Related papers: Rank one density property for a class of $M$-bases

In the early 1990s the works of Larson, Wogen and Argyros, Lambrou, Longstaff disclosed an example of a strong tridiagonal $M$-basis that was not rank one dense. Later Katavolos, Lambrou and Papadakis studied $k$ point density property of…

Inspired by the work of Borwein and Erdelyi \cite{BE1997JAMS} on generalizations of M\"{u}ntz's theorem, we investigate the properties of the system $\{x^{\lambda_n}\}_{n=1}^{\infty}$ in weighted $L^p (A)$ spaces, for $p\ge 1$, denoted by…

In this paper we give a method to associate a graph with an arbitrary density matrix referred to a standard orthonormal basis in the Hilbert space of a finite dimensional quantum system. We study the related issues like classification of…

Let $\mathcal{H}$ and $\mathcal{H}_0$ be Hilbert spaces and $\{A_n\}_n$ be a sequence of bounded linear operators from $\mathcal{H}$ to $\mathcal{H}_0$. The study frames for Hilbert spaces initiated the study of operators of the form…

We present a starting point for the search for a Lagrangian density for M-Theory using characteristic classes for flat foliations of bundles.

We provide a strengthened version of the famous Jakobson's theorem. Consider an interval map $f$ satisfying a summability condition. For a generic one-parameter family $f_t$ of maps with $f_0=f$, we prove that $t=0$ is a Lebesgue density…

It is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-$r$ minors have constant density. More precisely, the formulas are $\exists x_1 ... x_k \#y…

To understand sparse systems we must account for both strong local atom bonds and weak nonlocal van der Waals forces between atoms separated by empty space. A fully nonlocal functional form [H. Rydberg, B.I. Lundqvist, D.C. Langreth, and M.…

The usual examples of Bergman spaces consist of the closure of an algebra of holomorphic functions on a domain. One can also take the real part of such functions, but essentially one is looking at the same object. In this paper the author…

Given a graph $F$ and a positive integer $n$, the weak $F$-saturation number $\mathrm{wsat}(K_n,F)$ is the minimum number of edges in a graph $H$ on $n$ vertices such that the edges missing in $H$ can be added, one at a time, so that every…

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…

In this manuscript, we consider the extension of the Hilbert-Einstein action to analyze several interesting features of the theory. More specifically, the Lagrangian $f(R)$ is replaced by $f(R, L_m)$ in action, where $R$ is the Ricci…

In Ho, Russell, and Weiss, a Carleson measure criterion for admissibility of one-dimensional input elements with respect to diagonal semigroups is given. We extend their results from the Hilbert space situation $X=\ell_2$ and…

We generalize three main concepts of Gabor analysis for lattices to the setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's representation of the frame operator and Wexler-Raz biorthogonality relations. Utilizing the…

Fourth - order gravity theories have received much interest in recent years thanks to their ability to provide an accelerated cosmic expansion in a matter only universe. In these theories, the Lagrangian density of the gravitational field…

Three basic properties that standard graded artinian $k$-algebras may or may not enjoy are the Weak and Strong Lefschetz Properties and the Maximal Rank Property (respectively WLP, SLP, and MRP). In this paper we will assume that the base…

We consider extended slow-fast systems of N interacting diffusions. The typical behavior of the empirical density is described by a nonlinear McKean-Vlasov equation depending on , the scaling parameter separating the time scale of the slow…

Let $M$ be a random $m \times n$ matrix with binary entries and i.i.d. rows. The weight (i.e., number of ones) of a row has a specified probability distribution, with the row chosen uniformly at random given its weight. Let $N(n,m)$ denote…

Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…

We study the mass-richness relation using galaxy catalogues and images from the Sloan Digital Sky Survey. We use two independent methods, in the first one, we calibrate the scaling relation with weak-lensing mass estimates. In the second…