Unified Theory of Recurrence Formulas. I

Brane World Astronomy I Unified Theory

Unified theories suggest that space is intrinsically 10 dimensional, even though everyday phenomena seem to take place in only 3 large dimensions. In “Brane World” models, matter and radiation are localized to a “brane” which has a thickness less than ≈ (TeV) in all but the usual three dimensions, while gravity propagates in additional dimensions, some of which may extend as far as submillimete...

Basic formulas and languages Part I. The theory

Unified Theory of Source Coding: Part I -- Two Terminal Problems

Since the publication of Shannon’s theory of one terminal source coding, a number of interesting extensions have been derived by researchers such as Slepian-Wolf, Wyner, Ahlswede-Körner, Wyner-Ziv and Berger-Yeung. Specifically, the achievable rate or rate-distortion region has been described by a first order information-theoretic functional of the source statistics in each of the above cases. ...

An Assessment of Evans' Unified Field Theory I

Evans developed a classical unified field theory of gravitation and electromagnetism on the background of a spacetime obeying a Riemann-Cartan geometry. This geometry can be characterized by an orthonormal coframe θ and a (metric compatible) Lorentz connection Γ . These two potentials yield the field strengths torsion T and curvature R . Evans tried to infuse electromagnetic properties into thi...

Orthogonal Sampling Formulas: A Unified Approach

This paper intends to serve as an educational introduction to sampling theory. Basically, sampling theory deals with the reconstruction of functions (signals) through their values (samples) on an appropriate sequence of points by means of sampling expansions involving these values. In order to obtain such sampling expansions in a unified way, we propose an inductive procedure leading to various...