"值代入"与线面、积分的计算

讨论线、面积分中“值代入”问题,并对其在某类重积分计算中的消极影响给予关注。     

从"和值14"现象谈二项分布的典型应用

分析了"和值14"现象产生的主要原因是不少彩民应用二项分布知识于彩票,实际上概率在数字彩中的作用并不太明显.但二项分布在其他领域中却有着广泛的应用,譬如在人力资源管理和风险管理上就有典型的应用.     

"精确到"与"精确度"

新教材引入了二分法求函数的近似值,这就涉及到近似计算中的两个概念:"精确到"与"精确度".教材上用的是精确度,一般如精确度为0.1,是指函数f(x)在区间[a,b]上,有f(a)·f(b)<0,则在(a,b)上存在零点,如∣a-b∣<0.1,在区间上任取一点,包括两个端点,其精确度即为0.1.而"精确到",以精确到0.1为例,即我们平常所说的精确到小数点后一位,是指与精确值的误差不超过±0.05.     

"有关代数微分方程的Gackstatter和Laine的猜测"的补充

§ 1.　Introduction　　Inthispaperwewillconsidertheproblemoftheformofalgebraicdifferentialequationwithadmissiblemeromorphicsolution[Ω1 (z ,w) /Ω2 (z ,w) ] m =∑nj=0aj(z)wj,(1 )whereΩ1 (z,w) =∑(i)a(i) (z)wi0 (w′) i1… (w(n) ) in,Ω2 (z,w) =∑( j)b( j) (z)wj0 (w′) j1… (w(n) ) jn,(i) ,(j)arefiniteindexsets,{ai(z) } ,{a(i) (z) }and {a(i) (z) }aremeromorphicfunctions,T(r,a(i) ) =o(T(r,w) ) ,T(r,ai) =o(T(r ,w) ) ,T(r,b(j) ) =o(T(r ,w) ) .Letw(z)beameromorphicsolutionof (1 ) .Ifw(z)satisfies…     

有效商Myerson值的公理化刻画

在具有图结构的合作对策中，Myerson值(Myerson, 1977)是一个著名的分配规则，它可以由分支有效性和公平性或者平衡贡献性所唯一确定。在实际中，图结构可能并不影响大联盟的形成，只是由于参与者在网络中所处的位置不同，对其讨价还价能力会产生影响。换句话说，图结构会对分配格局产生影响，但对大联盟的形成没有影响。这促使人们开始考虑Myerson值的有效推广问题。文献中已经提出了Myerson的几种有效推广形式。2020年，Li和Shan提出了有效商Myerson值并给出了公理化刻画，它是Myerson值一种新的有效推广形式。本文首先引入了准商盈余公平性这一性质，然后结合有效性和Myerson值黏性给出了有效商Myerson值的新公理化刻画。其次，通过应用案例，将该值和其他值做了比较分析。     

"NCD"系统中保险双方的最优决策

在"NCD"系统中,利用Markov决策过程,获得了投保双方博弈行为的最优结果.对被保险人来说,确定了其最优临界损失值;对保险人来说,确定了最优保费与折扣值.     

"函数、极限与连续"教学中的两个问题

对于多值函数和复合函数极限的一些说法发表了看法。     

矩阵广义Schur补的复合矩阵的 L"owner偏序与奇异值

本文把矩阵广义Schur补和复合矩阵结合起来,研究了一个mn复矩阵的广义Schur补及其共轭转置之积的复合矩阵的Lowner偏序,并给出相关复合矩阵的奇异值不等式,推广了近期的一些结果.     

关於"Урысон算子正、负固有值的全局特征和应用"一文的注记

不设函数k(x,y,u)≥0(x,y∈G,u∈[0, ∞)),对於超幂型Урысон算子得出某种关於原点对称的两个无穷区间中的每一个实数皆为它的固有值.其结果也适用於一般的Урысон算子.     

从"费马点"谈起

法国数学家费马1640年前后向意大利物理学家托里拆利提出这样-个问题:在已知△ABC所在的平面上求一点P,使它到三角形三顶点的距离之和最小.这个问题中所求的点被人们称为"费马点".类似这样的最值问题令人着迷,催人思考,在平面几何中占居一席之地实施新课改以来,古老的最值问题以崭新的姿态频频出现在各地中考试卷上,笔者以近几年中考数学试题为例,介绍几种不同类型的线段最值问题及解题策略,仅供参考.     

模糊乘积的“失效”与“失真”的一个判定

给出模糊乘积"失真"的充要条件,并讨论模糊乘积的"失效"与"失真"的关系.     

模糊乘积的"失效"与"失真"的一个判定

给出模糊乘积"失真"的充要条件,并讨论模糊乘积的"失效"与"失真"的关系.     

