单位圆内拟亚纯映射的重值

单位圆内充满圆序列是一个复杂的问题,该文改进了现有一些证法,使单位圆内充满圆证法类似于平面上充满圆证法.同时得到单位圆内K-拟亚纯映射涉及重值的充满圆序列及相应的奇异半径     

单位圆内无限级拟亚纯映射的充满圆

本文研究了单位圆内无限级拟亚纯映射的充满圆，证明了单位圆内存在充满圆序列；Borel点邻域内存在充满圆序列．     

熟悉圆的性质用好基本辅助线

初中数学当中,圆是最优美的图形.它内涵丰富、性质多样.圆的性质定理有:圆的基本性质、垂径定理、圆周角性质定理、圆的对称性、圆的切线的性质等.它们对应了圆中的条基本辅助线.     

相交圆内一类内接蝶形的等积性质

笔者对相交圆内接蝶形进行探究时,得到了两个有趣的等积性质.为了陈述方便,先给出如下定义:定义 两圆相交,若一个圆的圆弧含于另一个圆内,则称此段圆弧为该圆的内弧;若一个圆的圆弧不含于另一个圆内,则称此段圆弧为该圆的外弧.其中内弧和外弧均不包含两圆交点.如图1所示,(⌒)AGB为圆O2的内弧,(⌒)ACB为圆O1的外弧.     

相交圆内接蝶形的等积性质

笔者对相交圆内接蝶形进行探究时,得到了两个有趣的等积性质.定义两圆相交,若一个圆的圆弧含于另一个圆内,则称此段圆弧为该圆的内弧;若一个圆的圆弧不含于另一个圆内,则称此段圆弧为该圆的外弧.其中内弧和外弧均不包含两圆交点.如图1所示,(AGB)为⊙O2的内弧,ACB为⊙O1的外弧.     

两圆相切的判定及应用

初中教科书在介绍圆和圆的位置关系时,给出了两圆相切的判定方法,即:设两圆的半径分别为R和r,圆心距为d,若d=R+r,则两圆外切;若d=R-r(R>r),则两圆内切.本文不妨统称为"圆心距法".下面介绍另一种判定方法,这里统称为"公切线法".一、两圆相切的判定1.两圆外切的判定过两圆的公共点作     

单位圆内亚纯函数的充满圆

本文推广了Ahlfors不等式，给出了亚纯函数的充满圆的一个几何特征，从而证明了单位圆内亚纯函数的充满圆序列的存在性.此外还举例说明了这些结果就充满圆的指数而言是最好的．     

构造辅助圆,解决“等长共点”问题

<正>由于圆具有丰富的性质:(1)圆的对称性;(2)等圆或同圆中不同名称量的转化;(3)与圆相关的角;(4)圆中比例线段.适当发现并添出辅助圆,就为圆的丰富性质的运用创造了条件,在解题时会收到意想不到的效果.添补辅助圆的常见方法有:1.利用圆的定     

串点连线，一题多变——以“圆”的综合复习为例

<正>圆是常见的几何图形之一,是进一步学习数学以及其他学科的重要基础.小学阶段初步学习了圆的概念,初中阶段系统地学习圆的概念和性质,高中阶段将继续学习圆的方程.由此可见圆在几何学习中的重要性.圆的有关性质是进一步研究圆与其他图形关系的主要依据,是学习圆的基础.近年来,圆的基本性质成为了广东省中考选择题、填空题或是解答题第24题的高频考点,也成了日常教学的重难点.1 教学目标本节课的教学任务是巩固圆中弧与角的关系,     

系列平行图的围长和圆可选性

本文讨论了系列平行图的圆可选性．令x_(c,l)表示圆可选性(或圆列表着色数)．本文证明了围长至少是4n 1的系列平行图的圆可选性至多为2 1/n．     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

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.     

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.     

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.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Unsteady motion of a spherical bubble in a complex fluid: Mathematical modelling and simulation

The nonlinear response of an oscillatory bubble in a complex fluid is studied. The bubble is immersed in a Newtonian liquid, which may have a dilute volume fraction of anisotropic additives such as fibers or few ppm of macromolecules. The constitutive equation for the fluid is based on a Maxwell model with an extensional viscosity for the viscous contribution. The model is considered new in the study of bubble dynamics in complex fluids. The numerical computation solves a system of three first order ordinary differential equations, including the one associated with the solution of the convolution integral, using a fifth order Runge–Kutta scheme with appropriated time steps. Asymptotic solutions of governing equation are developed for small values of the pressure forcing amplitude and for small values of the elastic parameter. A study of the bubble collapse radius is also presented. We compare the results predicted by our model with other model in the literature and a good agreement is observed. The calculated asymptotic solutions are also used to test the results of the numerical simulations. In addition, the orientation of the additives is considered. The angular probability density function is assumed to be a normal distribution. The results show that the model based on the fully aligned additives with the radial direction overestimates the tendency of the additives to stabilize the bubble motion, since the effect of extensional viscosity occurs due to the particle resistance to the movement throughout its longitudinal direction.     

基于NSGA-Ⅱ的应急储备库多目标

应急物资储备库选址问题是在近年世界灾害多发的现实背景下产生的,根据具体选址问题特点建立了多目标选址决策模型。该模型综合考虑了两种灾害风险下储备库的成本费用、覆盖效率以及对重点地区的备用覆盖,以使模型更加符合实际目标及约束情况。算法设计上,首次采用带精英策略的非支配排序遗传算法(Fast and elitist Non-dominated Sorting Genetic Algorithm Ⅱ,NSGA-Ⅱ)解决储备库多目标选址问题,得到了Pareto非劣解分布并同不带精英策略的常规NSGA算法下的仿真结果进行对比分析。验证了模型的可行性以及NSGA-Ⅱ在解决储备库多目标选址问题的有效性。     

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。     

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.

     

Mathematical modeling of time fractional reaction–diffusion systems

We study a fractional reaction–diffusion system with two types of variables: activator and inhibitor. The interactions between components are modeled by cubical nonlinearity. Linearization of the system around the homogeneous state provides information about the stability of the solutions which is quite different from linear stability analysis of the regular system with integer derivatives. It is shown that by combining the fractional derivatives index with the ratio of characteristic times, it is possible to find the marginal value of the index where the oscillatory instability arises. The increase of the value of fractional derivative index leads to the time periodic solutions. The domains of existing periodic solutions for different parameters of the problem are obtained. A computer simulation of the corresponding nonlinear fractional ordinary differential equations is presented. For the fractional reaction–diffusion systems it is established that there exists a set of stable spatio-temporal structures of the one-dimensional system under the Neumann and periodic boundary conditions. The characteristic features of these solutions consist of the transformation of the steady-state dissipative structures to homogeneous oscillations or space temporary structures at a certain value of fractional index and the ratio of characteristic times of system.