**Previous months:**

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2012 - 1202(2) - 1203(3) - 1204(2) - 1205(2) - 1206(2) - 1207(1) - 1208(3) - 1211(1) - 1212(1)

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2015 - 1501(7) - 1502(18) - 1503(6) - 1504(7) - 1505(1) - 1506(6) - 1507(1) - 1508(111) - 1509(18) - 1510(143) - 1511(16) - 1512(176)

2016 - 1601(65) - 1602(28) - 1603(33) - 1604(38) - 1605(17) - 1606(24) - 1607(45) - 1608(36) - 1609(39) - 1610(9) - 1611(21) - 1612(25)

2017 - 1701(235) - 1702(9) - 1703(11) - 1704(20) - 1705(53) - 1706(79) - 1707(1) - 1708(9) - 1709(23) - 1710(17) - 1711(132) - 1712(7)

2018 - 1801(31) - 1802(31) - 1803(129) - 1804(37) - 1805(37) - 1806(8) - 1807(8) - 1808(165) - 1809(77) - 1810(21) - 1811(8) - 1812(13)

2019 - 1901(9)

Any replacements are listed farther down

[2979] **viXra:1901.0296 [pdf]**
*submitted on 2019-01-20 01:15:19*

**Authors:** Aditya Raj

**Comments:** 3 Pages. Mathematical coincidences

Mathematical coincidences concerning the mathematical constant Pi (π) and Archimedes’ constant (√2), containing other mathematical constants i.e. The Golden Ratio (φ), the Silver Ratio (δ_s) and the Euler’s number (e).

**Category:** General Mathematics

[2978] **viXra:1901.0273 [pdf]**
*submitted on 2019-01-19 12:56:00*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

Here is a counter example of Riemann hypothesis.
I have shown six counter example so far, but it is likely that it was nothing more than the zero point on 0.5 when checked in the figure.
I thought that there should be a counter example to the high area and I found it.
Since this is a high area, it can not be confirmed in the figure.
You can check on the super-computer whether it is counter example.
zeta[0.5001+i9993939939.66587267099915568134]= 2.71601636452515... × 10^-19 - 2.378065787121017... × 10^-12 i

**Category:** General Mathematics

[2977] **viXra:1901.0267 [pdf]**
*submitted on 2019-01-18 09:55:56*

**Authors:** Timothy W. Jones

**Comments:** 6 Pages.

The full potential of elementary algebra is presented. A simple regression problem demonstrates how programming can be combined with linear regression. The math and programming are simple enough for any algebra class that uses a TI-83 family calculator.

**Category:** General Mathematics

[2976] **viXra:1901.0240 [pdf]**
*submitted on 2019-01-17 03:30:42*

**Authors:** Toshiro Takami

**Comments:** 10 Pages.

It presents counter exsample which is close to 0.5 of 3 Riemann hypothesis but not 0.5.
Somewhere on the net there is a memory that reads the mathematician's view that "there are countless zero points in the vicinity of 0.5", which seems to be.
This is the value I gave by hand calculation, and it seems that correction by supercomputer is necessary.
Among these five, it is presumed that a true counter example and a thing that is not mixed together.
zeta[0.5000866+i393939939.3731193515534038924]= -1.60917723458557... × 10^-18 - 1.428779604546702... × 10^-11 i
and
zeta[0.4999944+i393939958.90878694741368323631]= 9.30660314868779... × 10^-19 + 1.342928180878699... × 10^-12 i
and
zeta[0.4999964+i393939964.659437163857861]= -5.914628349384624... × 10^-16 + 6.504227267123851... × 10^-13 i

**Category:** General Mathematics

[2975] **viXra:1901.0209 [pdf]**
*submitted on 2019-01-14 17:11:15*

[2974] **viXra:1901.0154 [pdf]**
*submitted on 2019-01-11 06:25:44*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

Esta nota muestra una integral elemental.

**Category:** General Mathematics

[2973] **viXra:1901.0153 [pdf]**
*submitted on 2019-01-11 06:28:59*

**Authors:** Edgar Valdebenito

**Comments:** 69 Pages.

Esta nota muestra una colección de fractales.

