A control problem for Burgers' equation with bounded input/output

A stabilization problem for Burgers' equation is considered. Using linearization, various controllers are constructed which minimize certain weighted energy functionals. These controllers produce the desired degree of stability for the closed-loop nonlinear system. A numerical scheme for computing the feedback gain functional is developed and several numerical experiments are performed to illustrate the theoretical results.     

Complete Asymptotic Expansions of Solutions of the System of Elastostatics in the Presence of an Inclusion of Small Diameter and Detection of an Inclusion

We consider the system of elastostatics for an elastic medium consisting of an imperfection of small diameter, embedded in a homogeneous reference medium. The Lamé constants of the imperfection are different from those of the background medium. We establish a complete asymptotic formula for the displacement vector in terms of the reference Lamé constants, the location of the imperfection and its geometry. Our derivation is rigorous, and based on layer potential techniques. The asymptotic expansions in this paper are valid for an elastic imperfection with Lipschitz boundaries. In the course of derivation of the asymptotic formula, we introduce the concept of (generalized) elastic moment tensors (Pólya–Szegö tensor) and prove that the first order elastic moment tensor is symmetric and positive (negative)-definite. We also obtain estimation of its eigenvalue. We then apply these asymptotic formulas for the purpose of identifying with high precision the order of magnitude of the diameter of the elastic inclusion, its location, and its elastic moment tensors.     

Vanishing of Rabinowitz Floer homology on negative line bundles

Following Frauenfelder (Rabinowitz action functional on very negative line bundles, Habilitationsschrift, Munich/München, 2008), Albers and Frauenfelder (Bubbles and onis, 2014. arXiv:1412.4360) we construct Rabinowitz Floer homology for negative line bundles over symplectic manifolds and prove a vanishing result. Ritter (Adv Math 262:1035–1106, 2014) showed that symplectic homology of these spaces does not vanish, in general. Thus, the theorem \(\mathrm {SH}=0\Leftrightarrow \mathrm {RFH}=0\) (Ritter in J Topol 6(2):391–489, 2013), does not extend beyond the symplectically aspherical situation. We give a conjectural explanation in terms of the Cieliebak–Frauenfelder–Oancea long exact sequence Cieliebak et al. (Ann Sci Éc Norm Supér (4) 43(6):957–1015, 2010).     

微信用户数发展趋势的理论分析与因素探讨

给出Logistic,Gompertz,Usher和Von Bertalanffy 4种增长曲线的拐点、最大加速点和最大减速点的表达式.利用R语言编写程序,结合拟牛顿算法与随机优化算法,对微信月活跃用户数(WMAUs)的发展趋势进行分析与拟合.结果表明,4条曲线的拟合值在最大加速点到最大减速点时间段内基本吻合,但在初期和后期有所差别.Logistic曲线在初期的预测值偏大,而后期偏小,偏差相对较大;Von Bertalanffy曲线的偏差最小,且在饱和值、拐点、最大加速点、最大减速点及拟合优度的估计值方面都优于另外3种曲线;Usher和Gompertz曲线居于Logistic与Von Bertalanffy曲线之间,对后期的预测值有些保守.最后,基于价值理念的观点分析了影响WMAUs变动的主要因素.     

Modelling the Effects of Pest Control with Development of Pesticide Resistance

In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive different...     

Singular Functions and Characterizations of Field Concentrations: a Survey

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics(Laplace equation), linear elasticity(Lamé system), and viscous flow(Stokes system). This paper is to review such progress in a coherent way.     

一个具有三次非线性项的可积两分量Camassa-Holm系统解的持久性

研究了一个具有三次非线性项的可积的两分量Camassa-Holm系统Cauchy问题解的持久性.通过用权函数估计的方法证明:如果两分量Camassa-Holm系统的初值以及初值的空间导数都以指数形式衰减,则两分量Camassa-Holm系统的强解也在无穷远处以指数形式衰减,进一步,给出了动量的最优衰减估计.     

小尺寸管道内二氧化碳抑制甲烷爆炸效果的实验及数值模拟

为了有效防治矿井瓦斯爆炸事故, 以瓦斯的主要成分甲烷作为模拟气体, 运用自主设计改装的XKWB-S型小尺寸石英玻璃管道实验系统, 结合高速摄影仪, 并采用FLACS数值模拟软件, 研究惰性气体抑爆条件下甲烷燃烧爆炸特性, 进行体积分数为6%~27%的CO₂抑制体积分数为9%CH₄爆炸的实验及数值模拟, 结果表明:各组分混合气体在爆炸传播过程中, 爆炸压力、火焰锋面速度和气体运动速度均呈现一定程度的波动, 且压力和速度没有同时达到最大值; CO₂的加入有效抑制了甲烷/空气反应, 且添加CO₂体积分数越大, 抑爆效果越明显, 模拟结果与实验结果基本吻合。