Algebra

1807 Submissions

[3] 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

[2] 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

[1] 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