Volterra Integral Equations and Some Nonlinear Integral Equations with Variable Limit of Integration as Generalized Moment Problems

In this paper we will see that, under certain conditions, the techniques of generalized moment problem will apply to numerically solve an Volterra integral equation of first kind or second kind. Volterra integral equation is transformed into a one-dimensional generalized moment problem, and shall apply the moment problem techniques to find a numerical approximation of the solution. Specifically you will see that solving the Volterra integral equation of first kind f（t） = {a^t K（t, s）x（s）ds a ≤ t ≤ b or solve the Volterra integral equation of the second kind x（t） =f（t）＋{a^t K（t,s）x（s）ds a ≤ t ≤ b is equivalent to solving a generalized moment problem of the form un = {a^b gn（s）x（s）ds n = 0,1,2… This shall apply for to find the solution of an integrodifferential equation of the form x＇（t） = f（t） ＋ {a^t K（t,s）x（s）ds for a ≤ t ≤ b and x（a） = a0 Also considering the nonlinear integral equation： f（x）= {fa^x y（x-t）y（t）dt This integral equation is transformed a two-dimensional generalized moment problem. In all cases, we will find an approximated solution and bounds for the error of the estimated solution using the techniques ofgeneralized moment problem.

Coefficient Determination in Parabolic Equations Solved as a Moment Problem Two-Dimensional in a Rectangular Domain

The problem is to considerer a parabolic equation depending on a coefficient a (t), and find the solution of the equation and the coefficient. The objective is to solve the problem as an application of the inverse moment problem. An approximate solution and limits will be found for the error of the estimated solution using the techniques of inverse problem moments. In addition, the method is illustrated with several examples.

Parabolic Partial Differential Equations as Inverse Moments Problem

We considerer parabolic partial differential equations under the conditions on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse moments problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. Also we consider the one- dimensional one-phase inverse Stefan problem.

Partial Differential Equations as Three-Dimensional Inverse Problem of Moments

We considerer partial differential equations of second order, for example the Klein-Gordon equation, the Poisson equation, on a region E = （a1, b1 ） × （a2, b2 ） x （a3, b3 ）. We will see that with a common procedure in all cases, we can write the equation in partial derivatives as an Fredholm integral equation of first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.

On Polynomial Maximum EntropyMethod for ClassicalMoment Problem

The maximum entropy method for the Hausdorff moment problem suffers from ill conditioning as it uses monomial basis{1,x,x2,···,xn}.Themaximum entropy method for the Chebyshev moment probelm was studied to overcome this drawback in[4].In this paper we review and modify the maximum entropy method for the Hausdorff and Chebyshev moment problems studied in[4]and present the maximum entropy method for the Legendre moment problem.We also give the algorithms of converting the Hausdorff moments into the Chebyshev and Lengendre moments,respectively,and utilizing the corresponding maximum entropy method.

Solution of Partial Derivative Equations of Poisson and Klein-Gordon with Neumann Conditions as a Generalized Problem of Two-Dimensional Moments

It will be shown that finding solutions from the Poisson and Klein-Gordon equations under Neumann conditions are equivalent to solving an integral equation, which can be treated as a generalized two-dimensional moment problem over a domain that is considered rectangular. The method consists to solve the integral equation numerically using the two-dimensional inverse moments problem techniques. We illustrate the different cases with examples.

On the Condition of Operator-valued Moment Problem

In Ref. [1] it is discussed that the sequence {A_n} of operators on the Hilbertspace can be expressed in the formA_n=integral from n=R to (λ~nB(λ)dλ), (1)where B(λ) is the integrable operator-valued function with compact support. Asufficient and necessary condition is that there is another sequence {A′_m}such

Parabolic Partial Differential Equations with Border Conditions of Dirichlet as Inverse Moments Problem

We considerer parabolic partial differential equations: under the conditions , on a region . We will see that an approximate solution can be found using the techniques of generalized inverse moments problem and also bounds for the error of estimated solution. First we transform the parabolic partial differential equation to the integral equation . Using the inverse moments problem techniques we obtain an approximate solution of . Then we find a numerical approximation of when solving the integral equation , because solving the previous integral equation is equivalent to solving the equation .

Linear Partial Differential Equations of First Order as Bi-Dimensional Inverse Moments Problem

We consider linear partial differential equations of first order on a region . We will see that we can write the equation in partial derivatives as an Fredholm integral equation of the first kind and will solve this latter with the techniques of inverse problem moments. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on problem of moments.

Fourier Moment Method with Regularization for the Cauchy Problem of Helmholtz Equation

In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.

