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1.
In this paper, we consider a MUSIC algorithm for locating point-like scatterers contained in a sample on flat substrate. Based on an asymptotic expansion of the scattering amplitude proposed by Ammari et al., the reconstruction problem can be reduced to a calculation of Green function corresponding to the background medium. In addition, we use an explicit formulation of Green function in the MUSIC algorithm to simplify the calculation when the cross-section of sample is a half-disc. Numerical experiments are included to demonstrate the feasibility of this method.  相似文献   

2.
Let Cv be an algebraically closed non-archimedean field, complete with respect to a valuation v. Let ϕ : PN → PN be a morphism of degree greater than one defined over Cv, Φ a lift of ϕ. Let GΦ be the Green function of Φ and ρ the chordal metric on PN(Cv). In this paper, we first study the properties of reduction of points in high dimensional projective space and reduction of automorphisms of PN with degree one. With the help of Green function GΦ of Φ, we introduce the arithmetic distance of morphisms and investigate its property. The necessary and sufficient condition which Φ has good reduction is obtained in this paper. We also describe explicitly the Filled Julia set of Φ by its Green function. © 2022 Chinese Academy of Sciences. All rights reserved.  相似文献   

3.
NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION   总被引:1,自引:1,他引:0  
In this paper, we will introduce how to apply Green’s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen’s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green’s function of the linearized system and micro-local analysis, such as frequency decomposition and so on.  相似文献   

4.
We study the Green's function for a general hyperbolic-parabolic system, including the Navier-Stokes equations for compressible fluids and the equations for magnetohydrodynamics. More generally, we consider general systems under the basic Kawashima- Shizuta type of conditions. The first result is to make precise the secondary waves with subscale structure, revealing the nature of coupling of waves pertaining to different characteristic families. The second result is on the continuous differentiability of the Green's function with respect to a small parameter when the coefficients of the system are smooth functions of that parameter. The results significantly improve previous results obtained by the authors.  相似文献   

5.
闫杰生  杨刘  刘锡平 《数学季刊》2006,21(3):448-454
Using a fixed point theorem in cones, the paper consider the existence of positive solutions for a class of second-order m-point boundary value problem. Sufficient conditions to ensure the existence of double positive solutions are obtained. The associated Green function of this problem is also given.  相似文献   

6.
In this paper, using two fixed-point theorems, we consider the existence and mul- tiplicity results of solutions to a nonlinear two point boundary value problem. In argument, the properties of the Green function play an important role.  相似文献   

7.
In this paper, using the property of the corresponding Green’s function and fixed point index theory, some sufficient conditions for the multiplicity and nonexistence of positive solutions to a class of nonlinear fractional boundary value problem are obtained. Three examples are given to show the effectiveness of our results.  相似文献   

8.
A complete manifold is said to be nonparabolic if it does admit a positive Green’s function. To ?nd a sharp geometric criterion for the parabolicity/nonparbolicity is an attractive question inside the function theory on Riemannian manifolds. This paper devotes to proving a criterion for nonparabolicity of a complete manifold weakened by the Ricci curvature. For this purpose, we shall apply the new Laplacian comparison theorem established by the ?rst author to show the existence of a non-constant bounded subharmonic function.  相似文献   

9.
AbstractSome superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.  相似文献   

10.
We prove that some holomorphic functions on the moduli space of tori have only simple zeros.Instead of computing the derivative with respect to the moduli parameter τ, we introduce a conceptual proof by applying Painlevé Ⅵ equation. As an application of this simple zero property, we obtain the smoothness of the degeneracy curves of trivial critical points for some multiple Green function.  相似文献   

11.
格林函数法是数学物理方程中一种常用的方法,适用于求解狄利克雷问题.针对几种特殊区域上的上狄利克雷问题,采用几何对称法求取这些区域对应的格林函数,该方法对于该区域上格林函数的求解是有效的.  相似文献   

12.

We consider the pluricomplex Green function with multiple poles as introduced by Lelong. We give a partial solution to a question concerning the set where the multipole Green function coincides with the sum of the corresponding single pole Green functions.

