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

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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*

**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