General Mathematics

1610 Submissions

[9] viXra:1610.0379 [pdf] submitted on 2016-10-31 12:58:46

Ordinalcy Calculus: Entangled Avenues Nuanced

Authors: Arthur Shevenyonov
Comments: 7 Pages. new foundations--lativity

Ordinalcy does appear to suggest a minimalist meta-ToE, with the Ordual calculus generalizing beyond differential forms. Matter is all about relationships rather than elements.
Category: General Mathematics

[8] viXra:1610.0363 [pdf] submitted on 2016-10-29 19:32:17

An Introduction to New Foundations: The Ordual Calculus for Ultimate Search

Authors: Arthur Shevenyonov
Comments: 5 Pages. new foundations--a glimpse at

The Ordinalcy paradigm has been illustrated and tentatively formalized. The proposed calculus appears to generalize the Poisson brackets while complying with the Jacobi identity.
Category: General Mathematics

[7] viXra:1610.0361 [pdf] submitted on 2016-10-30 00:44:19

From Quaternionic Multiplication to Matrix Decomposition

Authors: Kohji Suzuki
Comments: 14 Pages.

We are led to certain kinds of matrix decompositions through quaternionic multiplication.
Category: General Mathematics

[6] viXra:1610.0320 [pdf] submitted on 2016-10-26 19:38:45

There Exists no Algorithm for Solving the Quadratic Equation with Real Coefficients Neither in ℝ Nor in ℂ

Authors: Giorgos Bougioukas
Comments: 5 Pages.

This paper proves that the problem of the equality of two real constants is undecidable and as a consequence there exists no algorithm for solving the (univariate) quadratic equation with real coefficients neither in ℝ nor in ℂ.
Category: General Mathematics

[5] viXra:1610.0149 [pdf] submitted on 2016-10-14 03:24:24

Introduction to Tensor Calculus

Authors: Taha Sochi
Comments: 84 Pages.

These are general notes on tensor calculus which can be used as a reference for an introductory course on tensor algebra and calculus. A basic knowledge of calculus and linear algebra with some commonly used mathematical terminology is presumed.
Category: General Mathematics

[4] viXra:1610.0148 [pdf] submitted on 2016-10-14 03:30:28

Tensor Calculus

Authors: Taha Sochi
Comments: 91 Pages.

These notes are the second part of the tensor calculus documents which started with the previous set of introductory notes. In the present text, we continue the discussion of selected topics of the subject at a higher level expanding, when necessary, some topics and developing further concepts and techniques. Unlike the previous notes which are largely based on a Cartesian approach, the present notes are essentially based on assuming an underlying general curvilinear coordinate system.
Category: General Mathematics

[3] viXra:1610.0147 [pdf] submitted on 2016-10-14 03:36:32

Principles of Differential Geometry

Authors: Taha Sochi
Comments: 161 Pages.

The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on tensor calculus as they are based on the materials and conventions given in those documents. They can be used as a reference for a first course on the subject or as part of a course on tensor calculus.
Category: General Mathematics

[2] viXra:1610.0121 [pdf] submitted on 2016-10-12 04:00:31

On Complex Interval Linear System

Authors: Kayalvizhi Lakshmanan, Sarangam Majumdar
Comments: 7 Pages.

Linear system of equations with crisp values are crucial filed of research. Several different technique are available to solve this type of equations. The parameter values are actually uncertain in nature because data are collected from experiment. Another aspect is error in calculation. To avoid errors and uncertain nature of the parameter values, we use interval analysis. In this work, we are addressed solution methods for complex interval linear system. We propose a new method for finding solution of complex linear system of equations (CLSE). Moreover we study the numerical experiments using the proposed different methods.
Category: General Mathematics

[1] viXra:1610.0120 [pdf] replaced on 2016-10-20 23:29:55

Inverse Polynomials for Nonzero Constant Jacobian

Authors: Dhananjay P. Mehendale
Comments: 22 Pages

The so called Jacobian problem [1] or Jacobian conjecture [2], [3] demands the existence of inverse functions of polynomial nature when the Jacobian is a nonzero constant (=1). Bass, Connell, Wright in there paper [3] have shown that it is enough to construct (or show the existence of) such inverse polynomials for special type of cubic polynomials whose Jacobian is a nonzero constant (=1).To settle Jacobian conjecture one needs to show the existence of inverse polynomials for special type of cubic polynomials whose Jacobian is a nonzero constant (=1) for all dimensions [3]. In this paper we explicitly give these inverse polynomials for two and three dimensions, i.e. for two and three variables cases. Any higher dimensional cases are no different than these special cases and it is possible to obtain such inverse polynomials in any higher dimensional cases also.
Category: General Mathematics