**Category:** General Mathematics

[2972] **viXra:1901.0100 [pdf]**
*submitted on 2019-01-09 01:40:30*

**Authors:** Jianwen Huang, Jianjun Wang, Feng Zhang, Hailin Wang

**Comments:** 17 Pages.

In this paper, we bring forward a completely perturbed nuclear norm minimization method to tackle a formulation of completely perturbed low-rank matrices recovery. In view of the matrix version of the restricted isometry property (RIP) and the Frobenius-robust rank null space property (FRNSP), this paper extends the investigation to a completely perturbed model taking into consideration not only noise but also perturbation, derives sufficient conditions guaranteeing that low-rank matrices can be robustly and stably reconstructed under the completely perturbed scenario, as well as finally presents an upper bound estimation of recovery error. The upper bound estimation can be described by two terms, one concerning the total noise, and another regarding the best $r$-approximation error. Specially, we not only improve the condition corresponding with RIP, but also ameliorate the upper bound estimation in case the results reduce to the general case. Furthermore, in the case of $\mathcal{E}=0$, the obtaining conditions are optimal.

**Category:** General Mathematics

[2971] **viXra:1901.0025 [pdf]**
*submitted on 2019-01-04 00:51:50*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

Every number, every equation carries profound meaning, not just physically, but in the bigger scheme of things. We set out to study and uncover them.

**Category:** General Mathematics

[2970] **viXra:1812.0480 [pdf]**
*submitted on 2018-12-31 00:05:05*

**Authors:** Kohji Suzuki

**Comments:** 28 Pages.

We explore classification of conics from a viewpoint of differential forms.

**Category:** General Mathematics

[2969] **viXra:1812.0410 [pdf]**
*submitted on 2018-12-24 16:22:46*

**Authors:** Kohji Suzuki

**Comments:** 4 Pages.

The interested reader is invited to solve these exercises.

**Category:** General Mathematics

[2968] **viXra:1812.0361 [pdf]**
*submitted on 2018-12-21 02:55:08*

**Authors:** Toshiro Takami

**Comments:** 2 Pages.

ζ (3) was obtained by another method.
\sum_{k=1}^\infty \frac{1}{k^2*2^(k-1)}+(log2)^2
=π^2/6 =ζ(2)
\sum_{k=1}^\infty \frac{1}{k^3*2^(k-1)}+(log2)^3≈1.40745
zeta(3)= 1.202056903160…..

**Category:** General Mathematics

[2967] **viXra:1812.0350 [pdf]**
*submitted on 2018-12-19 08:04:33*

**Authors:** Nicolò Rigamonti

**Comments:** 8 Pages.

This paper shows the importance of two properties, which are at the base of the Riemann hypothesis.
The key point of all the reasoning about the validity of the Riemann hypothesis is in the fact that only if the Riemann hypothesis is true, these two properties, which are satisfied by the non-trivial zeros, are both true.
In fact, only if these two properties are both true , all non-trivial zeros lie on the critical line

**Category:** General Mathematics

[2966] **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

[2965] **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

[2964] **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

[2963] **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

[2962] **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

[2961] **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

[2960] **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

[2959] **viXra:1812.0043 [pdf]**
*submitted on 2018-12-04 00:02:55*

**Authors:** Toshiro Takami

**Comments:** 5 Pages.

Since ζ(3) could be represented by sin, cos and π, we report here. I spelled
In wolframAlpha,
sum_(n=1)^infty [sin((6n-4)*pi/3) -sin((6n-2)*pi/3) + sin(6n*pi/3) ] / [sqrt(3)*n^3]
=1.2020569031595942853997381615114…...
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

[2958] **viXra:1811.0501 [pdf]**
*submitted on 2018-11-29 19:06:09*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

It is at a glance that pairs that can be thought of as twin prime exist at non-trivial zero points.
I considered it.

**Category:** General Mathematics

[2957] **viXra:1811.0434 [pdf]**
*submitted on 2018-11-26 06:21:05*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents a elementary integral formula.

