Rational approximation solution of the fractional Sharma–Tasso–Olever equation

In the paper, we implement relatively new analytical techniques, the variational iteration method, the Adomian decomposition method and the homotopy perturbation method, for obtaining a rational approximation solution of the fractional Sharma–Tasso–Olever equation. The three methods in applied mathematics can be used as alternative methods for obtaining an analytic and approximate solution for different types of differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. The numerical results demonstrate the significant features, efficiency and reliability of the three approaches.     

Parabolic finite volume element equations in nonconvex polygonal domains

We study spatially semidiscrete and fully discrete finite volume element approximations of the heat equation with homogeneous Dirichlet boundary conditions in a plane polygonal domain with one reentrant corner. We show that, as a result of the singularity in the solution near the reentrant corner, the convergence rate is reduced from optimal second order, similarly to what was shown for the finite element method in the earlier work 2 . Optimal order convergence may be restored by mesh refinement near the corners of the domain. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Weak Type Inequality for a Family of Singular Integral Operators Related with the Gaussian Measure

In this paper we study a family of singular integral operators that generalizes the higher order Gaussian Riesz Transforms and find the right weight w to make them continuous from L ¹(wdγ) into L ^1, ∞(dγ), being Some boundedness properties of these operators had already been derived by Urbina (Ann Scuola Norm Sup Pisa Cl Sci 17(4):531–567, 1990) and Pérez (J Geom Anal 11(3):491–507, 2001).      

基于DC分解的非凸二次规划SDP近似解

本文提出一类基于DC分解的非凸二次规划问题SDP松弛方法,并通过求解一个二阶锥问题得到原问题的近似最优解.我们首先对非凸二次目标函数进行DC分解,然后利用线性下逼近得到一个凸二次松弛问题,而最优的DC分解可通过求解一个SDP问题得到.数值试验表明,基于DC分解的SDP近似解平均优于经典SDP松弛和随机化方法产生的近似解。     

Sobolev type spaces in quantum calculus

In this paper q-Sobolev type spaces are defined on Rq by using the q-cosine Fourier transform and its inverse. In particular, embedding results for these spaces are established. Next we define the q-cosine potential and study some of its properties.     

The group reduction for bounded cosine functions on UMD spaces

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)^1/2 generates a bounded C ₀-group. The proof uses a transference principle for cosine functions.      

Solving fractional integral equations by the Haar wavelet method

Haar wavelets for the solution of fractional integral equations are applied. Fractional Volterra and Fredholm integral equations are considered. The proposed method also is used for analysing fractional harmonic vibrations. The efficiency of the method is demonstrated by three numerical examples.     

Gaussian density estimates for solutions to quasi-linear stochastic partial differential equations

In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [17]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic heat and wave equations in R^d${\mathbb{R}}^d$ (d≥1$d\ge 1$ and d≤3$d\le 3$, respectively) driven by a Gaussian noise which is white in time and has a general spatially homogeneous correlation.     

Some unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative

The aim of this paper is to present the analytical solutions corresponding to two types of unsteady unidirectional flows of a generalized Oldroyd-B fluid with fractional derivative between two parallel plates. The fractional calculus approach is used in solving the problems. The velocity distributions are determined by means of discrete Laplace transform and finite Fourier sine transform. The obtained results indicate that some well known solutions for the generalized second grade fluid, the generalized Maxwell fluid as well as the ordinary Oldroyd-B fluid appear as the limiting cases of the presented results.