导电介质中电磁波相移常数与振幅衰减常数的方向关系的讨论

对文献上给出的非均匀电磁波在同一均匀导电介质中传播时,电磁波的相移常数和振幅衰减常数方向之间满足定量关系的结论,重新进行了分析和推导,利用电磁波在导电介质界面的边界条件,给出了两种情况下的相移常数和振幅衰减常数的表达式,以及它们与界面法线的夹角正弦的表达式.结果表明,在同一均匀导电介质中,非均匀电磁波的相移常数的方向和振幅衰减常数的方向之间一般不满足定量关系.     

Viscosity solutions to a parabolic inhomogeneous equation associated with infinity Laplacian

We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut- ΔN∞u = f,where ΔN∞denotes the so-called normalized infinity Laplacian given by ΔN∞u =1|Du|2 D2 uD u, Du.     

Shape changing hydrogels and their applications as soft actuators

In nature, plants or animals change their geometric shapes and hence realize different functions or movements. Inspired by the shape changes of plants and animals, several hydrogels that can change their geometric shapes upon external stimuli have been developed. This article provides a brief overview of shape changing hydrogels. First, two strategies to realize the shape changes of hydrogels, that is, preparing hydrogels with inhomogeneous structures and applying inhomogeneous stimuli onto homogeneous hydrogels, are discussed. Then, external stimuli that can actuate the shape changes of the stimuli-responsive hydrogels are presented. The applications of shape changing hydrogels such as soft machines, soft robotics, drug carriers, microfluidic valves, and sensors have been provided in third part. Finally, we offer our perspective on open challenges and future areas of interest for the shape changing hydrogel actuators. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1314–1324     

Diffusion instability of a uniform cycle bifurcating from a separatrix loop

We consider the boundary value problem

Convergence theory of exact interpolation scheme for computing several eigenvectors

An asymptotic convergence analysis of a new multilevel method for numerical solution of eigenvalues and eigenvectors of symmetric and positive definite matrices is performed. The analyzed method is a generalization of the original method that has recently been proposed by R. Ku?el and P. Vaněk (DOI: 10.1002/nla.1975) and uses a standard multigrid prolongator matrix enriched by one full column vector, which approximates the first eigenvector. The new generalized eigensolver is designed to compute eigenvectors. Their asymptotic convergence in terms of the generalized residuals is proved, and its convergence factor is estimated. The theoretical analysis is illustrated by numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.     

Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes

The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process.     

Legendre spectral method for solving mixed boundary value problems on rectangle

In this paper, we develop a spectral method for mixed inhomogeneous Dirichlet/Neumann/Robin boundary value problems defined on rectangle. Some results on two‐dimensional Legendre approximation in Jacobi‐weighted Sobolev space are established. As examples of applications, spectral schemes are provided for two model problems with mixed inhomogeneous boundary conditions. The spectral accuracy in space of proposed algorithms are proved. Efficient implementations are presented. Numerical results demonstrate their high accuracy and confirm the theoretical analysis well. Copyright © 2016 John Wiley & Sons, Ltd.     

Cauchy problem for a quasilinear parabolic equation with a source term and an inhomogeneous density

The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered:

$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $

. The conditions on the parameters of the problem are found under which the solution to the Cauchy problem blows up in a finite time. A sharp universal (i.e., independent of the initial function) estimate of the solution near the blowup time is obtained.

     

两非均匀半平面粘结的非均匀平面的裂纹问题*

本文对两个非均匀半平面粘结的非均匀平面的裂纹问题作了分析,文中假定两种材料的泊松比v相同,但杨氏模量随坐标x按不同形式的指数函数变化.本文使用非均匀平面问题的单裂纹解及富氏变换方法, 使问题归为一个柯西型奇异积分方程,最后对应力强度因子的计算给出了若干数值例子.