**Category:** General Mathematics

[2956] **viXra:1811.0433 [pdf]**
*submitted on 2018-11-26 06:23:53*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

This note presents a elementary infinite product.

**Category:** General Mathematics

[2955] **viXra:1811.0409 [pdf]**
*submitted on 2018-11-27 03:59:39*

**Authors:** Toshiro Takami

**Comments:** 12 Pages.

At first, each prime number was related to each non-trivial zero point, we thought from equation (2).
However, when calculated, it turned out that each prime number is not related to the nontrivial zeros, and is related to trivial zeros.

**Category:** General Mathematics

[2954] **viXra:1811.0325 [pdf]**
*submitted on 2018-11-20 06:35:58*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

In this note we give some integrals.

**Category:** General Mathematics

[2953] **viXra:1811.0293 [pdf]**
*submitted on 2018-11-20 03:15:30*

**Authors:** Toshiro Takami

**Comments:** 17 Pages.

Tried to simulate the nontribial point of the Riemann zeta function.
At the beginning, we tried to be exactly the same value as the nontribial point of the Riemann Zeta function only with the degree of increase of the circle going up like wrapping x = 0.5, but the degree of increase varies from moment to moment extremely difficult It was judged impossible.
Then I created an expression that can take approximate values, but always take lower values than the nontribial zeros of the Riemann zeta function except for the initial values. However, by increasing the degree of increase of the circle going up like winding x = 0.5, it became possible to take a value which can be said to be an approximate value.
The degree of increase in circle was based on the formula of the nuclear energy value of uranium.
Since the degree of increase of the zero point changes from moment to moment, satisfactory approximate values can not be obtained yet.

**Category:** General Mathematics

[2952] **viXra:1811.0215 [pdf]**
*submitted on 2018-11-13 06:36:17*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

In this note we give some integrals.

**Category:** General Mathematics

[2951] **viXra:1811.0174 [pdf]**
*submitted on 2018-11-12 05:03:56*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 6 Pages.

This paper deals only with the Mellin transforms of some functions and their relationship with the gamma functions.

**Category:** General Mathematics

[2950] **viXra:1811.0044 [pdf]**
*submitted on 2018-11-03 23:46:55*

**Authors:** Felix M Lev

**Comments:** 5 Pages.

Classical mathematics (involving such notions as infinitely small/large and continuity)
is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We give a simple proof that the situation is the opposite: classical mathematics is only a degenerate special case of finite one. Motivation and implications are discussed.

**Category:** General Mathematics

[2949] **viXra:1810.0465 [pdf]**
*submitted on 2018-10-29 03:25:43*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 8 Pages.

Riemann and others have used the Poisson summation formula to prove Riemann’s functional equation. The opposite is actually true, the Poisson summation formula provides a refutation of Riemann’s functional equation. It is the purpose of this paper to disprove Riemann’s functional equation using the Poisson summation formula.

**Category:** General Mathematics

[2948] **viXra:1810.0434 [pdf]**
*submitted on 2018-10-25 06:29:22*

**Authors:** Agbo Felix Isaac

**Comments:** 17 Pages.

In this article, I propose a generalized method for obtaining a substitution for reducing a reducible linear ordinary differential equation with function coefficients (RLDEF) to a linear ordinary differential equation with constant coefficient (LDE). This proposed method was also used to obtain the already known substitutions for the Euler’s and Legendre’s homogeneous second order linear differential equation. The derived method is able to reduce quite a large number of RLDEF to LDE including the Euler’s and Legendre’s homogeneous second order linear differential equation. However, these RLDEF (homogeneous and inhomogeneous) must satisfy the condition for reducibility, which is also proposed before the substitution is derived. the condition for reducibility is based on the order of the differential equation. In this article, the condition for reducibility is presented for a second and third order LDEF. Keywords: reducibility, generalized, differential equations.

