[5] **viXra:1802.0267 [pdf]**
*submitted on 2018-02-19 17:56:17*

**Authors:** Ayal Sharon

**Comments:** 18 Pages.

Euler's formula is used to derive a trigonometric version of the Dirichlet series $\zeta(s)=\sum n^{-s}$, which is divergent in the half-plane $\sigma \le 1$, wherein $s \in \mathbb{C}$ and $s=\sigma +it$. Abel's lemma and Dirichlet's test incorrectly hold that trigonometric $\zeta(s)$ is convergent in the critical strip $0<\sigma \le 1$ at $t\ne0$, because they fail to consider a divergent monotonically decreasing series (e.g. the harmonic series) in combination with a bounded oscillating function having an increasing period duration (e.g. $f(t, n) = \sin(t \cdot \ln(n))$).

**Category:** Functions and Analysis

[4] **viXra:1802.0126 [pdf]**
*replaced on 2018-02-12 23:41:44*

**Authors:** Han Geurdes, Koji Nagata, Tadao Nakamura, Ahmed Farouk

**Comments:** 12 Pages.

In the paper it is demonstrated that Bells theorem is an unprovable theorem. This inconsistency is similar to concrete mathematical incompleteness. The inconsistency is purely mathematical. Nevertheless the basic physics requirements of a local model are fulfilled.

**Category:** Functions and Analysis

[3] **viXra:1802.0120 [pdf]**
*submitted on 2018-02-10 14:44:28*

**Authors:** Zeraoulia Rafik

**Comments:** 23 Pages. I wish my results w'd be considerable for any futur refeered journal

In this note we present some new results about the analyticity of the functional-differential equation $ f'=e^{{f}^{-1}}$ at $ 0$ with $f^{-1}$ is a compositional inverse of $f$ , and the growth rate of $f_-(x)$ and $f_+(x)$ as $x\to \infty$ , and we will check the analyticity of some functional equations which they were studied before and had a relashionship with the titled functional-differential and we will conclude our work with a conjecture related to Borel- summability and some interesting applications of some divergents generating function with radius of convergent equal $0$ in number theory

**Category:** Functions and Analysis

[2] **viXra:1802.0094 [pdf]**
*submitted on 2018-02-08 07:08:19*

**Authors:** Jesús Álvarez Lobo

**Comments:** 2 Pages. Revista Escolar de la Olimpiada Iberoamericana de Matemática. Volume 22. Spanish.

Upper bound for the product of the sum of the reciprocals of n real numbers greater than or equal to 1 by the product of those increased by 1, and some variants.
Se establece una cota superior para el producto del sumatorio de los recíprocos de n números reales mayores o iguales que 1 por el producto de éstos incrementados en 1, y para algunas variantes.

**Category:** Functions and Analysis

[1] **viXra:1802.0021 [pdf]**
*submitted on 2018-02-02 16:57:10*

**Authors:** Jesús Álvarez Lobo

**Comments:** 10 Pages.

Usually, the complexity of a fractional function increases significantly in its second derivative, so the calculation of the second derivative can be tedious and difficult to simplify and evaluate its value at a point, especially if the abscise isn't an integer.
However, to determine whether a point at which cancels the first derivative of a function is a relative extremum (maximum or minimum) of it, is not necessary to know the value of the second derivative at the point but only its sign.
Motivated by these facts, we define a signum function for the second derivative of fractional functions in the domain of the roots of the first derivative of the function.
The method can dramatically simplify the search for maximum and minimum points in fractional functions and can be implemented by means of a simple algorithm.

**Category:** Functions and Analysis