一个问题推广的探讨

笔者曾经在一本杂志上看到这样一个问题:甲乙两人进行射击游戏,规则如下:若一方射击一次击中目标,则此人继续下一次射击;若一方射击一次未击中目标,则由对方接替下一次射击.已知甲乙两人射击一次击中目标的概率都是31,且每次射击是否击中目标彼     

关于特征值的平方和的注记

探讨了特征值的平方和这一计算问题,指出了常用方法的不足之处,并在深入研究方阵相似的基础之上弥补了这一不足,彻底解决了这一问题,此外运用这种方法还能解决特征值高次幂之和与多项式之和的计算问题.最后文中给出了一种新的计算特征值平方和的方法,这种方法能够回避第一种方法的不足,但缺点是不易推广.     

餐桌上的数学

正经不住外婆隔三差五的邀请,妈妈一有空就带着我到外婆家蹭饭吃。今天一进门,一股香喷喷的鸭汤味就扑鼻而来,闻得我直流口水。外婆见我进门,赶紧给我盛了一个大鸭腿端过来。这时,妈妈笑着说:"嘉毅,每次你一来,外婆家的鸭子兔子们就要遭殃了,它们该管你叫‘无敌杀手’了。"我嘿嘿一笑,一边狼吞虎咽,一边小心地向外婆打探:"外婆,你家还有几只鸭子几只兔子呀?"外婆故弄玄     

怀念我的父亲李国平院士——灵魂的乐师生命的哲人

写我父亲李国平的文章太多了。作为1955年中国科学院的首批学部委员(院士)、一级教授,这位享誉海内外的著名数学家离开我们已经11年了。今天,我想写的是一位平凡的父亲,一位慈父,一位在儿女心中灵魂的乐师与生命的哲人。父亲的伟大就在于他在儿女心目中是这个家庭的精神支柱。在我儿时的记忆里,父亲总是里穿一套浅灰色的西装,外披一件深蓝色的灯芯线披风,左手拿着烟斗,右臂挎着阳伞,     

一个问题推广的探秘

笔者曾经在一本杂志上看到这样一个问题：甲乙两人进行射击游戏，规则如下：若一方射击一次击中目标，则此人继续下一次射击；若一方射击一次未击中目标，则由对方接替下一次射击．已知甲乙两人射击一次击中目标的概率都是1/3，且每次射击是否击中目标彼此相互独立，甲进行第1次射击，试推断甲乙两人谁在第3次射击的可能性较大．     

巫婆的戒指

有一位巫婆送你一只宝石戒指,这是一只不同予普通戒指的神奇戒指。当巫婆握住你双手的一瞬间,宝石会发出万丈光芒,你认为它会发出什么颜色的光芒昵？     

爱的概率

在寂静的大海边生长着一棵老松树。老松树每天都站在那里看着周围的风景。有一天，从海滩上的一个洞里爬出来一个小东西，老松树仟细一看，原来是一只小螃蟹。     

巫婆的戒指

有一位巫婆送你一只宝石戒指,这是一只不同予普通戒指的神奇戒指。当巫婆握住你双手的一瞬间,宝石会发出万丈光芒,你认为它会发出什么颜色的光芒昵？     

地下100层的房子

正今天上午,丁婷婷到我家来玩。她一进门,就被书架上掉下来的一本漂亮的书给吸引住了。书的名字叫《100层的房子》,它是我小时候非常喜欢的一本绘本呢。和其他绘本不一样的是,其他书都是横着翻的,可它却是竖着翻的。丁婷婷就是翻了几页后,马上发现了其中的奥妙。这本书讲的是一位男生多奇收到了一封奇怪的信,来到了一座100层的房子面前,     

奇妙的种子

很久很久以前，在某个地方，住着一个懒（lan）隋（dui）的男人。一年冬天，仙人对他说：“我给你两颗奇妙的种子吧。你把其中一颗烤（kao）烤吃掉的话，一整年你都不会觉得肚子饿。另外的一颗把它埋在地里，来年秋天一定能收获两颗种子的。”说完就给了他两颗奇妙的种子。这个男人把其中的一颗种子烤熟之后吃下去了。原本黑色的种子烤熟...     

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.     

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。     

Lattices of dominions of universal algebras

We fix a universal algebra A and its subalgebra H. The dominion of H in A (in a class M) is the set of all elements a ∈ A such that any pair of homomorphisms f, g: A → M ∈ M satisfies the following: if f and g coincide on H then f(a) = g(a). In association with every quasivariety, therefore, is a dominion of H in A. Sufficient conditions are specified under which a set of dominions form a lattice. The lattice of dominions is explored for down-semidistributivity. We point out a class of algebras (including groups, rings) such that every quasivariety in this class contains an algebra whose lattice of dominions is anti-isomorphic to a lattice of subquasivarieties of that quasivariety. __________ Translated from Algebra i Logika, Vol. 46, No. 1, pp. 26–45, January–February, 2007.     

完全偶图的星因子计数

图G的一个星因于是G的一个支撑子图，其中每一个分支是一个星图．本文研究完全偶图Km,n的星因子计数，给出了Km,x存在由K个分支构成的星因子的充要条件，进而给出了Km,n星因子计数的公式．     

Choice of the best alternative in case of a continuous set of states of nature-application of fuzzy numbers

On the basis of a known application of an order weighted averaging operator to the decision making in the case of a discrete set of states of nature, a general approach to the case of a continuous set of states of nature is proposed. The general approach encompasses various types of attitudes of the decision maker, expressed in the form of fuzzy numbers.     

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.     

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.     

Existence of normal Hall subgroups by means of orders of products

Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup 6 . As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.     

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.