Low regularity global well-posedness for the Zakharov and Klein-Gordon-Schrödinger systems

We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables and . The Zakharov system is known to be locally well-posed in and the Klein-Gordon-Schrödinger system is known to be locally well-posed in . Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the norm of and controlling the growth of via the estimates in the local theory.

     

老电影全局闪烁修复系统的设计与实现

针对老电影中褪色闪烁的现象,研究了一种基于颜色传递和色彩校正的全局闪烁修复方法.该方法主要分三个步骤对视频序列进行修复,首先对导入的图像序列进行分镜并判断是否存在闪烁,然后对闪烁序列进行参考帧选取,如果无参考帧,则采用色彩校正来产生参考帧,最后通过颜色传递进行全局颜色闪烁修复.在VS2013中使用OpenCV实现了相关算法,并详细介绍了系统实现的关键代码.实验表明,该系统能够较好地完成对老电影全局闪烁的交互式修复.     

多核学习融合局部和全局特征的人脸识别算法

提出一种基于词袋模型的新的人脸识别算法.该方法将词袋模型和词袋模型的全局模式分别作为人脸图像的局部特征和全局特征描述,最后使用多核学习方法将二者进行融合.AR、FERET、CMU PIE以及LFW公开人脸数据库上的实验结果表明,本文方法能够更好的解决小样本问题,并且对人脸的表情变化、姿态变化以及面部遮挡具有更优良的鲁棒性.     

THE IMPROVED FOURIER SPLITTING METHOD AND DECAY ESTIMATES OF THE GLOBAL SOLUTIONS OF THE CAUCHY PROBLEMS FOR NONLINEAR SYSTEMS OF FLUID DYNAMICS EQUATIONS

Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple together the elementary uniform energy estimates of the global weak solutions and a well known Gronwall''s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980''s to study the optimal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay estimates with sharp rates of the global weak solutions of the Cauchy problems for $n$-dimensional incompressible Navier-Stokes equations, for the $n$-dimensional magnetohydrodynamics equations and for many other very interesting nonlinear evolution equations with dissipations can be established.     

Microlocal analysis of quasianalytic Gelfand-Shilov type ultradistributions

We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients.     

Fast search algorithms for computational protein design

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state‐of‐the‐art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well‐established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of to produce conformations in increasing order of energy, we defined new strategies combining CFN lower bounds, with new side‐chain positioning‐based branching scheme. Beyond the speedups obtained in the new ‐CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms. © 2016 Wiley Periodicals, Inc.     

一类具有直接和间接传播的SIV传染病模型

传染病的传播途径是多种多样的,如:直接传播和间接传播等.在以往的传染病模型中,大多是只考虑直接传播对疾病的影响,而忽略了环境作用对疾病的影响,即间接传播的影响.其实,间接传播在传染病的传播中同样起着重要的作用,忽略间接传播的影响会低估基本再生数,从而错估传染病爆发的规模,给人类的健康带来更大的威胁.研究了一个既有直接传播又有间接传播的SⅣ传染病模型,通过研究模型的动力学行为,给出了无病平衡点和地方病平衡点全局渐近稳定的条件,并用数值模拟证实了该结果.     

一种确定整周模糊度搜索空间的方法

模糊度搜索空间的大小是影响模糊度解算效率的关键因素之一.针对传统确定模糊度搜索空间的方法较为保守,致使搜索空间过大,提出了一种基于最小二乘模糊度降相关平差法(LAMBDA)的改进方法.首先对目前模糊度搜索空间确定方法给予了介绍和深入的分析比较,评价了这些经典方法的优缺点.在此基础上,定义了搜索空间的一个影响因子η,并结合LAMBDA方提出了确定模糊度搜索空间的修正公式.基于仿真和实测数据对修正方法进行实验,结果表明方法在保证获得期望模糊度组数的前提下,其确定的模糊度搜索空间包含的整数点个数更小,可保证90%以上实际模糊度组数接近于期望值.     

具有泄漏时滞的复值神经网络的全局同步性

研究了一类具有泄漏时滞的复值神经网络的全局同步性问题.在不要求激励函数可分离为实部函数和虚部函数的条件下,通过构造合适的Lyapunov-Krasovskii泛函,并运用驱动-响应同步方法、自由权矩阵方法和矩阵不等式技巧,获得了具有泄漏时滞的复值神经网络全局同步性的充分条件和同步控制器设计方法.给出的判据是由复值线性矩阵不等式表示的,易于MATLAB软件的YALMIP Toolbox实现.数值仿真实例验证了获得结果的有效性.