**Previous months:**

2010 - 1003(1) - 1005(2) - 1008(2) - 1009(1) - 1010(2) - 1011(2) - 1012(1)

2011 - 1101(2) - 1103(3) - 1105(1) - 1108(1) - 1109(1) - 1111(2)

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

2013 - 1301(1) - 1302(2) - 1303(4) - 1304(3) - 1305(2) - 1306(4) - 1309(3) - 1310(2) - 1311(2) - 1312(2)

2014 - 1401(2) - 1402(3) - 1403(639) - 1404(85) - 1405(59) - 1406(1) - 1407(4) - 1408(1) - 1409(2) - 1411(54) - 1412(19)

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(16) - 1606(24) - 1607(45) - 1608(36) - 1609(39) - 1610(9) - 1611(21) - 1612(25)

2017 - 1701(233) - 1702(9) - 1703(11) - 1704(20) - 1705(53) - 1706(79) - 1707(1) - 1708(9) - 1709(23) - 1710(17) - 1711(131) - 1712(7)

2018 - 1801(31) - 1802(31) - 1803(119) - 1804(36) - 1805(37) - 1806(8) - 1807(8) - 1808(164) - 1809(77) - 1810(20) - 1811(5) - 1812(12)

2019 - 1901(7) - 1902(12) - 1903(4) - 1904(9) - 1905(11) - 1906(17) - 1907(13) - 1908(24) - 1909(9)

Any replacements are listed farther down

[3052] **viXra:1909.0483 [pdf]**
*submitted on 2019-09-22 08:27:44*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 4 Pages.

This tutorial parlays two simple properties of positive-integer powers of positive numbers into a closed formula for arbitrary real-valued powers of positive numbers. The two properties are the very familiar result for the derivative of a positive-integer power of a positive real variable, and the fact that positive-integer powers of unity equal unity. Extended to real values of the powers of positive numbers, these two properties comprise a set of first-derivative linear differential equations for functions of a positive real variable, together with their initial conditions, so it isn't surprising that a unique solution is in fact forthcoming via Taylor expansion methods. The additive property of multiplied powers emerges immediately from the two properties of powers that are initially assumed, and enters prominently into working out the closed-formula result, which turns out to be a creature of the exponential function and its inverse. Logarithms are defined in terms of the inverse operation of taking powers in the familiar way, and the special base whose powers reproduce the exponential function and whose logarithms reproduce the exponential function's inverse is pointed out and developed.

**Category:** General Mathematics

[3051] **viXra:1909.0439 [pdf]**
*submitted on 2019-09-20 12:25:01*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

The meaning (logical content) of the concept of numbers is revealed. Arithmetic operations are defined.

**Category:** General Mathematics

[3050] **viXra:1909.0421 [pdf]**
*submitted on 2019-09-19 07:58:13*

**Authors:** Viola Maria Grazia

**Comments:** Pages. Successions are successions with positive terms

In this pdf there is my point of view about successions and series. I talk about when a succession (and so a serie) is said convergent making attention to the succession's definition.

**Category:** General Mathematics

[3049] **viXra:1909.0359 [pdf]**
*submitted on 2019-09-18 06:27:24*

**Authors:** J Gerard Wolff

**Comments:** 61 Pages. Accepted for publication in the journal "Complexity", 2019-09-17.

This paper describes a novel perspective on the foundations of mathematics: how mathematics may be seen to be largely about 'information compression (IC) via the matching and unification of patterns' (ICMUP. That is itself a novel approach to IC, couched in terms of non-mathematical primitives, as is necessary in any investigation of the foundations of mathematics. This new perspective on the foundations of mathematics reects the idea that, as an aid to human thinking, mathematics is likely to be consonant with much evidence for the importance of IC in human learning, perception, and cognition. This perspective on the foundations of mathematics has grown out of a long-term programme of research developing the SP Theory of Intelligence and its realisation in the SP Computer Model, a system in which a generalised version of ICMUP -- the powerful concept of SP-multiple-alignment -- plays a central role. The paper shows with an example
how mathematics, without any special provision, may achieve compression of information. Then it describes examples showing how variants of ICMUP
may be seen in widely-used structures and operations in mathematics. Examples are also given to show how several aspects of the mathematics-related disciplines of logic and computing may be understood as ICMUP. Also discussed is the intimate relation between IC and concepts of probability, witharguments that there are advantages in approaching AI, cognitive science,
and concepts of probability via ICMUP. Also discussed is how the close relation between IC and concepts of probability relates to the established view that some parts of mathematics are intrinsically probabilistic, and how that latter view may be reconciled with the all-or-nothing, 'exact', forms of calculation or inference that are familiar in mathematics and logic. There are
many potential benefits and applications of the mathematics-as-IC perspective.

