Algebra

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Recent submissions

Any replacements are listed farther down

[278] viXra:1807.0240 [pdf] submitted on 2018-07-12 08:50:24

Some Finite Series and Their Application

Authors: Saikat sarkar
Comments: 4 Pages.

This is only for maths students
Category: Algebra

[277] viXra:1807.0131 [pdf] submitted on 2018-07-05 07:07:06

The Upper Bound of Composition Series

Authors: Abhijit Bhattacharjee
Comments: 9 Pages. The paper was submitted to journal of combinatorial theory a, after referee 's review they told me to submit it algebra related journal.

The upper bound of composition series for finite group is obtained .
Category: Algebra

[276] viXra:1807.0091 [pdf] submitted on 2018-07-03 11:10:16

Triple Conformal Geometric Algebra for Cubic Plane Curves (long CGI2017/ENGAGE2017 paper in SI of MMA)

Authors: Robert B. Easter, Eckhard Hitzer
Comments: 20 pages. Revision, 3 July 2018, with corrections and improvements to the published version, 18 Sep 2017 DOI:10.1002/mma.4597, in MMA 41(11)4088-4105, 30 July 2018, Special Issue: ENGAGE. 9 tables, 4 figures, 28 references.

The Triple Conformal Geometric Algebra (TCGA) for the Euclidean R^2-plane extends CGA as the product of three orthogonal CGAs, and thereby the representation of geometric entities to general cubic plane curves and certain cyclidic (or roulette) quartic, quintic, and sextic plane curves. The plane curve entities are 3-vectors that linearize the representation of non-linear curves, and the entities are inner product null spaces (IPNS) with respect to all points on the represented curves. Each IPNS entity also has a dual geometric outer product null space (OPNS) form. Orthogonal or conformal (angle-preserving) operations (as versors) are valid on all TCGA entities for inversions in circles, reflections in lines, and, by compositions thereof, isotropic dilations from a given center point, translations, and rotations around arbitrary points in the plane. A further dimensional extension of TCGA, also provides a method for anisotropic dilations. Intersections of any TCGA entity with a point, point pair, line or circle are possible. TCGA defines commutator-based differential operators in the coordinate directions that can be combined to yield a general n-directional derivative.
Category: Algebra

[275] viXra:1806.0467 [pdf] submitted on 2018-06-30 09:35:47

Clifford Algebras :New Results

Authors: Jean Claude Dutailly
Comments: 28 Pages.

The purpose of the paper is to present new results (exponential, real structure, Cartan algebra,...) but, as the definitions are sill varying with the authors, the paper covers all the domain, and can be read as a comprehensive presentation of Clifford algebras.
Category: Algebra

[274] viXra:1806.0430 [pdf] submitted on 2018-06-29 03:36:32

Note on Mathematical Inequality.

Authors: Saikat sarkar
Comments: 3 Pages.

This artical has been prepared for basic inequality concept.
Category: Algebra

[273] viXra:1806.0250 [pdf] submitted on 2018-06-16 20:42:30

The Pagerank Algorithm: Theory & Implementation in Scilab

Authors: Ayoub ABRACH, El Mehdi BOUCHOUAT
Comments: 27 Pages.

Search engines are huge power factors on the Web, guiding people to information and services. Google is the most successful search engine in recent years,his research results are very complete and precise. When Google was an early research project at Stanford, several articles have been written describing the underlying algorithms. The dominant algorithm has been called PageRank and is still the key to providing accurate rankings for search results. A key feature of web search engines is sorting results associated with a query in order of importance or relevance. We present a model allowing to define a quantification of this concept (Pagerank) a priori fuzzy and elements of formalization for the numerical resolution of the problem. We begin with a natural first approach unsatisfactory in some cases. A refinement of the algorithm is introduced to improve the results.
Category: Algebra

[272] viXra:1805.0528 [pdf] submitted on 2018-05-31 00:49:48

The Matricial Clifford Algebras

Authors: Antoine Balan
Comments: 1 page, written in french

We introduce here the notion of matricial Clifford algebras with help of the product of matrices and the tensor product.
Category: Algebra

[271] viXra:1805.0355 [pdf] submitted on 2018-05-20 05:12:52

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 8 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 3 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[270] viXra:1805.0337 [pdf] submitted on 2018-05-18 14:29:00

On the Locality of Fields

Authors: Jacob Klumberg, Boris Kyrasov
Comments: 10 Pages.

