Related papers: Some remarks about homeomorphisms, "energy", and s…
In the last decade, an explosive attention has been paid to piezoelectric harvesters due to their flexibility in design and increasing need to small-scale energy generation. As a result, various energy review papers have been presented by…
Network reconstruction is a well-developed sub-field of network science, but it has only recently been applied to production networks, where nodes are firms and edges represent customer-supplier relationships. We review the literature that…
This is a short review, aimed at a general audience, of several current subjects of research in cosmology. The topics discussed include the cosmic microwave background (CMB), with particular emphasis on its relevance for testing inflation;…
This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques…
This paper presents a survey of recent and not so recent results concerning the study of smooth homeomorphisms of the circle with a finite number of non-flat critical points, an important topic in the area of One-dimensional Dynamics. We…
This paper is a survey dedicated to the analogy between the notions of {\it complexity} in theoretical computer science and {\it energy} in physics. This analogy is not metaphorical: I describe three precise mathematical contexts, suggested…
We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain…
Illuminating the nature of dark energy is one of the most important challenges in cosmology today. In this review I discuss several promising observational approaches to understanding dark energy, in the context of the recommendations by…
This paper is devoted to show the advantages of introducing a geometric viewpoint and a non extensive formulation in the description of apparently unrelated phenomena: combustion and earthquakes. Here, it is shown how the introduction of a…
This is a survey article to appear in the "Handbook on Teichmueller Theory".
The goal of these talks was to explain how cohomology and other tools of algebraic topology are seen through the lens of n-category theory. Special topics include nonabelian cohomology, Postnikov towers, the theory of "n-stuff", and…
The survey contains a brief description of the ideas, constructions, results, and prospects of the theory of hypergroups and generalized translation operators. Representations of hypergroups are considered, being treated as continuous…
In this text we expose basic cases of some fundamental ideas and methods of topology. Namely, of homotopy, degree, fundamental group, covering, Whitehead invariant, etc. This is done by considering the elementary example: closed polygonal…
We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.
These lectures were addressed to nonspecialists willing to learn some basic facts, approaches, tools and observational evidence which conform modern cosmology. The aim is also to try to complement the many excellent treatises that exists on…
The aim of this work is to describe the set of fixed point free homeomorphisms of the plane under certain expansive conditions.
In this paper the concept of a partial cone metric space is investigated, some continuity type theorems, and fixed point theorems of contractive mappings in this generalized setting are proved as well as some theorems related to topological…
This is an almost self-contained monograph (containing some new results) on left-orderable groups which mostly rely on dynamical and probabilistic aspects, but also on geometric, combinatorial, analytic, and topological ones. This new…
We provide justifications for two questions on special maps on subgroups of the reals. We will show that the questions can be treated from different points of view. We also discuss two versions of Anderson's Involution Conjecture.
Topological insulators are a new class of materials that have engendered considerable research interest among the condensed matter community owing primarily to their application prospects in quantum computations and spintronics. Many of the…