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[3088] viXra:2001.0374 [pdf] submitted on 2020-01-19 12:35:05
Division by Zero Dzielenie Przez Zero
Authors: Leszek Mazurek
Comments: 49 Pages. Text in Polish, English version soon
Since the beginning of time, the ban on dividing by zero has been a serious problem for all thinking people, who have found this restriction hard to accept. Moreover, intuitively it seems very artificial and unjustified. In this work, I have made the effort to analyze this problem very carefully, to try and finally understand where it comes from, why it is a problem, a limitation, and what should be done to solve it. By a very detailed analysis of multiplication and division, I have found out that these operations are the same. Combined with the selection operation they are transformations that perform the change of a pair of numbers into another pair of numbers. After the analysis, I've found out that a ratio of two numbers, that can represent such a transformation, is the most natural form of a number. I'm proposing a new understanding of fractions and explaining why 1/2 should not be equal to 2/4. I presented an explanation to the problem of why division by zero is not possible in real numbers' domain and how easy it can be understood in the domain of rational numbers. The results that I have obtained not only solve this problem but also shed a whole new light on understanding the numbers and operations of numbers. My work fixes one of the foundations of mathematics, it is difficult to predict all consequences which this change can bring, to everything, what was created based on this wrong foundation.
Category: General Mathematics
Letter Nº4 :On pi
Authors: Edgar Valdebenito
Comments: 2 Pages.
We give a formula involving Pi.
Letter Nº5 :Integrals
We give some elementary integrals.
Approximation-Degree-Based Interpolation: A New Interpolation Method
Authors: Shiyou Lian
Comments: 26 Pages.
This paper introduces the measure of approximate-degree and the concept of approximate-degree function between numerical values, thus developing a new interpolation method —— approximation-degree-based interpolation, i.e., AD interpolation. One-dimensional AD interpolation is done directly by using correlative interpolation formulas; n(n>1)-dimensional AD interpolation is firstly separated into n parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the n-dimensional interpolation. If the parallel processing is used, the efficiency of n-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.
`(st)ringy' Proof the Poincar\'{e} Conjecture
Authors: Kohji Suzuki
We prove the Poincar\'{e} Conjecture using `(st)ring theory'.
From Periods to Anabelian Geometry and Quantum Amplitudes
Authors: Lucian M. Ionescu
Comments: 14 Pages. IHES GP May 2019
To better understand and investigate Kontsevich-Zagier conjecture on abstract periods, we consider the case of algebraic Riemann Surfaces representable by Belyi maps. The category of morphisms of Belyi ramified maps and Dessins D'Enfant, will be investigated in search of an analog for periods, of the Ramification Theory for decomposition of primes in field extensions, controlled by theirs respective algebraic Galois groups. This suggests a relation between the theory of (cohomological, Betti-de Rham) periods and Grothendieck's Anabelian Geometry (homotopical/ local systems), towards perhaps an algebraic analog of Hurwitz Theorem, relating the the algebraic de Rham cohomology and algebraic fundamental group, both pioneered by A. Grothendieck. There seem to be good prospects of better understanding the role of absolute Galois group in the physics context of scattering amplitudes and Multiple Zeta Values, with their incarnation as Chen integrals on moduli spaces, as studied by Francis Brown, since the latter are a homotopical analog of de Rham Theory. The research will be placed in the larger context of the ADE-correspondence, since, for example, orbifolds of finite groups of rotations have crepant resolutions relevant in String Theory, while via Cartan-Killing Theory and exceptional Lie algebras, they relate to TOEs. Relations with the author's reformulation of cohomology of cyclic groups as a discrete analog of de Rham cohomology and the Arithmetic Galois Theory will provide a purely algebraic toy-model of the said algebraic homology/homotopy group theory of Grothendieck as part of Anabelian Geometry. It will allow an elementary investigation of the main concepts defining periods and algebraic fundamental group, together with their conceptual relation to algebraic numbers and Galois groups. The Riemann surfaces with Platonic tessellations, especially the Hurwitz surfaces, are related to the finite Hopf sub-bundles with symmetries the ``exceptional'' Galois groups. The corresponding Platonic Trinity leads to connections with ADE-correspondence, and beyond, e.g. TOEs and ADEX-Theory. Quantizing "everything" (cyclotomic quantum phase and finite Platonic-Hurwitz geometry of qubits/baryons) could perhaps be The Eightfold (Petrie polygon) Way to finally understand what quark flavors and fermion generations really are.
An Theorem About Square Root
Authors: Shinichi Kumakura, Rose Redrabbit
Use Properties of exponents and Characteristic equation to derive an formula of square root.
Letter Nª3: Elementary Formula
We recall a elementary formula involving Pi.
