It is well known that Kirchhoff equations admit infinitely many simple modes, i. e. time periodic solutions with only one Fourier component in the space variables. We prove that, for some choices of the nonlinearity, these simple modes are unstable provided that their energy is large enough. This result, stated in an abstract Hilbert space setting, and proved by reducing to a system of two seco...

The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the ti...

In this paper we illustrate the use of the Beckmann-Kirchhoff model for analysing rough surface reflectance. The Beckmann-Kirchhoff model is a physical model that describes the reflectance of light from rough surfaces. The parameter of the model is the surface slope, or ratio of the surface roughness to the correlation length. We show how this parameter may be estimated using pairs of surface i...

This paper introduces a fast high-resolution imaging algorithm designed for ultra-wideband radar, and combines modified Kirchhoff migration and frequency-wavenumber (F-K) migration. The proposed algorithm also uses the texture method and inverse boundary scattering transform to calculate efficiently the integral arising in modified Kirchhoff migration, and thus enabling the integral in the F-K ...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow fie ld are modeled with the aid of Spalart-Alimaras one-equation turbulence modeL Appropriate acoustic and outflow boundary conditions were implemented to ...

WE DERIVE FIELD EQUATIONS for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order sheardeformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Ki...

For the SEG-EAGE salt data set, common-azimuth migration produces better images in the subsalt than single-arrival Kirchhoff migration, at a similar computational cost. Subsalt reflectors are better imaged and the typical Kirchhoff artifacts caused by severe multipathing disappear. We show how angle-domain Common Image Gathers (CIG) can be easily extracted from prestack wavefield downward conti...

Method of Moments (MOM) combining with the Kirchhoff Approximation(KA) for analysis of the problem of optical wave scattering by a stack of two one-dimensional Gaussian rough interfaces is solved. The scattered field from the upper interface is solved by MOM and the transmitted field from the lower one is expressed from the Kirchhoff approximation where the multiple scattering phenomenon is neg...