ii APPROVAL of a dissertation submitted by Nicomedes Alonso III This dissertation has been read by each member of the dissertation committee and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the MSU Division of Graduate Education. In presenting this dissertation in partial fulfillment o...

We extend our new approach for numeric evaluation of Feynman diagrams to integrals that include fermionic and vector propagators. In this initial discussion we begin by deriving the Sinc function representation for the propagators of spin1 2 and spin-1 fields and exploring their properties. We show that the attributes of the spin-0 propagator which allowed us to derive the Sinc function represe...

We show that a variety of trigonometric sums have unexpected closed forms by relating them to cognate integrals. 1 Motivation Recall that sinc(x) := sin(x)/x when x 6= 0 and sinc(0) := 1. In [4] and [8], it was shown that, for N = 0, 1, 2, 3, 4, 5, and 6, ∫ ∞

We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The are given in terms convolution, our proposed numerical approach is not only super-algebraically convergent, but it also satisfies an important property convolution—namely, preservation bandwidth. Furthermore, accuracy depends how well source field approx...

‎In this paper‎, ‎the numerical solutions of linear and nonlinear Volterra integral‎ ‎equations with nonvanishing delay are considered by two methods‎. ‎The methods are developed by means of‎ ‎the sinc approximation with the single exponential (SE) and double exponential (DE)‎ ‎transformations‎. ‎The existence and uniqueness of sinc-collocation solutions for these equations are provided‎. ‎Thes...

The aim of the present paper is to present a numerical algorithm for the time-dependent generalized regularized long wave equation with boundary conditions. We semi-discretize the continuous problem by means of the Crank–Nicolson finite difference method in the temporal direction and exponential B-spline collocation method in the spatial direction. The method is shown to be unconditionally stab...

OFDM is a form of multicarrier modulation technique with high spectral efficiency, robustness to channel fading, immunity to impulse interference, uniform average spectral density capacity of handling very strong echoes and non-linear distortion. Despite of its many advantages, one major disadvantage of OFDM is that the time domain OFDM signal which is a sum of several sinusoids leads to high p...

A newly developed distributed approximating functional ~DAF!-wavelet, the Dirichlet–Gabor DAF-wavelet ~DGDW!, is applied in a calculation of the state-to-state reaction probabilities for the three-dimensional ~3-D! (J50)H1H2 reaction, using the time-independent wave-packet reactant-product decoupling ~TIWRPD! method. The DGDWs are reconstructed from a rigorous mathematical sampling theorem, and...