Pi , A Short Letter
Comments: 1 Page.
We give a formula for Pi.
Refutation of Anticommutative Hypercomplex Number Systems
Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.
We evaluate a fragment of two rows of the multiplication table for the quaternion as not tautologous and not equivalent. This refutes the hypercomplex product and hence the conjecture of quadratic anticommutative hypercomplex number systems. These results form a non tautologous fragment of the universal logic VŁ4.
Properties of Quadratic Anticommutative Hypercomplex Number Systems
Authors: Katheryn Menssen
Comments: 30 Pages. Professor Karen Shuman was my faculty advisor for this research project, which I did as an undergraduate. Although she helped greatly with editing throughout the process, all the research is my own ideas.
Hypercomplex numbers are, roughly speaking, numbers of the form x_1 + i_1x_2 + … + i_nx_{n+1} such that x_1 + i_1x_2 + … + i_nx_{n+1} = y_1 + i_1y_2 + … + i_ny_{n+1} if and only if x_j = y_j for all j in {1,2,…,n}. I define a quadratic anticommutative hypercomplex numbers as hypercomplex numbers x_1 + i_1x^2 + … + i_nx_{n+1} such that i_j^2 = p_j for all j (where p_j is a real number) and i_ji_k = - i_ki_j for all k not equal to j. These numbers have some interesting properties. In particular, in this paper I prove a generalized form of the Demoivre's formula for these numbers, and determine certain conditions required for a function on a Quadratic Anticommutative Hypercomplex plane to be analytic—including generalizations of the Cauchy-Riemann equations.
Санация комплексного исчисления
Authors: Райков Александр Геннадьевич
Comments: 4 Pages. Язык русский. Лекция-презентация является фрагментом печатного издания «ТОМ ТРЕТИЙ»
Настоящее просветительское издание подготовлено для ознакомления широких кругов общественности и научного сообщества с переводом Комплексного Исчисления на язык объективно-статусного описания качественно-количественных форм и причинно-следственных периодических процессов материи, на основе разработанного автором принципиально нового операционно-аналитического (математического) аппарата философии диалектического материализма в качестве универсального языка научной коммуникации. Лекция-презентация является фрагментом печатного издания «ТОМ ТРЕТИЙ»
A Second Note on a Possible Anomaly in the Complex Numbers
Authors: Han Geurdes
Comments: 3 Pages. Response to VRA discussion
The paper gives an additional reason why, initially, there are two different solutions associated to a quadratic equation that indicates an anomaly in complex numbers. It is demonstrated that one of the solutions is impossible but plausible \& necessary.
Number Pi , Bernoulli Numbers
Authors: Edgar Valdebenito, Rodrigo Valdebenito
This note presents some formulas for Pi.
Mathematics as Information Compression Via the Matching and Unification of Patterns
Authors: J Gerard Wolff
Comments: Now published in "Complexity", vol. 2019, Article ID 6427493, 25 pages, 2019, https://doi.org/10.1155/2019/6427493 (PDF, bit.ly/2LqUHIr).
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 reflects 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, with arguments 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.
Kryptos - Hidden Hill Cipher
Authors: Robert Mereau
This paper is intended to provide support for those working to solve Kryptos. The hope is that the content, be it in part or complete, contains novel discoveries and mechanics that can assist the greater communities development of new approaches.
In New Mathematics, Riemann Hypothesis is Mistake
Authors: Toshiro Takami
In classical mathematics there will be a complete zero.\\ But in new mathematics there is no perfect zero. At the same time, there is no perfect 1/2 in new mathematics.\\ Hence, Riemann hypothesis is false.\\ In new mathematics, there is no perfect 1 or 2.\\ They are 1 or 2 as close as possible to 1 or 2, and not 1 or 2.\\ I think we should break away from classical mathematics and think about new mathematics.\\ These can be said from quantum mechanics.\\ New mathematics doesn't have perfect zero, 1/2, 1, 2 and so on.\\ There are only numbers close to zero, 1/2, 1, and 2.\\ 1/2 is 0.499999999..... or 0.5000000000.....\\ A perfect 1/2 cannot exist.\\
Authors: Viola Maria Grazia
I talk about functions in particolar I study the behavior of this near infinity
Elementary Integrals: Report 21/11/2019 6:21:49
We give some elementary integrals
Zero is only a Mathematical Fantasy
Mathematics returns to Ancient Times.\\ Perfect Zero cannot exist.\\ In physics, there are many particles in a vacuum.\\ 0 is not perfect zero.\\ 0 is almost zero.\\ Zero is only a mathematical fantasy.\\ There is no Zero.\\ 0 may be a return to the womb.\\ And, love is 0 and infinite.\\
Fractal for :F(z)=z-Arctanh(1-z)
We give a simple formula for Pi
A Method of Determining the Extreme Points of a Function Defined on the Integers
Authors: Stanley Korn
The standard method of determining the extreme points of a function ��(��) is to set its first derivative equal to zero and solve for x. However, this method requires that the function be continuous (at least piecewise) and differentiable; it won't work for a function defined on the integers. Described herein is a method of determining the extreme points of a function defined on the integers. This method is illustrated by using it to solve two example problems.
