The mathematics of the grand unified theory

This paper surveys the mathematics of GUT and highlights the author’s new real number system which is a continuum, non-Archimedean and non-Hausdorff, but its subspace of decimals is countably infinite, discrete, Archimedean and Hausdorff. The paper also proves Goldbach’s conjecture in and provides an overview of GUT and qualitative and computational models of many of the presently ill-defined physical concepts, e.g., gravity.     

Qualitative model of the atom,its components and origin in the early universe

This paper is the first qualitative model of the atom and its components as well as its origin in our early universe. The atom’s components–proton, neutron (with its neutrino) and electron–are built on the prima, units of visible matter. Their qualitative models are obtained using some laws of nature. They yield new information such as the mass of the neutrino and how heavy isotopes of an atom form as well as the arrangement of the nucleons. It clarifies some presently unresolved issues such as what happens in thermonuclear explosion and whether it can be controlled to generate energy. It also explains the wave-particle duality of the primum and photon, metal fatigue, matter-anti-matter interaction and brittle and malleable materials and reviews the early phase of the development of our universe beyond the formation of the first atom up to its rapid formation at the present time in the Cosmos and tissues of living organisms.     

Revisiting the hybrid real number system

The hybrid real number system consisting of terminating and nonterminating decimals, dark numbers, dual dark numbers, involving the notions of personal infinities and the impersonal infinity has been discussed. Some algebraic properties of dark numbers and dual dark numbers are discussed.