Related papers: A note on Gurzadyan theorem
The purpose of this paper is to expound and clarify the mathematics and explanations commonly employed in certain notable areas of astronomy and astrophysics. The first section concentrates upon the mathematics employed to represent and…
We will present several examples in which ideas from ergodic theory can be useful to study some problems in arithmetic and algebraic geometry.
We lay the groundwork for a formal framework that studies scientific theories and can serve as a unified foundation for the different theories within physics. We define a scientific theory as a set of verifiable statements, assertions that…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
The parameters of any model that satisfies the cosmological principle (the universe is homogeneous and isotropic on large scale), can be expressed through cosmographic parameters. In this paper, we perform this procedure for the Cardassian…
We show a possibility to apply certain philosophical concepts to the analysis of concrete mathematical structures. Such application gives a clear justification of topological and geometric properties of considered mathematical objects.
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
The aim of this note is to show that the "usual" proof of the Maschke Theorem in the case of a real and complex field can not be generalized at least to the case of a field of rational functions on a non-singular curve.
An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…
We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.
This is an overview of higher structural constructions in physics. The main motivations of our current attempt are as follows: (i) to provide a brief introduction to derived algebraic geometry, (ii) to understand how derived objects…
The formula for dark energy density derived by Gurzadyan and Xue provides a value of density parameter of dark energy in remarkable agreement with current cosmological datasets, unlike numerous phenomenological dark energy scenarios where…
The expansion of the Universe is the basis of modern cosmology. This chapter outlines the theory behind the expansion of the universe, including the cosmological principle, distances, velocities, and accelerations. We provide basic…
We note that in general there exist two basic aspects in any branch of physics, including cosmology - one dealing with the attributes of basic constituents and forces of nature, the other dealing with how structures arise from them and how…
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so…
The purpose of this paper is to introduce a new way to inquire the quantum cosmology for a certain gravitational theory. Normally, the quantum cosmological model is introduced as the minisuperspace theory which is obtained by reducing the…
This is a pedagogical introduction to original Kaluza-Klein theory and its salient features. Most of the technical calculations are given in detail and the nature of gravitons is discussed.
This thesis aims to review the cosmological mass function problem, both from the theoretical and the observational point of view, and to present a new mass function theory, based on realistic approximations for the dynamics of gravitational…
I give a concise introduction into high energy cosmic ray physics, including also few related aspects of high energy gamma-ray and neutrino astrophysics. The main emphasis is placed on astrophysical questions, and the level of the…
After a short history of the $\Lambda$-term it is explained why the (effective) cosmological constant is expected to obtain contributions from short-distance physics, corresponding to an energy at least as large as the Fermi scale. The…