[5] **viXra:1310.0255 [pdf]**
*submitted on 2013-10-29 20:39:08*

**Authors:** Roxana Bujack, Eckhard Hitzer, Gerik Scheuermann

**Comments:** 5 Pages. In T. Simos, G. Psihoyios and C. Tsitouras (eds.), Numerical Analysis and Applied Mathematics ICNAAM 2013, AIP Conf. Proc. 1558, pp. 525-528 (2013). DOI: 10.1063/1.4825543, with minor revisions.

As it will turn out in this paper, the recent hype about most of the Clifford Fourier transforms is not worth the pain.
Almost every one that has a real application is separable and these transforms can be decomposed into a sum of real valued
transforms with constant multivector factors. This fact makes their interpretation, their analysis and their implementation
almost trivial.

**Keywords:** geometric algebra, Clifford algebra, Fourier transform, trigonometric transform, convolution theorem.

**Category:** Functions and Analysis

[4] **viXra:1310.0249 [pdf]**
*submitted on 2013-10-29 03:30:11*

**Authors:** Eckhard Hitzer

**Comments:** 4 Pages. In T. Simos, G. Psihoyios and C. Tsitouras (eds.), Numerical Analysis and Applied Mathematics ICNAAM 2013, AIP Conf. Proc. 1558, pp. 529 -532 (2013). DOI: 10.1063/1.4825544. 2 figures.

We show how Fourier transformations can be extended to Hamilton’s algebra of quaternions. This was initially
motivated by applications in nuclear magnetic resonance and electric engineering. Followed by an ever wider range of
applications in color image and signal processing. Hamilton’s algebra of quaternions is only one example of the larger class
of Clifford’s geometric algebras, complete algebras encoding a vector space and all its subspace elements. We introduce how
Fourier transformations are extended to Clifford algebras and applied in electromagnetism, and in the processing of images,
color images, vector field and climate data.

**Keywords:** Clifford geometric algebra, quaternion Fourier transform, Clifford Fourier transform, Clifford Fourier-Mellin transform,
Mulitvector wavepackets, Spacetime Fourier transform.

AMS Subj. Class. 15A66, 42A38

**Category:** Functions and Analysis

[3] **viXra:1310.0248 [pdf]**
*submitted on 2013-10-29 03:33:41*

**Authors:** Eckhard Hitzer

**Comments:** 4 Pages. In T. Simos, G. Psihoyios and C. Tsitouras (eds.), Numerical Analysis and Applied Mathematics ICNAAM 2013, AIP Conf. Proc. 1558, pp. 30-33 (2013). DOI: 10.1063/1.4825413

Conformal geometric algebra is preferred in many applications. Clifford Fourier transforms (CFT) allow holistic signal processing of (multi) vector fields, different from marginal (channel wise) processing: Flow fields, color fields, electromagnetic
fields, ... The Clifford algebra sets (manifolds) of $\sqrt{-1}$ lead to continuous manifolds of CFTs. A frequently asked
question is: What does a Clifford Fourier transform of conformal geometric algebra look like? We try to give a first answer.

**Keywords:** Clifford geometric algebra, Clifford Fourier transform, conformal geometric algebra, horosphere.

AMS Subj. Class. 15A66, 42A38

**Category:** Functions and Analysis

[2] **viXra:1310.0176 [pdf]**
*submitted on 2013-10-20 10:06:59*

**Authors:** Sidharth Ghoshal

**Comments:** 11 Pages.

The goal of the following document is to highlight an idea for generating new infinite series besides the ones that the standard mauclarin approach produce:

**Category:** Functions and Analysis

[1] **viXra:1310.0080 [pdf]**
*submitted on 2013-10-12 19:32:01*

**Authors:** A.A.Salama, S.A.Albolwi, Mohmed Eisa

**Comments:** 8 Pages. New neutrosophic sets and possible Applications

In this paper we will introduce and study some types of neutrosophic sets. Finally, we extend the concept of intuitionistic fuzzy ideal [8] to the case of neutrosophic sets. We can use the new of neutrosophic notions in the following
applications: compiler, networks robots, codes and database.

**Category:** Functions and Analysis