[3] **viXra:1602.0246 [pdf]**
*replaced on 2017-02-03 06:23:46*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 53 Pages. Article (english version) published in J. Phys. Math (2016) 7: 196. The digitation or conversion of this paper in J. Phys. Math. need revision and many typographical corrections. I'm sorry.

A solution to the 6th millenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy. We have proved that there are initial velocities u^0(x) and forces f(x,t) such that there is no physically reasonable solution to the Navier-Stokes equations for t>0, which corresponds to the case (C) of the problem relating to Navier-Stokes equations available on the website of the Clay Institute.

**Category:** Functions and Analysis

[2] **viXra:1602.0235 [pdf]**
*submitted on 2016-02-19 06:00:15*

**Authors:** Oleh Kyrhan

**Comments:** 6 Pages.

The article discusses the representation of discrete functions defined in an analytic form without the use of approximations, namely the Heaviside function, identity function, the Dirac delta function and the prime-counting function.

**Category:** Functions and Analysis

[1] **viXra:1602.0044 [pdf]**
*submitted on 2016-02-04 07:36:02*

**Authors:** Eckhard Hitzer

**Comments:** 19 Pages. Submitted to Adv. in Appl. Cliff. Algs., 1 figure.

In this paper we use the general steerable two-sided Clifford Fourier transform (CFT), and relate the classical convolution of Clifford algebra-valued signals over $\R^{p,q}$ with the (equally steerable) Mustard convolution. A Mustard convolution can be expressed in the spectral domain as the point wise product of the CFTs of the factor functions. In full generality do we express the classical convolution of Clifford algebra signals in terms of finite linear combinations of Mustard convolutions, and vice versa the Mustard convolution of Clifford algebra signals in terms of finite linear combinations of classical convolutions.

**Category:** Functions and Analysis