Suppose we are given a reversible, nonnegative, ultra-partially sub-null arrow r. A central problem in arithmetic is the characterization of unconditionally universal numbers. Recent interest in Artinian subalgebras has centered on describing multiply associative numbers. Recently, there has been much interest in the derivation of super-reducible, extrinsic hulls.
Category: Algebra

[269] viXra:1804.0093 [pdf] submitted on 2018-04-06 07:41:06

None Complex Numbers

Authors: Said Amharech
Comments: 5 Pages. the work is written in french

This work is dealing with something that we’re not sure it exists, but it’s just an attempt to solve some problems in algebra, it gives a general idea about the complexe numbers we got from the great mathematicians of all times, I believe that these complexe numbers we notice in algebra, calculus or even quantum physics are not enough, in general, i think there is another infinite dimension of numbers, and real or complexe numbers are just a simple projection of the complexity of that world. As a method of work instead of adding a function of rotation pi over two as we did with the real line to expand the complexe plan, i’ve thought to make a function of translation… But the importance in here is that the function we need is not a linear function to solve some kind of problems like for example dividing over zero, and as you may notice if the function isn’t linear so that the neutral element of the complexe plan for the additive law which it the trivial zero we know is completely different of the neutral element of the new mother group. at the end we can find some roots easily of riemann’s zeta function but it is not a complexe roots.
Category: Algebra

[268] viXra:1804.0003 [pdf] submitted on 2018-04-01 04:40:39

About the Hamilton Numbers

Authors: Antoine Balan
Comments: 4 pages, written in french

We introduce here some algebraic theory about the Hamilton numbers and develop a quaternionic geometry of fiber bundles.
Category: Algebra

[267] viXra:1802.0294 [pdf] submitted on 2018-02-21 10:54:53

Solution of a High-School Algebra Problem to Illustrate the Use of Elementary Geometric (Clifford) Algebra

Authors: James A. Smith
Comments: 5 Pages.

This document is the first in what is intended to be a collection of solutions of high-school-level problems via Geometric Algebra (GA). GA is very much "overpowered" for such problems, but students at that level who plan to go into more-advanced math and science courses will benefit from seeing how to "translate" basic problems into GA terms, and to then solve them using GA identities and common techniques.
Category: Algebra

[266] viXra:1802.0096 [pdf] submitted on 2018-02-08 06:48:35

Solution to the Problem Pmo33.5. Problema Del Duelo Matemático 08 (Olomouc – Chorzow Graz).

Authors: Jesús Álvarez Lobo
Comments: 3 Pages. Spanish.

Solution to the problem PMO33.5. Problema del Duelo Matemático 08 (Olomouc – Chorzow - Graz). Let a, b, c in ℝ. Prove that V = 4(a² + b² + c² ) - (a + b)² - (b + c)² - (c + a)² >= 0, and determine all values of a, b, c for which V = 0.
Category: Algebra

[265] viXra:1802.0022 [pdf] submitted on 2018-02-02 16:54:13

Discarding Algorithm for Rational Roots of Integer Polynomials (DARRIP).

Authors: Jesús Álvarez Lobo
Comments: 20 Pages.

The algorithm presented here is to be applied to polynomials whose independent term has many divisors. This type of polynomials can be hostile to the search for their integer roots, either because they do not have them, or because the first tests performed have not been fortunate. This algorithm was first published in Revista Escolar de la Olimpíada Iberoamericana de Matemática, Number 19 (July - August 2005). ISSN – 1698-277X, in Spanish, with the title ALGORITMO DE DESCARTE DE RAÍCES ENTERAS DE POLINOMIOS. When making this English translation 12 years later, some erratum has been corrected and when observing from the perspective of time that some passages were somewhat obscure, they have been rewritten trying to make them more intelligible. The algorithm is based on three properties of divisibility of integer polynomials, which, astutely implemented, define a very compact systematic that can simplify significantly the exhaustive search of integer roots and rational roots. Although there are many other methods for discarding roots, for example, those based on bounding rules, which sometimes drastically reduce the search interval, for the sake of simplicity, they will not be considered here. The study presented here could be useful to almost all the young people of the planet, since at some stage of their academic training they will have to solve polynomial equations with integer coefficients, looking for rational solutions, integer or fractional. The author thinks that DARRIP's algorithm should be incorporated into the curricula of all the elementary study centers over the world.
Category: Algebra

[264] viXra:1801.0106 [pdf] submitted on 2018-01-09 08:48:03

A Simpler Classification Paradigm for Finite Simple Groups and an Application to the Riemann Hypothesis

Authors: A.Polorovskii
Comments: 2 Pages.

