Related papers: Sharp Elements and Apartness in Domains
We investigate local entropy theory, particularly the property of having completely positive entropy (CPE), from a descriptive set-theoretic point of view. We aim to determine descriptive complexity of different families of dynamical…
We study varieties with a term-definable poset structure, "po-groupoids". It is known that connected posets have the "strict refinement property" (SRP). In [arXiv:0808.1860v1 [math.LO]] it is proved that semidegenerate varieties with the…
We develop a constructive theory of continuous domains from the perspective of program extraction. Our goal that programs represent (provably correct) computation without witnesses of correctness is achieved by formulating correctness…
We develop two unfitted finite element methods for the Stokes equations using $H^{\text{div}}$-conforming finite elements. Both methods achieve optimal convergence for velocity, ensure pointwise divergence-free velocity fields, and produce…
This paper investigates the interplay between algebraic structure, topology, and differentiability in Clifford semigroups. The study is developed along three main themes. First, in the compact Hausdorff setting, we provide an explicit…
Differential calculus on discrete sets is developed in the spirit of noncommutative geometry. Any differential algebra on a discrete set can be regarded as a `reduction' of the `universal differential algebra' and this allows a systematic…
Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…
We derive an inequality for the linear entropy, that gives sharp bounds for all finite dimensional systems. The derivation is based on generalised Bloch decompositions and provides a strict improvement for the possible distribution of…
We prove that if $G$ is a noncompact connected real reductive linear Lie group, then any discrete subgroup of $G$ acting properly discontinuously and cocompactly on some homogeneous space $G/H$ of $G$ is quasi-isometrically embedded and…
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are…
Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the…
Suppose $Y$ is a continuum, $x\in Y$, and $X$ is the union of all nowhere dense subcontinua of $Y$ containing $x$. Suppose further that there exists $y\in Y$ such that every connected subset of $X$ limiting to $y$ is dense in $X$. And,…
This paper presents a pressure-robust and element-wise divergence-free nonconforming finite element method for the Stokes problem on curved domains. The discrete element is constructed by mapping the Fortin-Soulie element from a reference…
To test a possible relation between the topological entropy and the Arnold complexity, and to provide a non trivial example of a rational dynamical zeta function, we introduce a two-parameter family of two-dimensional discrete rational…
The ability to automatically discover interpretable mathematical models from data could forever change how we model soft matter systems. For convex discovery problems with a unique global minimum, model discovery is well-established. It…
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps the discrete velocity space onto the the discrete pressure…
Piecewise-linear (PL) Morse theory and discrete Morse theory are used in shape analysis tasks to investigate the topological features of discretized spaces. In spite of their common origin in smooth Morse theory, various notions of critical…
Exceptional points are universal level degeneracies induced by non-Hermiticity. Whereas past decades witnessed their new physics, the unified understanding has yet to be obtained. Here we present the complete classification of generic…
We study properties of strongly separately continuous mappings defined on subsets of products of topological spaces equipped with the topology of pointwise convergence. In particular, we give a necessary and sufficient condition for a…
Working in the soft-element (classical) viewpoint, we introduce \emph{soft bitopological groups}: soft groups endowed with two soft topologies such that the induced topologies on the set of soft elements make the soft-element group into a…