[11] **viXra:1812.0238 [pdf]**
*submitted on 2018-12-13 21:08:50*

**Authors:** Stephen Moore

**Comments:** 2 Pages.

rThe stopping time of an integer X is the number of steps in a Collatz sequence which lead to an integer value less than X. This note details an algorithm for deriving X from a list of the steps in a stopping time sequence, thus inverting the operation.
sfmoorex@gmail.com

**Category:** General Mathematics

[10] **viXra:1812.0237 [pdf]**
*submitted on 2018-12-13 21:45:15*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

It proved the Riemann hypothesis.
I used Euler's formula.

**Category:** General Mathematics

[9] **viXra:1812.0227 [pdf]**
*submitted on 2018-12-12 06:32:19*

**Authors:** Edgar Valdebenito

**Comments:** 14 Pages.

Esta nota presenta una imagen fractal.

**Category:** General Mathematics

[8] **viXra:1812.0219 [pdf]**
*submitted on 2018-12-12 13:19:51*

**Authors:** Ranjan Kumar, S A Edaltpanah, Sripati Jha, Said Broumi, Arindam Dey

**Comments:** 11 Pages.

Neutrosophic set theory provides a new tool to handle the uncertainties in shortest path problem (SPP). This paper introduces the SPP from a source node to a destination node on a neutrosophic graph in which a positive neutrosophic number is assigned to each edge as its edge cost. We define this problem as neutrosophic shortest path problem (NSSPP). A simple algorithm is also introduced to solve the NSSPP. The proposed algorithm finds the neutrosophic shortest path (NSSP) and its corresponding neutrosophic shortest path length (NSSPL) between source node and destination node. Our proposed algorithm is also capable to find crisp shortest path length (CrSPL) of the corresponding neutrosophic shortest path length (NSSPL) which helps the decision maker to choose the shortest path easily. We also compare our proposed algorithm with some existing methods to show efficiency of our proposed algorithm. Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical and graphical results demonstrate that the novel methods are superior to the existing method.

**Category:** General Mathematics

[7] **viXra:1812.0164 [pdf]**
*submitted on 2018-12-10 03:05:02*

**Authors:** Kim Geon Hack

**Comments:** 6 Pages. Proof of Goldbach conjecture

According to Goldbach's conjecture, every even number is the sum of two.Prime .This conjecture was proposed in 1742,
In fact, it remains unproven. I prove Goldbach's conjecture.. It is related to the integer system and when the number expands to infinity it is concluded that Goldbach speculation is proven.

**Category:** General Mathematics

[6] **viXra:1812.0131 [pdf]**
*replaced on 2018-12-09 13:58:06*

**Authors:** Toshiro Takami

**Comments:** 7 Pages.

Euler's formula is generally expressed as follows.
\zeta(1-s)={\frac{2}{(2*pi)^s}\Gamma(s)\cos(\frac{pi*s}{2})\zeta(s))}
However, I substitute (-2,-4,-6) in this and do not become zero.
There is not it and approaches only for a zero when I surely substitute Non trivial zero point (0.5+14.1347i, 0.5+21.0220i) for this formula.
It is either whether the formula of the Euler is wrong whether a misprint is sold as for this. I am convinced misprints are circulating.
I am convinced that it is sold It is make a mistake with cos, and to have printed sin.
Suppose you replace cos with sin.
\zeta(1-s)={\frac{2}{(2*pi)^s}\Gamma(s)\sin(\frac{pi*s}{2})\zeta(s))}

**Category:** General Mathematics

[5] **viXra:1812.0092 [pdf]**
*submitted on 2018-12-05 13:22:24*

**Authors:** Zaid Laadjal

**Comments:** 7 Pages.

In this short note, we present the sharp estimate for the existence of a unique solution for a Hadamard-type fractional differential equations with two-point boundary conditions. The method of analysis is obtained by the Banach contraction principle. An exmple is presented to clarify the principle result.

**Category:** General Mathematics

[4] **viXra:1812.0088 [pdf]**
*submitted on 2018-12-06 02:46:35*

**Authors:** Tangyin Wu Ye

**Comments:** 2 Pages.

Abstract, simulates basic arithmetic logic, reasoning judgment and hypothesis contradiction.

**Category:** General Mathematics

[3] **viXra:1812.0072 [pdf]**
*submitted on 2018-12-04 20:55:33*

**Authors:** 1

**Comments:** 23 Pages. Welcome to comment on my article

Reference: proof of the infinite size of Euclidean prime numbers
The twin prime number

**Category:** General Mathematics

[2] **viXra:1812.0062 [pdf]**
*submitted on 2018-12-03 06:39:33*

**Authors:** Edgar Valdebenito

**Comments:** 33 Pages.

This note presents the newton fractal for the function: f(z)=ln(ln(ln z))-1.

**Category:** General Mathematics

[1] **viXra:1812.0043 [pdf]**
*replaced on 2018-12-05 02:08:54*

**Authors:** Toshiro Takami

**Comments:** 3 Pages.

Since ζ(3) could be represented by sin, cos and π, we report here. I spelled
In wolframAlpha,
and, ζ(5), ζ(7), ζ(9), ζ (11), ζ(13) considered.
From these equations, it can be said that ζ(3), ζ (5), ζ (7), ζ (9), ζ (11), ζ(13) are irrational numbers.
ζ (15), ζ (17) etc. can also be expressed by these equations.

**Category:** General Mathematics