Functions and Analysis

    

Additive-Contingent Nonlinearity, Asymptotic Behaviors and Quantum-Causality in a Group of Covariant Systems

Authors: Michael C. I. Nwogugu

Some properties of the equations x2+y2+z2+v2= rXYZ, x2+y2+z2= rXYZ, x2+y2+z2+v2+u2=rXYZ, X2+Y2+Z2+V2= rXYZ, X2+Y2+Z2 = rXYZ, X2+Y2+Z2+V2 +U2 = rXYZ, Xi+Yi+Zi+Vi= rXYZ, x3+y3+z3=rXYZ, x3+y3+z3+x6+y6+z6=rXYZ, x6+y6+z6=rXYZ, [(x12+y12+z12)-(x6+y6+z6)]=rXYZ, and xi+yi+zi=rXYZ, (i is a positive integer), where x│X (ie. X is a multiple of x), y│Y, and z│Z are real numbers. This article also summarizes the relationships to Homotopy Theory, PDEs, Mathematical Cryptography and Analysis. The proofs are within the context of Sub-Rings. The additional common factor is that each of the variables x,y,z, v and dXYZ are multiples of (n-f), where n and f are real numbers. The solutions derived herein can be extended to other problems wherein (n-f) can take the form of polynomials/functions such as (6d-3), (14-5c), (ai-b2i), etc.. Some of the results are applicable where all variables are Integers.

Comments: 31 Pages. The copyright license-type for this article is CC-BY-NC-ND

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[v1] 2022-08-04 01:30:42

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