**Category:** General Mathematics

[3048] **viXra:1909.0330 [pdf]**
*submitted on 2019-09-15 08:15:06*

**Authors:** Louiz Akram

**Comments:** 1 Page.

I present my contribustion in three Claymath Millenium problems.

**Category:** General Mathematics

[3047] **viXra:1909.0288 [pdf]**
*submitted on 2019-09-13 12:22:55*

**Authors:** Suraj Deshmukh

**Comments:** 2 Pages.

In this paper I have defined primes on the basis of "skip function" which basically is nothing but tells you how many numbers are skipped between two numbers. And we define a collection of set which I call skip set. The occurrence of a number decides weather it is prime or not.

**Category:** General Mathematics

[3046] **viXra:1909.0283 [pdf]**
*submitted on 2019-09-14 00:46:51*

**Authors:** A.I.Somsikov

**Comments:** 4 Pages. -

Definition is given to concepts of number and arithmetic action.

**Category:** General Mathematics

[3045] **viXra:1909.0215 [pdf]**
*submitted on 2019-09-09 08:08:04*

**Authors:** Zeolla Gabriel Martín

**Comments:** 25 Pages.

The Simple Tesla algorithm, is the art of multiplying by adding.
We can use this method to calculate the product of any number with true accuracy. It has indisputable applications in various areas such as polynomials, complex numbers, binary numbers and many more.
Basically multiplying is an act of repeated sums, and true to this concept is how this algorithm is developed.

**Category:** General Mathematics

[3044] **viXra:1909.0080 [pdf]**
*submitted on 2019-09-04 22:40:00*

**Authors:** Toshiro Takami

**Comments:** 5 Pages.

tan(π)=0, 0 =1, 1 =z =0 2000
When I saw this expression, I was surely suspicious.
But I knew intuitively that Next infinity is zero.
For me, infinite and zero were equal, that’s true now.
The universe did not start with the Big Burn. The universe has existed for an infinite
amount of time, and has repeated an infinite number of big burns.
In other words, the universe is a repetition of Next infinity is zero.

**Category:** General Mathematics

[3043] **viXra:1908.0619 [pdf]**
*submitted on 2019-08-30 15:59:20*

**Authors:** Anamitra Palit

**Comments:** 7 Pages.

In this article we derive an anomalous result that with curved space time transformations have to be linear. Technical difficulties with infinitesimal space time coordinates as tensors are exposed. Analysis with the Taylor series brings out a stupendous fact that it considers only such functions as are linear in the independent variables.

**Category:** General Mathematics

[3042] **viXra:1908.0588 [pdf]**
*submitted on 2019-08-28 08:29:01*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

En esta nota mostramos algunas integrales relacionadas con la constante Pi:pi=3.1415926535...

**Category:** General Mathematics

[3041] **viXra:1908.0587 [pdf]**
*submitted on 2019-08-28 08:32:25*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

This note present some Elementary integrals and series.

**Category:** General Mathematics

[3040] **viXra:1908.0584 [pdf]**
*submitted on 2019-08-28 08:45:25*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

En esta nota mostramos algunas fórmulas relacionadas con las raíces de la ecuación: n*z=1+i*z*z*z,i=sqrt(-1),n=1,2,3,...,Re(z)>0,Im(z)>0.

**Category:** General Mathematics

[3039] **viXra:1908.0502 [pdf]**
*submitted on 2019-08-24 06:49:05*

**Authors:** Viola Maria Grazia

**Comments:** 1 Page.

In this article the author talk about convergent series using ordinal number.

