PHYSICS, RELATIVITY, GRAVITATION, COSMOLOGY AND MATHEMATICS  NEW THEORIES AND FORMULATIONS. The purpose of this site is the presentation of new theories and mathematical formulations of Atomic Structure, Albert Einstein's Special Theory of Relativity, Gravitation and Cosmology. The Section on Mathematics presents new ideas in number theory and analysis. The content is therefore of a technical nature, requiring a good knowledge of mathematics, physics and applied mechanics up to graduate level.  
Links to the Papers.
Changes in Last Updates.
New Mathematics Paper Added : (i) Assuming Convergence, (as suggested in paper M21), Determination of the Closed Form of the Harmonic Series New Mathematics Paper Added : (ii) A Second Deliberation on the Closed Form of the Harmonic Series, and the True Nature of the Euler  Mascheroni Constant Last Update 4 February 2019. Note: This site displays best in Internet Explorer 7 et seq and Chrome. 
The current literature on the physics theories above primarily works with such techniques as Quantum Mechanics and Quantum Electrodynamics, (Atomic Stucture), Riemannian Geometry and the Tensor Calculus etc. (Relativity, Gravitation and Cosmology), and while these are extremely powerful mathematical tools, they are also very complex. Therefore, when applied to Atomic Structure Theory, the theories of Special and General Relativity, and Cosmology, they result in a formulation quite difficult to follow, for even the most accomplished post graduate student. In the presentations here, nothing more complex than first and second order differential equations of functions of a complex variable are used, to initially develop the Special Theory of Relativity from first principles, using a new representation of Minkowski spacetime designated Relativistic Domains. This forms the basis from which additional papers are developed, extending the technique into further relativistic, gravitational and cosmological matters. This extension includes the development of mathematically rigorous new theories for Gravitation, the origin and existence of the Universe, and Atomic Structure theory. The latter is based upon a combination of modern Quantum Mechanics and the old Quantum Theory of Niels Bohr and Arnold Sommerfeld. In the Section on Mathematics, the subjects addressed are: (i) A simple proof of Fermat's Last Theorem. (ii) A Resolution of the Riemann Hypothesis, (iii) The generation of prime numbers via single variable polynomial equations. New methods of testing for (a) primality, and (b) the determination of the number of primes between two limiting numbers, (iv) The closed forms of convergent infinite series, and (v) Ensuring the absolute convergence of the Bairstow Method of finding the roots of high order polynomials. The precise determination of the multiple roots of high order polynomials is also addressed. All papers are in PDF format. The links at the top left connect with introductory pages to the six categories of papers presented. Because they largely follow on from one another, for maximum appreciation, all papers in each category should be read in the order listed.
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