Unknown Summations
Authors: Yuly Shipilevsky
We introduce a set of finite and infinite summations which looks like were never considered yet.
A Note on a Possible Anomaly in the Complex Numbers
In the present paper a conflict in basic complex number theory is reported. The ingredients of the analysis are Euler's identity and the DeMoivre rule for $n=2$. The outcome is that a quadratic equation only has one single solution because one of the existing solutions gives rise to an impossibility.
Catalan's Constant and pi :Integrals
Numbers: Part 6, Three Integrals .
We give three definite integrals
Numbers Do Not Exist
Authors: Averky Glebov
In this paper we discuss how numbers, are just not real, and do not exist in the world.
Refutation of Multiplication, Addition, and Subtraction by Zero Calculus
Comments: 1 Page. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.
We evaluate the conjecture of the following equations: (a×0)≠0 ; (a×0)<a; and (a−0)<a<(a+0). None is tautologous, and the first two are contradictory. This refutes the conjectures to form a non tautologous fragment of the universal logic VŁ4.
Multiplication by Zero Calculus, Addition by Zero Calculus, and Subtraction by Zero Calculus
In physics, there are many particles in a vacuum.\\ Perfect zero cannot exist.\\ 0 is not perfect zero.\\ 0 is almost zero.\\ Perfect zero is only a mathematical fantasy.\\ $a\times0\approx0$, but $a\times0\neq0$.\\ $a\times0\times0\times0\times0\times0<a\times0\times0\times0\times0<a\times0\times0\times0<a\times0\times0<a\times0<a$.\\ $a-0-0-0<a-0-0<a-0<a<a+0<a+0+0<a+0+0+0$.\\
Finite-Time Lyapunov Exponents in the Instantaneous Limit and Material Transport
Authors: Peter J. Nolan, Mattia Serra, Shane D. Ross
Comments: 43 Pages. Submitted for publication
Lagrangian techniques, such as the Finite-Time Lyapunov Exponent (FTLE) and hyperbolic Lagrangian coherent structures, have become popular tools for analyzing unsteady fluid flows. These techniques identify regions where particles transported by a flow will converge to and diverge from over a finite-time interval, even in a divergence-free flow. Lagrangian analyses, however, are time consuming and computationally expensive, hence unsuitable for quickly assessing short-term material transport. A recently developed method called OECSs rigorously connected Eulerian quantities to short-term Lagrangian transport. This Eulerian method is faster and less expensive to compute than its Lagrangian counterparts, and needs only a single snapshot of a velocity field. Along the same line, here we define the instantaneous Lyapunov Exponent (iLE), the instantaneous counterpart of the finite-time Lyapunov exponent (FTLE), and connect the Taylor series expansion of the right Cauchy-Green deformation tensor to the infinitesimal integration time limit of the FTLE. We illustrate our results on geophysical fluid flows from numerical models as well as analytical flows, and demonstrate the efficacy of attracting and repelling instantaneous Lyapunov exponent structures in predicting short-term material transport.
SCIS- Traffic Congestion Optimisation using River Formation Dynamics
Authors: Kunal Verma, Vishal Paike
The raising level of traffic imposes a great demand in the growth of intelligent traffic systems. With increase in complexity of alleviation, finding solutions to traffic congestion problem have become one of the challenges. Various optimization techniques have been proposed in literature to meet these challenges. This paper surveys different optimization techniques based on heuristics for automated traffic congestion control. Moreover, an approach based on River Formation Dynamics scheme is introduced to analyze the optimization problem for traffic congestion control and a scheme to extract real time information through Internet of Things is presented for superior efficiency and productivity
О парадоксе при классическом подходе к доказательству теорем и непригодности общепринятых стереотипных тавтологий классической математики для доказательства теорем
Authors: Victoria Kondratenko Виктория Александровна Кондратенко
Аннотация. В текущее время в естественных и прикладных науках в большинстве публикаций доказательство теорем осуществляется: во-первых, содержательным способом, что противоречит настоятельному требованию философов науки использовать исключительно формальное доказательство, которое является критерием оценки корректности и достоверности доказательства; во-вторых, при содержательном доказательстве в 95% случаев используются исключительно стандартный перечень тавтологий, который по определению некорректен для целей доказательства теорем о явлениях и процессах мироздания на основе истинных аксиом, полученных в результате натурного экспериментирования с этими явлениями и процессами. В статье анализируется часто используемый стандартный перечень тавтологий, доказывается непригодность этих тавтологий для доказательства теорем, что порождает очередной неразрешимый парадокс в началах математики. Автором предлагается выход из создавшегося тупика.
