[6] **viXra:1608.0432 [pdf]**
*replaced on 2016-09-01 12:40:33*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

We present two proofs of theorems on solutions of the Navier-Stokes equations for incompressible case with a conservative external force in n = 3 spatial dimensions. Without major difficulties, it can be adapted to any spatial dimension, n>=1.

**Category:** Functions and Analysis

[5] **viXra:1608.0394 [pdf]**
*submitted on 2016-08-29 06:04:21*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 2 Pages.

Using sliding hump-type techniques, we prove some Schur, Vitali-Hahn-Saks and Nikodým-type theorems for lattice group-valued k-triangular set functions.

**Category:** Functions and Analysis

[4] **viXra:1608.0229 [pdf]**
*submitted on 2016-08-21 11:27:59*

**Authors:** Fu Yuhua

**Comments:** 12 Pages.

Unlike Dirac operator method, this paper discusses one dimensional method for Clifford analysis, namely the n-dimensional problem is simplified into n problems of one dimension, even reduced to only one problem of one dimension. For example, the typhoon track is a two-dimensional problem related to latitude and longitude, but as forecasting typhoon track, it can be simplified into two problems of one dimension: forecasting longitude and forecasting latitude respectively. Again, the stock index is effected by various factors, however as forecasting stock index we may assume that it is only a function of time. In order to improve the effect of one dimensional method, we can change finding the solution suitable for whole space or a domain, into finding the solution suitable for one point only with single point method. As applying one dimensional method, the fractal model is very effective.

**Category:** Functions and Analysis

[3] **viXra:1608.0155 [pdf]**
*submitted on 2016-08-16 03:44:17*

**Authors:** L. A. N. de Paula

**Comments:** 5 Pages.

A large number of methods have been proposed for solving nonlinear differential equations. The
Jacobi elliptic function method and the f-expansion methods are generalizations from a few of
them. These methods produce not only single-solitons but also multi-soliton solutions. In this work
we applied the f -expansion method and found novel solutions besides those known for three main
equations of the kind sine-Gordon: Triple Sine-Gordon (TSG), Double Sine-Gordon (DSG) and
Simple Sine-Gordon (SSG).

**Category:** Functions and Analysis

[2] **viXra:1608.0090 [pdf]**
*replaced on 2016-12-14 21:10:19*

**Authors:** Stephen Crowley

**Comments:** 9 Pages.

There is shown to exist a unique solutions to the LeClaire-França exact equation for the first 98,020 of the first 100,000 zeros of the Hardy Z Function via the construction of Cauchy sequences whose accumulation points are guaranteed via an application of the Newton-Kantorovich theorem applied to a Newton-like map

**Category:** Functions and Analysis

[1] **viXra:1608.0065 [pdf]**
*submitted on 2016-08-05 21:34:41*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

This article explores a case of signal based chaos generation, using the Carotid-Kundalini function, shown in literature to possess fractal artifacts. Specifically, we set the input to a two tone signal, with the frequency ratio between the sinusoids acting as the control parameter. We explore the iterative map using the time derivatives, and upon plotting the bifurcation plot, observe the chaotic nature of the generated signal. Phase portraits are plotted for different orders, and presence of rich patterns are observed. True to the nonlinear nature, the frequency spectrum shows a horde of new frequency components generated at the output. Lyapunov Exponents also quantitatively confirm the presence of generated chaos in the Carotid-Kundalini signal.

**Category:** Functions and Analysis