Related papers: Homogeneity
Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In this study we show that any outcome of…
In this paper we prove a general homogenization result for monotone parabolic problems with an arbitrary number of microscopic scales in space as well as in time, where the scale functions are not necessarily powers of epsilon. The main…
We will generalize the concept of aggregation function for mathematical structures as a certain function between quantales. In fact, these functions turn to be exactly the lax morphism of quantales. This provides a global framework for the…
The basic notions related to coherence phenomena are formulated. Two types of coherence are described, state coherence and transition coherence. Useful characteristics for quantifying coherence are defined, such as coherence functions,…
Many recursive functions can be defined elegantly as the unique homomorphisms, between two algebras, two coalgebras, or one each, that are induced by some universal property of a distinguished structure. Besides the well-known applications…
We study the behavior of various set-functions under holomorphic motions. We show that, under such deformations, logarithmic capacity varies continuously, while analytic capacity may not.
It is proved that harmonic functions are characterized by harmonicity of their spherical means, for which purpose the iterated spherical means are used. The similar characterization of solutions to the modified Helmholtz equation…
Agglomeration economies drive urban growth at different spatial scales by enabling productivity gains, knowledge spillovers, and shared inputs among proximate firms and amenities. To develop a unified science of cities it is thus important…
The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…
This work deals with the homogenization of functionals with linear growth in the context of $\mathcal{A}$-quasiconvexity. A representation theorem is proved, where the new integrand function is obtained by solving a cell problem where the…
This paper studies the average gradient over the local region of a function and constructs the homogenization function of a function. It is found that there are some good properties about the local extreme points and the global extreme…
Solutions of nonlinear functional equations are generally not expressed as a finite number of combinations and compositions of elementary and known special functions. One of the approaches to study them is, firstly, to find formal solutions…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
Linear fractional transformations on the extended complex plane are classified up to topological conjugacy. Recall that two transformations f and g are called topologically conjugate if there exists a homeomorphism h such that hg=fh.
We apply a probabilistic approach to study the computational complexity of analog computers which solve linear programming problems. We analyze numerically various ensembles of linear programming problems and obtain, for each of these…
It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in…
We characterize cohomogeneity one manifolds and homogeneous spaces with a compact Lie group action admitting an invariant metric with positive scalar curvature.
We study the homogeneous involutions on the full square matrices over an algebraically closed field endowed with a division grading with commutative support. We obtain the classification of the isomorphism and equivalence classes for the…
Feature generation is an open topic of investigation in graph machine learning. In this paper, we study the use of graph homomorphism density features as a scalable alternative to homomorphism numbers which retain similar theoretical…
The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main…