Algebra

1911 Submissions

[8] viXra:1911.0479 [pdf] submitted on 2019-11-28 13:22:22

Policies for Constraining the Behaviour of Coalitions of Agents in the Context of Algebraic Information Theory

Authors: Christopher Goddard
Comments: 27 Pages.

This article takes an oblique sidestep from two previous papers, wherein an approach to reformulation of game theory in terms of information theory, topology, as well as a few other notions was indicated. In this document a description is provided as to how one might determine an approach for an agent to choose a policy concerning which actions to take in a game that constrains behaviour of subsidiary agents. It is then demonstrated how these results in algebraic information theory, together with previous investigations in geometric and topological information theory, can be unified into a single cohesive framework.
Category: Algebra

[7] viXra:1911.0452 [pdf] submitted on 2019-11-26 11:57:04

Press Release: Multiplication of Triplets

Authors: Clumsy Foo
Comments: 8 Pages. Every mathematical proof is only valid for the range of the few axioms, on which its construction is based! English and German press release.

To all appearances mathematicians are not interested in mathematics, but they are only interested in constructing proofs. After having found a proof that a mathematical statement is correct or wrong, or that a mathematical construction is possible or impossible, mathematicians stop thinking about these statements or constructions. This is problematic for a science which is axiomatically founded in such a severe way.
Category: Algebra

[6] viXra:1911.0345 [pdf] submitted on 2019-11-20 11:53:48

"Can You Multiply Triplets?" "Yes, I Can."

Authors: Clumsy Foo
Comments: 15 Pages. Shorter equations will result in better mathematics.

It is possible to model rotations in three-dimensional space with triplets.
Category: Algebra

[5] viXra:1911.0275 [pdf] replaced on 2019-11-17 23:52:46

Exponential Factorization and Polar Decomposition of Multivectors in $Cl(p,q)$, $p+q \leq 3$

Authors: Eckhard Hitzer, Stephen J. Sangwine
Comments: 18 Pages. Submitted to Adv. in Appl. Cliff. Algs., 2019.

In this paper we consider general multivector elements of Clifford algebras $Cl(p,q)$, $n=p+q \leq 3$, and study multivector equivalents of polar decompositions and factorization into products of exponentials, where the exponents are frequently blades of grades zero (scalar) to $n$ (pseudoscalar).
Category: Algebra

[4] viXra:1911.0258 [pdf] submitted on 2019-11-15 06:50:19

Refutation of Fundamental Sets for Algebraic Subgroups

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 fundamental sets for algebraic subgroups by way of the seminal Theorem 6.12. It is not tautologous and refutes the conjecture. What follows is refutation of quantitative reduction theory and unlikely intersections. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Algebra

[3] viXra:1911.0226 [pdf] submitted on 2019-11-12 10:50:35

Hypercomplex Numbers of Dimension 11

Authors: Valery Timin
Comments: timinva@yandex.ru, 3 pages in Russian

This work is devoted to the search, study and compilation of the multiplication table of a compound hyperbolic (Hypercomplex) number of dimension nine (11): q = {1, i1, i2, i3, …, i10, }: in2 = 1. On this basis, as a template, you can choose other multiplication tables with a different target or arbitrary arrangement of plus (+) and minus (-) characters in the cells of the multiplication table. The disadvantage of multiplication tables of dimension 11 is that they are neither associative nor commutative (not even anticommutative). But this is their fundamental property.. Эта работа посвящена поиску, изучению и составлению таблицы умножения составного гиперболического (гиперкомплексного) числа размерностью девять (11): q = {1, i1, i2, i3, …, i11, }: in2 = 1. На этой основе как на шаблоне можно подобрать другие таблицы умножения с другой целевой или произвольной расстановкой знаков "плюс" (+) и "минус" (-) в ячейках таблицы умножения. Ассоциативных и коммутативных таблиц умножения не имеется.
Category: Algebra

[2] viXra:1911.0174 [pdf] submitted on 2019-11-09 04:11:04

On the Construction of a Regular Heptagon by Straightedge and Compass

Authors: Henry Wong
Comments: 1 Page.

An addendum to field theory.
Category: Algebra

[1] viXra:1911.0023 [pdf] submitted on 2019-11-01 12:27:07

Cheating with Complex Numbers Der Selbstbetrug Mit Den Komplexen Zahlen

Authors: Martin Erik Horn
Comments: 6 pages, bilingual version (in English and German)

Together with complex conjugation, complex numbers are misused to model anti-commutative structures. German Abstract: Komplexe Zahlen werden zur Modellierung anti-kommutativer Strukturen missbraucht, wenn die komplexe Konjugation genutzt wird.
Category: Algebra