Functions and Analysis

1511 Submissions

[5] viXra:1511.0302 [pdf] submitted on 2015-11-30 20:55:26

The Quaternion Domain Fourier Transform and its Properties

Authors: Eckhard Hitzer
Comments: 16 Pages. Published in Advances in Applied Clifford Algebras, pp. 1-16, Online First: 02 Nov. 2015, DOI: 10.1007/s00006-015-0620-3..

So far quaternion Fourier transforms have been mainly defined over $\mathbb{R}^2$ as signal domain space. But it seems natural to define a quaternion Fourier transform for quaternion valued signals over quaternion domains. This quaternion domain Fourier transform (QDFT) transforms quaternion valued signals (for example electromagnetic scalarvector potentials, color data, space-time data, etc.) defined over a quaternion domain (space-time or other 4D domains) from a quaternion position space to a quaternion frequency space. The QDFT uses the full potential provided by hypercomplex algebra in higher dimensions and may moreover be useful for solving quaternion partial differential equations or functional equations, and in crystallographic texture analysis. We define the QDFT and analyze its main properties, including quaternion dilation, modulation and shift properties, Plancherel and Parseval identities, covariance under orthogonal transformations, transformations of coordinate polynomials and differential operator polynomials, transformations of derivative and Dirac derivative operators, as well as signal width related to band width uncertainty relationships.
Category: Functions and Analysis

[4] viXra:1511.0247 [pdf] replaced on 2017-01-03 15:13:28

General Method for Summing Divergent Series Using Mathematica and a Comparison to Other Summation Methods

Authors: Sinisa Bubonja
Comments: 22 Pages. Removed an entire sentence from section 1, corrected typos, results unchanged.

We are interested in finding sums of some divergent series using the general method for summing divergent series discovered in our previous work and symbolic mathematical computation program Mathematica. We make a comparison to other five summation methods implemented in Mathematica and show that our method is the stronger method than methods of Abel, Borel, Cesaro, Dirichlet and Euler.
Category: Functions and Analysis

[3] viXra:1511.0246 [pdf] submitted on 2015-11-25 07:46:15

ACourse of Numerical Analysis and Applied Mathematics

Authors: Abdelmajid Ben Hadj Salem
Comments: 93 Pages. In French.

It is a course of numerical analysis and applied mathematics for the students of the geomatic and topography option of the ESAT School, Tunis, Tunisia.
Category: Functions and Analysis

[2] viXra:1511.0077 [pdf] submitted on 2015-11-10 07:45:51

Abscissa and Weights for Gaussian Quadratures of Modified Bessel Functions Integrated from Zero to Infinity

Authors: Richard J. Mathar
Comments: Few text; the majority of pages show pairs of abscissae and weights.

We tabulate the abscissae and associated weights for numerical integration of integrals with kernels which contain a power of x and Modified Bessel Functions K_nu(x). The first family of integrals contains the factor x^m K_nu(x) with integer indices nu=0 or 1 and integer powers nu <= m <= 3. The second family of integrals contains the factor x^m K_nu(x)K_nu'(x) with integer indices 0 <= nu, nu' <= 1 and integer powers nu+nu' <= m <= 3.
Category: Functions and Analysis

[1] viXra:1511.0071 [pdf] submitted on 2015-11-09 06:26:54

A Critique to Otelbaev Solution for the Sixth Millenium Problem (Navier-Stokes Equation)

Authors: Valdir Monteiro dos Santos Godoi
Comments: 2 Pages. In portuguese.

A critique to Otelbaev solution for the sixth millenium problem (Navier-Stokes equation). Begins with a dialogue with the teacher Odilon in the IME-USP library.
Category: Functions and Analysis