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[11] viXra:2001.0473 [pdf] replaced on 2024-10-04 02:09:12
Authors: Theophilus Agama, Gael Kibiti
Comments: 12 Pages. This paper has been substantially revised.
In this paper we introduce a particular class of matrices. We study the concept of a matrix to be balanced. We study some properties of this concept in the context of matrix operations. We examine the behaviour of various matrix statistics in this setting. The crux will be to understanding the determinants and the eigenvalues of balanced matrices. It turns out that there does exist a direct communication among the leading entry, the trace, determinants and, hence, the eigenvalues of these matrices of order $2times 2$. These matrices have an interesting property that enables us to predict their quadratic forms, even without knowing their entries but given their spectrum.
Category: Algebra
[10] viXra:2001.0463 [pdf] submitted on 2020-01-22 07:33:42
Authors: Theophilus Agama
Comments: 11 Pages.
In this paper we give a proof of Sendov's conjecture. We start by establishing the uniformly diminishing state of the mass of an expansion.
Category: Algebra
[9] viXra:2001.0451 [pdf] submitted on 2020-01-21 10:28:12
Authors: Alberto Mananga Bifica
Comments: 3 Pages. Este Artigo Científico está Escrito em Português
A matriz é considerada como uma tabela que contem linhas (m) e colunas (n) dos números reais ou funções que serve para estudo de cálculos de área, equações e entre outros. O método proposto neste artigo é uma combinação do método de grammer e de Laplace válida para uma matriz de ordem três onde obtém-se somas de três matrizes de ordem dois.
Category: Algebra
[8] viXra:2001.0438 [pdf] submitted on 2020-01-21 16:38:08
Authors: Saeid Jafari, L. Mariapresenti, I. Arockiarani
Comments: 8 Pages.
In this paper, the notion of direct product of vague set in BCK- algebra is introduced and some related properties are investigated. Also we introduce some of the properties of direct product of finite vague ideal and vague subalgebras of BCK- algebras.
Category: Algebra
[7] viXra:2001.0435 [pdf] replaced on 2022-03-01 16:36:44
Authors: Mantzakouras Nikos
Comments: 26 Pages.
The Pythagorean theorem is perhaps the best known theorem in the vast world of mathematics.A simple relation of square numbers, which encapsulates all the glory of mathematical science, isalso justifiably the most popular yet sublime theorem in mathematical science. The starting pointwas Diophantus’ 20 th problem (Book VI of Diophantus’ Arithmetica), which for Fermat is for n= 4 and consists in the question whether there are right triangles whose sides can be measuredas integers and whose surface can be square. This problem was solved negatively by Fermat inthe 17 th century, who used the wonderful method (ipse dixit Fermat) of infinite descent. Thedifficulty of solving Fermat’s equation was first circumvented by Willes and R. Taylor in late1994 ([1],[2],[3],[4]) and published in Taylor and Willes (1995) and Willes (1995). We presentthe proof of Fermat’s last theorem and other accompanying theorems in 4 different independentways. For each of the methods we consider, we use the Pythagorean theorem as a basic principleand also the fact that the proof of the first degree Pythagorean triad is absolutely elementary anduseful. The proof of Fermat’s last theorem marks the end of a mathematical era; however, theurgent need for a more educational proof seems to be necessary for undergraduates and students ingeneral. Euler’s method and Willes’ proof is still a method that does not exclude other equivalentmethods. The principle, of course, is the Pythagorean theorem and the Pythagorean triads, whichform the basis of all proofs and are also the main way of proving the Pythagorean theorem in anunderstandable way. Other forms of proofs we will do will show the dependence of the variableson each other. For a proof of Fermat’s theorem without the dependence of the variables cannotbe correct and will therefore give undefined and inconclusive results . It is, therefore, possible to prove Fermat's last theorem more simply and equivalently than the equation itself, without monomorphisms.
Category: Algebra
[6] viXra:2001.0407 [pdf] submitted on 2020-01-20 17:20:57
Authors: Cicily Flora, S., Arockiarani, I., Saeid Jafari
Comments: 7 Pages.
The notion of bipolar vague A-ideals of BCI-algebra is introduced and their properties are investigated.
Characterizations of bipolar vague A-ideals are given. Relationship between bipolar vague ideal and the newly defined ideals are analyzed. Moreover, we studied some equivalent conditions for bipolar vague A-ideals. Finally, we prove a result in bipolar A-ideal using bipolar vague level cut.
Category: Algebra
[5] viXra:2001.0239 [pdf] submitted on 2020-01-14 10:00:00
Authors: Zeolla Gabriel
Comments: 11 Pages.
This document develops and demonstrates the discovery of a new potentiation algorithm that works absolutely with all the numbers using the formula of the square of a binomial, trinomial, tetranomial and pentanomial
Category: Algebra
[4] viXra:2001.0160 [pdf] submitted on 2020-01-09 15:09:47
Authors: Theophilus Agama
Comments: 44 Pages.
In this paper we introduce and develop the concept of expansivity of a tuple whose entries are elements from the polynomial ring R[x]. As an inverse problem, we examine how to recover a tuple from the expanded tuple at any given phase of expansion. We convert the celebrated Sendov conjecture concerning the distribution of zeros of polynomials and their critical points into this language and prove some weak variants of this conjecture. We also apply this to the existence of solutions to differential equations. In particular, we show that a certain system of differential equation has no non-trivial solution.
Category: Algebra
[3] viXra:2001.0067 [pdf] submitted on 2020-01-05 00:46:10
Authors: Henry Wong
Comments: 2 Pages.
An addendum to set theory.
Category: Algebra
[2] viXra:2001.0035 [pdf] submitted on 2020-01-03 00:59:30
Authors: Henry Wong
Comments: 1 Page.
An addendum to group theory.
Category: Algebra
[1] viXra:2001.0028 [pdf] submitted on 2020-01-03 05:31:24
Authors: Mehsin Jabel Atteya
Comments: 48 Pages.
In this article, we introduce new generators of a permuting n-derivations to improve and
increase the action of usual derivation. We produce a permuting n-generalized semiderivation,
a permuting n-semigeneralized semiderivation, a permuting n-antisemigeneralized semiderivation
and a permuting skew n-antisemigeneralized semiderivation of non-empty rings with their
applications. Actually, we study the behaviour of those types and present their results of semiprime ring R. Examples of various results have also been included. That is, many of the branches of science
such as business, engineering and quantum physics, which used a derivation, have the opportunity
to invest them in solving their problems.
Category: Algebra
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