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13.
The purpose of this paper is to find optimal estimates for the Green function of a half-space of the relativistic α -stable process with parameter m on ℝ d space. This process has an infinitesimal generator of the form mI–(m 2/α IΔ) α/2, where 0<α<2, m>0, and reduces to the isotropic α-stable process for m=0. Its potential theory for open bounded sets has been well developed throughout the recent years however almost nothing was known about the behaviour of the process on unbounded sets. The present paper is intended to fill this gap and we provide two-sided sharp estimates for the Green function for a half-space. As a byproduct we obtain some improvements of the estimates known for bounded sets. Our approach combines the recent results obtained in Byczkowski et al. (Bessel Potentials, Hitting Distributions and Green Functions (2006) (preprint). ), where an explicit integral formula for the m-resolvent of a half-space was found, with estimates of the transition densities for the killed process on exiting a half-space. The main result states that the Green function is comparable with the Green function for the Brownian motion if the points are away from the boundary of a half-space and their distance is greater than one. On the other hand for the remaining points the Green function is somehow related the Green function for the isotropic α-stable process. For example, for d≥3, it is comparable with the Green function for the isotropic α-stable process, provided that the points are close enough. Research supported by KBN Grants.  相似文献   

14.
The harmonic Robin function is redefined as interpolation between the related Green and Neumann functions and explicitly constructed for the unit disc and a circular ring.  相似文献   

15.
We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. Our main goal is construct the Green function for the operator with mixed boundary conditions in a Lipschitz domain. Thus we specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We require a corkscrew or non-tangential accessibility condition on the set where we specify Dirichlet boundary conditions. Our proof proceeds by defining a variant of the space BMO(Ω) that is adapted to the boundary conditions and showing that the solution exists in this space. We also give a construction of the Green function with Neumann boundary conditions and the fundamental solution in the plane.  相似文献   

16.
偶数维的线性化Navier—Stokes方程解之逐点估计   总被引:1,自引:1,他引:0  
徐红梅 《数学杂志》1998,18(2):201-208
道德对偶数维线性化Navier-Stokes方程的格林函数作出估计,再用格林函数得出了其解的逐点估计。  相似文献   

17.
In this paper, we derive the non-singular Green’s functions for the unbounded Poisson equation in one, two and three dimensions using a spectral cut-off function approach to impose a minimum length scale in the homogeneous solution. The resulting non-singular Green’s functions are relevant to applications which are restricted to a minimum resolved length scale (e.g. a mesh size h) and thus cannot handle the singular Green’s function of the continuous Poisson equation. We furthermore derive the gradient vector of the non-singular Green’s function, as this is useful in applications where the Poisson equation represents potential functions of a vector field.  相似文献   

18.
In this work, we present an explicit expression for the Green function in a visco‐elastic medium. We choose Szabo and Wu's frequency power law model to describe the visco‐elastic properties and derive a generalized visco‐elastic wave equation. We express the ideal Green function (without any viscous effect) in terms of the viscous Green function using an attenuation operator. By means of an approximation of the ideal Green function, we address the problem of reconstructing a small anomaly in a visco‐elastic medium from wavefield measurements. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

19.
We explicitly construct the Green’s function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Green’s function are of interest in their own right. In particular, the explicit representations for a solution to the Dirichlet problem for the biharmonic equation are important in elasticity.  相似文献   

20.
A Green function of time-independent multi-channel Schrödinger equation is considered in matrix representation beyond a perturbation theory. Nonperturbative Green functions are obtained through the regular in zero and at infinity solutions of the multi-channel Schrödinger equation for different cases of symmetry of the full Hamiltonian. The spectral expansions for the nonperturbative Green functions are obtained in simple form through multi-channel wave functions. The developed approach is applied to obtain simple analytic equations for the Green functions and transition matrix elements for compound multi-potential system within quasi-classical approximation. The limits of strong and weak inter-channel interactions are studied.  相似文献   

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