Relaxation of a Bolza Problem Governed by a Time-Delay Sweeping Process

We study in an infinite dimensional Hilbert space a Bolza problem in which the dynamics are given by a time-delay perturbed sweeping process. This is a differential inclusion whose right-hand side involves a normal cone to a moving set, along with a time-delay perturbation. A relaxation result is established from which we deduce a sufficient condition ensuring the existence of an optimal solution.     

Existence and Upper Semicontinuity of the Attractor for a Singularly Perturbed Navier-Stokes Equation

Suppose Rn, n = 2,3 be a smooth bounded domain, we consider the perturbed Navier-Stokes equationequation ut - ut - u + (u )u + p = F, in ,equationequation div u = 0, in ,equationequation u = 0, on .equation The study of this equation for = 0 has a long and richhistory. In the two-dimensional case, the study is very successful and it iswell known that the solutions of the equation define a C0-semigroupS(t): t 0 inthe space H = PL2() (where P is the projection onto the space ofdivergence-free vector fields) and which has a global attractor A0 on H(see ［1］). But, in the three-dimensional case, things are quitedifference, although some progress has been made recently,there are many problems still open, i.e., the global regularity of thesolutions and the existence of the global attractors (see ［1--7］ andthe references therein). The machanical background ofthe equation in the case of > 0 can be found in ［8］     

A Maximum Principle for the Controlled Sweeping Process

We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin’s Maximum Principle type. The results are also discussed through an example. We combine techniques from Sene and Thibault (Journal of Nonlinear and Convex Analysis 15, 647–663, 2014) and from Brokate and Krej?í (Discrete and Continuous Dynamical Systems Series B 18, 331–348, 2013), which in particular deals with a different but related control problem. Our assumptions include the smoothness of the boundary of the moving set C(t), but, differently from Brokate and Krej?í, do not require strict convexity and time independence of C(t). Rather, a kind of inward/outward pointing condition is assumed on the reference optimal trajectory at the times where the boundary of C(t) is touched. The state space is finite dimensional.     

由偏微支配的系统的最优控制理论中的奇异摄动方法*

本文介绍了由偏微分方程支配的系统的最优控制理论中有关应用奇异摄动方法时出现的各种问题。考虑了渐近分析来自状态方程。或来自性能指标函数,也考虑了状态方程是定义在摄动域内的情形。     

A Minimal Candidate for the Existence of a Weakly-Ruinous Set

We show that Richard Thompson's group F is nonamenable if and only if the three element set A ₂ = {x ₀ x ₀ x ₀, x ₀ x ₀ x ₁, x ₀ x ₀ x ₂} is weakly-ruinous. We then show that no two element set is weakly-ruinous, thereby showing that A ₂ is minimal in both the number of elements that a weakly-ruinous set must contain and also in the number of carets that each tree in a weakly-ruinous set must have.     

Nonexistence and Existence of an Optimal Control Problem Governed by a Class of Semilinear Elliptic Equations

An optimal control problem governed by a class of semilinear elliptic equations is considered in this paper. Using relaxed controls, the nonexistence and existence results of an optimal control are obtained.     

一类有小扰动项的二阶哈密尔顿系统的多重解的存在性

基于变分法,运用三临界点定理,得到了一类有小扰动项的二阶哈密尔顿系统的多重解的存在性,推广了已有文献的相关结果.     

Some Results for the Compound Poisson Process That Is Perturbed by Diffusion

Abstract In the present paper surplus process perturbed by diffusion are considered.The distributions ofthe surplus immediately before and at ruin corresponding to the probabilities of ruin caused by oscillation andruin caused by a claim are studied.Some joint distribution densities are obtained.Techniques from martingaletheory and renewal theory are used.     

一类非紧算子正不动点的存在唯一性

本文利用锥理论和选代技巧,研究了一类非紧混合单调算子正不动点的存在唯一性,改进和推广了混合单调算子、增算子与减算子的某些相应结果．     

On the Existence of the Global Smooth Process for One-dimensional Nonlinear Thermoviscoelastic Materials with Fixed and Thermally Insulated Endpoints

The system of balance laws of mass, momentum and energy for one- dimensional nonlinear thermoviscoelastic material with fixed and thermally insulated endpoints is considered, and the problem of whether there exists a globally defined smooth thermoviscoelastic process is sloved, i.e there exists such a process.     

α凸算子(α>1)的正不动点存在性及其应用

通过构造一个特殊的锥,利用锥拉伸与压缩不动点定理对α凸算子(α>1)正不动点的存在性与不可比较性作了研究,并将其结果应用到超线性多项式型Hammerstein积分方程．     

Existence and genericity problems for dynamical systems with nonzero Lyapunov exponents

This is a survey-type article whose goal is to review some recent results on existence of hyperbolic dynamical systems with discrete time on compact smooth manifolds and on coexistence of hyperbolic and non-hyperbolic behavior. It also discusses two approaches to the study of genericity of systems with nonzero Lyapunov exponents.      

Banach空间中一类周期非线性受控系统最优控制的存在性

研究一类强非线性发展方程的周期解及相应的最优控制问题的存在性，首先，证明了Banach空间中一类包含非线性单调算子和非线性非单调扰动的强非线性发展方程周期解的存在性；其次，给出了保证相应的Lagrange最优控制的充分条件；最后，举例说明理论结果在拟线笥抛物方程周期问题及相应的最优控制问题中的应用。     

On the Existence and Construction of Common Lyapunov Functions for Switched Discrete Systems

Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach.     

带干扰古典风险模型的一些分布

该文主要讨论带干扰古典风险模型的破产瞬间余额和破产赤字的边际及联合分布.借助于修正阶梯高度的结果,得到了它们的表达式.当索赔服从指数分布时,给出它们的精确表达.     

A Controllability Problem for a System Governed by the Heat Equation

A control system described by the one-dimensional heat equationwith a boundary control is considered. The problem of findinga control which drives the system, in finite time T, to a constantfinal temperature distribution is discussed. A simple boundfor the norm of the control in terms of the final time T isderived, and a numerical example is presented.     

关于最近点对及近渡点存在性与唯一性

给定两个不主集合Ｆ，Ｇ研究最近点对（ｘ，ｙ）存在性及与近距映射Ｐ_Ｇｘ_０，Ｐ_rｙ０的关系，以及与近渡点存在的关系。又引入严凸集，它对研究最近点对唯一性与近渡点唯一性起重要作用，而Ｆ，Ｇ一个严凸，一个凸的仍不保证唯一性，除非在严凸空间情形．     

单值映射对与集值映射对的公共不动点

在度量空间中,引进了单值映射对与集值映射对的调和概念,对调和单值映射对与集值映射对建立了公共不动点定理及相应的随机公共不动点定理。     

相关带干扰风险模型的破产概率

本文引进了含相关类带干扰经典风险过程, 研究类之间的相关性对破产概率的影响, 主要研究类之间的相关性对其Lundberg指数的大小关系的影响.     

带有随机干扰和确定投资回报风险过程下的一些分布

我们考虑既带有随机干扰又带有确定投资回报的风险过程, 得到了破产前瞬间盈余的分布$F_{\delta}(u,x)$及破产前瞬间盈余和破产时赤字的联合分布$H_{\delta}(u,x,y)$所满足的积分表达, 连续性及二次连续可微性和积分--微分方程. 同时, 只有随机干扰的风险模型下的破产前瞬间盈余的分布及破产前瞬间盈余和破产时赤字的联合分布所满足的性质也被得到. 已有文献中的诸多有关结果均可以通过令我们结论中的某些参数特殊化为零而得到.