Related papers: Atomic density of arithmetical congruence monoids
Let $R$ be a local ring and $M,N$ be finitely generated $R$-modules. The complexity of $(M,N)$, denoted by $\cxx RMN$, measures the polynomial growth rate of the number of generators of the modules $\Ext nRMN$. In this paper we study…
We describe how one can explicitly obtain all atoms of an arbitrary root-closed monoid, whose quotient group is isomorphic to $\mathbb{Z}^2$. For this purpose, we solve this task for three special types of such monoids in Theorems 5 and 6,…
We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes, 2) absolutely irreducible elements that are not prime, and…
We show that there are sets of integers with asymptotic density arbitrarily close to 1 in which there is no solution to the equation ab=c, with a,b,c in the set. We also consider some natural generalizations, as well as a specific numerical…
We consider the set of monic irreducible polynomials $P$ over a finite field $\mathbb{F}_q$ such that the multiplicative order modulo $P$ of some a in $\mathbb{F}_q(T)$ is divisible by a fixed positive integer $d$. Call $R_q(a,d)$ this set.…
We propose and demonstrate an experimental method to measure by absorption imaging the size and local column density of a cloud of atoms, even when its smallest dimension is smaller than the resolution of the imaging system. To do this, we…
A broad array of interstellar absorption features that appear in the ultraviolet spectra of bright sources allows us to measure the abundances and ionization states of many important heavy elements that exist as free atoms in the…
Given a complete noncompact Riemannian manifold $N^n$, we investigate whether the set of bounded Sobolev maps $(W^{1, p} \cap L^\infty) (Q^m; N^n)$ on the cube $Q^m$ is strongly dense in the Sobolev space $W^{1, p} (Q^m; N^n)$ for $1 \le p…
A numerical set $T$ is a subset of $\mathbb N_0$ that contains $0$ and has finite complement. The atom monoid of $T$ is the set of $x \in \mathbb N_0$ such that $x+T \subseteq T$. Marzuola and Miller introduced the anti-atom problem: how…
We consider a piecewise smooth expanding map of the interval possessing two invariant subsets of positive Lebesgue measure and exactly two ergodic absolutely continuous invariant probability measures (ACIMs). When this system is perturbed…
This paper proposes a formalization of the class of sentences quantified by \textit{most}, which is also interpreted as {\em proportion of} or {\em majority of} depending on the domain of discourse. We consider sentences of the form…
A commutative cancellative monoid is atomic if every non-invertible element factors into irreducibles (also called atoms), while an integral domain is atomic if its multiplicative monoid is atomic. Back in the eighties, Gilmer posed the…
We investigate the mass fractions and in-medium properties of heavy nuclei in stellar matter at characteristic densities and temperatures for supernova (SN) explosions. The individual nuclei are described within the compressible liquid-drop…
The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We…
It is shown that when a magnetic field is used to support neutral atoms against the gravitational force mg, the total curvature of the field magnitude B must be larger than m^2 g^2/(2 \mu^2 B), where mu is the magnetic moment of the atoms.…
Focusing of atoms with light potentials is studied. In particular, we consider strongly confined, cylindrical symmetric potential, and demonstrate their applications in both red and blue-detuned focusing of atoms. We also study the…
Nuggets---very large stable bound objects arising in the presence of a sufficiently attractive and long-range force and in the absence of a dark Coulomb force---are a smoking gun signature for Asymmetric Dark Matter (ADM). The cosmology of…
Let $\mathbb{A}$ denote the Alexandroff-Urysohn double arrow space. We prove the following results: (a) $\mathbb{A}\times{}^\omega{2}$ is not countable dense homogeneous; (b) ${}^{\omega}{\mathbb{A}}$ is not countable dense homogeneous; (c)…
In this paper, we use density functional theory to calculate the electronic structure and properties of 46 metallic and semi-metallic elements. The binding energy and bond charge model (BBC) model is combined with the tight binding and…
For A a separable unital C*-algebra and M a separable McDuff II_1-factor, we show that the space Hom_w(A,M) of weak approximate unitary equivalence classes of unital *-homomorphisms A \rightarrow M may be considered as a closed, bounded,…