[5] **viXra:1508.0214 [pdf]**
*submitted on 2015-08-27 06:58:21*

**Authors:** Alex Patterson

**Comments:** 5 Pages. Special thanks to many

Abstract
This short paper is a simple attempt to see whether the Lorentz Gamma Factor, when restrained by Wittgenstein’s TLP (Tractatus Logico Philosophicus) 3.333 proposition on a Function containing a function which he supposes rather imperatively that it excises Russell’s Paradox in Principia Mathematica, may be ‘a rationalist/rational under-study’ on that very of excisement, and vice versa. Further, potentially moot but nonetheless by Vico’s Dictum attention is given to what the consequences of finalizing the Under-Study might entail, be consequent on, pertain to, maybe even elucidate, etc.
Such under-studies are abundant in the classics, for example Vico to Petrarch. That’s sufficient and needs more of in the author’s view.

**Category:** Functions and Analysis

[4] **viXra:1508.0204 [pdf]**
*submitted on 2015-08-25 14:15:46*

**Authors:** Kunle Adegoke, Olawanle Layeni

**Comments:** 22 Pages.

We state and prove a general summation identity. The identity is then applied to derive various summation formulas involving the generalized harmonic numbers and related quantities. Interesting results, mostly new, are obtained for both finite and infinite sums. The high points of this paper are perhaps the discovery of several previously unknown infinite summation results involving {\em non-linear} generalized harmonic number terms and the derivation of interesting alternating summation formulas involving these numbers.

**Category:** Functions and Analysis

[3] **viXra:1508.0152 [pdf]**
*replaced on 2016-01-24 06:06:48*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 14 Pages. See viXra:1601.0312: "Breakdown of Navier-Stokes Solutions – Unbounded Energy for t > 0", by Valdir M.S. Godoi

Considerations on (and solution to) the 6th millenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy.

**Category:** Functions and Analysis

[2] **viXra:1508.0096 [pdf]**
*replaced on 2015-09-03 08:41:14*

**Authors:** Han Geurdes

**Comments:** 5 Pages.

It is demonstrated that the Navier Stokes equation has a smooth nontrivial exact solution in (3+1). All the required characteristics of a type B solution are verified.

**Category:** Functions and Analysis

[1] **viXra:1508.0083 [pdf]**
*submitted on 2015-08-11 10:24:30*

**Authors:** Carlos Armando De Castro

**Comments:** 7 pages, one column, 8 figures

In this paper it is shown a simple approximation of the function exp(x) for positive values of x, deduced from the implicit Euler numerical solution of first order lineal differential equations (ODE). The results show that the approximation has an error of less than 10% for exp(x) when x < 0.35 and for exp(-x) when x < 0.5, which is acceptable for many engineering applications, and helps facilitate the analysis of some systems without the use of computers.
Keywords: approximation, Euler implicit method, exponential function, first order ODE.

**Category:** Functions and Analysis