نتایج جستجو برای: eigenfunction expansion

تعداد نتایج: 142226  

Journal: :Journal of Sound and Vibration 2021

This paper develops an averaging technique based on the combination of eigenfunction expansion method and collaboration to investigate multiple scattering effect SH wave propagation in a porous medium. The semi-analytical is conducted using Monto Carlo understand macroscopic dispersion attenuation phenomena stress solid due effects. verified by finite element analysis. Finally, simple homogeniz...

Journal: :International Journal of Applied Mathematics 2022

We investigate an initial-boundary value problem for a time-fractional subdiffusion equation with the Caputo derivatives on $N$-dimensional torus by classical Fourier method. Since our solution is established eigenfunction expansion of elliptic operator, method proposed in this article can be used to arbitrary domain and operator variable coefficients. It should noted that conditions existence ...

2006
FRITZ GESZTESY VADIM TKACHENKO

We derive necessary and sufficient conditions for a Hill operator (i.e., a one-dimensional periodic Schrödinger operator) H = −d/dx + V to be a spectral operator of scalar type. The conditions show the remarkable fact that the property of a Hill operator being a spectral operator is independent of smoothness (or even analyticity) properties of the potential V . In the course of our analysis we ...

2007
D. Borisov

We consider the Dirichlet Laplacian in a domain two three-dimensional parallel layers having common boundary and coupled by a window. The window produces the bound states below the essential spectrum; we obtain two-sided estimates for them. It is also shown that the eigenvalues emerge from the threshold of essential spectrum as the window passes through certain critical shapes. We prove the nec...

2007
W. C. Sue J. Y. Liou J. C. Sung

The order of the stress singularity of a magnetoelectroelastic bonded antiplane wedge is analyzed by complex potential function and eigenfunction expansion method. Contrary to the familiar problem of elastic anisotropic bonded wedges which always produce real values for the order of singularity, the results of the magnetoelectroelastic bonded wedges may be real or complex. Numerical results are...

2012
Mourad E.H. ISMAIL Erik KOELINK

The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey– Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynom...

1999
C. F. Lo P. H. Yuen

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute numerical results from the formula. The numerical results are...

Journal: :Physical review letters 2013
Olivier Morin Claude Fabre Julien Laurat

The characterization or subsequent use of a propagating optical quantum state requires the knowledge of its precise temporal mode. Defining this mode structure very often relies on a detailed a priori knowledge of the used resources, when available, and can additionally call for an involved theoretical modeling. In contrast, here we report on a practical method enabling us to infer the optimal ...

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