General Mathematics

1912 Submissions

[13] viXra:1912.0532 [pdf] submitted on 2019-12-31 00:58:08

`(st)ringy' Proof the Poincar\'{e} Conjecture

Authors: Kohji Suzuki
Comments: 7 Pages.

We prove the Poincar\'{e} Conjecture using `(st)ring theory'.
Category: General Mathematics

[12] viXra:1912.0430 [pdf] submitted on 2019-12-24 09:23:16

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.
Category: General Mathematics

[11] viXra:1912.0356 [pdf] submitted on 2019-12-19 05:53:35

An Theorem About Square Root

Authors: Shinichi Kumakura, Rose Redrabbit
Comments: 4 Pages.

Use Properties of exponents and Characteristic equation to derive an formula of square root.
Category: General Mathematics

[10] viXra:1912.0301 [pdf] submitted on 2019-12-16 15:24:11

Letter Nª3: Elementary Formula

Authors: Edgar Valdebenito
Comments: 2 Pages.

We recall a elementary formula involving Pi.
Category: General Mathematics

[9] viXra:1912.0271 [pdf] submitted on 2019-12-14 05:02:48

Pi , A Short Letter

Authors: Edgar Valdebenito
Comments: 1 Page.

We give a formula for Pi.
Category: General Mathematics

[8] 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
Comments: 4 Pages.

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.
Category: General Mathematics

[7] viXra:1912.0209 [pdf] submitted on 2019-12-10 22:08:44

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.
Category: General Mathematics

[6] viXra:1912.0181 [pdf] submitted on 2019-12-09 11:43:58

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.
Category: General Mathematics

[5] viXra:1912.0163 [pdf] submitted on 2019-12-08 12:44:14

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»
Category: General Mathematics

[4] viXra:1912.0143 [pdf] submitted on 2019-12-08 09:10:53

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.
Category: General Mathematics

[3] viXra:1912.0140 [pdf] submitted on 2019-12-07 10:38:22

Number Pi , Bernoulli Numbers

Authors: Edgar Valdebenito, Rodrigo Valdebenito
Comments: 2 Pages.

This note presents some formulas for Pi.
Category: General Mathematics

[2] viXra:1912.0100 [pdf] submitted on 2019-12-05 08:48:18

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.
Category: General Mathematics

[1] viXra:1912.0024 [pdf] submitted on 2019-12-02 16:04:37

Kryptos - Hidden Hill Cipher

Authors: Robert Mereau
Comments: 23 Pages.

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.
Category: General Mathematics