This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...

in this paper we have solved analytically the schrödinger equation for a microscopic particle in a one-dimensional box with two infinite walls, which the potential function inside it, has a linear form. based on the solutions of this special quantum mechanical system, we have shown that as the quantum number approaches infinity the expectation values of microscopic particle position and square ...

Final Project Report Jungwoo Lee (610-21-4670) Reference : An Improved Gridding Method for Spiral MRI Using Nonuniform Fast Fourier Transform Authors: Liewei Sha, Hua Guo, and Allen W.Song Introduction The objective of this project is to develop improved reconstruction algorithm using nonuniform fast Fourier transform(NUFFT) for spiral MRI. In conventional gridding methods, while explicit forms...

By using the three-term recurrence equation satisfied by a family of orthogonal polynomials, the Christoffel-Darboux-type bilinear generating function and their asymptotic expressions, we obtain quadrature formulas for integral transforms generated by the classical orthogonal polynomials. These integral transforms, related to the so-called Poisson integrals, correspond to a modified Fourier Tra...

This paper proposes the Fourier-Bessel cepstral coefficients (FBCC) as features for robust text-independent speaker identification. Fourier-Bessel (FB) expansion is used instead of Fourier transform for representing the signal in frequency domain. FB expansion can be viewed as two-dimensional Fourier transform. Change in the kernel of the transform from exponential to decaying exponentials help...

Purpose Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based complete orthonormal system of Dunkl kernels generalizing classical exponential defining Fourier series. Design/methodology/approach Although difficulties related to settings, techniques used by K. Sato were still efficient in this case establish inequalities which have expected simila...

einstein, möbius, and proper velocity gyrogroups are relativistic gyrogroups that appear as three different realizations of the proper lorentz group in the real minkowski space-time $bbb{r}^n$. using the gyrolanguage we study their gyroharmonic analysis. although there is an algebraic gyroisomorphism between the three models we show that there are some differences between them. our study focus ...

This dissertation consists of two independent parts: oscillatory data analysis (Part I) and fast algorithms for integral operators in computational harmonic analysis (Part II). The first part concentrates on developing theory and efficient tools in applied and computational harmonic analysis for oscillatory data analysis. In modern data science, oscillatory data analysis aims at identifying and...