相关论文: From homogeneity to discrete homogeneity

In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some…

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…

A mostly expository account of old questions about the relationship between polyhedra and topological manifolds. Topics are old topological results, new gauge theory results (with speculations about next directions), and history of the…

A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play main role instead of thin or finite sets which removes some…

We propose continuum percolation theory to study homogenization problems of elliptic equations.Our aim is to improve and extend similar results that have been obtained for periodic domains using modeling for non-periodic domains with…

The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

This paper is my 2014 Cornell Senior Thesis, written under the supervision of R. Keith Dennis. It contains results on homogeneous covers and generating sequences of finite groups.

These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…

We investigate the homogeneity of topological subspaces of separable Hilbert space, akin to the spaces with all points rational or all points irrational, so-called Erd\H{o}s spaces. We provide a non-homogeneous example, that is based on one…

Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued…

This paper is devoted to the study the $m$-point homogeneity property and the point homogeneity degree for finite metric spaces. Since the vertex sets of regular polytopes, as well as of some their generalizations, are homogeneous, we pay…

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

We study possibilities for semantic and syntactic rigidity, i.e., the rigidity with respect to automorphism group and with respect to definable closure. Variations of rigidity and their degrees are studied in general case, for special…

This paper is devoted to the horizontal (``characteristic'') cohomology of systems of differential equations. Recent results on computing the horizontal cohomology via the compatibility complex are generalized. New results on the Vinogradov…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

We count integer points on bihomogeneous varieties using the Hardy-Littlewood method. The main novelty lies in using the structure of bihomogeneous equations to obtain asymptotics in generically fewer variables than would be necessary in…

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…

The transition from hard/soft turbulence to deterministic chaos in freely decaying fluid dynamics (incompressible and compressible) has been studied using the results of laboratory measurements and numerical simulations. The notion of…

Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…