Using a mixed-type Fourier transform of a general form in the case of water of infinite depth and the method of eigenfunction expansion in the case of water of finite depth, several boundary-value problems involving the propagation and scattering of time harmonic surface water waves by vertical porous walls have been fully investigated, taking into account the effect of surface tension also. Kn...

In this paper, the dynamic response of a viscoelastic beam subjected to a moving distributed load has been studied. The viscoelastic properties of the beam have been considered as linear standard model in shear and incompressible in bulk. The stress components have been separated to the shear and dilatation components and as a result the governing equations in viscoelastic form has been obtaine...

Many combinatorial configurations (for example, perfect codes, latin squares and hypercubes, combinatorial designs and their q-ary generalizations — subspace designs) can be defined as an eigenfunction on a graph with some discrete restrictions. The study of these configurations often leads to the question about the minimum possible difference between two configurations from the same class (it ...

1. Introduction. The main purpose of this article is to give a stronger counterexample to the " hot spots " conjecture than the one presented in Burdzy and Werner [7]. Along the way we define and partly analyze a new process, which we call fiber Brownian motion, and which may have some interest of its own. Consider a Euclidean domain that has a discrete spectrum for the Laplacian with Neumann b...

We propose a new method to solve the Hartree-Fock-Bogoliubov equations for weakly bound nuclei whose purpose is to improve the treatment of the continuum when a finite range two-body interaction is used. We replace the traditional expansion on a discrete harmonic oscillator basis by a mixed eigenfunction expansion associated with a potential that explicitely includes a continuous spectrum. We o...

This article presents an assessment of alternative forms of the Green’s function for boundary element simulations of acoustic wave propagation in shallow water. It is assumed that the problem is two-dimensional, the source of acoustic disturbance is time-harmonic, the velocity of sound is constant and the medium in the absence of perturbations is quiescent. Efficient implementations of the boun...

We study the critical points of Laplace eigenfunctions on polygonal domains with a focus second Neumann eigenfunction. show that if each convex quadrilaterals has no eigenfunction an interior point, then there exists quadrilateral unstable point. also point second-Neumann Lip-1 polygon orthogonal sides is acute vertex.

Directional emission from a slit surrounded by rectangular grooves on the exit surface in a conducting plane is investigated. An electromagnetic boundaryvalue problem dealing with a slit surrounded by rectangular grooves on the exit surface in a conducting plane is rigourously solved based on the Fourier transform, eigenfunction expansion, and mode-matching method. The radiation pattern from th...

In this article we develop new techniques for studying concentration of Laplace eigenfunctions $\phi_\lambda$ as their frequency, $\lambda$, grows. The method consists controlling $\phi_\lambda(x)$ by decomposing into a superposition geodesic beams that run through the point $x$. Each beam is localized in phase-space on tube centered around whose radius shrinks slightly slower than $\lambda^{-\...

Relativistic shocks provide an efficient method for high-energy particle acceleration in many astrophysical sources. Multiple shock systems are even more effective and of importance, for example, in the internal shock model of gamma-ray bursts. We investigate the reacceleration of pre-existing energetic particles at such relativistic internal shocks by the first order Fermi process of pitch ang...