自由群的直积的检验元素的注记

本文研究了自由群的直积的检验元素,通过对直积的自同态的分解,得到了直积中的元素为检验元素的充分必要条件,改进了O'neill和Turner的结果.此外,构造了两类具体的检验元素.     

环的投射自由性的研究

引进了两类新环,进而研究了其投射自由性,得到了群环上的模结构,推广了Quillen-Suslin定理.     

幂格与商格的关系的注记

研究了分配格上的幂格,给出了格的相对凸子格的概念,得到了分配格上的幂格的一个充要条件,建立了幂格与商格的联系.     

基于GRA-DEA模型的有关农民收入的九城市的评价

有关农民收入,文章以山西省九个城市为例进行了评价.首先用灰色关联分析法分析了2016年这些城市的有关数据,筛选出影响农民收入的主要因素;其次构建了指标体系,利用数据包络分析法对有关农民收入九个城市进行了DEA有效性评价;再次对非DEA有效的城市,借助投影公式探索了改进方法;最后得出了九城市分为两类的结论,提出了针对性的建议.     

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.     

由自然数的因子构成的半群

本文首先介绍了半群、群的定义,研究了自然数n取何值时,通过定义相应的代数运算,使得它的因子集构成半群、群,从而为半群的代数理论提供了一个有趣的实例.     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

基于小波变换的信号突变检测的方法

本文利用高斯函数的正整数阶导函数的一个性质,给出了一种探测信号奇异性的方法,得到了奇异点的位置,阶数α以及相应的平滑因子a和k,推导出了α满足的方程,对文献[8]的结论进行了推广.最后进行了数值试验,相对Mallat定理的10%的误差,取得了较好的效果.     

含有共轭三键的高聚物的掺杂机制的探讨

本文从实验事实出发,对含有共轭三键的共轭高聚物——聚丁二炔的掺杂及电导的特点进行了详细的分析;对聚丁二炔晶体掺杂的机制进行了初步的探讨;从结构相变的角度出发,提出了一个掺杂模型,并从能量的角度估算了由于掺杂引起链段结构改变所需的能量,较好地解释了聚丁二炔晶体掺杂未取得成功的原因.     

基于FAHP的择偶偏好的探讨

择偶是社会成员以婚恋为目的选择异性对象的一种行为,是婚姻过程中一个十分重要的环节,如何选择一个适合自己的配偶就成为了当今社会的一个重要问题.从解决多属性决策问题的角度来思考择偶问题,并采用了层次分析法与模糊理论相结合的方法对择偶的评价与选择进行了分析,初次提出了择偶吻合度的概念,并在此基础上建立了择偶指标评价体系模型.通过案例具体分析了择偶的评价与选择的过程,分析结果表明方法处理择偶问题是有效的.     

Boundary-Value Problems of the Theory of Thin and Nonthin Orthotropic Shells with Account of Nonlinearly Elastic Properties and Low Shear Rigidity of Composite Materials

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.     

On the hyperbolicity of the period-doubling fixed point

We give a new proof of the hyperbolicity of the fixed point for the period-doubling renormalization operator using the local dynamics near a semi-attractive fixed point (in a Banach space) and the theory of holomorphic motions. We also give a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the period-doubling fixed point: our proof uses the non-existence of invariant line fields in the period-doubling tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument.

     

颤振分析中的特征值排序问题

颤振分析中判断颤振临界速度的重要依据是系统V-g和V-f图,即系统特征值随参数的变化曲线.在几乎所有商用软件及自编程序的输出结果中,有时会出现所谓的"窜支"现象,这给颤振临界速度和颤振穿越分支及耦合形式的判断带来很大不便.通过隐函数定理可以证明,除重特征值点以外,系统特征值连续依赖于系统参数变化.依据多元向量值函数连续性,建立对特征值的排列算法,给出系统特征根轨迹的正确曲线,再输出V-g和V-f图数据,从而避免"窜支"现象.编制应用程序,通过几个典型算例对算法进行了验证.该工作能够有效简化颤振分析的后处理工作,提高分析效率.     

Effects of permeability and viscosity in linear polymeric gels

We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum of the polymer and liquid components of the gel. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a fluid. The problems that we study are motivated by predictions of the life cycle of body‐implantable medical devices. Scaling arguments suggest neglecting inertia terms, and therefore, we consider the quasi‐static approximation to the dynamics. We focus on the linearized system about stress‐free states, uniform expansions, and compressions and derive sufficient conditions for the solvability of the time‐dependent problems. These turn out to be conditions that guarantee local stability of the equilibrium solutions. We also consider non‐stress free equilibria and states with residual stress and derive an energy law for the corresponding time‐dependent system. The conditions that guarantee stability of solutions provide a selection criteria of the material parameters of devices. The boundary conditions that we consider are of two types, displacement‐traction and permeability of the gel surface to the fluid. We address the cases of viscous and inviscid solvent, assume Newtonian dissipation for the polymer component, and establish existence of weak solutions for the different boundary permeability conditions and viscosity assumptions. We present two‐dimensional, finite element numerical simulations to study stress concentration on edges, this being the precursor to debonding of the gel from its substrate. Copyright © 2015 John Wiley & Sons, Ltd.     

