[5] **viXra:1210.0146 [pdf]**
*replaced on 2014-06-09 10:10:42*

**Authors:** Bertrand Wong

**Comments:** 16 Pages.

The motion of fluids which are incompressible could be described by the Navier-Stokes differential equations. However, the
three-dimensional Navier-Stokes equations for modelling turbulence misbehave very badly although they are relatively simplelooking. The solutions could wind up being extremely unstable even with nice, smooth, reasonably harmless initial conditions. A mathematical understanding of the outrageous behaviour of these equations would greatly affect the field of fluid mechanics.
In this paper, which had been published in the International Journal of Nonlinear Science, Vol. 10 (2010) No. 3, pp.264-278, a reasoned, practical approach towards resolving the issue is adopted and a practical, statistical kind of mathematical solution is proposed.

**Category:** Functions and Analysis

[4] **viXra:1210.0111 [pdf]**
*replaced on 2013-04-18 16:34:34*

**Authors:** J.A.J. van Leunen

**Comments:** 76 Pages.

This is a compilation of formula of quaternionic algebra and quaternionic differentials
Two types of quaternionic differentiation exist.
Flat differentiation uses the quaternionic nabla and ignores the curvature of the parameter space.
Full differentiation uses the distance function ℘(x) that defines the curvature of the parameter space.
The text focuses at applications in quantum mechanics, in electrodynamics and in fluid dynamics.

**Category:** Functions and Analysis

[3] **viXra:1210.0069 [pdf]**
*submitted on 2012-10-13 04:32:55*

**Authors:** Imanol Pérez

**Comments:** 1 Page.

In this paper I introduce a new method to find the roots of a function with two known values a and b such that sgn(f(a)) = -sgn(f(b)).

**Category:** Functions and Analysis

[2] **viXra:1210.0068 [pdf]**
*submitted on 2012-10-13 04:38:34*

**Authors:** Imanol Pérez

**Comments:** 3 Pages.

This paper shows a relationship between spiral and the roots of complex numbers.

**Category:** Functions and Analysis

[1] **viXra:1210.0041 [pdf]**
*submitted on 2012-10-09 02:27:46*

**Authors:** Pierre-Yves Gaillard

**Comments:** 1 Page.

We give a short proof of l'Hospital's Rule.

**Category:** Functions and Analysis