Given a finite set of points in Rn and a radius parameter, we study the Čech, Delaunay–Čech, Delaunay (or alpha), and Wrap complexes in the light of generalized discrete Morse theory. Establishing the Čech and Delaunay complexes as sublevel sets of generalized discrete Morse functions, we prove that the four complexes are simple-homotopy equivalent by a sequence of simplicial collapses, which a...

We exhibit a countably infinite family of simple, separable, nuclear, and mutually non-isomorphic C-algebras which agree on K-theory and traces. The algebras do not absorb the Jiang-Su algebra Z tensorially, answering a question of N. C. Phillips. They are also pairwise shape and Morita equivalent, confirming a conjecture from our earlier work. The distinguishing invariant is the radius of comp...

Radiometry is the measurement of radiant electromagnetic energy, especially that associated with the IR spectrum. It can be more simply defined as an absolute measurement of radiant flux. The typical unit of measure for imaging radiometry is radiance, which is expressed in units of Watts/(sr-cm2). (The abbreviation “sr” stands for steradian; a non-dimensional geometric ratio expressing the soli...

We present a novel relativistic density-functional approach to modeling quark matter with mechanism mimic confinement. The quasiparticle treatment of quarks provides their suppression due large selfenergy already at the mean-field level. demonstrate that our is equivalent chiral model medium-dependent couplings. dynamical restoration symmetry ensured by construction density functional. Suppleme...

We consider the topological and geometric reconstruction of a geodesic subspace [Formula: see text] both from Čech Vietoris-Rips filtrations on finite, Hausdorff-close, Euclidean sample. Our technique leverages intrinsic length metric induced by geodesics subspace. distortion convexity radius as our sampling parameters for problem. For with finite positive radius, we guarantee correct computati...

This paper characterizes when a Delone setX in Rn is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the hetereogeneity of their distribution. For a Delone set X, let NX(T ) count the number of translation-inequivalent patches of radius T in X and let MX(T ) be the minimum radius such that every closed ball of radius MX(T ) contains the center ...

The bulk composition of an exoplanet is commonly inferred from its average density. For small planets, however, the average density is not unique within the range of compositions. Variations of a number of important planetary parameters—which are difficult or impossible to constrain from measurements alone—produce planets with the same average densities but widely varying bulk compositions. We ...

Bohr’s theorem ([10]) states that analytic functions bounded by 1 in the unit disk have power series ∑ anz n such that ∑ |an||z| < 1 in the disk of radius 1/3 (the so-called Bohr radius.) On the other hand, it is known that there is no such Bohr phenomenon in Hardy spaces with the usual norm, although it is possible to build equivalent norms for which a Bohr phenomenon does occur! In this paper...