树脂基复合材料粘接的优化设计

本文在试验数据和理论分析的基础上,提出树脂基复合材料单搭接的优化设计的原则,胶粘剂的选择、被粘物的设计,粘接长度的选择、胶层厚度的选择等.认为通过优化设计可以提高粘接强度,减轻产品的重量,提高其质量.     

EPR制度下的家电以旧换新回收策略优化模型

研究生产者责任延伸制度(EPR)约束下,家电生产销售企业集中决策下实施以旧换新进行废旧产品回收的问题。在对家电消费者市场结构进行分析基础上,建立以企业利润最大化为目标的实施以旧换新回收策略的优化模型,并根据我国家电行业EPR制度的特点,构建政府与企业间竞争的Stackelberg博弈模型,研究在政府环境效益最优时的补贴和基金征收标准下,企业以旧换新回收产品最优定价决策;同时,与企业不直接参与废旧产品回收时单一定价相应结果进行比较。结果表明:在EPR约束下,政府环境效益最优时的补贴和基金征收标准,对企业实施以旧换新回收策略的产品销量、总利润和废旧产品回收量的影响取决于企业成本结构、消费者结构、消费者效用和废旧产品回收处理能力。企业决策者需根据不同情形决定是否参与以旧换新回收实践。     

拍卖机制设计在区块链中的应用与挑战

区块链是新一代信息技术的重要组成部分,是分布式网络、加密技术、智能合约等多种技术集成的新型数据库软件。过去的十多年,区块链技术在全球范围内产生广泛影响。如今的区块链技术,已从最初的关注于解决货币和支付的去中心化问题,转入到解决市场的去中心化问题。智能合约的出现使得基于区块链技术的去中心化金融进入高速发展状态,也涌现出区块链环境下的各类拍卖场景。本文首次从机制设计角度,以区块链交易费机制,非同质化代币(Non-Fungible Token,NFT)拍卖和矿工可提取价值(Miner-Extractable Value,MEV)交易位置拍卖为主要对象,总结和剖析近些年来区块链上特有的拍卖机制;并针对区块链特性,提出区块链上拍卖机制设计所面临的挑战和未来亟待解决的问题。     

The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation

In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions at the irregular singular point for the unfolded system. Our study covers a full neighborhood of the origin in the confluence parameter space. In particular, we show how the divergence of solutions at the irregular singular point explains the presence of logarithmic terms in the solutions at a regular singular point of the unfolded system. For this study, we consider values of the confluence parameter taken in two sectors covering the complex plane. In each sector, we study the monodromy of a first integral of a Riccati system related to the hypergeometric equation. Then, on each sector, we include the presence of logarithmic terms into a continuous phenomenon and view a Stokes multiplier related to a 1-summable solution as the limit of an obstruction that prevents a pair of eigenvectors of the monodromy operators, one at each singular point, to coincide.     

Comparison principle and analogues of the phragmen—lindelöf theorem for solutions of parabolic inequalities

It is well known that a Monotonicity Condition and a Coerciveness Condition principally lie in the basis of most results of the Theory of PDE's. The necessity of these important assumptions for the validity of a comparison principle and analogues of the Phragmen-Lindelöf theorem for solutions of quasilinear parabolic inequalities is discussed in the paper. In the first part of the work we introduce a new concept of monotonicity for nonlinear differential operators-nonlinear monotonicity concept-and on its basis we obtain new phenomena for solutions, subsolutions and supersolutions of the well-known quasilinear differential equations. In the second part we omit the current coerciveness condition and change it by a weaker one. In spite of this we obtain a series of new qualitative properties of solutions for wide classes of quasilinear parabolic inequalities. Most of these properties are also new for solutions of the well-known equations, which we consider in the paper.     

公众参与视角下的央地环境规制博弈分析

本文首先构建环境规制中中央政府和地方政府的两方演化博弈模型,并在此基础上将公众作为第三方参与主体,构建中央政府、地方政府和公众三方演化博弈模型,详细比较两方和三方博弈模型的区别,探究各个主体策略行为的影响因素。研究发现:(1)未有公众参与下,地方政府策略选择主要受地方政府积极执行成本、环境收益、经济损失,消极执行的环境政绩损失,中央政府监管力度、治理补贴和对地方政府的处罚等因素影响;中央政府的监管策略主要受到严格监管的成本以及对地方政府的治理补贴和处罚等因素影响。引入公众参与后,在央地两方博弈的基础上,地方政府环境规制执行策略的影响因素还增加了地方政府被举报后所受到的追加处罚,中央政府监管策略的影响因素还增加了中央政府监管力度、对地方政府的追加处罚以及中央政府的公信力损失。(2)未有公众参与下,中央政府严格监管的概率随地方政府积极执行概率的增大而减小。引入公众参与后,中央政府严格监管率随地方政府积极执行概率的增大而增大。说明在公众参与下,地方政府积极执行环境规制对中央政府严格监管产生的抑制作用转变成了促进作用。(3)地方政府积极执行的概率、中央政府严格监管的概率都随公众举报概率的增大而增大。说明公众参与不仅对地方政府承担环保责任具有促进作用,而且有利于促使中央政府落实环境治理政策。