Related papers: Some remarks about homeomorphisms, "energy", and s…
A class of Cantor-type spaces and related geometric structures are discussed.
We review the problem of dark energy, including a survey of theoretical models and some aspects of numerical studies.
Based on a simple example, it is explained how the homological analysis may be applied for modeling of the electric circuits. The homological branch, mesh and nodal analyses are presented. Geometrical interpretations are given.
It has, quite recently, become fashionable to study a certain class of holographic-inspired models for the dark energy. These investigations have, indeed, managed to make some significant advances towards explaining the empirical data.…
This review on dark energy is intended for a wider audience, beginners as well as experts. It contains important notes on various aspects of dark energy and its alternatives. The section on Newtonian cosmology followed by heuristic…
This work presents a tentative discussion of certain aspects of energy behavior in the context of mathematical fluid dynamics. While some observations are made regarding certain patterns in energy behavior under particular conditions, the…
This abstract provides up-to-date insights into fusion (thermonuclear) research, detailing ongoing projects and planned devices. The document also explores alternative sources of energy, offering a comprehensive overview of the current…
The study of algebraic properties of groups of transformations of a manifold gives rise to an interplay between different areas of mathemathics such as topology, geometry, and dynamical systems. Especially, in this paper, we point out some…
These lectures aim to highlight the remarkable symbiosis that currently exists between the physics of the very small and the physics of the very large, using the unsolved puzzle of the nature of Dark Energy as a vehicle for so doing. The…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
In an introductory manner, the nature of dark energy is addressed, how it is observed and what further tests are needed to reconstruct its properties. Several theoretical approaches to dark energy will be discussed.
The purpose of this paper is to study how small orbits of periodic homemorphisms of spheres can be.
Let M be a closed simply connected 2n-dimensional manifold. The present paper is concerned with the cohomology of classifying spaces of connected groups of homeomorphisms of M.
The statistical tools of Complex Network Analysis are of great use to understand salient properties of complex systems, may these be natural or pertaining human engineered infrastructures. One of these that is receiving growing attention…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
We determine the homeomorphism type of the set of real points of a smooth projective toric surface. This note may serve as an expository introduction to some of the ideas and techniques in C. Delaunay's work on real toric varieties.
This paper is a survey about recent developments in the local entropy theory for topological dynamical systems and continuous group actions, with particular emphasis on the connections with other areas of dynamical systems and mathematics.
This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects.
A brief general picture of the world, european and italian energy situations is made, analyzing several different energy sources and paying attention to the relations energy-quality of life, energy-environment and energy-health. Then will…
We present mathematical details of several cosmological models, whereby the topological and the geometrical background will be emphasized.