￣［２］；０＜π≤１为幼虫到成虫的成活...     

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.     

管状曲面在曲线论中的应用

研究了围绕曲线的管状曲面上的曲率线,渐近线与测地线,给出它们的方程,揭示了这些曲线与Bertrand曲线或Mannheim曲线之间的关系,采用新的方法给出一条曲线是Bertrand曲线或Mannheim曲线的充要条件的另一种证明以及Mannheim侣线的曲率与挠率之间的关系．     

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。     

Products of operators of multidimensional structured model of systems

The author has previously defined the concept of a general system in terms of operators and operands. An operand is a mapping defined on a subset of an m-fold Cartesian product instead of the usual set and collection of k-ary relations on it. An operator is a kind of mapping between two collections of operands. Here subsystems, extensions, and the notion of P-semiexactness is studied. In particular we derive conditions such that P-semiexactness of a composition of operators, and of one factor, implies P-semiexactness of the other factor.     

Admissibility of estimators of the probability of unobserved outcomes

The problem of estimating the probability of unobserved outcomes or, as it is sometimes called, the conditional probability of a new species, is studied. Good's estimator, which is essentially the same as Robbins' estimator, namely the number of singleton species observed divided by the sample size, is studied from a decision theory point of view. The results obtained are as follows: (1) When the total number of different species is assumed bounded by some known number, Good's and Robbins' estimators are inadmissible for squared error loss. (2) If the number of different species can be infinite, Good's and Robbins' estimators are admissible for squared error loss. (3) Whereas Robbins' estimator is a UMVUE for theunconditional probability of a new species obtained in one extra sample point, Robbins' estimator is not a uniformly minimum mean squared error unbiased estimator of the conditional probability of a new species. This answers a question raised by Robbins. (4) It is shown that for Robbins' model and squared error loss, there are admissible Bayes estimators which do not depend only on a minimal sufficient statistic. A discussion of interpretations and significance of the results is offered. Research supported by NSF Grant DMS-88-22622.     

Geometry of the Space of Phylogenetic Trees

We consider a continuous space which models the set of all phylogenetic trees having a fixed set of leaves. This space has a natural metric of nonpositive curvature, giving a way of measuring distance between phylogenetic trees and providing some procedures for averaging or combining several trees whose leaves are identical. This geometry also shows which trees appear within a fixed distance of a given tree and enables construction of convex hulls of a set of trees. This geometric model of tree space provides a setting in which questions that have been posed by biologists and statisticians over the last decade can be approached in a systematic fashion. For example, it provides a justification for disregarding portions of a collection of trees that agree, thus simplifying the space in which comparisons are to be made.     

Some properties of c-covers of a pair of Lie algebras

In [H. Safa and H. Arabyani, On c-nilpotent multiplier and c-covers of a pair of Lie algebras, Commun. Algebra 45(10) (2017), 4429–4434], we characterized the structure of the c-nilpotent multiplier of a pair of Lie algebras in terms of its c-covering pairs and discussed some results on the existence of c-covers of a pair of Lie algebras. In the present paper, it is shown under some conditions that a relative c-central extension of a pair of Lie algebras is a homomorphic image of a c-covering pair. Moreover, we prove that a c-cover of a pair of finite dimensional Lie algebras, under some assumptions, has a unique domain up to isomorphism and also that every perfect pair of Lie algebras admits at least one c-cover. Finally, we discuss a result concerning the isoclinism of c-covering pairs.     

Results of the maximum genus of graphs

In this paper,we provide a new class of up-embeddable graphs,and obtain a tight lower bound on the maximum genus of a class of 2-connected pseudographs of diameter 2 and of a class of diameter 4 multi-graphs.This extends a result of Skoviera.     

On Location and Approximation of Clusters of Zeros of Analytic Functions

At the beginning of the 1980s, M. Shub and S. Smale developed a quantitative analysis of Newton's method for multivariate analytic maps. In particular, their α-theory gives an effective criterion that ensures safe convergence to a simple isolated zero. This criterion requires only information concerning the map at the initial point of the iteration. Generalizing this theory to multiple zeros and clusters of zeros is still a challenging problem. In this paper we focus on one complex variable function. We study general criteria for detecting clusters and analyze the convergence of Schroder's iteration to a cluster. In the case of a multiple root, it is well known that this convergence is quadratic. In the case of a cluster with positive diameter, the convergence is still quadratic provided the iteration is stopped sufficiently early. We propose a criterion for stopping this iteration at a distance from the cluster which is of the order of its diameter.     

Capability of Crossed Modules of Lie Algebras

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module.