In this paper we propose a new system of classification that greatly simplifies the task of classifying (or setifying) all finite simple groups (Hereafter referred to as FSGs.) We propose classification of FSGs by identifying each group with the equivalence class of certain groups up to isomorphism. Furthermore, it is shown that every FSG belongs to at least one of the equivalence classes herein. Using our new classification, the Generalized Riemann Hypothesis is proven.
Category: Algebra

[263] viXra:1712.0575 [pdf] submitted on 2017-12-24 00:18:53

Approximate A Slice of Pi Essay

Authors: Cres Huang
Comments: Pages.

A simple way of approximating π by slice.
Category: Algebra

[262] viXra:1712.0140 [pdf] submitted on 2017-12-06 10:51:29

On Fermat's Last Theorem. Revised.

Authors: Richard Wayte
Comments: 8 Pages.

A solution of Fermat’s Last Theorem is given, using elementary function arithmetic and inference from worked examples.
Category: Algebra

[261] viXra:1710.0247 [pdf] submitted on 2017-10-22 16:35:07

Mathematical Closure

Authors: Paris Samuel Miles-Brenden
Comments: 1 Page. None.

Mathematical Closure.
Category: Algebra

[260] viXra:1709.0131 [pdf] submitted on 2017-09-11 11:21:53

The Difference of Any Real Transcendental Number and Complex Number E^i is Always a Complex Transcendental Number.

Authors: Charanjeet Singh Bansrao
Comments: 4 Pages.

The difference of any real transcendental number and complex number e^i is always a complex transcendental number.
Category: Algebra

[259] viXra:1708.0417 [pdf] submitted on 2017-08-28 08:38:14

The Quintic Equation: X^5+10*x^3+20*x-1=0

Authors: Edgar Valdebenito
Comments: 11 Pages.

This note presents the roots (in radicals) of the equations:x^5+10*x^3+20*x-1=0 , x^5-20*x^4-10*x^2-1=0 and related fractals.
Category: Algebra

[258] viXra:1708.0256 [pdf] submitted on 2017-08-21 18:38:34

Discussion Sur Les Structures Algébriques Des Infinis Réels et L’irrationalité de la Constante D’Euler-Mascheroni

Authors: F.L.B.Périat
Comments: 3 Pages.

Proposition sur l'infini imaginé comme un espace vectoriel, permettant par distribution des vecteurs de démontrer l'irrationalité de certaines valeurs.
Category: Algebra

[257] viXra:1708.0188 [pdf] submitted on 2017-08-16 12:49:22

Real Roots of the Equation: X^6-3x^4-2x^3+9x^2+3x-26=0

Authors: Edgar Valdebenito
Comments: 5 Pages.

This note presents the real roots (in radicals)of the equation:x^6-3x^4-2x^3+9x^2+3x-26=0.
Category: Algebra

[256] viXra:1706.0508 [pdf] submitted on 2017-06-27 07:33:39

3D Matrix Ring with a “Common” Multiplication

Authors: Orgest ZAKA
Comments: 11 Pages.

In this article, starting from geometrical considerations, he was born with the idea of 3D matrices, which have developed in this article. A problem here was the definition of multiplication, which we have given in analogy with the usual 2D matrices. The goal here is 3D matrices to be a generalization of 2D matrices. Work initially we started with 3×3×3 matrix, and then we extended to m×n×p matrices. In this article, we give the meaning of 3D matrices. We also defined two actions in this set. As a result, in this article, we have reached to present 3-dimensional unitary ring matrices with elements from a field F.
Category: Algebra

[255] viXra:1705.0019 [pdf] submitted on 2017-05-02 04:07:01

Double Conformal Geometric Algebra (long CGI2016/GACSE2016 paper in SI of AACA)

Authors: Robert B. Easter, Eckhard Hitzer
Comments: 25 Pages. Published online First in AACA, 20th April 2017. DOI: 10.1007/s00006-017-0784-0. 2 tables, 26 references.

