A probabilistic approach to spectral analysis of growth-fragmentation equations

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation concern the asymptotic behaviour of solutions at large times: at what rate do they converge to zero or infinity, and what does the asymptotic profile of the solutions look like? Does the rescaled solution converge to its asymptotic profile at an exponential speed? These questions have traditionally been studied using analytic techniques such as entropy methods or splitting of operators. In this work, we present a probabilistic approach: we use a Feynman–Kac formula to relate the solution of the growth-fragmentation equation to the semigroup of a Markov process, and characterise the rate of decay or growth in terms of this process. We then identify the Malthus exponent and the asymptotic profile in terms of a related Markov process, and give a spectral interpretation in terms of the growth-fragmentation operator and its dual.     

面向工程应用的单片机课程教学改革与实践

在分析传统单片机教学存在问题的基础上,提出面向工程应用,聚焦企业需要,构建能力递进、面向应用的内容体系,搭建资源共享、实践创新、师生互动的自主学习平台,组建培养兴趣,突出技能的“双师型”教学团队,实践表明,在传授知识的同时,能有效提升学习兴趣,优化人才素质结构。     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Perturbative manifolds and the Noether generators of nth-order Poisson equations

A manifold that contains small perturbations will induce a perturbed partial differential equation. The partial differential equation that we select is the Poisson equation – in order to explore the interplay between the geometry of the manifold and the perturbations. Specifically, we show how the problem of symmetry determination, for higher-order perturbations, can be elegantly expressed via geometric conditions.     

Two-dimensional vortex sheets for the nonisentropic Euler equations: Nonlinear stability

We show the short-time existence and nonlinear stability of vortex sheets for the nonisentropic compressible Euler equations in two spatial dimensions, based on the weakly linear stability result of Morando and Trebeschi (2008) [20]. The missing normal derivatives are compensated through the equations of the linearized vorticity and entropy when deriving higher-order energy estimates. The proof of the resolution for this nonlinear problem follows from certain a priori tame estimates on the effective linear problem in the usual Sobolev spaces and a suitable Nash–Moser iteration scheme.     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

2.5GHz低相位噪声CMOS LC VCO的设计

用0 .35μm、一层多晶、四层金属、3.3V的标准全数字CMOS工艺设计了一个全集成的2 .5 GHz L C VCO,电路采用全差分互补负跨导结构以降低电路功耗和减少器件1/ f噪声的影响.为了减少高频噪声的影响,采用了在片L C滤波技术.可变电容采用增强型MOS可变电容,取得了2 3%的频率调节范围.采用单个16边形的对称片上螺旋电感,并在电感下加接地屏蔽层,从而减少芯片面积,优化Q值.取得了在离中心频率1MHz处- 118d Bc/ Hz的相位噪声性能.电源电压为3.3V时的功耗为4 m A.     

串行16位DAC转换芯片在流量手操器中的应用

本文介绍串行16位D／A转换芯片MAX541及其与AT89C52单片机的接口电路、相应的转换子程序，并给出其在过程流量手操器中的应用。