1011 Submissions

[3] viXra:1011.0038 [pdf] submitted on 17 Nov 2010

Interval Linear Algebra

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 249 pages

This Interval arithmetic or interval mathematics developed in 1950's and 1960's by mathematicians as an approach to putting bounds on rounding errors and measurement error in mathematical computations. However no proper interval algebraic structures have been defined or studies. In this book we for the first time introduce several types of interval linear algebras and study them.
Category: Algebra

[2] viXra:1011.0037 [pdf] submitted on 14 Nov 2010

Lattice Rationals

Authors: Nathaniel S. K. Hellerstein
Comments: 17 pages

This paper redefines the addition of rational numbers, in a way that allows division by zero. This requires defining a "compensator" on the integers, plus extending least-common-multiple (LCM) to zero and negative numbers. "Compensated addition" defines ordinary addition on all ratios, including the 'infinities' n/0, and also 'zeroids' 0/n. The infinities and the zeroids form two 'double ringlets'. The lattice rationals modulo the zeroids yields the infinities plus the 'wheel numbers'. Due to the presence of the 'alternator' @ = 0/-1, double-distribution does not apply, but triple-distribution still does.
Category: Algebra

[1] viXra:1011.0019 [pdf] submitted on 11 Nov 2010

On Reduction

Authors: Nathaniel S. K. Hellerstein
Comments: 33 pages

In this paper I discuss "reduction", a.k.a. "reciprocal addition"; addition conjugated by reciprocal. I discuss reduction's definition, its laws, its graphs, its geometry, its algebra, its calculus, and its practical applications. This paper contains a problem set with answer key.
Category: Algebra