Value function and optimality condition for semilinear control problems. II: Parabolic case

In this paper we continue to study properties of the value function and of optimal solutions of a semilinear Mayer problem in infinite dimensions. Applications concern systems governed by a state equation of parabolic type. In particular, the issues of the joint Lipschitz continuity and semiconcavity of the value function are treated in order to investigate the differentiability of the value function along optimal trajectories.The research of P. Cannarsa was partially supported by the Italian National Project MURST Equazioni di Evoluzione e Applicazioni Fisico-Matematiche.     

阶跃伏安法离散数据连续化及导数卷积的方法 Ⅰ.样条插值法

本文对采用样条函数插值法解决阶跃伏安法中离散数据连续化及进一步的导数卷积处理进行了详细讨论。用模拟数据和实验数据进行了该方法的效果测试。结果表明,样条函数插值法处理连续化问题,具有显著的优越性,能成功地解决阶跃伏安法在大阶梯增量(△E)快速扫描时存在的由于采样点不多而造成的波形显示、导数卷积后波形杂散等问题。     

On the factor sets of measures and local tightness of convolution semigroups over Lie groups

It is shown that for a large class of Lie groups (called weakly algebraic groups) including all connected semisimple Lie groups the following holds: for any probability measure on the Lie group the set of all two-sided convolution factors is compact if and only if the centralizer of the support of inG is compact. This is applied to prove that for any connected Lie groupG, any homomorphism of any real directed (submonogeneous) semigroup into the topological semigroup of all probability measures onG is locally tight.     

On the characterization of the stationary state of a class of dynamical semigroups

We consider a representation of the entropy production for a completely positive, trace-preserving dynamical semigroup satisfying detailed balance with respect to its faithful stationary state denned on aW*-algebra(): it is expressed as a positive Hermitian form on(), which is analogous to the quantum correlation functions used in the Kubo theory. By considering this Hermitian form as a variation function of a vector in(), an exact characterization of the stationary states of semigroups in a certain class is obtained. On this basis, the problem of characterizing the stationary states discussed by Spohn and Lebowitz for manyreservoir open systems is solved without the restriction to situations near thermal equilibrium.     

Generalized result with a unified proof of global existence to a class of reaction‐diffusion systems

We prove in this paper a generalized result with a unified proof of global existence in time of classical solutions to a class of a reaction diffusion system with triangular diffusion matrix on a bounded domain in . The system in question is u_t=aΔu ? f(x,t,u,v), v_t=cΔu + dΔv + ρf(x,t,u,v), , t > 0 with f(x,t,0,η) = 0  and  f(x,t,ξ,η)≤Kφ(ξ)e^ση, for all  x∈Ω, t > 0, ξ≥0, η≥0; where  ρ, K  and  σ  are real positive constants. Copyright © 2016 John Wiley & Sons, Ltd.     

Non-Nehari manifold method for periodic discrete superlinear Schrödinger equation

We consider the nonlinear difference equations of the form Lu=f(n, u), n∈Z, where L is a Jacobi operator given by(Lu)(n)=a(n)u(n+1)+a(n-1)u(n-1)+b(n)u(n) for n∈Z, {a(n)} and {b(n)} are real valued N-periodic sequences, and f(n, t) is superlinear on t. Inspired by previous work of Pankov [Discrete Contin. Dyn. Syst., 19, 419-430(2007)] and Szulkin and Weth [J. Funct. Anal., 257, 3802-3822(2009)], we develop a non-Nehari manifold method to find ground state solutions of Nehari-Pankov type under weaker conditions on f. Unlike the Nehari manifold method, the main idea of our approach lies on finding a minimizing Cerami sequence for the energy functional outside the Nehari-Pankov manifold by using the diagonal method.     

从离散速度模型到矩方法

为了求解动理学方程,我们通过研究一维情形下的离散速度模型,发现通过对离散速度点使用自适应技术可以直接得到Grad矩方程组.作为一个统一的认识,矩方程组可以看作是对离散速度点自适应的离散速度模型,而离散速度模型可以看作是取特别形式的"矩"的矩方程组.这使得我们可以在一致的框架下来理解离散速度模型和矩方法,而不是将它们对立起来.为了建立这样的一致框架,最近在[2]中发展的正则化理论是根本性的.     

离散小波变换耦合静电场理论的图像快速伪造检测算法

为了解决当前图像伪造检测算法主要是在图像空域中定位伪造区域,难以降低图像维数,使其复杂度大;且不能有效检测几何变换篡改形式的伪造区域,导致其鲁棒性不佳的不足,本文提出了离散小波变换耦合静电场理论的图像伪造检测算法。首先,引入离散小波变换,提取伪造图像的低频子带,降低图像空间;再基于静电场理论,将提取子带映射到虚拟电场中,提取鲁棒性较强的特征,利用Radix排序算法对特征完成重组,形成特征矩阵;最后,定义相同仿射变换,并用其处理排序矩阵,完成伪造区域检测。实验测试结果显示：与当前的移动复制伪造检测技术相比,本文算法具有更高的定位效率与检测精度;同时拥有较强的鲁棒性,有效抗击几何变换篡改。     

一个二次多项式混沌系统的均匀化及其熵分析

利用已有理论给出了一个二次多项式混沌系统,证明了该系统与Tent映射拓扑共轭,给出了该混沌系统的概率密度函数;并根据此概率密度函数,得到了轨道均匀分布的反三角函数映射;对均匀化前后的混沌系统在不同参数下产生序列的信息熵、Kolmogorov熵、离散熵的特性进行了分析,结果显示均匀化后产生的混沌序列混沌程度不改变且具有更好的均匀性.