General Mathematics

2606 Submissions

[3] viXra:2606.0117 [pdf] submitted on 2026-06-30 20:47:17

Parapose, Triggering for Transition of Matrix and Principles of an Object to Round Around the Chord or the Point

Authors: Binay Krishna Maity
Comments: 8 Pages.

In the Transpose mode of a matrix we can see thearrangement of the literals of the matrix in a specific manner. If we rearrange these literals in another specific manner and combine the resulting matrix with original and/or transpose as we need, then, there will be different patterns of matrix and we may call this way of transition of the literals of the matrix as Parapose of matrix and the way of combination of the matrices as the Triggering for transition. Then there are three kinds of triggering of transitions. Such as - 1) The Triggering for Transition in First kind, 2) The Triggering for Transition in Second kind and 3) The Triggering for Transition in Third kind. This triggering of Transition may exhibit the principle of any set of objects rounding centering the point or around the chord.
Category: General Mathematics

[2] viXra:2606.0114 [pdf] submitted on 2026-06-30 09:11:32

Deriving the Dot Product From Polar Coordinates

Authors: Timothy Jones
Comments: 1 Page. This derivation doesn't seem to be in the literature.

Using polar coordinates the dot product is easily derived.
Category: General Mathematics

[1] viXra:2606.0071 [pdf] submitted on 2026-06-19 03:08:51

Identifying Natural Limits to Infinite Algebraic Singularities with Null Algebra

Authors: Robert S. Miller
Comments: 22 Pages. (Note by viXra Admin: Please cite and listed scientific references)

This paper introduces a framework which regularizes the classical algebraic singularity, using the essential hyperbola y=1/x to illustrate its application. Traditional, classical mathematics leaves the behavior at the origin for this function undefined due to divergence toward unachievable infinities. By using the transformational matrix defined in Null Algebra to map u=-1/y, the defined subspace of y, we may focus on a rate of information transfer implied by the function, as x→0. This is achieved by imposing a strict constraint upon dy/du which is required for any function y=f(x) and based upon chosen scale for the system defined by y=f(x). This shall show the singularity cannot actually be achieved due to natural self-limiting properties unique to a given function which emerge from Null Algebra, leaving a function, that is piecewise defined and continuous.
Category: General Mathematics