**Category:** General Mathematics

[2947] **viXra:1810.0408 [pdf]**
*submitted on 2018-10-24 14:59:24*

**Authors:** Zaid Laadjal

**Comments:** 9 Pages.

In this paper, we describe the solution approaches based on Homotopy Analysis Method for the follwing Nonlinear Mixed Volterra-Fredholm integro-differential equation of fractional order $$\begin{array}{l} ^{C}D^{\alpha }u(t)=\varphi (t)+\lambda \int_{0}^{t}\int_{0}^{T}k(x,s)F\left( u(s\right) )dxds, \\ u(0)=c,\text{}u^{(i)}(0)=0,i=1,...,n-1, \end{array}$$ where $t\in \Omega =\left[ 0;T\right] ,\ k:\Omega \times \Omega \longrightarrow \mathbb{R},$ $\varphi :\Omega \longrightarrow \mathbb{R},$ are known functions,\ $F:C\left(\Omega, \mathbb{R}\right) \longrightarrow \mathbb{R}$ is nonlinear function, $c$ and $\lambda $ are constants, $^{C}D^{\alpha }$ is the Caputo derivative of order $\alpha $ with $n-1<\alpha \leqslant n.$ In addition some examples are used to illustrate the accuracy and validity of this approach.

**Category:** General Mathematics

[2946] **viXra:1810.0407 [pdf]**
*submitted on 2018-10-24 15:31:00*

**Authors:** Colin James III

**Comments:** 2 Pages. © Copyright 2018 by Colin James III All rights reserved. Respond to the author by email at: info@ersatz-systems dot com.

Definitions of neutrosophy as further embellished with probability and (in)dependency share the same result as denied of tautology. This means neutrosophic logic as a general framework for unification of many existing logics, such as intuitionistic fuzzy logic) and paraconsistent logic, is refuted.

**Category:** General Mathematics

[2945] **viXra:1810.0398 [pdf]**
*submitted on 2018-10-23 06:05:17*

**Authors:** Rebeca Escobar Jara, Maikel Leyva Vázquez, Cesar Ernesto Roldan Martínez

**Comments:** 13 Pages.

Objective. Social learning analytics is a subset of learning analysis as it attempts to demonstrate how new skills and ideas are not just individual achievements, but are developed, carried forward and transmitted through interaction and collaboration.

**Category:** General Mathematics

[2944] **viXra:1810.0397 [pdf]**
*submitted on 2018-10-23 06:06:49*

**Authors:** Neilys González Benítez

**Comments:** 9 Pages.

The mental upsets are affections or psychic syndromes and conduct ales, opposed to the town of the individuals that enjoy good mental health. They are varied the causes of the mental illnesses. The biological factors are one of the more common causes. Of similar form a traumatic injury of the brain can conduct to a mental upset. The exposition of the mother during the embarrassments to virus or chemical toxics constitutes other causes, of similar form exist other factors capable of increase the risk of suffering of mental upsets, just as the use of illegal drugs or suffer a medical serious condition.

**Category:** General Mathematics

[2943] **viXra:1810.0395 [pdf]**
*submitted on 2018-10-23 06:09:58*

**Authors:** Rodolfo González Ortega, Maikel Leyva Vázquez, João Alcione Sganderla Figueiredo

**Comments:** 14 Pages.

The Sinos River Basin is one of the most contaminated water basin in Bra-zil which leads to tremendous efforts for its recovery through adequate integral management. The management of water quality through the analysis of the interrelations between the different factors could be difficult. In this paper, the authors
present Fuzzy Cognitive Maps and Neutrosophic Cogntive Maps for a better choice of environmental management i by the Basin Management Committee of the Sino River. With this method it’s possible to use FCM/NCM to model the complex system of variables involved into the determination of water quality,
according to the water quality index (WQI).

**Category:** General Mathematics

[2942] **viXra:1810.0394 [pdf]**
*submitted on 2018-10-23 06:11:20*

**Authors:** Maikel Leyva Vázquez, Florentin Smarandache

**Comments:** 7 Pages.

Recommendation models are useful in the decision-making process that allow the user a set of options that are expected to meet their expectations. Recommendation models are useful in the decision-making process that offer the user a set of options that are expected to meet their SVN expectations to express linguistic terms.