**Category:** General Mathematics

[3038] **viXra:1908.0453 [pdf]**
*submitted on 2019-08-21 09:50:23*

**Authors:** Zeolla Gabriel Martín

**Comments:** 7 Pages.

Este documento demuestra el descubrimiento de patrones ocultos en los cuadrados mágicos, estos forman figuras geométricas sorprendentes
Cuando reducimos los valores de un cuadrado mágico a los 9 principales dígitos, este forma 3 patrones. Dos opuestos complementarios, (estos se necesitan entre sí para lograr la armonía) y un tercero llamado equitativo el cual está organizado y en equilibrado en sí mismo

**Category:** General Mathematics

[3037] **viXra:1908.0391 [pdf]**
*submitted on 2019-08-18 16:34:48*

**Authors:** Bheemaiah, Anil Kumar

**Comments:** 3 Pages.

Abstract:
We consider the world of scientific publications, from their journey of inception in an editor to a publication server like the DOI server. Publications live in an interactive fiction universe of text and hyper-media. We define closure operations on Camera streams, IF based Rooms and arrays of publication urls. Since we believe in open science and technology, the publications are not subjected to undue scrutiny, judgement and review by peers. They find freedom in an open repository.
Formal theory of closure theorems are presented.
Keywords: Publication Space, Camera Readiness, Interactive Fiction, Open Publishing, OCR, Digital Repositories, Closure Theorems, Isomorphism, Homeomorphism

**Category:** General Mathematics

[3036] **viXra:1908.0389 [pdf]**
*submitted on 2019-08-18 17:03:48*

**Authors:** Zeolla Gabriel Martín

**Comments:** 6 Pages. Idioma Español

Este documento demuestra el descubrimiento de patrones ocultos en los cuadrados mágicos, estos forman figuras geométricas sorprendentes
Cuando reducimos los valores de un cuadrado mágico a los 9 principales dígitos, este forma 3 patrones. Dos opuestos complementarios, (estos se necesitan entre sí para lograr la armonía) y un tercero llamado equitativo el cual está organizado y en equilibrado en sí mismo.

**Category:** General Mathematics

[3035] **viXra:1908.0387 [pdf]**
*submitted on 2019-08-18 22:30:24*

**Authors:** Addie bint Ishak

**Comments:** 1 Page.

I discovered an evidence of the existence of God as the mathematically beautiful equality of the sum of all natural numbers.

**Category:** General Mathematics

[3034] **viXra:1908.0365 [pdf]**
*submitted on 2019-08-17 19:07:07*

**Authors:** Bheemaiah, Anil Kumar

**Comments:** 7 Pages.

Abstract. Let ̃z be a bare-foot dependent path. Recently, there has been much interest in the derivation of isomorphisms on strange groups that come in the way of ~z. Let there exist a countable infinity of such groups, [[G]]. We show that [[G]] has one or more isomorphisms to a Dojo D.
Keywords; Bare-foot paths, Measure Theory, Higher Operators, Strange Groups, Techno Gibberish, model theory, Dojo Theory

**Category:** General Mathematics

[3033] **viXra:1908.0332 [pdf]**
*submitted on 2019-08-17 05:06:48*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is definition ⑦

**Category:** General Mathematics

[3032] **viXra:1908.0327 [pdf]**
*submitted on 2019-08-15 22:31:43*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is definition⑥

**Category:** General Mathematics

[3031] **viXra:1908.0321 [pdf]**
*submitted on 2019-08-16 04:31:44*

**Authors:** Wiroj Homsup

**Comments:** 2 Pages.

Based on the functional equation of the Dirichlet eta function, Sondow’s conjecture is proved. The advantage of a method is that it only use undergraduate mathematics.

**Category:** General Mathematics

[3030] **viXra:1908.0272 [pdf]**
*submitted on 2019-08-14 05:45:24*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is definition ⑤

**Category:** General Mathematics

[3029] **viXra:1908.0252 [pdf]**
*submitted on 2019-08-13 00:21:59*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is definition ④.

**Category:** General Mathematics

[3028] **viXra:1908.0214 [pdf]**
*submitted on 2019-08-11 12:12:46*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is Definition III;

**Category:** General Mathematics

[3027] **viXra:1908.0213 [pdf]**
*submitted on 2019-08-11 12:42:25*

**Authors:** Kenny Peluso

**Comments:** 29 Pages. Amended version of the author's undergraduate thesis, submitted 4/18

How may we find a transition matrix that guarantees the long-run convergence of a Markov Chain to a given stationary distribution? Solving for this (usually) undetermined system is non-trivial and presents unique computational challenges. Five different of methods of directly solving for a transition matrix are presented along with their limitations. Relaxations of the two core assumptions underlying these direct methods - the Identityless and Independence Assumptions - are considered. A method of generating a Mass Matrix - the transition matrix underlying hops between entire population states - is described while developing the notion of successively-bounded weak compositions. An algorithm for their exhaustive generation is also presented. Applications of some methods are provided with respect to optimizing firm profit via optimally distributing workers among wage brackets and optimizing measures of national wealth via manipulation of class distribution and immigration policy. A generalization of all applications is formulated.

