The vertical structure of the low-level atmospheric response to an elevated large-scale, low-frequency heat source in the Tropics is explored using linear tidal theory on an equatorial beta plane. Through the calculation of the projection of a large-scale, low-frequency thermal source onto the meridional eigenfunctions, the contributions from a set of discrete meridional eigenfunctions with pos...

This paper deals with the construction of discrete numerical solutions of mixed problems for the telegraph equation. After discretization, the two-variables partial difference mixed problem is solved by means of a discrete eigenfunctions method that mimics the advantages of the continuous eigenfunction method while eliminating its computational disadvantages. The solution is based on a closed f...

This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions which are eigenfunctions of the continuous Fourier transform and by performing a novel error removal procedure. Then, the result of the eigendecomposition of the DFT matrix...

Abstract In this paper we discuss spectral properties of operators associated with the least-squares finite-element approximation elliptic partial differential equations. The convergence discrete eigenvalues and eigenfunctions towards corresponding continuous eigenmodes is studied analyzed help appropriate $L^2$ error estimates. A priori a posteriori estimates are proved.

The linearized Vlasov equation for a plasma system in an external constant magnetic field and the corresponding linear Vlasov operator are studied. The solution of the Vlasov equation is found by the resolvent method. The spectrum and eigenfunctions of the Vlasov operator are also found. The spectrum of this operator consists of two parts: one is continuous and real; the other is discrete and c...

We construct new examples of bispectral dual Hahn polynomials, i.e., orthogonal polynomials with respect to certain superposition Christoffel and Geronimus transforms the measure which are also eigenfunctions a higher order difference operator. The have novelty that they depend on an arbitrary number continuous parameters. These first this property constructed from classical discrete families.

We decompose time-varying beta for stock into beta for continuous systematic risk and beta for discontinuous systematic risk. Brownian motion is assumed as nature of price movements in our modeling. Our empirical research is based on high-frequency data for stocks from Tehran Stock Exchange. Our market portfolio experiences 136 days out of 243 trading days with jumps which is a considerable rat...

A brief introduction to discrete quantum mechanics is given together with the main results on various exactly solvable systems. Namely, the intertwining relations, shape invariance, Heisenberg operator solutions, annihilation/creation operators and dynamical symmetry algebras, including the q-oscillator algebra and the Askey-Wilson algebra. A simple recipe to construct exactly and quasi-exactly...

Ant colony optimization algorithms (ACOs) have been basically introduced to discrete variable problems and applied to different research domains in several engineering fields. Meanwhile, abundant studies have been already involved to adapt different ant models to continuous search spaces. Assessments indicate competitive performance of ACOs on discrete or continuous domains. Therefore, as poten...