相关论文: From homogeneity to discrete homogeneity
We consider problems involving rich homotheties in a set S of n points in the plane (that is, homotheties that map many points of S to other points of S). By reducing these problems to incidence problems involving points and lines in R^3,…
This paper presents a discrete homotopy theory and a discrete homology theory for finite posets. In particular, the discrete and classical homotopy groups of finite posets are always isomorphic. Moreover, this discrete homology theory is…
This paper defines homology in homotopy type theory, in the process stable homotopy groups are also defined. Previous research in synthetic homotopy theory is relied on, in particular the definition of cohomology. This work lays the…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
The purpose of this article is to give an exposition of topological properties of spaces of homomorphisms from certain finitely generated discrete groups to Lie groups $G$, and to describe their connections to classical representation…
It is shown that a connected non-compact metrizable manifold of dimension $\ge 2$ is strongly discrete homogeneous if and only if it has one end (in the sense of Freudenthal compactification).
Cellular heterogeneity is an immanent property of biological systems that covers very different aspects of life ranging from genetic diversity to cell-to-cell variability driven by stochastic molecular interactions, and noise induced cell…
Our original results refer to multivariate recurrences: discrete multitime diagonal recurrence, bivariate recurrence, trivariate recurrence, solutions tailored to particular situations, second order multivariate recurrences, characteristic…
In this paper we present an overview of results for discrete trigonometric and hyperbolic systems. These systems are discrete analogues of trigonometric and hyperbolic linear Hamiltonian systems. We show results which can be viewed as…
We report on recent developments in the dynamics and rigidity of infinite-volume homogeneous spaces, viewed through the lens of circles. By addressing four natural questions about circle packings, we highlight the interplay between…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
We present a new density functional, which is the result of a natural evolution and improvement of previous density functional theories for liquid helium. We focus on the key ingredients of the theory, showing how they determine important…
This is a survey on recent results regarding singularities that occur on higher dimensional stable varieties.
We analyze the relationship between Hausdorffness and homogeneity in the frame of manifolds, not confined to be Hausdorff. We exhibit examples of homogeneous non-Hausdorff manifolds and prove that a Lindel\"of homogeneous manifold is…
We perform the homogenization process avoiding the necessity of testing the weak formulation of the initial and homogenized systems by corresponding weak solutions. We show that the stress tensor for homogenized problem depends on the…
Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depend on the context and…
Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.
In a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
A structure is called homogeneous if every isomorphism between finite substructures of the structure extends to an automorphism of the structure. Recently, P. J. Cameron and J. Ne\v{s}et\v{r}il introduced a relaxed version of homogeneity:…