**Category:** General Mathematics

[2941] **viXra:1810.0393 [pdf]**
*submitted on 2018-10-23 06:12:22*

**Authors:** Artemio Leyva-Aguilera, Adalys Ray Hayne

**Comments:** 7 Pages.

In the present work it is demonstrated that the construction of the media agenda is a process whose structure does not behave in a rigid manner, whose application foundations have a dialectical character, since it assumes the eventualities of coverage which demands a content management that corresponds.
Additionally, the possibilities of using neutrosophical cognitive maps in the construction of the media agenda are explored. It explores neutrosophical cognitive maps for the analysis of causality.

**Category:** General Mathematics

[2940] **viXra:1810.0389 [pdf]**
*submitted on 2018-10-23 07:33:43*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some definite integrals.

**Category:** General Mathematics

[2939] **viXra:1810.0388 [pdf]**
*submitted on 2018-10-23 07:36:02*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note presents some integrals for pi^3.

**Category:** General Mathematics

[2938] **viXra:1810.0363 [pdf]**
*submitted on 2018-10-22 23:44:04*

**Authors:** Boram Han

**Comments:** 7 Pages. This paper is my first paper in High School life.

In many places of life today, the use of mathematics is increasing. In particular, the use of mathematics in various fields such as science, economics, and biotechnology is becoming more and more popular as the natural science advances. This paper briefly grasps the essence of vectors and matrices that play a key role in mathematics, and explains the vector approach is effective for controlling the robot through how vector-based methods are used in recognizing and solving the problems of input and output of EV3 robots.
As a result of using vector analytical methods to overcome defects in hardware and software, many defects could be overcome in many areas. The result of using the concept of the vector which is able to conclude the recognized color of the color sensor with certainty was obtained satisfactory result, the program that controls the omni wheel can also overcome the hardware difficulties in a vector interpretive manner. Also, when attempting to use re-parameterization to create an unit speed curve to overcome the hardware defect of the motor, it was necessary to know the concept of the vector. Therefore, it can be said that the vector was used successfully to overcome the shortcomings and difficulties of EV3.
Nonetheless, the decline of the computation function could not be avoided by the vector approach, because it was a problem that was closer to engineering and physical part rather than mathematical part. Therefore, although it was able to achieve some degree of success in overcoming the disadvantages and difficulties of EV3, it came to the conclusion that it was impossible to overcome it completely. In addition, solving problems using vectors means being more dependent on mathematics, so it relies more heavily on the computation function of EV3. Thus, if the underlying computational function of the EV3, that is, the processing speed is not improved, the vector interpretation approach will show its limitations again.

**Category:** General Mathematics

[2937] **viXra:1810.0333 [pdf]**
*submitted on 2018-10-20 15:20:00*

**Authors:** Waldemar Zieliński

**Comments:** 5 Pages.

We will derive the formulas for the N-th element of the union of two arithmetic progressions with rational and real common differences.

**Category:** General Mathematics

[164] **viXra:1901.0240 [pdf]**
*replaced on 2019-01-17 03:44:57*

**Authors:** Toshiro Takami

**Comments:** 8 Pages.

It presents counter exsample which is close to 0.5 of 2 Riemann hypothesis but not 0.5.
Somewhere on the net there is a memory that reads the mathematician's view that "there are countless zero points in the vicinity of 0.5", which seems to be.
This is the value I gave by hand calculation, and it seems that correction by supercomputer is necessary.
Among these 2, it is presumed that a true counter example and a thing that is not mixed together.
zeta[0.4999944+i393939958.90878694741368323631]= 9.30660314868779... × 10^-19 + 1.342928180878699... × 10^-12 i
and
zeta[0.4999964+i393939964.659437163857861]= -5.914628349384624... × 10^-16 + 6.504227267123851... × 10^-13 i