Metrology of the Circle and the Royal Cubit: Deciphering the Ancient 360 Degree Circle Design
Authors: Mark Anthony Musgrave
Design of the ancient 360-degree circle is proposed to be the result of using a scientific length standard, the Egyptian Royal cubit, to define the dimensions of the circle reference frame. The ancient length standard is subdivided into its own sub-units of palms and fingers, but it is the equivalence to other ancient length units (inches, feet) in proportions that match specific circle features that allow underling design aspects to be identified. The available evidence suggests that the original circle design described by Hipparchus, as being based on "a radius of 3438 minutes", should be interpreted to mean that the design circle radius was actually 3438 Royal cubits. From this framework it is possible to observe direct metrological relationships between the design of the Royal cubit and the design of the 360-degree circle, as well as the origin of the inch and feet units. Multiple shared features between the circle and the Royal cubit suggest a common design principle was involved, and the evidence suggests that an understanding of electromagnetic physics was in place when the sexagesimal circle was created. If verified, the hypothesis presented here infers that a new frequency standard could be implemented in modern metrology that would provide both the time and length units and allow for complete integration with the 360-degree circle reference frame. This step may also then provide deeper insights into astronomical physics as dimensional features are examined under a suitable length unit
Proof of the Riemann Hypothesis [final Edition]
Up to now, I have tried to expand this equation and prove Riemann hypothesis with the equation of cos, sin, but the proof was impossible. However, I realized that a simple formula before expansion can prove it. The real value is zero only when the real part of s is 1/2. Non-trivial zeros must always have a real value of zero. The real part of s being 1/2 is the minimum requirement for s to be a non-trivial zeros.
Non-Negative in Value, but Absolute in Function by a Magnum and Parabolin—the Cogent Value Function
Authors: William F. Gilreath
Comments: 34 Pages. Published in the General Science Journal
The absolute value function is a fundamental mathematical concept taught in elementary algebra. In differential calculus, the absolute value function has certain well-known mathematical properties that are often used to illustrate such concepts of—a continuous function, differentiability or the existence of a derivative, the limit, and etcetera. An alternative to the classical definition of absolute value is given to define a new function that is mathematically equivalent to the absolute value, yet the different mathematically. This new mathematical formalism, the cogent value function, does not have the same mathematical properties of the absolute value function. Two other new mathematical functions are used in the definition of the cogent value function—the parabolin function, and the magnum function. The cogent value function and the absolute value function have the same domain and range, but both are mathematically very different. The cogent value function demonstrates that the same mathematical concept when formally defined by an alternative method has different mathematical properties. The functions by operation are mathematically similar, but in mathematical formalism each is unique.
Remainder Theorem and the Division by Zero Calculus
Authors: Saburou Saitoh
Comments: 4 Pages. In this short note, for the elementary theorem of remainder in polynomials we recall the division by zero calculus that appears naturally in order to show the importance of the division by zero calculus.
In this short note, for the elementary theorem of remainder in polynomials we recall the division by zero calculus that appears naturally in order to show the importance of the division by zero calculus.
Replacements of recent Submissions
[193] viXra:1912.0210 [pdf] replaced on 2019-12-11 12:28:52
Teoremas de Engenharia Analítica e Propriedades Hiperbólicas Restritas
Authors: Ordepte Ezurk; Síul Hodrad
A utilização das conjecturas demonstradas na matemática contemporânea, submetida à progressivas sentenças direcionadas à resolução de problemas, demonstra fatores errôneos no quesito de seus axiomas, a partir de vias hiperbólicas restritas. A engenharia analítica, fundamentada na adesão de axiomas definidos segundo a restritividade de Herbert K., 1987, contrapõe as perspectivas algébricas atuais, correlacionando campos do estudo previamente não unificados e possibilitando a proposição e a demonstração de teoremas anteriormente impossibilitados pela incompletude de Gödel. Este documento busca comprimir os fundamentos da teoria da engenharia analítica, os quais terão suas proposições posteriormente comprovadas por meio dos fatores restritivos hiperbólicos.
Comments: 4 Pages. After further discussion
In the present paper a conflict in basic complex number theory is reported. The ingredients of the analysis are Euler's identity and the DeMoivre rule for n=2. The outcome is that a quadratic equation only has one single solution because one of the existing solutions gives rise to an impossibility.
Comments: 3 Pages. Sharpened the write-up after first round of discussion VRA
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