Related papers: A note on Gurzadyan theorem
We consider a new and simpler proof of an inequality of A.S. Gasparyan, which was originally derived in terms of complex algebraical objects --- multidimensional hyperdeterminants. Our proof is much simpler and use only standard technics…
The arguments surrounding the Galactic component of the cosmic rays, the energy budget, questions of composition, spectral features, anisotropy, sources etc, will be critically examined. We are moving into a new phase in the study of the…
Cosmology contributes a good deal to the investigation of variation of fundamental physical constants. High resolution data is available and allows for detailed analysis over cosmological distances and a multitude of methods were developed.…
A modest aim of this pedagogical presentation is to analyze, critically, certain fundamental physical concepts to illustrate the physical principles behind the special theory of relativity and, hence, to also illustrate the limitations of…
This thesis addresses two major problems in the philosophy of physics. The first is how to identify the minimal physical content of a theory; that is, what features of a theory are truly needed to make predictions, and what can be removed…
A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.
The $\Lambda$CDM cosmology passes demanding tests that establish it as a good approximation to reality. The theory is incomplete, of course, and open issues are being examined in active research programs. I offer a review of less widely…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
A description of physical reality in which wholeness is the foundation is discussed along with the motivation for such an attempt. As a possible mathematical framework within which a physical theory based on wholeness may be expressed,…
The purpose of this lecture is to describe the KAM theorem in its most basic form and to give a complete and detailed proof. This proof essentially follows the traditional lines laid out by the inventors of this theory, and the emphasis is…
We present an educational proposal which aims to illustrate the elegant, refined and coherent physics contained in Thermodynamics, through a path which assigns to the microscopic description of the physical systems a constantly privileged…
This text aims at discussing the relations between the cosmic acceleration and the theory of gravitation and more generally with the hypotheses underlying the construction of our cosmological model, such as the validity of general…
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…
In a present note we give a new proof of Etingof-Kazhdan quantization theorem.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.
The $\Lambda$CDM cosmology passes demanding tests that establish it as a good approximation to reality, but it could be improved. I present a list of possibly interesting and less well explored things that might yield hints to a better…
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
An overview is given of the current status of the theory and observations of the acceleration of the expansion of the observable part of the Universe. Contents 1. Historical Introduction 2. Friedmann equations and cosmological acceleration…