**Category:** General Mathematics

[163] **viXra:1812.0361 [pdf]**
*replaced on 2018-12-21 14:13:22*

**Authors:** Toshiro Takami

**Comments:** 2 Pages.

ζ (3) was obtained by another method.
\begin{equation}
\zeta(3) =\frac{-17.74063+\pi^3 log(4)}{21}= \end{equation}
and
\begin{equation}
\zeta(3) =\frac{11.5610 +\pi^2\log(4)}{21} \end{equation}

**Category:** General Mathematics

[162] **viXra:1812.0361 [pdf]**
*replaced on 2018-12-21 02:58:52*

**Authors:** Toshiro Takami

**Comments:** 2 Pages.

ζ (3) was obtained by another method.
\sum_{k=1}^\infty \frac{1}{k^2*2^(k-1)}+(log2)^2
=π^2/6 =ζ(2)
\sum_{k=1}^\infty \frac{1}{k^3*2^(k-1)}+(log2)^3≈1.40745
=
zeta(3)= 1.202056903160…..

**Category:** General Mathematics

[161] **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

[160] **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

[159] **viXra:1811.0409 [pdf]**
*replaced on 2018-11-28 00:48:19*

**Authors:** Toshiro Takami

**Comments:** 15 Pages.

At first, each prime number was related to each non-trivial zero point, we thought from equation (2).
However, when calculated, it turned out that each prime number is not related to the nontrivial zeros, and is related to trivial zeros.

**Category:** General Mathematics

[158] **viXra:1811.0044 [pdf]**
*replaced on 2019-01-12 12:43:10*

**Authors:** Felix M. Lev

**Comments:** 9 Pages. Statement 2 in Sec. 3 has been considerably elaborated

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. In our previous publications we argue that the situation is the opposite: classical mathematics is only a special degenerate case of finite one in the formal limit when the characteristic of the ring or field in finite mathematics goes to infinity.
In the present paper we give a simple and rigorous proof of this fundamental fact. In general, introducing infinity automatically implies transition to a degenerate theory because in that case all operations modulo a number are lost. So, {\it even from the pure mathematical point of view}, the very notion of infinity cannot be fundamental, and theories involving infinities can be only approximations to more general theories. We also prove that standard quantum theory based on classical mathematics is a special degenerate case of
quantum theory based on finite mathematics. Motivation and implications are discussed.

**Category:** General Mathematics

[157] **viXra:1811.0044 [pdf]**
*replaced on 2018-12-13 23:09:36*

**Authors:** Felix M. Lev

**Comments:** 8 Pages. A section discussing philosophy of arithmetic added

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. In our previous publications we argue that the situation is the opposite: classical mathematics is only a special degenerate case of finite one in the formal limit when the characteristic of the ring or field in finite mathematics goes to infinity. In the present paper we give a simple and rigorous proof of this fundamental fact. In general, introducing infinity automatically implies transition to a degenerate theory because in that case all operations modulo a number are lost. So, {\it even from the pure mathematical point of view}, the very notion of infinity cannot be fundamental, and theories involving
infinities can be only approximations to more general theories. We also prove that standard quantum theory based on classical mathematics is a special degenerate case of quantum theory based on finite mathematics. Motivation and implications are discussed.

**Category:** General Mathematics

[156] **viXra:1811.0044 [pdf]**
*replaced on 2018-11-23 18:29:06*

**Authors:** Felix M Lev

**Comments:** 6 Pages. A more rigorous proof of the main statement is given

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. In our previous publications we argue that the situation is the opposite: classical mathematics is only a special degenerate case of finite one in the formal limit when the characteristic of the ring or field in finite mathematics goes to infinity. In the present paper we give a simple and rigorous proof of this fundamental fact. In general, introducing infinity automatically implies transition to a degenerate theory because in that case all operations modulo a number are lost. So, even from the pure mathematical point of view, the very notion of infinity cannot be fundamental, and theories involving infinities can be only approximations to more general theories. We also prove that standard quantum theory based on classical mathematics is a special degenerate case of quantum theory based on finite mathematics. Motivation and implications are discussed.