**Category:** General Mathematics

[3026] **viXra:1908.0166 [pdf]**
*submitted on 2019-08-09 15:26:29*

**Authors:** Zeolla Gabriel Martín

**Comments:** 149 Pages.

Una obra inspirada en los misteriosos y enigmáticos cuadrados Mágicos y los números
de la magnificencia a los que hacía referencia Nikola Tesla.(3,6,9)
Los cuadrados Mágicos eran usados como amuletos de protección, estos se forman utlizando números ordenados en armonía.

**Category:** General Mathematics

[3025] **viXra:1908.0144 [pdf]**
*submitted on 2019-08-07 08:26:09*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

We give a formula for Pi.

**Category:** General Mathematics

[3024] **viXra:1908.0141 [pdf]**
*submitted on 2019-08-07 08:39:34*

**Authors:** Edgar Valdebenito

**Comments:** 4 Pages.

We give four series for Pi.

**Category:** General Mathematics

[3023] **viXra:1908.0102 [pdf]**
*submitted on 2019-08-06 15:17:18*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

First, ±∞ is constant at any observation point (position).

**Category:** General Mathematics

[3022] **viXra:1908.0100 [pdf]**
*submitted on 2019-08-06 20:03:01*

**Authors:** Saburou Saitoh

**Comments:** 18 Pages. The contents in this paper seem to be serious for our mathematics and for our world history with the materials in \cite{sur}. So, the author hopes that the related mathematicians, mathematical scientists and others check and consider the topics from vari

Based on the preprint survey paper (\cite{sur}), we will discuss the theoritical point of the division by zero calculus. We will need a new axiom for our mathematics. The contents in this paper seem to be serious for our mathematics and for our world history with the materials in \cite{sur}.
So, the author hopes that the related mathematicians, mathematical scientists and others check and consider the topics from various viewpoints.

**Category:** General Mathematics

[3021] **viXra:1908.0018 [pdf]**
*submitted on 2019-08-01 13:15:35*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

±∞ is constant at any observation point (position).

**Category:** General Mathematics

[3020] **viXra:1908.0015 [pdf]**
*submitted on 2019-08-01 22:59:14*

**Authors:** Felix M Lev

**Comments:** 9 Pages.

In our previous publications we have proved that quantum theory based on finite mathematics is more fundamental than standard quantum theory, and, as a consequence, finite mathematics is more fundamental than classical one. The goal of the present paper is to explain without formulas why those conclusions are natural.

**Category:** General Mathematics

[3019] **viXra:1907.0534 [pdf]**
*submitted on 2019-07-26 08:31:02*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

We recall some Elementary sums for Pi.

**Category:** General Mathematics

[3018] **viXra:1907.0531 [pdf]**
*submitted on 2019-07-26 08:35:13*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

We give three series for Pi.

**Category:** General Mathematics

[3017] **viXra:1907.0527 [pdf]**
*submitted on 2019-07-26 10:43:36*

**Authors:** Egger Mielberg

**Comments:** 12 Pages.

The Sense Theory is not a part of traditional mathematics. It is a new paradigm of how we can formalize complex cognitive processes of the human brain. The basis of the theory is a sense function which determines sense conformity between a set of objects or/and events and a single subject (described object/event).
The sense function has a series of unique properties that can help find associative connections between trillions different-type objects/events.
By the function, we can investigate a whole process of forming a single sense of big data set of different business or scientific events.

**Category:** General Mathematics

[3016] **viXra:1907.0346 [pdf]**
*submitted on 2019-07-17 08:27:21*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents some formulas for Pi.

**Category:** General Mathematics

[3015] **viXra:1907.0320 [pdf]**
*submitted on 2019-07-16 16:39:05*

**Authors:** Vinicius Teixeira do Nascimento, Angel Ramon Sanchez Delgado, Sergio Drumond Ventura

**Comments:** 11 Pages.

Nowadays integrated crop-livestock production systems have been presented as a viable and sustainable alternative in economic, social and environmental terms. This work develops and implements a mixed integer programming model (MIXP) that represents or simulates numerically the optimum operational conditions of an integrated crop-livestock system with no-tillage (iCLS-NT), including animal transit. For the computational implementation of the model, data on the fitness of the live weight gain of each animal of the herd considered, in each period and area of the (iCLS-NT), (confinement, pasture and annual crop), as well as marginal net income of each crop and the costs per unit of food considered. In order to test the validity of the developed mathematical model, data were randomly generated. To solve each MIXP, we used the solver INTLINPROG in the software MATLAB. Thus, after the computational implementation, it was verified that the program meets all restrictions imposed, maximizes the weight gain of each animal, provides the best selection of annual crops and minimizes feeding costs in the confinement area.

