In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

farmers are now more interested in application of weed control methods and tools with less environmental side effects. flame weeding using propane gas is an approach with almost no any chemical residue on the soil and plant surfaces or underground water. in this research, a flame weeding machine with the ability of uniform and also discrete flaming was developed and evaluated in laboratory and ...

We discuss the absolutely continuous spectrum of H = — d 2 /dx 2 + V(x) with F almost periodic and its discrete analog (hu)(n) = u(n +1) + u(n — 1) + V(ri)u(ri). Especial attention is paid to the set, A, of energies where the Lyaponov exponent vanishes. This set is known to be the essential support of the a.c. part of the spectral measure. We prove for a.e. Fin the hull and a.e. E in A, H and h...

Abstract. The Stieltjes–Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pear...

We present a simple recipe to construct exactly and quasi-exactly solvable Hamiltonians in one-dimensional ‘discrete’ quantum mechanics, in which the Schrödinger equation is a difference equation. It reproduces all the known ones whose eigenfunctions consist of the Askey scheme of hypergeometric orthogonal polynomials of a continuous or a discrete variable. The recipe also predicts several new ...

Abstract In this work, we construct different classes of coherent states related to a quantum system, recently studied in [1], an electron moving plane uniform external magnetic and electric fields which possesses both discrete continuous spectra. The eigenfunctions are realized as orthonormal basis suitable Hilbert space appropriate for building the states. These latter achieved context where ...

We develop general expressions for the raising and lowering operators that belong to the orthogonal polynomials of hypergeometric type with discrete and continuous variable. We construct the creation and annihilation operators that correspond to the normalized polynomials and study their algebraic properties in the case of the Kravchuk/Hermite Meixner/Laguerre polynomials. 1. Introduction. In a...

Two approaches for optimal control of diffusion-convection-reaction processes based on reduced-order models are presented. The approaches differ in the way spatial discretization is carried out to compute a reduced-order model suitable for controller design. In the first approach, the partial differential equation (PDE) that describes the process is first discretized in space and time using the...

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...

Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discret...