Linearized filtering of affine processes using stochastic Riccati equations

We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for the law of $X_t$, for some $t>0$, conditional on all observations up to time $t$. This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential equations depending on the observation and the process characteristics of $X$. The quality of the approximation can be controlled by easily observable quantities in terms of a macro location of the signal in state space. Asymptotic techniques as well as maximization techniques can be directly applied to the solutions of the Riccati equations leading to novel very tractable filtering formulas. The efficiency of the method is illustrated with numerical experiments for Cox–Ingersoll–Ross and Wishart processes, for which Gaussian approximations usually fail.     

PN结物理特性的开放式测量实验方法研究

开放式、综合性量测实验的设计与应用,在巩固基础理论知识的同时,能够有效培养学生的动手实践能力、数据处理及分析能力,一定程度代表着大学物理实验课程的教学模式改革方向。以PN结物理特性的测量实验为例,基于通用型仪器与元器件的积木式组合,设计出简单、适用的实验电路;t=17.95℃时所采集的原始实验数据经三种模式回归分析,比较验证了PN结扩散电流与电压间遵循的玻尔兹曼分布律;计算出的玻尔兹曼常数与FD-PN-4测定仪的量测值相比,其结果说明了开放式测量实验方法的有效性。     

“曼德拉”现象对于监狱工作的启示

纳尔逊·罗利赫拉赫拉·曼德拉，于北京时间2013年12月6日凌晨与世长辞。曼德拉是一名传奇人物，人生道路坎坷。曼德拉44岁时被当时政府以“煽动”罪和“非法越境”罪判处5年监禁，以此为起点开始了他长达27年的“监狱生涯”。在狱中，面对大量具有种族歧视倾向的狱警，曼德拉非但没有为他们的种种羞辱、暴力所屈服。相反，狱中27年，他用自己独特的方式“感化”了一些狱警，这一现象对我国的监狱行刑改造工作是有一定启示作用的。     

Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.     

Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.     

γ-variable first-order logic of uniform attachment random graphs

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with m edges joining the new vertex with m different vertices chosen uniformly at random from $1,\dots ,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m?2$ variables.     

一种改进的基于人体静电冲击模型应力的瞬态功率模型

提出一种改进的基于人体静电冲击模型(Human Body Model, HBM)应力的瞬态功率模型。利用HSPICE仿真软件, 模拟MOS管遭受的HBM应力, 得到对应的等效直流电压。HBM电路的预充电电压与MOS管对应的等效直流电压值的散点图表明, 两者保持线性关系, 并通过拉普拉斯变化得到证明。与现有的瞬态功率模型相比, 改进后的模型降低了在HBM应力作用下的计算复杂度, 可以更加简便地从统计学上预测MOS管栅氧击穿的发生, 给HBM冲击作用下MOS管栅氧化层可靠性的评估提供参考。     

区域法治视角下法官的权力赋予与国家作为

区域法治既是对中国千年统治形态的否定，又是对市场经济繁荣发展的积极回应。区域经济社会发展进程中个人自由交易的权利内省必然导致基于私人契约的社会纠纷处断方式选择与国家统一范式的司法之间发生规制和自由的冲突。就国家法治背景下的区域法治而言，国家制式立法和司法无法回应经济交易的多元自由。没有得到社会认可的审判，就不能产生社会接受的规则之治。区域法治建设的核心应是赋予法官认定区域判例，根据案件行使司法解释权，给予法官无法可依情势下输出规则的权力。为此，国家应善待区域法治建设的现实要求，作出积极性的权力让渡，赋予法官特别司法权，从而推动地方治理的法治化与现代化。没有政治体制改革的先行，区域法治的建设将难以奏效。而政治体制改革能否成功的突破口，不能缺失法治的在场。     

Existence and uniqueness of the entropy solution of a stochastic conservation law with a Q-Brownian motion

In this paper, we prove the existence and uniqueness of the entropy solution for a first-order stochastic conservation law with a multiplicative source term involving a $Q$-Brownian motion. After having defined a measure-valued weak entropy solution of the stochastic conservation law, we present the Kato inequality, and as a corollary, we deduce the uniqueness of the measure-valued weak entropy solution, which coincides with the unique weak entropy solution of the problem. The Kato inequality is proved by a doubling of variables method; to that purpose, we prove the existence and the uniqueness of the strong solution of an associated stochastic nonlinear parabolic problem by means of an implicit time discretization scheme; we also prove its convergence to a measure-valued entropy solution of the stochastic conservation law, which proves the existence of the measure-valued entropy solution.