**Category:** General Mathematics

[3014] **viXra:1907.0264 [pdf]**
*submitted on 2019-07-15 20:00:11*

**Authors:** Halina dos Santos Salles, Paulo Frederico Souza Lomeu, Franciane Conceição Peters, Webe João Mansur

**Comments:** 9 Pages.

In building design, the designers aim a better and safer project, regarding several structural aspects, besides the reduction of the costs of the inputs. Optimization methods can be used for this purpose without compromising structural safety. Thus, this article aims at the structural optimization by genetic algorithms of reinforced concrete 3D frames. In this study a Genetic Algorithm was developed, containing the specifications for the dimensioning of the structural elements reinforcement. The objective function is formed by the costs of concrete, molds and steel and will be minimized, according to the restrictions of NBR 6118:2014 (Concrete Structures Project - Procedure). The structural model is processed in the Ansys ® software, where discretization occurs through the finite element method, to analyze and obtain the stresses and deformations of the structure. The study consideres design variables: height of beams and columns. The results show that this methodology provided responses consistent when compared to the practice and also surprised with solutions that could be rejected by designers.

**Category:** General Mathematics

[3013] **viXra:1907.0263 [pdf]**
*submitted on 2019-07-15 20:01:49*

**Authors:** Antônio Chicharo Prata Lisboa, Claudia Mazza Dias, Julio Henrique Lopes de Almeida

**Comments:** 14 Pages.

This work has the purpose of performing the Dual Cycle analysis, suitable for high rotation engines, with the objective of obtaining its Energetic and Exergetic efﬁciencies, as well as quantifying the destruction of exergy in the processes. The results are obtained through parametric studies, which allow the evaluation of the behavior of parameters of interest. The calculations are developed in an open code written in Python® with the support of libraries numpy and scipy.

**Category:** General Mathematics

[3012] **viXra:1907.0262 [pdf]**
*submitted on 2019-07-15 20:04:02*

**Authors:** Wilian Jeronimo dos Santos, Rosane Ferreira de Oliveira, Marcos Bacis Ceddia, Juliana Lima de Almeida

**Comments:** 10 Pages.

The present work aimed to create a tool that can contribute to the prediction of moisture content in heterogeneous and well-drained plots of soil over a given period of time. To characterise the water balance, which is a criterion for the redistribution of water in the soil, an analogy is made to the competition model in population dynamics. This analogy can be explained by “competition” for water among the different soil compartments. The different layers “compete” with each other for water due to difference in hydraulic potential. In this sense, the model proposed is based on models of interspecific competition. Furthermore, the numerical methodology proposed is characterized to be solved more easily than the traditional and highly non-linear Richards’ equation. Numerical results were compared against simulation results from the Hydrus-1D program.

**Category:** General Mathematics

[3011] **viXra:1907.0261 [pdf]**
*submitted on 2019-07-15 20:05:32*

**Authors:** Carlos Andrés Reyna Vera-Tudela

**Comments:** 12 Pages.

The Boundary Element Method transforms partial differential equations that govern the problem domain into integral equations involving only contour values after the introduction of weighting functions called fundamental solutions. When the problem studied involves internal loads, such as self weight, one must search for a solution that preserves the philosophy of the method. For this purpose, the Dual Reciprocity technique is used. This work illustrates dual reciprocity with Navier’s equation with a self-weight load term. Numerical results are presented.

**Category:** General Mathematics

[3010] **viXra:1907.0216 [pdf]**
*submitted on 2019-07-14 03:02:59*

**Authors:** Colin James III

**Comments:** 3 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The equation of the weak duality theorem, (Ax≤b, x≥0) ≤ (A^Ty≥c, y≥0), is confirmed as tautologous. Three proofs of it in the literature are not tautologous. The equation of the strong duality theorem, (Ax≤b, x≥0) = (A^Ty≥c, y≥0), is refuted as not tautologous. These form a non tautologous fragment of the universal logic VŁ4. What follows is the weak duality theorem could just as easily exclude the “or equal to” relation to read (Ax≤b, x≥0) < (A^Ty≥c, y≥0) as the corrected weak duality theorem.

