Quasi-compact operator,pseudo-essential spectra and some perturbation results

In this paper, we use the concept of quasi-compact operators, as a generalization of the class of Riesz operators, to improve the definition of the pseudo-Schechter essential spectrum of a closed densely defined operator acting on Banach space. Moreover, we discuss the incidence of some perturbation results on the behavior of pseudo-essential spectra of the sum of two bounded linear operators.     

On the general expression of Fredholm Integral Equations Method in elasticity

In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.     

Phragmen-Lindelöf alternative results for the initial boundary problem of stokes equation

In this paper we prove Phragmén-Lindelöf type alternative for the initial boundary problem of Stokes equation, i. e. we show that the energy expression for the solution of the initial boundary problem must either grow exponentially or decay exponentially with axial distance from the end of a semi-infinite strip. For the case of decay, we also establish the pointwise estimate for the maximum module of the Stokes flow and present a method for obtaining explicit bounds for the total energy.Project supported by the National Natural Science Foundation of China and Zhongshan University Science Foundation     

Non-axisymmetrical vibration of elastic circular plate on layered transversely isotropic saturated ground

The non-axisymmetrical vibration of elastic circular plate resting on a layered transversely isotropic saturated ground was studied.First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soils were transformed into a group of governing differential equations with 1-order by the technique of Fourier ex- panding with respect to azimuth,and the state equation is established by Hankel integral transform method,furthermore the transfer matrixes within layered media are derived based on the solutions of the state equation.Secondly,by the transfer matrixes,the general solutions of dynamic response for layered transversely isotropic saturated ground excited by an arbitrary harmonic force were established under the boundary conditions, drainage conditions on the surface of.ground as well as the contact conditions.Thirdly, the problem was led to a pair of dual integral equations describing the mixed boundary- value problem which can be reduced to the Fredholm integral equations of the second kind solved by numerical procedure easily.At the end of this paper,a numerical result concerning vertical and radical displacements both the surface of saturated ground and plate is evaluated.     

Function-valued Padé-type approximant via E-algorithm and its applications in solving integral equations

The function-valued Padé-type approximant (FPTA) was defined in the inner product space [8]. In this work, we choose the coefficients in the Neumann power series to make the inner product with both sides a function-valued system of equations to yield a scalar system. Then we express an FPTA in the determinant form. To avoid the direct computation of the determinants, we present the E-algorithm for FPTA based on the vector-valued E-algorithm given by Brezinski [4]. The method of FPTA via E-algorithm (FPTAVEA) not only includes all previous methods but overcomes their essential difficulties. The numerical experiment for a typical integral equation [1] illustrates that the method of FPTAVEA is simpler and more effective for obtaining the characteristic values and the characteristic functions than all previous methods. In addition, this method is also applicable to other Fredholm integral equations of the second kind without explicit characteristic values and characteristic functions. A corresponding example [12] is given and the numerical result is the same as that in [12].     

Numerical solution of the two-dimensional Fredholm integral equations using Gaussian radial basis function

In this paper, we introduce a numerical method for the solution of two-dimensional Fredholm integral equations. The method is based on interpolation by Gaussian radial basis function based on Legendre-Gauss-Lobatto nodes and weights. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.     

A Hermite collocation method for the approximate solutions of high‐order linear Fredholm integro‐differential equations

In this study, a Hermite matrix method is presented to solve high‐order linear Fredholm integro‐differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707–1721, 2011     

An intermediate wavelength, weakly nonlinear theory for the evolution of capillary gravity waves

A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid-air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity.     

Acoustic scattering of a plane wave by a circular penetrable cone

The paper is devoted to the diffraction of a plane wave by an acoustically transparent semi-infinite cone. The problem of diffraction is reduced to a singular integral equation in the framework of the incomplete separation of variables. The Fredholm property and regularization of the integral equation are discussed. Some important integral representations of the wave field are considered. The detailed study of the far-field asymptotics is given. Expressions for the diffraction coefficient of the spherical wave scattered from the vertex of the cone are considered. The reflected from the conical surface waves and those transmitted across the surface are also discussed.     

多元分布下单边备择假设的两步检验

x~2检验是熟知的拟合优度检验.它适用于任意的备择假设,尤其是适用于一般的备择假设"H_0不真"的情况.但是,当备择假设是一个单边假设时,x~2检验没有用到单边假设所提供的信息.因此,一个充分利用单边备择假设信息的检验是有可能优于传统的x~2检验的.本文就是利用单边备择假设的信息给出了一个两步检验,并通过一个例子,详细介绍了两步检验法的实施,说明了其应用.