Functions and Analysis

1508 Submissions

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

An Under-Study of Both in Terms of the Other – Wittgenstein’s TLP Proposition 3.333 & the Lorentz Gamma-Factor γ

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

New Finite and Infinite Summation Identities Involving the Generalized Harmonic Numbers

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

Breakdown of Navier-Stokes Solutions – Bounded Energy

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

A Type B Solution to the 3 Dimensional Navier Stokes Equation

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

Approximation of Exp(x) Deduced from the Implicit Euler Numerical Solution of First Order Linear Differential Equations

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