A three level linearized compact difference scheme for the Cahn-Hilliard equation

This article is devoted to the study of high order accuracy difference methods for the Cahn-Hilliard equation.A three level linearized compact difference scheme is derived.The unique solvability and unconditional convergence of the difference solution are proved.The convergence order is O(τ 2 + h 4 ) in the maximum norm.The mass conservation and the non-increase of the total energy are also verified.Some numerical examples are given to demonstrate the theoretical results.     

Asymptotic analysis of the p-Laplacian flow in an exterior domain

We consider the Dirichlet problem for the p  -Laplacian evolution equation, ut=Δpu$u_t={\mathrm{\Delta }}_{p}u$, where p>2$p>2$, posed in an exterior domain in RN${\mathbf{R}}^N$, with zero Dirichlet boundary condition and with integrable and nonnegative initial data. We are interested in describing the influence of the holes of the domain on the large time behaviour of the solutions. Such behaviour varies depending on the relative values of N and p  . We must distinguish between the behaviour near infinity of space (outer analysis), and near the holes (inner analysis). We obtain that the outer analysis is given in all cases by certain self-similar solutions and the inner analysis is given by quasi-stationary states. Logarithmic corrections to exact self-similarity appear in the critical case N=p$N=p$, which is mathematically more interesting. In this first paper we treat only the cases N>p$N>p$ and N=p$N=p$, the case N<p$N<p$ will be considered in a companion work.     

The D-property in unions of scattered spaces

We show in a direct way that a space is D if it is a finite union of subparacompact scattered spaces. This result cannot be extended to countable unions, since it is known that there is a regular space which is a countable union of paracompact scattered spaces and which is not D. Nevertheless, we show that every space which is the union of countably many regular Lindelöf C-scattered spaces has the D-property. Also, we prove that a space is D if it is a locally finite union of regular Lindelöf C-scattered spaces.     

Convergence theorems of common elements for equilibrium problems and fixed point problems

In this paper, we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of two asymptotically nonexpansive mappings in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the two sets.     

Bilinear biorthogonal expansions and the Dunkl kernel on the real line

We study an extension of the classical Paley–Wiener space structure, which is based on bilinear expansions of integral kernels into biorthogonal sequences of functions. The structure includes both sampling expansions and Fourier–Neumann type series as special cases, and it also provides a bilinear expansion for the Dunkl kernel (in the rank 1 case) which is a Dunkl analogue of Gegenbauer’s expansion of the plane wave and the corresponding sampling expansions. In fact, we show how to derive sampling and Fourier–Neumann type expansions from the results related to the bilinear expansion for the Dunkl kernel.     

Hlder Norm Estimate for a Hilbert Transform in Hermitean Clifford Analysis

A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.     

Existence and asymptotic behavior for a singular parabolic equation

We prove global existence of nonnegative solutions to the singular parabolic equation 0 \} } ( -u^{-\beta} + \lambda f(u) )=0$"> in a smooth bounded domain with zero Dirichlet boundary condition and initial condition , . In some cases we are also able to treat . Then we show that if the stationary problem admits no solution which is positive a.e., then the solutions of the parabolic problem must vanish in finite time, a phenomenon called ``quenching'. We also establish a converse of this fact and study the solutions with a positive initial condition that leads to uniqueness on an appropriate class of functions.

     

Tangent algebraic subvarieties of vector fields

An algebraic commutative group is associated to any vector field on a complete algebraic variety . The group acts on and its orbits are the minimal subvarieties of which are tangent to . This group is computed in the case of a vector field on .

     

Numerical Analysis of the Behaviour of Tooth Intrarradial Posts by the Finite Element Method

The aim of this work is to study the behaviour of a carbon/epoxi post housed in a canine tooth after endodontic treatment in order to support the typical loads present during mastication. The three-D basic design of the dental piece consisting of tooth + post was carried out with a three-dimensional parametric design program. We study the stresses and displacements of the different elements of the dental piece under normal load conditions, and present the results and conclusions.     

两个安全第一思想模型的比较分析

针对投资者可能的投资需求确立了基于安全第一思想下两个相近的投资目标:1、极大化投资末期总收益率超过给定水平α的概率;2、极小化投资末期总收益率与给定水平α的距离.并分别就这两个目标建立了优化决策模型,得到了模型解析解,最后对两个模型结果进行了比较分析和经济解释.