[7] **viXra:1604.0376 [pdf]**
*submitted on 2016-04-29 06:12:02*

**Authors:** Antonio Boccuto, Xenofon Dimitriou

**Comments:** 13 Pages.

We give necessary and sufficient
conditions for exchange of limits of
double-indexed families, taking values in sets
endowed with an abstract structure of convergence, and for preservation
of continuity or semicontinuity of the limit family, with respect to filter convergence.
As consequences, we give some filter
limit theorems and some characterization of
continuity and semicontinuity of
the limit of a pointwise convergent family of set functions.

**Category:** Functions and Analysis

[6] **viXra:1604.0369 [pdf]**
*submitted on 2016-04-28 08:05:07*

**Authors:** Claude Michael Cassano

**Comments:** 4 Pages.

The Homogeneous , Reduction of Order Homogeneous , and Inhomogeneous Second Order Linear Ordinary Differential Equations Solution may be established in one analytical proof-process.

**Category:** Functions and Analysis

[5] **viXra:1604.0244 [pdf]**
*replaced on 2017-04-03 08:56:40*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 14 Pages.

We find an exact solution for the system of Navier-Stokes equations, supposing that there is some solution, following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, it is possible that there are infinite solutions for pressure and velocity, given only the condition of initial velocity.

**Category:** Functions and Analysis

[4] **viXra:1604.0235 [pdf]**
*replaced on 2016-06-12 04:36:26*

**Authors:** Danil Krotkov

**Comments:** 13 Pages.

We derive some new formulas, connecting some series with Möbius function with Sine Integral and Cosine Integral functions, give the formal proof for full version of Stirling's formula with remainder term in form of definite integral of elementary function; investigate the values of new Dirichlet series function at natural numbers >1 and its behavior at the pole at s=1, connecting it with elementary constants.

**Category:** Functions and Analysis

[3] **viXra:1604.0204 [pdf]**
*submitted on 2016-04-13 02:17:14*

**Authors:** Bing He

**Comments:** 16 Pages.

Let \begin{equation*}
A_{q}^{(\alpha)}(a;z)=\sum_{k=0}^{\infty}\frac{(a;q)_{k}q^{\alpha k^2} z^k}{(q;q)_{k}},
\end{equation*}
where $\alpha >0,~0<q<1.$ In a paper of Ruiming Zhang, he asked under what conditions the zeros of the entire
function $A_{q}^{(\alpha)}(a;z)$ are all real and established some results on the zeros of $A_{q}^{(\alpha)}(a;z)$ which present a partial answer to that question. In the present paper, we will set up some results on certain entire functions which includes that $A_{q}^{(\alpha)}(q^l;z),~l\geq 2$ has only infinitely many negative zeros that gives a partial answer to Zhang's question. In addition, we establish some results on zeros of certain entire functions involving the Rogers-Szeg\H{o} polynomials and the Stieltjes-Wigert polynomials.

**Category:** Functions and Analysis

[2] **viXra:1604.0107 [pdf]**
*replaced on 2016-11-18 06:21:50*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 17 Pages.

We seek some attempt solutions for the system of Navier-Stokes equations for spatial dimensions n = 2 and n = 3. These solutions have the principal objective to provide a better numerical evaluation of the exact analytical solution, thus contributing to the solution not only from a theoretical mathematical problem, but from a practical problem worldwide.

**Category:** Functions and Analysis

[1] **viXra:1604.0001 [pdf]**
*submitted on 2016-04-01 02:42:01*

**Authors:** Eckhard Hitzer

**Comments:** 16 Pages. 1 figure

In this paper we use the general steerable one-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 a linear combination of Mustard convolutions, and vice versa the Mustard convolution of Clifford algebra signals in terms of a linear combination of classical convolutions.

**Category:** Functions and Analysis