Related papers: Divisorial Multiplicative Lattices
This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…
We describe the associative multilinear polynomial functions over commutative integral domains. This extends Marichal and Mathonet's result on infinite integral domains and provides a new proof of Andres's classification of two-element…
We prove that for any two lattices $L, M \subseteq \mathbb{R}^d$ of the same volume there exists a measurable, bounded, common fundamental domain of them. In other words, there exists a bounded measurable set $E \subseteq \mathbb{R}^d$ such…
We introduce and study a new class of integral domains which we call irreducible divisor pair domains (IDPDs). In particular, we show how IDPDs fit in with other classes of integral domains defined in terms of factorization conditions. For…
In this paper, we introduce the zero divisor graph of a multiplicative lattice. We provide a counter example to Beck's conjecture for multiplicative lattices. Further, we prove that Beck's conjecture is true for reduced multiplicative…
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
A novel basis of discrete analytic polynomials on a rhombic lattice is introduced and the associated convolution product is studied. A class of discrete analytic functions that are rational with respect to this product is also described.
Divisible residuated lattices are algebraic structures corresponding to a more comprehensive logic than Hajek's basic logic with an important significance in the study of fuzzy logic. The purpose of this paper is to investigate commutative…
We describe the spectrum structure for the restricted Dirichlet fractional Laplacian in multi-tubes, i.e. domains with cylindrical outlets to infinity. Some new effects in comparison with the local case are discovered. In this version,…
We prove the existence of two-dimensional good lattice points in thick multiplicative subgroups modulo $p$.
We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a,b in L.
We consider planar curved strictly convex domains with no or very weak smoothness assumptions and prove sharp bounds for square-functions associated to the lattice point discrepancy.
We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…
We derive determinant expressions for the partition functions of spin-k/2 vertex models on a finite square lattice with domain wall boundary conditions.
We prove some basic results on the dimension theory of algebraic stacks, and on the multiplicities of their irreducible components, for which we do not know a reference.
Coincidence Site Lattices (CSLs) are a well established tool in the theory of grain boundaries. For several lattices up to dimension $d=4$, the CSLs are known explicitly as well as their indices and multiplicity functions. Many of them…
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…
We extend the classical Titchmarsh theorems to the Fourier transform of two types of H\"older-Lipschitz functions - additive and multiplicative - defined on fundamental domains of lattices in $\mathbb{R}^d$. Our approach is based on…
Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for…
Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…