Related papers: The Euclidean Universe
Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
In this work we propose an alternative scheme for an Emergent Universe scenario where the universe is initially in a static state supported by a scalar field located in a false vacuum. The universe begins to evolve when, by quantum…
We provide the full classification of equidistant decomposition of a two-dimensional Euclidean plane and a two-dimensional sphere.
We use Herbrand's theorem to give a new proof that Euclid's parallel axiom is not derivable from the other axioms of first-order Euclidean geometry. Previous proofs involve constructing models of non-Euclidean geometry. This proof uses a…
Non-Euclidean method of the generalized geometry construction is considered. According to this approach any generalized geometry is obtained as a result of deformation of the proper Euclidean geometry. The method may be applied for…
The article presents a new approach to euclidean plane geometry based on projective geometric algebra (PGA). It is designed for anyone with an interest in plane geometry, or who wishes to familiarize themselves with PGA. After a brief…
A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new…
In this article, I develop an elementary system of axioms for Euclidean geometry. On one hand, the system is based on the symmetry principles which express our a priori ignorant approach to space: all places are the same to us (the…
The search for new computational machines beyond the traditional von Neumann architecture has given rise to a modern area of nonlinear science -- development of unconventional computing -- requiring the efforts of mathematicians, physicists…
Universe structure emerges in the unreduced, complex-dynamical interaction process with the simplest initial configuration (two attracting homogeneous fields). The unreduced interaction analysis avoiding any perturbative model gives…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
An approach to modelling the universe based on the requisites of gravitational energy. This model is explained as it relates to the stages of the universal life cycle and the continued existence of the universe as it is known today. The…
The large-scale structure of the Universe is well approximated by the Friedmann equations, parametrized by several energy densities which can be observationally inferred. A natural question to ask is: How different would the Universe be if…
A new class of self-similar ordered structures with non-crystallographic point symmetries is presented. Each of these structures, named superquasicrystals, is given as a section of a higher-dimensional "crystal" with recursive superlattice…
This text consists on a series of introductory lectures on cosmology for mathematicians and physicists who are not specialized on the subject.
Assuming a cellular structure for the space-time, we propose a model in which the expansion of the universe is understood as a decrumpling process, much like the one we know from polymeric surfaces. The dimension of space is then a…
We study the statistical mechanics of the early radiation dominated universe in the context of a generalized uncertainty principle which supports the existence of a minimal length scale. Utilizing the resultant modified thermodynamical…
In this review, the formation, evolution, and decay of the large-scale structure of the Universe is discussed in the context of observational data, numerical simulations, and the Cosmological Standard Model (CSM). Problems concerning…
We study the Wasserstein space (with quadratic cost) of Euclidean spaces as an intrinsic metric space. In particular we compute their isometry groups. Surprisingly, in the case of the line, there exists a (unique) "exotic" isometric flow.…