Related papers: Attainable numbers and the Lagrange spectrum
It is argued that every measurement is made in a certain scale. The scale in which present measuments are made is called present scale which gives present knowledge. Quantities at the limits to present measurement may be observables in…
We construct the potentials that describe the spectrum and decay of electromagnetic bound states of hadrons, and are consistent with ChPT. These potentials satisfy the matching condition which enables one to express the parameters of the…
It is known that a $2\times 2$ quaternionic matrix has one, two or an infinite number of left eigenvalues, but the available algebraic proofs are difficult to generalize to higher orders. In this paper a different point of view is adopted…
The Harper equation describes an electron on a 2D lattice in magnetic field and a particle on a 1D lattice in a periodic potential, in general, incommensurate with the lattice potential. We find the distribution of the roots of Bethe ansatz…
$\lambda$-Scale is an enrichment of lambda calculus which is adapted to emergent algebras. It can be used therefore in metric spaces with dilations.
Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts lattice points in polytopes and we deduce an effective algorithm in order to compute…
In this article we give a survey on open problems and conjectures concerning L^2-invariants. We cover the whole portfolio and not only certain aspects as they are considered in the previous more specialized (and within their scope more…
The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…
The distance of a binary operation from being associative can be "measured" by its associative spectrum, an appropriate sequence of positive integers. Particular instances and general properties of associative spectra are studied.
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
We call an $\alpha \in \mathbb{R}$ regainingly approximable if there exists a computable nondecreasing sequence $(a_n)_n$ of rational numbers converging to $\alpha$ with $\alpha - a_n < 2^{-n}$ for infinitely many $n \in \mathbb{N}$. We…
We study the relation between the spectrum of a self-adjoint operator and its multidimensional numerical range. It turns out that the multidimensional numerical range is a convex set whose extreme points are sequences of eigenvalues of the…
Recent results in light hadron spectroscopy are reviewed. Attention is given to the requirements of precision determinations in lattice gauge theory. Different methods for extracting the running coupling constant $\alpha_S$ are compared.…
In this paper we consider the one-dimensional Schrodinger operator L(q) with a periodic real and locally integrable potential q. We study the bands and gaps in the spectrum and explicitly write out the first and second terms of the…
We introduce the notion of almost realizability, an arithmetic generalization of realizability for integer sequences, which is the property of counting periodic points for some map. We characterize the intersection between the set of…
Recent developments in lattice QCD calculations of the light hadron spectrum and quark masses are reviewed.
The location and width of the time window in which a sequence of processes converges to equilibrum are given under conditions of exponential convergence. The location depends on the side: the left-window and right window cutoffs may have…
A complete characterization of near subnormality for bilateral weighted shifts is obtained. As an application of the main results, many new answers to the Hilbert space problem 160 are presented at the end of the paper.