Computational Results for Seamount Imaging in a Water Waveguide

This article presents our computational results for imaging a seamount in a waveguide. We assume that there is no knowledge of what kind of boundary condition on the unknown seamount. The incident waves are sent from point sources along a straight line and the corresponding scattered fields are measured from a line above the unknown seamount. Analysis and numerical results are presented.     

Noninvariant Boundary Conditions

It is generally believed that in order to solve initial and boundary value problems using Lie symmetry methods, the boundary and initial conditions need to be left invariant by the infinitesimal symmetry generator which admits the invariant solution. In this article we give less restrictive conditions on the imposed initial and boundary values in order that they be recoverable with a particular symmetry generator.     

Boundedness of Solutions of Dirichlet Problem for a Class of Nonlinear Elliptic Equations with Weights

In this article, under some Hypotheses on weights and on coefficients, using a modification of Moser's method, we establish the boundedness of solutions of Dirichlet Problem for a class of nonlinear elliptic equations.     

Extracting the Convex Hull of an Unknown Inclusion in the Multilayered Material

We consider the problem of extracting information about an unknown inclusion embedded in a background layered material that has different constant conductivities across finitely many parallel planes, from the Dirichlet-to-Neumann map. For this purpose we construct the exponentially growing solutions of the governing equation for the background material. The leading coefficient of the equation has discontinuity across finitely many planes that are parallel to each other. Using the property of those solutions, we give an extraction formula of the support function of the inclusion from the Dirichlet-to-Neumann map.     

Correction to the Paper - Determination of a Domain in Complex Space by its Automorphism Group

The author offers some corrections to his article which appeared in Vol. 47, No. 3 of this journal.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.     

On the Error of the Optical Response Approximation in Chiral Media

We study the equations modelling the evolution of electromagnetic fields in chiral media with dispersion. We prove existence and uniqueness of solutions of these equations and provide estimates for the error of the optical response approximation for chiral media.     

On the Laplacian Spectrum and Walk-regular Hypergraphs

We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on hypergraphs. For instance, we obtain upper bounds on the eccentricity and the excess of any vertex of hypergraphs. We extend to the case of hypergraphs the concepts of walk regularity and spectral regularity, showing that all walk-regular hypergraphs are spectrally-regular. Finally, we obtain an upper bound on the mean distance of walk-regular hypergraphs that involves all the Laplacian spectrum.     

On the Laplacian Spectrum and Walk-regular Hypergraphs

We use the generalization of the Laplacian matrix to hypergraphs to obtain several spectral-like results on hypergraphs. For instance, we obtain upper bounds on the eccentricity and the excess of any vertex of hypergraphs. We extend to the case of hypergraphs the concepts of walk regularity and spectral regularity, showing that all walk-regular hypergraphs are spectrally-regular. Finally, we obtain an upper bound on the mean distance of walk-regular hypergraphs that involves all the Laplacian spectrum.     

On a nonstandard problem for heat conduction in a cylinder

Decay bounds are derived for the solution of a heat conduction problem in a semi-infinite cylinder when the lateral surface is held at zero temperature, a nonzero temperature is prescribed on the finite base, and the temperature at time T is prescribed to be a constant multiple of the temperature at initial time. Both energy and pointwise decay bounds are computed for a range of values of the constant multiple. Such problems were originally introduced as a means of stabilizing the backward-in-time problem for the heat equation.     

On the Two-dimensional Inverse Scattering Problems in Electromagnetics

In recent years, inverse scattering problems have received much attention because of their important applications. Given the incident and scattered waves, an inverse scattering problem in general is to determine the properties of the scatterer. In radar or sonar a known incident wave and observed scattered wave are used to detect the properties and the presence of aircraft or submarine objects; in MRI scanning, tomography X-rays and ultrasound, scattered waves are used to determine the presence or properties of tumors by detecting density variations, to name a few. In this article, we are concerned with the two-dimensional electromagnetic inverse scattering problem. An iterative algorithm for the transversal electric waves will be given based on a singular domain integral equation formulation. Basic features of a scattering object such as shape, location and index of refraction will be recovered from measurements of the field scattered by the object (when illuminated by electromagnetic waves with the magnetic vector polarized along the cylinder axis). Some numerical experiments are included to illustrate the efficiency of the algorithm.     

Carleman estimate for a stationary isotropic Lamé system and the applications

For the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L ²-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement.     

随机化均匀设计在股票交易上的应用

本文首先利用Bundschuh和朱尧辰(1993)的偏差精确计算公式,给出了某些二维均匀设计的生成元.其次,利用随机化均匀设计提出了一种可以提高以移动平均线进行股票交易的赚钱概率的方法.     

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.