**Category:** General Mathematics

[155] **viXra:1811.0044 [pdf]**
*replaced on 2018-11-15 23:29:07*

**Authors:** Felix M Lev

**Comments:** 6 Pages.

Classical mathematics (involving such notions as infinitely small/large and continuity)
is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. In our previous publications we argue that the situation is the opposite: classical mathematics is only a special degenerate case of finite one in the formal limit when the characteristic of the ring or field in finite mathematics goes to infinity. In the present paper we give a simple and rigorous proof of this fundamental fact. In general, introducing infinity automatically implies transition to a degenerate theory because in this case all operations modulo a number are lost. So, even from the pure mathematical point of view, the the very notion of infinity cannot be fundamental, and theories involving
infinities can be only approximations to more general theories. We also prove that standard quantum theory based on classical mathematics is a special degenerate case of quantum theory based on finite mathematics. Motivation and implications are discussed.

**Category:** General Mathematics

[154] **viXra:1810.0465 [pdf]**
*replaced on 2018-10-30 07:49:09*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 8 Pages.

Riemann and others have used the Poisson summation formula to prove Riemann’s functional equation. The opposite is actually true, the Poisson summation formula provides a refutation of Riemann’s functional equation. It is the purpose of this paper to disprove Riemann’s functional equation using the Poisson summation formula.

**Category:** General Mathematics

[153] **viXra:1810.0408 [pdf]**
*replaced on 2018-11-17 09:34:46*

**Authors:** Zaid Laadjal

**Comments:** 10 Pages.

In this paper, we describe the solution approaches based on Homotopy Analysis Method for the follwing Nonlinear Mixed Volterra-Fredholm integro-differential equation of fractional order $$^{C}D^{\alpha }u(t)=\varphi (t)+\lambda \int_{0}^{t}\int_{0}^{T}k(x,s)F\left( u(s\right) )dxds,$$ $$u^{(i)}(0)=c_{i},i=0,...,n-1,$$ where $t\in \Omega =\left[ 0;T\right] ,\ k:\Omega \times \Omega \longrightarrow \mathbb{R},$ $\varphi :\Omega \longrightarrow \mathbb{R},$ are known functions,\ $F:C\left(\Omega, \mathbb{R}\right) \longrightarrow \mathbb{R}$ is nonlinear function, $c_{i} (i=0,...,n-1),$ and $\lambda $ are constants, $^{C}D^{\alpha }$ is the Caputo derivative of order $\alpha $ with $n-1<\alpha \leq n.$ In addition some examples are used to illustrate the accuracy and validity of this approach.

**Category:** General Mathematics

[152] **viXra:1810.0384 [pdf]**
*replaced on 2018-12-10 16:10:06*

**Authors:** Toshiro Takami

**Comments:** 7 Pages.

If divided by 12, 18, 24, 30, 48, and the remainder is a multiple of 3.
This is a multiple of 3.
And,
when dividing by 48, the remainders are 35.
This is multiplication of prime numbers or prime mumber.
As a postscript
If the sum of the digits of the natural number is 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39......(Multiples of 3, Except 3)it is definitely not a prime number. Except 3.

**Category:** General Mathematics

[151] **viXra:1810.0384 [pdf]**
*replaced on 2018-10-23 21:46:31*

**Authors:** Toshiro Takami

**Comments:** 7 Pages.

If the sum of the digits of the natural number is 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39......(Multiples of 3, Except 3)it is definitely not a prime number. Except 3.
And have a divisor of 3.

**Category:** General Mathematics

[150] **viXra:1810.0333 [pdf]**
*replaced on 2018-10-23 12:19:41*

**Authors:** Waldemar Zieliński

**Comments:** 5 Pages.

We will derive the formulas for the N-th element of the union of two arithmetic progressions with rational and real common differences.

**Category:** General Mathematics

[149] **viXra:1810.0333 [pdf]**
*replaced on 2018-10-22 14:34:26*

**Authors:** Waldemar Zieliński

**Comments:** 5 Pages.

We will derive the formulas for the N-th element of the union of two arithmetic progressions with rational and real common differences.

**Category:** General Mathematics