In this paper, we will introduce a new algorithm for calculating the Green’s function of Schrödinger equation in a block layered potential, which has various and practical application in the quantum modeling of electron transport in a nano-MOSFET transistor. The proposed method is based on expansion of eigenfunctions of some Sturm-Liouville problems and collocation matching procedure. Numerical...

In stochastic modelling of flow in porous media, the medium properties that produce random trajectories of fluid elements are modelled by the assumed correlation kernel. For numerical simulation of the flow, the stochastic differential equation (SDE) is expanded using a Karhunen-Loeve expansion in terms of eigenvalues and eigenfunctions of the correlation function. In real world problems such a...

We examine the null boundary controllability of diffusion problems (with non-local conditions) arising from morphogen concentration process and electrochemistry. Two different types semi-periodic conditions are addressed. Also, towards further applications to biological chemical problems, we comment on anti-semi-periodic conditions. Such make auxiliary spectral non-self-adjoint and, therefore c...

Hough functions are the eigenfunctions of the Laplace tidal equation governing fluid motion on a rotating sphere with a resting basic state. Several numerical methods have been used in the past. In this paper, we compare two of those methods: normalized associated Legendre polynomial expansion and Chebyshev collocation. Both methods are not widely used, but both have some advantages over the co...

This study is on the fuzzy eigenvalues and fuzzy eigenfunctions of the Sturm-Liouville fuzzy problem with fuzzy eigenvalue parameter. We find fuzzy eigenvalues and fuzzy eigenfunctions of the problem under the approach of Hukuhara differentiability. We solve an example. We draw the graphics of eigenfunctions. We show that eigenfunctions are valid fuzzy functions or not.

Multiresolution analysis for problems involving random parameter fields is considered. The random field is discretized by a Karhunen-Loève expansion. The eigenfunctions involved in this representation are computed by a wavelet expansion. The wavelet expansion allows to control the spatial resolution of the problem. Fine and coarse scales are defined, and the fine scales are taken into account b...

Spectral theory for transition operators of one-dimensional symmetric Lévy process killed upon hitting the origin is studied. Under very mild assumptions, an integraltype formula for eigenfunctions is obtained, and eigenfunction expansion of transition operators and the generator is proved. As an application, and the primary motivation, integral fomulae for the transition density and the distri...

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal. In this paper, we give the spectral theory for eigenvalues and eigenfunctions...

We have obtained a general solution of evolution equations for QCD twist-2 string operators in form of expansion over complete set of orthogonal eigenfunctions of evolution kernels in coordinate-space representation. In the leading logarithmic approximation the eigenfunctions can be determined using constraints imposed by conformal symmetry. Explicit formulae for the LO scale-dependence of quar...

First we give a compact treatment of the Jacobi polynomials on a simplex in IR which exploits and emphasizes the symmetries that exist. This includes the various ways that they can be defined: via orthogonality conditions, as a hypergeometric series, as eigenfunctions of an elliptic pde, as eigenfunctions of a positive linear operator, and through conditions on the Bernstein–Bézier form. We the...