**Category:** General Mathematics

[3009] **viXra:1907.0215 [pdf]**
*submitted on 2019-07-12 10:03:19*

**Authors:** John Mark Vincent

**Comments:** 5 Pages.

A new method for multi-dimensional global optimization is presented. The fundamental idea is to obtain the Chebyshev norm from a set of L_p=norms; an original extrapolation procedure is used to converge to the optimum value, which is identical to the Chebyshev norm. This allows the optima to be efficiently pin-pointed by repeatedly bisecting the domain. Estimates of computational cost indicate that the method is fast.

**Category:** General Mathematics

[3008] **viXra:1907.0149 [pdf]**
*submitted on 2019-07-10 03:16:40*

**Authors:** Li xiaohong

**Comments:** 14 Pages.

Chord mathematics is a mathematical model of chord language. The main features are: octave duodecimal number system, symmetric, mirror phase, and spatial expression of chord language, also known as "chord geometry".
Chord mathematics is scattered in various disciplines related to chord language, such as musicology, chord colorology, meridian science (life expression), etc. In this paper, quantitative, number system, positive and negative, coordinate, formula, calculation method and so on are integrated and unified.
Chord language is composed of chord spectrum, with quantum, string (opening, closed string, N string), symmetry, mirroring and other physical, mathematical (geometric) characteristics, manifested in music (time expression), painting (space expression), meridian (life expression) and other disciplines, with spiritual, physical duality, it has thousands of years of accumulation of understanding, The more mature mathematical model, which can be observed and verified, should be the characteristic of the theory of everything.
Key words: chord mathematics, chord geometry, duodecimal system, discrete, symmetric, mirror image

**Category:** General Mathematics

[3007] **viXra:1907.0044 [pdf]**
*submitted on 2019-07-02 08:45:44*

**Authors:** Edgar Valdebenito

**Comments:** 2 Pages.

This note presents some formulas for Pi.

**Category:** General Mathematics

[193] **viXra:1909.0080 [pdf]**
*replaced on 2019-09-18 22:02:27*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

tan(π)=0, 0 =1, 1 =z =0 2000
When I saw this expression, I was surely suspicious.
But I knew intuitively that Next infinity is zero.
For me, infinite and zero were equal, that’s true now.
The universe did not start with the Big Burn. The universe has existed for an infinite
amount of time, and has repeated an infinite number of big burns.
In other words, the universe is a repetition of Next infinity is zero.

**Category:** General Mathematics

[192] **viXra:1909.0080 [pdf]**
*replaced on 2019-09-08 16:25:04*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

tan(π)=0, 0 =1, 1 =z =0 2000
When I saw this expression, I was surely suspicious.
But I knew intuitively that Next infinity is zero.
For me, infinite and zero were equal, that’s true now.
The universe did not start with the Big Burn. The universe has existed for an infinite
amount of time, and has repeated an infinite number of big burns.
In other words, the universe is a repetition of Next infinity is zero.

**Category:** General Mathematics

[191] **viXra:1908.0214 [pdf]**
*replaced on 2019-08-13 00:20:19*

**Authors:** Yuji Masuda

**Comments:** 1 Page.

This is Definition ③.

**Category:** General Mathematics

[190] **viXra:1907.0216 [pdf]**
*replaced on 2019-07-17 17:09:07*

**Authors:** Colin James III

**Comments:** 3 Pages. © Copyright 2019 by Colin James III All rights reserved. Respond to author by email only: info@cec-services dot com. See updated abstract at ersatz-systems.com.

The equation of the weak duality theorem, (Ax≤b, x≥0) ≤ (A^Ty≥c, y≥0), is confirmed as tautologous. Three proofs of it in the literature are not tautologous. The equation of the strong duality theorem, (Ax≤b, x≥0) = (A^Ty≥c, y≥0), is refuted as not tautologous. These form a non tautologous fragment of the universal logic VŁ4. What follows is the weak duality theorem could just as easily exclude the “or equal to” relation to read (Ax≤b, x≥0) < (A^Ty≥c, y≥0) as the corrected weak duality theorem.

**Category:** General Mathematics