"Freezing" and "defreezing" effects in the photoelastic investigation of temperature stresses

The "freezing" and "defreezing" temperature limits of an optically active material based on an epoxy resin have been experimentally investigated. A method of determining the mean value of the optical coefficient when the material is heated on the "freezing" temperature range is considered. The lower "defreezing" temperature limit has been experimentally established. The results of the investigation are presented in the form of graphs.Translated from Mekhanika Polimerov, No. 3, pp. 501–506, May–June, 1976.     

“数学模型”课程教学模式的探讨

本文介绍了开设“数学模型”课程在工科院校数学教学改革中的重要性．并讨论如何组织“数学模型”课程的教学．     

“准最优基”程序实现与应用探讨

在利用"准最优基"简化单纯形法的求解过程的基础上,采用matlab将"准最优基"方法程序化,并采用程序进行了模型.求解原采用两阶段法求解的线性规划问题,用"准最优基"方法,不必加入人工变量,改两阶段为一阶段,简化了求解过程,并针对只能将其目标函数系数为正的变量进基、约束条件都为正的局限性进行了探讨."准最优基"方法对目标函数的系数有正有负的情况,约束条件的系数有正有负的情况都适用.借助"bland法则"的思想,按下标顺序进基取代变量强度系数进基,得出了同样的结果,并对E.Beale的循环例子进行计算,一步得出最优解."准最优基"方法既可以提高运算速度,同时具有很好的适用性.     

Subspace partitions of Fqn containing direct sums

Let $q$ be a prime power and $n$ be a positive integer. A subspace partition of $V={\mathbb{F}}_q^n$, the vector space of dimension $n$ over ${\mathbb{F}}_q$, is a collection $\Pi$ of subspaces of $V$ such that each nonzero vector of $V$ is contained in exactly one subspace in $\Pi$; the multiset of dimensions of subspaces in $\Pi$ is then called a Gaussian partition of $V$. We say that $\Pi$contains a direct sum if there exist subspaces $W_1,\dots ,W_k\in \Pi$ such that $W_1\oplus ?\oplus W_k=V$. In this paper, we study the problem of classifying the subspace partitions that contain a direct sum. In particular, given integers $a_1$ and $a_2$ with $n>a_1>a_2\ge 1$, our main theorem shows that if $\Pi$ is a subspace partition of ${\mathbb{F}}_q^n$ with $m_i$ subspaces of dimension $a_i$ for $i=1,2$, then $\Pi$ contains a direct sum when $a_1{x}_1+a_2{x}_2=n$ has a solution $(x_1,x_2)$ for some integers $x_1,x_2\ge 0$ and $m_2$ belongs to the union $I$ of two natural intervals. The lower bound of $I$ captures all subspace partitions with dimensions in $\{a_1,a_2\}$ that are currently known to exist. Moreover, we show the existence of infinite classes of subspace partitions without a direct sum when $m_2?I$ or when the condition on the existence of a nonnegative integral solution $(x_1,x_2)$ is not satisfied. We further conjecture that this theorem can be extended to any number of distinct dimensions, where the number of subspaces in each dimension has appropriate bounds. These results offer further evidence of the natural combinatorial relationship between Gaussian and integer partitions (when $q\to 1$) as well as subspace and set partitions.     

“一站式”远程开放实验平台的设计与实现

"一站式"远程开放实验平台需要集成和整合分别多个来自不同厂商的实践教学软件,而不同的实践教学软件又有各自不同的用户系统与管理平台.针对这一情况,阐述了"一站式"远程开放实验平台的设计思路,并论述了"一站式"远程开放实验平台通过单点登录解决跨平台接口技术,通过Web Service方法实现平台对实践教学软件的数据的采集以及平台的权限设计与实现等关键技术.     

High Order Energy-Preserving Method of the "Good" Boussinesq Equation

The fourth order average vector field (AVF) method is applied to solve the "Good" Boussinesq equation. The semi-discrete system of the "good" Boussinesq equation obtained by the pseudo-spectral method in spatial variable, which is a classical finite dimensional Hamiltonian system, is discretized by the fourth order average vector field method. Thus, a new high order energy conservation scheme of the "good" Boussinesq equation is obtained. Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the "good" Boussinesq equation exactly and simulate evolution of different solitary waves well.     

The Dvoretzky-Hanani Theorem for the Group "ax + b"

Let G be the group "ax + b" of affine transformations of the line and let U be a neighbourhood of 1 in G. It is proved that there is another neighborhood V of 1 such that to each finite sequence g1,...,gn V there corresponds a sequence of signs 1,...,n = ±1 with U for k = 1,...,n. This implies that G satisfies the following analogue of the Dvoretzky-Hanani theorem: to each sequence converging to 1 in G there corresponds a sequence of signs k = ±1 such that the infinite product is convergent.