In this paper, the unsteady MHD Couette flow through a porous medium of viscous incompressible fluid bounded by two parallel plates under influence thermal radiation and chemical reaction is investigated. A uniform suction injection are applied perpendicular to while motion subjected time dependent pressure gradient. The transformed conservation equations solved analytically subject physically ...

In the present study, diffraction and radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on capability structures to dissipate wave energy minimize environmental impact, developing attenuation protection. context linear theory, three-dimensional solution eigenfunction expansion method developed for determination velocity p...

We present a simplified theory of generalized eigenfunction expansions for a commuting family of bounded operators and with finitely many unbounded operators. We also study the convergence of these expansions, giving an abstract type of uniform convergence result, and illustrate the theory by giving two examples: The Fourier transform on Hecke operators, and the Laplacian operators in hyperboli...

Generalized eigenfunctions may be regarded as vectors of a basis in a particular direct integral of Hilbert spaces or as elements of the antidual space Φ× in a convenient Gelfand triplet Φ ⊆ H ⊆ Φ×. This work presents a fit treatment for computational purposes of transformations formulas relating different generalized bases of eigenfunctions in both frameworks direct integrals and Gelfand tripl...

It is proved that the first eigenfunction of the mixed boundary-value problem for the Laplacian in a thin domain Ωh is localized either at the whole lateral surface Γh of the domain, or at a point of Γh, while the eigenfunction decays exponentially inside Ωh. Other effects, attributed to the high-frequency range of the spectrum, are discussed for eigenfunctions of the mixed boundary-value and N...

In this paper we consider the analogue of the Courant nodal domain theorem for the nonlinear eigenvalue problem for the p-Laplacian. In particular we prove that if uln is an eigenfunction associated with the nth variational eigenvalue, ln, then uln has at most 2n−2 nodal domains. Also, if uln has n+k nodal domains, then there is another eigenfunction with at most n−k nodal domains. © 2002 Elsev...

This paper proposes a novel scheme for reduced-rank Gaussian process regression. The method is based on an approximate series expansion of the covariance function in terms of an eigenfunction expansion of the Laplace operator in a compact subset of R. On this approximate eigenbasis the eigenvalues of the covariance function can be expressed as simple functions of the spectral density of the Gau...

In this paper we analyze the behavior of quantum random walks. In particular we present several new results for the absorption probabilities in systems with both one and two absorbing walls for the one-dimensional case. We compute these probabilities both by employing generating functions and by use of an eigenfunction approach. The generating function method is used to determine some simple pr...

In this paper, the eigenfunction expansion method combined with local contact models are presented to analyze repeated impact behaviors between sphere and beam. The simulations verified experimental results of a simply-supported beam struck 91 times by sphere. order clarify validity solve transverse impacts on beams, simulation spring-mass also compared experiments. It shows that appropriate mo...