Singularities of the Radon Transform of a Class of Piecewise Smooth Functions in R2

The Radon transform is the mathematical foundation of Computerized Tomography[1](CT).Its important applications includes medical CT,noninvasive test and etc.If one is specially interested in the places at which the image function changed largely such as the interfaces of two different tissues,tissue and ill tissue and the interfaces of two difierent matters,and want to reconstruct the outlines of the interfaces,one should reconstruct the singularities of the image function.The exact inversion of the Radon transform is valid only for smooth function[2].The singularity places of the reconstructed function should be studied specially.The research includes the propagation and inversion of singularity of the Radon transform.If one use convolutionbackprojection method to reconstruct the image function,the reconstructed function become blurring at the singularity places of the original function.M.Jiang and etc[3]developed a blind deconvolution method deblurring reconstructed image.By[4]and following research,we see that one can use a neighborhood data of the singularities of the Radon transform to inverse the singularity of the Radon transform,and therefore the reconstruction is available for some incomplete data reconstructions.     

非线性偏微分方程的约化和精确解

§ 1　IntroductionSeeking the exact solutions of the nonlinear partial differential equation is one of thevery importantsubjectin PDE research.Up to now,many methods offinding the exact so-lutions for NLPDE are constructed,such as inverse scattering transformation(IST) [1 ] ,Liepoint symmetry and similar reductions[2 ,3] ,B cklund[4— 6] and Cole-Hofe transformations,Hirota s bilinear method[7] ,the homogeneous balance method[8,9] ,tanh function method[1 0 ]and so on.In this paper,we giv…     

随机变量函数的矩估计不等式

Literature[1] obtained an upper bound inequality for the variance of a function of a standard normal random variable,using Hermite polynomials.In this paper we extend and improve the result of [1] and obtain an upper bound inequality for the rth absolute moment of a function of a random variable and an upper bound for the variance of a random variable function is also given.     

A MODIFICATION OF POWELL-ZANGWILL'S METHOD AND ITS RATE OF CONVERGENCE

In this paper,a modified version of Powell-Zangwill's method for function minimizationwithout calculating derivatives is proposed.The new method possesses following properties:quadratic termination,global convergence for strictly convex function and Q-linearconvergence rate for uniformly convex function.Furthermore,the main part of this paperis to show that the rate of convergence of the new method is quadratic for every n(2n 1)line searches if the objective function is a uniformly convex and suitably smooth functionon R~n.     

Superlinear convergence of affine scaling interior point newton method for linear inequality constrained minimization without strict complementarity

In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementarity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine sealing matrix in [2] for solving the linear inequlity constrained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.     

On the convergence of sequential number-theoretic method for optimization

1. IntroductionIn the papers [l] and [2] H. Niederreiter and K. McCurley gave a quasi-Monte Carlolnethod for the approxiInate computation of the extreme values of a mu1tivariab1e function.In l989 K.T. Fa11g and Y. Wang["'l proposed a sequential algorithm fOr optinlization bya number-theoretic method (abbr. SNTO), which is nlore effective than the Niederreiter'smethod in some cases, but it lacks a complete convergence result concerlling the a1gorithm.In the present note we will approach…     

SUPERLINEAR CONVERGENCE OF THE DFP ALGORITHM WITHOUT EXACT LINE SEARCH

Broyden algorithms are very efficient methods for solving the nonlinear programmingproblem:minWith exact line search, Powell[1] proved that the rate of convergence of these algorithms isone-step Q-superlinear for a twice continuously differentiable and uniformly convex function,and Pu[2] extended this result for LC1 function. Pu and Yu[3] proved that if the points whichare given by these algorithms are convergent they are globally convergent for continuouslydifferentiable functions without c…     

A QP Free Feasible Method

In [12], a QP free feasible method was proposed for the minimization of a smooth function subject to smooth inequality constraints. This method is based on the solutions of linear systems of equations, the reformulation of the KKT optimality conditions by using the Fischer-Burmeister NCP function. This method ensures the feasibility of all iterations. In this paper, we modify the method in [12] slightly to obtain the local convergence under some weaker conditions. In particular, this method is implementable and globally convergent without assuming the linear independence of the gradients of active constrained functions and the uniformly positive definiteness of the submatrix obtained by the Newton or Quasi Newton methods. We also prove that the method has superlinear convergence rate under some mild conditions. Some preliminary numerical results indicate that this new QP free feasible method is quite promising.     

ON LIAPUNOV FUNCTIONAL IN THEORY OF STABILITY OF SYSTEMS WITH TIME-LAG

It is well known,that in the theory of stability in differential equations,Liapunov's second method may be the most important The center problem of Liapunov's second method is construction of Liapunov function for concrete problems.Beyond any doubt,construction of Liapunov functions is an art.In the case of functional differential equations,there were also many attempts to establish various kinds of Liapunov type theorems.Recently Burton[2]presented an excellent theorem using the Liapunov functional to solve the asymptotic stability of functional differential equation with bounded delay. However,the construction of such a Liapunov functional is still very hard for concrete problems. In this paper, by utilizing this theorem due to Burton,we construct concrete Liapunov functional for certain and nonlinear delay differential equations and derive new sufficient conditions for asymptotic stability.Those criteria improve the result of literature[1]and they are with simple forms,easily checked and applicable.     