This paper introduces the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), based in the $\mathcal{G}_{8, 2}$ Clifford geometric algebra. DCGA is an extension of CGA and has entities representing points and general (quartic) Darboux cyclide surfaces in Euclidean 3D space, including circular tori and all quadrics, and all surfaces formed by their inversions in spheres. Dupin cyclides are quartic surfaces formed by inversions in spheres of torus, cylinder, and cone surfaces. Parabolic cyclides are cubic surfaces formed by inversions in spheres that are centered on points of other surfaces. All DCGA entities can be transformed by versors, and reflected in spheres and planes. Keywords: Conformal geometric algebra, Darboux Dupin cyclide, Quadric surface Math. Subj. Class.: 15A66, 53A30, 14J26, 53A05, 51N20, 51K05
Category: Algebra

[254] viXra:1702.0234 [pdf] submitted on 2017-02-18 21:44:17

On the K-Macga Mother Algebras of Conformal Geometric Algebras and the K-Cga Algebras

Authors: Robert B. Easter
Comments: 8 Pages.

This note very briefly describes or sketches the general ideas of some applications of the G(p,q) Geometric Algebra (GA) of a complex vector space C^(p,q) of signature (p,q), which is also known as the Clifford algebra Cl(p,q). Complex number scalars are only used for the anisotropic dilation (directed scaling) operation and to represent infinite distances, but otherwise only real number scalars are used. The anisotropic dilation operation is implemented in Minkowski spacetime as hyperbolic rotation (boost) by an imaginary rapidity (+/-)f = atanh(sqrt(1-d^2)) for dilation factor d>1, using +f in the Minkowski spacetime of signature (1,n) and -f in the signature (n,1). The G(k(p+q+2),k(q+p+2)) Mother Algebra of CGA (k-MACGA) is a generalization of G(p+1,q+1) Conformal Geometric Algebra (CGA) having k orthogonal G(p+1,q+1):p>q Euclidean CGA (ECGA) subalgebras and k orthogonal G(q+1,p+1) anti-Euclidean CGA (ACGA) subalgebras with opposite signature. Any k-MACGA has an even 2k total count of orthogonal subalgebras and cannot have an odd 2k+1 total count of orthogonal subalgebras. The more generalized G(l(p+1)+m(q+1),l (q+1)+m(p+1)):p>q k-CGA algebra, for even or odd k=l+m, has any l orthogonal G(p+1,q+1) ECGA subalgebras and any m orthogonal G(q+1,p+1) ACGA subalgebras with opposite signature. Any 2k-CGA with even 2k orthogonal subalgebras can be represented as a k-MACGA with different signature, requiring some sign changes. All of the orthogonal CGA subalgebras are corresponding by representing the same vectors, geometric entities, and transformation versors in each CGA subalgebra, which may differ only by some sign changes. A k-MACGA or a 2k-CGA has even-grade 2k-vector geometric inner product null space (GIPNS) entities representing general even-degree 2k polynomial implicit hypersurface functions F for even-degree 2k hypersurfaces, usually in a p-dimensional space or (p+1)-spacetime. Only a k-CGA with odd k has odd-grade k-vector GIPNS entities representing general odd-degree k polynomial implicit hypersurface functions F for odd-degree k hypersurfaces, usually in a p-dimensional space or (p+1)-spacetime. In any k-CGA, there are k-blade GIPNS entities representing the usual G(p+1,q+1) CGA GIPNS 1-blade entities, but which are representing an implicit hypersurface function F^k with multiplicity k and the k-CGA null point entity is a k-point entity. In the conformal Minkowski spacetime algebras G(p+1,2) and G(2,p+1), the null 1-blade point embedding is a GOPNS null 1-blade point entity but is a GIPNS null 1-blade hypercone entity.
Category: Algebra

[253] viXra:1702.0057 [pdf] submitted on 2017-02-03 16:53:05

Levi-Civita Rhymes with Lolita

Authors: William O. Straub
Comments: 6 Pages.

