[5] **viXra:1705.0391 [pdf]**
*submitted on 2017-05-27 11:05:35*

**Authors:** Wilson Torres Ovejero

**Comments:** 11 Pages.

Since 2013 I have dedicated my life to the study of the famous Riemann hypothesis, which is one of the 6 thousand-year-old problems that exist. This conjecture in addition to allowing me to deepen my knowledge in complex analysis, I had the opportunity to finish my degree in mathematics with an excellent thesis. Based on all of this, today I pose a possible demonstration of this hypothesis and hope that it has succeeded.

**Category:** Functions and Analysis

[4] **viXra:1705.0249 [pdf]**
*submitted on 2017-05-16 08:26:20*

**Authors:** Andrej Liptaj

**Comments:** 6 Pages.

A set of functions which allows easy derivative-matching is proposed. Several examples of approximations are shown.

**Category:** Functions and Analysis

[3] **viXra:1705.0165 [pdf]**
*submitted on 2017-05-09 17:00:33*

**Authors:** Nicholas R. Wright

**Comments:** 6 Pages.

We prove the Navier-Stokes equations, by means of the Metabolic Theory of Ecology and the Rule of 72. Macroecological theories are proof to the Navier-Stokes equations. A solution could be found using Kleiber’s Law. Measurement is possible through the heat calorie. A Pareto exists within the Navier-Stokes equations. This is done by superposing dust solutions onto fluid solutions. In summary, the Navier-Stokes equations require a theoretical solution. The Metabolic Theory of Ecology, along with Kleiber’s Law, form a theory by such standards.

**Category:** Functions and Analysis

[2] **viXra:1705.0028 [pdf]**
*submitted on 2017-05-02 15:33:07*

**Authors:** Morad Ahmad; Shaher Momani; Omar Abu Arqub; Mohammed Al-Smadi; Ahmed Alsaedi

**Comments:** 13 Pages.

In this paper, a powerful computational algorithm is developed for the solution of classes of singular second-order, three-point Volterra integrodifferential equations in favorable reproducing kernel Hilbert spaces. The solutions is represented in the form of series in the Hilbert space W₂³[0,1] with easily computable components. In finding the computational solutions, we use generating the orthogonal basis from the obtained kernel functions such that the orthonormal basis is constructing in order to formulate and utilize the solutions. Numerical experiments are carried where two smooth reproducing kernel functions are used throughout the evolution of the algorithm to obtain the required nodal values of the unknown variables. Error estimates are proven that it converge to zero in the sense of the space norm. Several computational simulation experiments are given to show the good performance of the proposed procedure. Finally, the utilized results show that the present algorithm and simulated annealing provide a good scheduling methodology to multipoint singular boundary value problems restricted by Volterra operator.

**Category:** Functions and Analysis

[1] **viXra:1705.0001 [pdf]**
*submitted on 2017-05-01 02:13:42*

**Authors:** Kolosov Petro

**Comments:** 12 pages, 6 figures

Calculating the value of $C^{k\in\{1,\infty\}}$ class of smoothness real-valued function's derivative in point of $\mathbb{R}^+$ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and $q$-difference operator. $(P,q)$-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using $q$-difference and $p,q$-power difference is shown.

**Category:** Functions and Analysis