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.     

The energy-critical nonlinear wave equation with an inverse-square potential

We study the energy-critical nonlinear wave equation in the presence of an inverse-square potential in dimensions three and four. In the defocussing case, we prove that arbitrary initial data in the energy space lead to global solutions that scatter. In the focusing case, we prove scattering below the ground state threshold.     

为什么要引入溶剂的渗透因子

阐明了引入溶剂渗透因子的必要性,较详细地介绍了两种渗透因子及它们间的关系。     

Decay rate for viscoelastic wave equation of variable coefficients with delay and dynamic boundary conditions

In this paper, we consider a viscoelastic wave equation of variable coefficients in the presence of past history with nonlinear damping and delay in the internal feedback and dynamic boundary conditions. Under suitable assumptions, we establish an explicit and general decay rate result without imposing restrictive assumption on the behavior of the relaxation function at infinity by Riemannian geometry method and Lyapunov functional method.     

平面阵列波导光栅波导模式参量的分析

用周期波导的方法分析平面阵列波导光栅(AWG)的本征方程及波导模式参数,结果表明波导传播常数是带状分布的,与波导间隔有关。分析结果对器件的优化设计有一定的指导意义。     

The 4D Klein-Gordon, Dirac and Quantization Equations from 5D Null Paths

Results from 5D induced-matter and membrane theory with null paths are extended to show that a particle obeys the 4D Klein-Gordon equation but with a variable mass. The Dirac equation also follows, but raises concerns about 4D quantization in the two natural 5D gauges, and reopens the question of a Regge-like trajectory for the spin angular momenta and squared masses of gravitationally-dominated systems.     

一种二元域上的快速计算哈希函数

论文从映射的角度,将哈希函数分为三类:严格哈希函数、计算哈希函数和实用哈希函数。在此基础上,根据二元域上二次方程x2 x c=0的部分不可解的性质,构造了一种计算哈希函数,它满足单向性和一一对应性,同时具有运算速度快的优点。     

双频抽运提高SBS相位共轭保真度

相位共轭保真度是相位共轭镜技术用于强激光系统中的一个重要指标。采用四波混频加强SBS的方法 ,其相干拍频驱动声子场 ,能提高SBS相位共轭保真度。对于双频单池结构 ,使用列阵相机测量激光束能量远场角分布 ,在SBS转换效率最佳时 ,对相干驱动SBS相位共轭保真度进行了实验研究     

卷积码的线性系统

介绍了卷积码的线性离散时不变系统模型。从建立卷积码的状态变量方程出发,研究了卷积码的代数结构,并详细论述了基于状态变量方程描述的迭代译码算法。     

非线性互补问题的一种全局收敛的显式光滑Newton方法

本针对Po函数非线性互补问题，给出了一种显式光滑Newton方法，该方法将光滑参数μ进行显式迭代而不依赖于Newton方向的搜索过程，并在适当的假设条件下，证明了算法的全局收敛性。