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.     

关于工科“线性代数”课程中的反问题

讨论了工科"线性代数"课程中涉及到的几类简单的反问题,给出了解的存在条件与一般解法.     

Enlargement of Monotone Operators with Applications to Variational Inequalities

Given a point-to-set operator T, we introduce the operator T defined as T(x)= {u: u – v, x – y – for all y Rn, v T(y)}. When T is maximal monotone T inherits most properties of the -subdifferential, e.g. it is bounded on bounded sets, T(x) contains the image through T of a sufficiently small ball around x, etc. We prove these and other relevant properties of T, and apply it to generate an inexact proximal point method with generalized distances for variational inequalities, whose subproblems consist of solving problems of the form 0 H(x), while the subproblems of the exact method are of the form 0 H(x). If k is the coefficient used in the kth iteration and the k's are summable, then the sequence generated by the inexact algorithm is still convergent to a solution of the original problem. If the original operator is well behaved enough, then the solution set of each subproblem contains a ball around the exact solution, and so each subproblem can be finitely solved.     

Local symmetries and conservation laws

Starting with Lie's classical theory, we carefully explain the basic notions of the higher symmetries theory for arbitrary systems of partial differential equations as well as the necessary calculation procedures. Roughly speaking, we explain what analogs of higher KdV equations are for an arbitrary system of partial differential equations and also how one can find and use them. The cohomological nature of conservation laws is shown and some basic results are exposed which allow one to calculate, in principle, all conservation laws for a given system of partial differential equations. In particular, it is shown that symmetry and conservation law are, in some sense, the dual conceptions which coincides in the self-dual case, namely, for Euler-Lagrange equations. Training examples are also given.Translated from the Russian by B. A. Kuperschmidt.     

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.     

Mutational equations in metric spaces

This paper summarizes an extension of differential calculus to a mutational calculus for maps from one metric space to another. The simple idea is to replace half-lines allowing to define difference quotients of maps and their various limits in the case of vector space by transitions with which we can also define differential quotients of a map. Their various limits are called mutations of a map. Many results of differential calculus and set-valued analysis, including the Inverse Function Theorem, do not really rely on the linear structure and can be adapted to the nonlinear case of metric spaces and exploited. Furthermore, the concept of differential equation can be extended tomutational equation governing the evolution in metric spaces. Basic Theorems as the Nagumo Theorem, the Cauchy-Lipschitz Theorem, the Center Manifold Theorem and the second Lyapunov Method hold true for mutational equations.This work was motivated by evolution equations of tubes in visual servoing on one hand, mathematical morphology on the other, when the metric spaces are power spaces. This paper begins by listing some consequences of general theorems concerning mutational equations for tubes.     

Homological finiteness properties of monoids, their ideals and maximal subgroups

We consider the general question of how the homological finiteness property left-(resp. right-) holding in a monoid influences, and conversely depends on, the property holding in the substructures of that monoid. This is done by giving methods for constructing free resolutions of substructures from free resolutions of their containing monoids, and vice versa. In particular, we show that left- is inherited by the maximal subgroups in a completely simple minimal ideal, in the case that the minimal ideal has finitely many left ideals. For completely simple semigroups, we prove the converse, and as a corollary, show that a completely simple semigroup is of type left- and right- if and only if it has finitely many left and right ideals and all of its maximal subgroups are of type . Also, given an ideal of a monoid, we show that if the ideal has a two-sided identity element then the containing monoid is of type left- if and only if the ideal is of type left-. Applying this result, we obtain necessary and sufficient conditions for a Clifford monoid (and more generally a strong semilattice of monoids) to be of type left-. Examples are provided showing that for each of the results all of the hypotheses are necessary.