Elementary overview of the Levi-Civita symbol, emphasizing its dependence on the Kronecker delta
Category: Algebra

[252] viXra:1702.0038 [pdf] submitted on 2017-02-02 16:32:16

Solving Inconsistent Systems of Linear Equations (Part I)

Authors: Martin Erik Horn
Comments: 12 Pages.

Using Geometric Algebra consistent solutions of inconsistent systems of linear equations can be found.
Category: Algebra

[251] viXra:1612.0259 [pdf] submitted on 2016-12-16 07:05:01

A Two-Dimensional Vector Space Algebra with Identity 2x2 Matrix Basis Matrix Multiplication Homomorphism

Authors: Claude Michael Cassano
Comments: 3 Pages.

A two-dimensional vector space algebra with identity 2x2 matrix basis matrix multiplication homomorphism There exists a homomorphism between any two-dimensional vector space algebra with identity and a 2x2 matrix basis under ordinary matrix multiplication. This is a statement of constructive existence of an algebra. Given that the vector space of the algebra is known to be 2-dimensional, the algebra product determines the constants: A,B,b ; determining the basis of the algebra. And showing that the basis of a two-dimensional vector space unitary algebra is a cyclic group of order 2
Category: Algebra

[250] viXra:1612.0221 [pdf] submitted on 2016-12-12 03:18:52

Conic and Cyclidic Sections in Double Conformal Geometric Algebra G_{8,2}

Authors: Robert Benjamin Easter, Eckhard Hitzer
Comments: 6 Pages. Proceedings of SSI 2016, Session SS11, pp. 866-871, 6-8 Dec. 2016, Ohtsu, Shiga, Japan, 10 color figures.

The G_{8,2} Geometric Algebra, also called the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA), has entities that represent conic sections. DCGA also has entities that represent planar sections of Darboux cyclides, which are called cyclidic sections in this paper. This paper presents these entities and many operations on them. Operations include projection, rejection, and intersection with respect to spheres and planes. Other operations include rotation, translation, and dilation. Possible applications are introduced that include orthographic and perspective projections of conic sections onto view planes, which may be of interest in computer graphics or other computational geometry subjects.
Category: Algebra

Replacements of recent Submissions

[42] viXra:1805.0355 [pdf] replaced on 2018-06-12 05:12:19

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 10 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 4 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[41] viXra:1805.0355 [pdf] replaced on 2018-06-06 15:20:33

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 10 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 4 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[40] viXra:1805.0355 [pdf] replaced on 2018-06-02 05:19:02

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 8 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 3 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[39] viXra:1805.0355 [pdf] replaced on 2018-06-01 17:03:00

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 8 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 3 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[38] viXra:1805.0355 [pdf] replaced on 2018-05-24 17:28:18

Boundary Matrices and the Marcus-de Oliveira Determinantal Conjecture

Authors: Ameet Sharma
Comments: 8 Pages.

We present notes on the Marcus-de Oliveira conjecture. The conjecture concerns the region in the complex plane covered by the determinants of the sums of two normal matrices with prescribed eigenvalues. Call this region ∆. This paper focuses on boundary matrices of ∆. We prove 3 theorems regarding these boundary matrices. We propose 2 conjectures related to the Marcus-de Oliveira conjecture.
Category: Algebra

[37] viXra:1804.0003 [pdf] replaced on 2018-04-07 11:38:11

About the Hamilton Numbers

Authors: Antoine Balan
Comments: 4 pages, written in french

We introduce here some algebraic theory about the Hamilton numbers and develop a quaternionic geometry of fiber bundles.
Category: Algebra

[36] viXra:1709.0131 [pdf] replaced on 2018-03-09 07:22:47

The Difference of Any Real Transcendental Number and Complex Number E^i is Always a Complex Transcendental Number.

Authors: Charanjeet Singh Bansrao
Comments: 8 Pages.

The Difference of Any Real Transcendental Number and Complex Number E^i is Always a Complex Transcendental Number.
Category: Algebra

[35] viXra:1709.0131 [pdf] replaced on 2018-01-09 00:03:03

The Difference of Any Real Transcendental Number and Complex Number is Always a Complex Transcendental Number.

Authors: Charanjeet Singh Bansrao
Comments: 4 Pages.

The difference of any real transcendental number and complex number is always a complex transcendental number.
Category: Algebra