Related papers: Attainable numbers and the Lagrange spectrum
Contrary to popular misconception, the question in the title is far from simple. It involves sets of numbers on the first level, sets of sets of numbers on the second level, and so on, endlessly. The infinite hierarchy of the levels…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
Recurrent representations for an electron transmission and reflection amplitudes for a one-dimensional chain are obtained. The linear differential equations for scattering amplitudes of an arbitrary potential are found.
We extend a recent breakthrough result relating expectation thresholds and actual thresholds to include some rainbow versions.
We give some new bounds for the clique and independence numbers of a graph in terms of its eigenvalues.
Some outstanding issues in high energy scattering are discussed. Particular emphasis is placed on recent developments concerning the next-to-leading log corrections to the BFKL equation.
The validity range of the time-honored effective range expansion can be very limited due to the presence of a left-hand cut close to the two-particle threshold. Such a left-hand cut arises in the two-particle interaction involving a light…
We discuss the distribution of the spectrum at infinity of a convenient and nondegenerate Laurent polynomial (singularity side) and the distribution of the Newton spectrum of a polytope (Ehrhart theory side). To this end, we study a hard…
We obtain sequences of inclusion sets for the spectrum, essential spectrum, and pseudospectrum of banded, in general non-normal, matrices of finite or infinite size. Each inclusion set is the union of the pseudospectra of certain…
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
Eigenvalue estimates that are optimal in some sense have self-evident appeal and leave estimators with a sense of virtue and economy. So, it is natural that ongoing searches for effective strategies for difficult tasks such as estimating…
Observability inequalities on lattice points are established for non-negative solutions of the heat equation with potentials in the whole space. As applications, some controllability results of heat equations are derived by the…
Let $G$ be a semidirect product of a simply connected nilpotent Lie group and $\R$. For a left invariant control system on $G$ with a convex cone as a control domain, it is proved that the attainable sets coincides with a "halfspace" if the…
In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…
The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-theoretic properties, but also have numerous connections to geometry and topology. We discuss basic properties of these integer-valued invariants, as…
We provide an introductory review of some topics in spectral theory of Laplacians on metric graphs. We focus on three different aspects: the trace formula, the self-adjointness problem and connections between Laplacians on metric graphs and…
In recent literature there are an increasing number of papers where the forbidden sets of difference equations are computed. We review and complete different attempts to describe the forbidden set and propose new perspectives for further…
We relate scattering amplitudes in particle physics to maximum likelihood estimation for discrete models in algebraic statistics. The scattering potential plays the role of the log-likelihood function, and its critical points are solutions…
We obtain spectral inequalities and asymptotic formulae for the discrete spectrum of the operator $\frac12\, \log(-\Delta)$ in an open set $\Omega\in\Bbb R^d$, $d\ge2$, of finite measure with Dirichlet boundary conditions. We also derive…
We continue the investigation on the spectrum of operators arising from the discretization of partial differential equations. In this paper we consider a three field formulation recently introduced for the finite element least-squares…