Algebra

1910 Submissions

[4] viXra:1910.0613 [pdf] submitted on 2019-10-29 00:18:26

The Two Couriers Problem

Authors: William F. Gilreath
Comments: 6 Pages. Published in Transmathematica 2019

The Two Couriers Problem is an algebra problem, originally stated in 1746 by the French mathematician Clairaut. For over a century, the Two Couriers Problem has been re-used in various forms as a mathemat- ical problem, in textbooks and journals, by different mathematicians and authors. The Two Couriers Problem involves cases where division by zero arises in practice, where each has a real-world, actual result for the solution. Thus the Two Couriers Problem is a centuries old algebra problem with actual applied results that involve division by zero. It is an excellent mathematical problem to evaluate different methods for dividing by zero. Division by zero has many different mathematical approaches. Conventional mathematics handles division by zero as an indeterminate or undefined result. Transmathematics defines division by zero as either nul- lity or explicitly positive or negative infinity. Two other approaches are by Saitoh, who defines division by zero simply as zero, and Barukčić who defines division by zero as either unity or explicitly positive or implicitly negativity infinity. The question is, which approach is best to solve the mathematical problem of division by zero? The paramount goal of this paper is to use the Two Couriers Problem as an objective test to examine and evaluate mathematical approaches to division by zero – and find which one is best.
Category: Algebra

[3] viXra:1910.0345 [pdf] submitted on 2019-10-19 11:43:49

Unimodular Rotation of E8 to H4 600-Cells

Authors: J Gregory Moxness
Comments: 5 Pages.

We introduce a unimodular Determinant=1 8x8 rotation matrix to produce four 4 dimensional copies of H4 600-cells from the 240 vertices of the Split Real Even E8 Lie group. Unimodularity in the rotation matrix provides for the preservation of the 8 dimensional volume after rotation, which is useful in the application of the matrix in various fields, from theoretical particle physics to 3D visualization algorithm optimization.
Category: Algebra

[2] viXra:1910.0293 [pdf] replaced on 2019-10-18 07:34:11

Motivating Abstract with Elementary Algebra

Authors: Timothy W. Jones
Comments: 9 Pages. Additional material added with corrections.

There are natural lead-ins to abstract algebra that occur in elementary algebra. We explore function composition using linear functions and permutations on letters in misspellings of words. Groups and the central idea of abstract algebra, proving 5th degree and greater polynomials are unsolvable, are put into focus for college students.
Category: Algebra

[1] viXra:1910.0037 [pdf] submitted on 2019-10-05 09:50:32

Hypercomplex Numbers of Dimension 10

Authors: Valery Timin
Comments: timinva@yandex.ru, 4 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 (10): q = {1, i1, i2, i3, …, i9, }: 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 10 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 (10): q = {1, i1, i2, i3, …, i9, }: 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. Только коммутативных таблиц размерности 10 может быть до 1750, а ассоциативных – до 65201 (не окончательно). Все коммутативные таблицы имеют эластичную ассоциативность (Am).
Category: Algebra