关于带W权Drazin逆的表示定理及迭代方法

To study singular linear system, Cline and Greville[8] proposed the concept of W-weighted Drazin inverse for the rectangular matrices,where the properties were also discussed. The computation for the W-weighted Drazin inverse is of much interest, which is mainly divided into two kinds of methods: direct method[2,4,6] and iterative method[3,5,7,9,12,13]. In this paper, we study the iterative method and successive matrix squaring(SMS) method for the W-weighted Drazin inverse and generalize the main results in [12,13].     

Long time behavior of solutions to the mKdV

In this paper we consider the long time behavior of solutions to the modified Korteweg-de Vries equation on ?. For sufficiently small, smooth, decaying data we prove global existence and derive modified asymptotics without relying on complete integrability. We also consider the asymptotic completeness problem. Our result uses the method of testing by wave packets, developed in the work of Ifrim and Tataru on the 1d cubic nonlinear Schrödinger and 2d water wave equations.     

The multi elliptic-localized solutions and their asymptotic behaviors for the mKdV equation

We mainly construct and analyze the multi elliptic-localized solutions under the background of elliptic function solutions for the focusing modified Korteweg-de Vries (mKdV) equation. Based on the Darboux–Bäcklund transformation, we provide a uniform expression for these solutions by the Jacobi theta functions. The asymptotic behaviors of multi elliptic-localized solutions are provided directly in two categories. By the consistent asymptotic expression of those solutions, we obtain that the collisions between the elliptic-breathers/solitons are elastic. Moreover, a sufficient condition of the strictly elastic collision between the solitons and breathers has been given by the symmetric analysis. In addition, as $k\to 0^{+}$, the multi elliptic-localized solutions degenerate into solitons, breathers, or soliton-breather solutions, which implies that we extend the solutions from the constant and vanishing backgrounds to the periodic solutions backgrounds. Moreover, we illustrate figures of the multi elliptic-localized solutions to visualize the above analysis.     

Sub-ODE method and soliton solutions for the variable-coefficient mKdV equation

In this work, an auxiliary equation is used for an analytic study on the time-variable coefficient modified Korteweg-de Vries (mKdV) equation. Five sets of new exact soliton-like solutions are obtained. The results show that the pulse parameters are time-dependent variable coefficients. Moreover, the basic conditions for the formation of derived solutions are presented.     

Superposition formulas for vector generalizations of the mKdV equation

Using the Bäcklund transformations, we obtain superposition formulas for vector generalizations of the mKdV equation.     

ILL-POSEDNESS OF MODIFIED KAWAHARA EQUATION AND KAUP-KUPERSHMIDT EQUATION

In this article,we consider the Cauchy problems for the modified Kawahara equation (6)tu + μ(6)x(u3) + α(6)5xu + β(6)3xu + γ(6)xu =0and the Kaup-Kupershmidt equation (6)tu + μu(6)2xu + α(6)5xu + β(6)3x...     

THE PROPERTIES OF MODIFIED NAVIER-STOKES EQUATION

1 Introduction'As we know, when velocity gradient is not large, and Newton's viscosity hypothesis holds, then the governing equation of motion of viscous incompressiblefluid is the classical Navier--Stokes equationIK = vAV~ (V' V)V ~ ~VP F, V' V = 0. (1)PThe Eq.(1) is very important in practice, but it is also rather licitted in applying and theoreticsll],[2]. In order to describe the motion of fluid more preciselyand more perfectly in mathematics and mechanics, Ladyzhenskaya gave a m…     

ON A FUNCTIONAL EQUATION

In this article, the author derives a functional equation η（s）=[（π/4）^s-1/2√2/π Г（1-s）sin（πs/2）]η（1-s） （1） of the analytic function η（s） which is defined by η（s）=1^-s-3^-s-5^-s＋7^-s＋… （2） for complex variable s with Re s 〉 1, and is defined by analytic continuation for other values of s. The author proves （1） by Ramanujan identity （see [1], [3]）. Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.     

mKdV方程和mKP方程组的新的精确孤立波解

用三角函数假设法和一种新辅助方程的解构造mK dV方程和mKP方程组的精确孤立波解.这种方法也可用于寻找其它非线性发展方程的新的孤立波解.     

时间分数阶扩散-反应方程

1、引言 当前,对含有非整数阶导数和积分的方程的研究正引起越来越多学者的关注,这类分数阶导数和积分将广泛应用于科学和工程的各个领域．     

N维多重非齐次调和方程及其边界积分方程

对n维多重非齐次调和方程△~((k))u=f(x),x∈R~n,给出了基本解的递推公式以及多重调和函数的积分关系式.在非齐次项f(x)为m次调和的情形下将域上的积分转化为沿边界的积分,进而应用直接法给出了基本边界积分方程.对f(x)为一般光滑函数的情形,给出了用泰勒多项式逼近时相应的误差估计并证明了含误差项的积分是收敛的.