[9] **viXra:1709.0442 [pdf]**
*submitted on 2017-09-30 11:38:21*

**Authors:** Antoine Warnery

**Comments:** 11 Pages. French

The purpose of this study is to explore the mathematical principle of causality.

**Category:** Functions and Analysis

[8] **viXra:1709.0393 [pdf]**
*submitted on 2017-09-26 07:41:30*

**Authors:** Andrej Liptaj

**Comments:** 8 Pages. Text presents known results.

Multiplicative coefficients of a series of Bessel functions of the first kind can be adjusted so as to match desired values corresponding to a derivatives of a function to be expanded. In this way Neumann series of Bessel functions is constructed. Text presents known results.

**Category:** Functions and Analysis

[7] **viXra:1709.0357 [pdf]**
*replaced on 2018-01-22 03:40:51*

**Authors:** Johan Aspegren

**Comments:** 3 Pages.

In this article we will give a proof that the Kakeya tube conjecture implies the Kakeya conjecture.

**Category:** Functions and Analysis

[6] **viXra:1709.0310 [pdf]**
*submitted on 2017-09-20 13:49:06*

**Authors:** Misha Mikhaylov

**Comments:** 2 Pages.

This is the Russian version of my previous publication.

**Category:** Functions and Analysis

[5] **viXra:1709.0305 [pdf]**
*submitted on 2017-09-20 13:07:26*

**Authors:** Misha Mikhaylov

**Comments:** 2 Pages.

This sum for natural values is, of course, already calculated by Bernoulli himself – at least modern or relatively recent authors that deal with it usually refer to take into account Bernoulli numbers. But, apparently, this method is rather cumbersome. Therefore, there can be suggested another, easier way to do this, but without claiming of its superfluous rigidity.

**Category:** Functions and Analysis

[4] **viXra:1709.0304 [pdf]**
*submitted on 2017-09-20 07:24:33*

**Authors:** Richard J. Mathar

**Comments:** 48 Pages. Most of the content is the source code listing

Boys' Function F_m(z) that appears in the quantum mechanics of Gaussian Type Orbitals is
a special case of Kummer's confluent hypergeometric function. We evaluate its integral representation
of a product of a power and an exponential function over the unit interval
with the numerical Gauss-Jacobi quadrature. We provide an implementation in C for real values
of the argument z which basically employs a table of the weights and abscissae of the
quadrature rule for integer quantum numbers m <= 129.

**Category:** Functions and Analysis

[3] **viXra:1709.0281 [pdf]**
*submitted on 2017-09-18 20:00:56*

**Authors:** Johan Aspegren

**Comments:** 3 Pages.

In this paper we will prove a theorem that implies the Kakeya conjecture.

**Category:** Functions and Analysis

[2] **viXra:1709.0113 [pdf]**
*replaced on 2018-07-22 15:18:50*

**Authors:** Johan Aspegren

**Comments:** 7 Pages.

In this article we will prove the Kakeya set conjecture. In addition we will prove that in the usual approach to the Kakeya maximal function conjecture we can assume that the tube-sets are maximal. Moreover, we will construct a tube- set were the well known L2 bound for the Kakeya maximal function is attained.

**Category:** Functions and Analysis

[1] **viXra:1709.0047 [pdf]**
*replaced on 2017-09-19 07:48:27*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

We describe a fluid in three-dimensional motion with at most one spatial variable by rectangular coordinate, beyond time, and conclude on the breakdown of Euler and Navier-Stokes solutions and the necessity of use of vector pressure.

**Category:** Functions and Analysis