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We give formulas for the density of visible points of several families of planar quasicrystals, which include the Ammann-Beenker point set and vertex sets of some rhombic Penrose tilings. These densities are used in order to calculate the…

This paper investigates regularity properties of two non-negative sparsity sets: non-negative sparse vectors, and low-rank positive semi-definite matrices. Novel formulae for their Mordukhovich normal cones are given and used to formulate…

In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…

We estimate the number of composite elements in the $n$-th grade of the group semiring of finite boolean groups. In view of this result we may conjecture that the composites in the semiring of finite groups are thinly dispersed.

We formulate some problems and conjectures about semigroups of rational functions under composition. The considered problems arise in different contexts, but most of them are united by a certain relationship to the concept of amenability.

To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…

Abstract polytopes generalize the face lattice of convex polytopes. A polytope is semiregular if its facets are regular and its automorphism group acts transitively on its vertices. In this paper we construct semiregular, facet-transitive…

We introduce analysis of orbital parities as a concept and a tool for understanding radicals. Based on fundamental reduced one- and two-electron density matrices, our approach allows us to evaluate a total measure of radical character and…

We consider various decision problems for automatic semigroups, which involve the provision of an automatic structure as part of the problem instance. With mild restrictions on the automatic structure, which seem to be necessary to make the…

This paper is the third in a series of manuscripts that examine the combinatorics of the Kunz polyhedron $P_m$, whose positive integer points are in bijection with numerical semigroups (cofinite subsemigroups of $\mathbb Z_{\ge 0}$) whose…

After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…

We address a problem posed in [1] by demonstrating through an example that, in the absence of separability, the property of sequential cone compactness does not generally imply cone compactness.

A numerical semigroup is a cofinite subset of $\mathbb Z_{\ge 0}$ containing $0$ and closed under addition. Each numerical semigroup $S$ with smallest positive element $m$ corresponds to an integer point in the Kunz cone $\mathcal C_m…

The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this…

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection…

Recall that an element $x\in R$ is {\bf complemented} if there is a $y\in R$ such that $xy = 0$ and $x + y \in {\rm reg}(R)$. In a recent article [1], the authors investigated those rings for which every non-nilpotent element is…

This paper is concerned with the density of rational points of bounded height lying on a variety defined by an integral quadratic form Q. In the case of four variables, we give an estimate that does not depend on the coefficients of Q. For…

Let $R$ be a polynomial ring over a field. We describe the extremal rays and the facets of the cone of local cohomology tables of finitely generated graded $R$-modules of dimension at most two. Moreover, we show that any point inside the…

Using elementary duality properties of positive semidefinite moment matrices and polynomial sum-of-squares decompositions, we prove that the convex hull of rationally parameterized algebraic varieties is semidefinite representable (that is,…

In this paper, we discuss characterizations of common fixed points of commutative semigroups of nonexpansive mappings. We next prove convergence theorems to a common fixed point. We finally discuss nonexpansive retractions onto the set of…