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

**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*

**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*

**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*

**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*

**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