A Method of Moment Approach in Solving Boundary Value Problems

Several available methods, known in literatures, are available for solving nth order differential equations and their complexities differ based on the accuracy of the solution. A successful method, known to researcher in the area of computational electromagnetic and called the Method of Moment (MoM) is found to have its way in this domain and can be used in solving boundary value problems where differential equations are resulting. A simplified version of this method is adopted in this paper to address this problem, and two differential equations examples are considered to clarify the approach and present the simplicity of the method. As illustrated in this paper, this approach can be introduced along with other methods, and can be considered as an attractive way to solve differential equations and other boundary value problems.

Analysis of a Cavity Used for Medical Purposes with the Dyadic Green's Functions and the Moment method

The structure of a microwave radiator used for medical purposes is described. The dyadic Green's function and the method are used to analyze this Kind of multimode rectangular medium-filled cavity. The distribution of electromagnetic field intensity and the power density,as well as the temperature effect in the biological sample load are obtained.OPtimization of the size of cavity and the position of the input aperture have been performed with the computer to optimize the uniformity or microwave effect and the input VSWR.Necessary experiments were performed to compare the data obtained with theoretical analysis.

NUMERICAL INVERSION OF MULTIDIMENSIONAL LAPLACE TRANSFORMS USING MOMENT METHODS

This paper develops a numerical method to invert multi-dimensional Laplace transforms. By a variable transform, Laplace transforms are converted to multi-dimensional Hansdorff moment problems so that the numerical solution can be achieved. Stability estimation is also obtained. Numerical simulations show the efficiency and practicality of the method.

Direct method for a Cauchy problem with application to a Tokamak

This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition.Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations.Four examples are used to study the applicability of the method with the presence of noise.

On One Possibility of Closuring the Chain of Equations for Statistical Moments in Turbulence Theory

The paper concerns the problem on statistical description of the turbulent velocity pulsations by using the method of characteristic functional. The equations for velocity covariance and Green’s function, which describes an average velocity response to external force action, have been obtained. For the nonlinear term in the equation for velocity covariance, it has been obtained an exact representation in the form of two terms, which can be treated as describing a momentum transport due to turbulent viscosity and action of effective random forces (within the framework of traditional phenomenological description, the turbulent viscosity is only accounted for). Using a low perturbation theory approximation for high statistical moments, a scheme of closuring the chain of equations for statistical moments is proposed. As the result, we come to a closed set of equations for velocity covariance and Green’s function, the solution to which corresponds to summing up a certain infinite subsequence of total perturbation series.

Extending the Behrens-Fisher Problem to Testing Equality of Slopes in Linear Regression: The Bayesian Approach

Testing the equality of means of two normally distributed random variables when their variances are unequal is known in the statistical literature as the “Behrens-Fisher problem”. It is well-known that the posterior distributions of the parameters of interest are the primitive of Bayesian statistical inference. For routine implementation of statistical procedures based on posterior distributions, simple and efficient approaches are required. Since the computation of the exact posterior distribution of the Behrens-Fisher problem is obtained using numerical integration, several approximations are discussed and compared. Tests and Bayesian Highest-Posterior Density (H.P.D) intervals based upon these approximations are discussed. We extend the proposed approximations to test of parallelism in simple linear regression models.

航空护林中的关键技术问题探讨

针对航空护林作业中的航站管理人员、航行管制员、空中观察员、作业航空公司机组等一线工作人员,提出航空护林作业中常见的坐标计算问题、重要作业点数据库问题、航空器通信导航监视问题等关键重点的技术问题并进行讨论,最后提出相应改进建议,为航空护林作业能安全、高效进行提供保障和参考,更好地满足“低空经济”政策要求。

N[a,b]类中Nevanlinna-Pick插值与Hausdorff矩量问题

利用Hankel向量方法建立N [a ,b]类中Nevanlinna Pick插值与相关Hausdorff矩量问题解集之间的一一对应 ,从而获得前者问题的可解性准则和解的描述 .

一维热传导反问题的条件稳定性与正则化

一类热传导方程初始值问题的反问题。通过变量代换,将该问题转化为一维Hausdorff矩问题。基于一维Hausdorff矩问题的条件稳定性和稳定算法,获得该热传导反问题的条件稳定性和正则化求解方法。

数值Laplace逆变换的矩方法

首先将Laplace变换转化成Hausdorff矩问题,然后基于矩问题的稳定化算法,由像函数F(s)的N+1个数据F(1),F(2),…,F(N+1)获得Laplace逆变换的数值解及其稳定性估计。数值模拟显示了算法是有效的和实用的。