运输问题"悖论"存在的条件及解决方法

首先探讨了运输问题"悖论"存在的条件和表上作业法的调整方法,然后指出了通过运输问题数学模型挖潜的方法,最后给出了"多反而少"现象存在的对偶条件.     

隐含条件的"藏身"处

隐含条件指题目中不易观察到的条件,因其"身形"隐蔽,给审清题意、正确解答制造了障碍.可以这样说,能否发现、挖掘并正确利用隐含条件是顺利解题的关键.笔者现将一些中考题中隐含条件的藏"身"处"一一揭穿",以飨读者.     

计算数学期望和概率的条件化方法

借助于条件数学期望和随机事件A的示性函数IA,通过对随机变量的适当"条件化"处理,应用全期望公式和推广的全概率公式,讨论了计算数学期望和概率的条件化方法.     

时滞格微分方程组的行波解

文利用Schauder不动点定理的方法和上、下解技巧,研究了时滞格微分方程组的行波解,给出了当系统的非线性项满足"拟单调条件"和"指数拟单调条件"时行波解的存在性.     

无穷多海洋表面波共振的Zakharov方程

从基本的波之"能量、动量、作用量"守恒定律出发,遵照普适的"对称性决定相互作用"法则和"Hamilton"结构,运用Hamilton海洋表面波复正则方程、正则变换及其Poisson括号条件,并结合经典的3-4-5-波共振条件,推导出两大类"无穷多海洋表面波相互作用的共振条件";相应地就建立了两大类"无穷多海洋表面波共振的Zakharov方程".以此,就为最具根本性、普遍性的海洋波湍流搭建了一个必备、先行和完备的理论框架.     

当等号不能成立时

我们知道,在应用均值不等式求有关函数的最值时,必须注意"一正(各项均为正数)、二定(和或积为定值)、三相等(等号能否取到)"三个条件.若忽略了某个条件,应用它求最值就会出错,特别是"取得等号"这个条件最易被忽视.或者说,当不能取等号时,求函数最值就显得无能为力了.事实     

BL代数的fantastic滤子和normal滤子

滤子是研究逻辑代数的有效工具.本文研究了BL代数的fantastic和normal滤子的等价条件,得到了在MV-代数中两种滤子之间的等价性,给出了两个公开问题:"在什么样的合适条件下,一个normal滤子成为一个fantastic滤子?"和"在什么合适的条件下,normal滤子的拓展性成立?"结论成立的一种条件.     

一类具漂移的“跳-停”奇异型随机控制

以随机分析和最优控制理论为基础,讨论了一类带停时的奇异型随机控制问题.在原模型状态过程的基础上添加了漂移因子,并将原模型中的控制费用函数推广为一般的费用函数.在某些条件下,得到"跳一停"策略是其最优控制策略,并给出了"跳一停"策略存在的条件以及控制方法,所得的结论在实际中有较深的应用背景.     

“同心协力”策略研究

针对"同心协力"拓展项目中队员的协同控制问题,建立了在理想条件下的最优策略模型,以及在非精确控制条件下的鼓面倾斜模型,讨论了稳定性要求对最优策略的影响,给出当球跳动方向偏离竖直方向后,鼓的控制方法及效果.最后对2019年"高教社杯"全国大学生数学建模竞赛B题的参赛论文予以简要评述.     

对问题204评析中《选登2》一文的思考

《数学通讯》(教师版)2011年第11期发表了邓超老师对问题204的评析,即评析中的《选登2》一文.邓超老师在该文中认为只要将函数f(x)的定义域由"实数集R"改为"闭区间[0,1]",而其它条件不变,则符合题目条件的函数f(x)就存在了,且     

A Comparison of Methods for Estimating the Extremal Index

The extremal index, (01), is the key parameter when extending discussions of the limiting behavior of the extreme values from independent and identically distributed sequences to stationary sequences. As measures the limiting dependence of exceedances over a threshold u, as u tends to the upper endpoint of the distribution, it may not always be informative about the extremal dependence at levels of practical interest. Therefore we also consider a threshold-based extremal index, (u). We compare the performance of a range of different estimators for and (u) covering processes with < 1 and = 1. We find that the established methods for estimating actually estimate (u), so perform well only when (u) . For Markov processes, we introduce an estimator which is as good as the established methods when (u) but provides an improvement when (u) < = 1. We illustrate our methods using simulated data and daily rainfall measurements.     

血液分组化验问题二次分组化验法最佳分组方式的算法

针对血液分组化验问题,进行了严密的数学分析和数学证明,给出了一次分组化验法最佳k_1值的简单精确计算方法;特别是通过对引理及定理3证明推导出二次分组化验法中每人平均化验次数计算公式;通过对定理4-5证明,总结出二次分组化验法最佳分组时k1和k2的计算方法.同时给出了二次分组化验法最佳分组时p与k_1和k_2对照表,以及一次分组化验法最佳分组时p与k_1对照表.     

Computations in choice groupoids

Defining achoice as a mapping of the subsets of a setX into their respective subsets, a one-to-one (and naturally) corresponding binary operation,sequential choice, is identified under which the power set ofX is closed as achoice groupoid. A complete logical diagram is given, exhibiting all the implications between conjunctions of the seven conditions: (1) idempotence, (2) consistency, (3) absorbence, and (4) homomorphism of a choice, and (5) commutativity, (6) associativity, and (7) path-independence of the corresponding sequential choice.     

Common complements of two subspaces of a Hilbert space

In this paper we find a necessary and sufficient condition for two closed subspaces, and , of a Hilbert space to have a common complement, i.e. a subspace having trivial intersection with and and such that .Unlike the finite-dimensional case the condition is significantly more subtle than simple equalities of dimensions and codimensions, and non-trivial examples of subspaces without a common complement are possible.     

Comodules and Landweber exact homology theories

We show that, if E is a commutative MU-algebra spectrum such that is Landweber exact over , then the category of -comodules is equivalent to a localization of the category of -comodules. This localization depends only on the heights of E at the integer primes p. It follows, for example, that the category of -comodules is equivalent to the category of -comodules. These equivalences give simple proofs and generalizations of the Miller-Ravenel and Morava change of rings theorems. We also deduce structural results about the category of -comodules. We prove that every -comodule has a primitive, we give a classification of invariant prime ideals in , and we give a version of the Landweber filtration theorem.