General Relativity in a generalized differential calculus – a candidate for quantum gravity

Abstract. I propose to apply my generalized limit theory and generalized partial differential equations to (unchanged) general relativity equations, changing the set of solutions to a different vector field than real numbers. So, I’ve formulated another variant of general relativity. Whether the resulting theory is non-contradictory in the case of singularities, is yet unknown. This…… Continue reading General Relativity in a generalized differential calculus – a candidate for quantum gravity

“Not Science” – a new method to gain knowledge that is not science

Developing a future not scientific method to replace scientific method and traditional mathematics. The method to be developed is to be highly selective and inclusive, economically effective, requiring interdisciplinarity. Not science is like science based on mathematics, but a different kind of mathematics, with an algorithm that is “not logic”.

Modelling the global war in the case if an efficient NP-complete algorithm is published

Lemme model what happens if somebody finds an efficient NP-complete algorithm. In layman terms an efficient NP-complete algorithm is: an algorithm that reaches any given decision accomplishment if what “to accomplish” is exactly (mathematically) described and is accomplishable (e.g. accordingly laws of physics). [That’s is oversimplified and inexact.] So, the first thing is that somebody…… Continue reading Modelling the global war in the case if an efficient NP-complete algorithm is published

I’ve proved that if P=NP, it’s a constructive problem.

Victor Porton A new proof that if P=NP, it’s a constructive problem (that is an algorithm that is polynomial-time NP-complete under the supposition that polynomial-time NP-complete algorithms exist). PDF This is my first significant CS theorem. My previous results were in general topology and something related with logic.

Axiomatic Theory of Formulas

Victor Porton Part 1. Axiomatic Theory of Formulas Preface Overview This new mathematical theory developed by the book author researches the properties of mathematical formulas (aka expressions). Naturally this theory is essential for the mathematics. Formulas are encountered in all areas of mathematics. Probably of special interest are propositional formulas in math logic. Using Operator…… Continue reading Axiomatic Theory of Formulas

Algebraic Theory of General Topology and Discontinuous Analysis book

An earlier version of this work was published by scientific publisher INFRA-M. Introduced several new axiomatic systems not less general than group theory and discontinuous analysis. In this work I introduce and study in details the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces, and generalizations thereof. The concept of…… Continue reading Algebraic Theory of General Topology and Discontinuous Analysis book