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This article is about finding the limit set for banded Toeplitz matrices. Our main result is a new approach to approximate the limit set Λ(b), where b is the symbol of the banded Toeplitz matrix. The new approach is geometrical and based on the formula Λ(b) = ∩ρ∊(0, ∞) sp T (bρ), where ρ is a scaling factor, i.e., bρ(t):= b(ρt), and sp(∙) denotes the spectrum. We show that the full intersection ca

Currently, local regulations governing hydrogen installations vary by geographical region and by country, leading to discrepancies in safety and separation distance requirements for similar hydrogen systems. This work carried out in the frame of IEA TCP H2 Task 43 (IEA TCP H2 2022) aims to provide an overview of various methodologies and recommendations established for risk management and conseque

This book attempts to reconstruct elementary physics in full compliance with reason, thus continuing the work of philosophers (experimental and mathematical) throughout the centuries. The unabridged Newton's mechanics is recovered, Gauss intuitions about relational electromagnetism are developed and completed and Schrödingers undulatory quantum theory is reproposed, unifying all three theories in

The symmetric Al-Salam-Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second-order difference operator on 2(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christiansen a

We study the spectral properties of a class of Sturm-Liouville type operators on the real line where the derivatives are replaced by a q-difference operator which has been introduced in the context of orthogonal polynomials. Using the relation of this operator to a direct integral of doubly-infinite Jacobi matrices, we construct examples for isolated pure point, dense pure point, purely absolutely

The Stieltjes-Wigert polynomials, which correspond to an indeterminate moment problem on the positive half-line, are eigenfunctions of a second order q-difference operator. We consider the orthogonality measures for which the difference operator is symmetric in the corresponding weighted L2-spaces. Under some additional assumptions these measures are exactly the solutions to the q-Pearson equation

We consider Jacobi matrices whose essential spectrum is a finite union of closed intervals. We focus on Szego{double acute}'s theorem, Jost solutions, and Szego{double acute} asymptotics for this situation. This announcement describes talks the authors gave at OPSFA 2007.

Classical graphical modeling of random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some coordinate processes of the multivariate stochastic process are unobserved, the local independence graph of the observed coordinate processes is a directed mixed graph (DMG). Tw

Let e ⊂ ℝ be a finite union of disjoint closed intervals. We study measures whose essential support is e and whose discrete eigenvalues obey a 1/2-power condition. We show that a Szego{double acute} condition is equivalent to (this includes prior results of Widom and Peherstorfer-Yuditskii). Using Remling's extension of the Denisov-Rakhmanov theorem and an analysis of Jost functions, we provide a

This is the first of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 1 contains most of the material on orthogonal polynomials, from the classical orthogonal polynomials of Hermite, Laguerre and Jacobi to the Askey–Wilson polynomials, which are the most general basic hypergeometric orthogonal polynomials. Separate chapter

Co- and post-translational modifications can significantly impact the structure, dynamics, and function of proteins. In this study, we investigate how N-terminal acetylation affects misfolding and self-assembly of the enzyme superoxide dismutase 1 (SOD1), implicated in amyotrophic lateral sclerosis (ALS). Studies of protein inclusions in patient samples and animal models have shown that wild-type

Background: Available fluid biomarkers, neuroimaging techniques, and clinical assessments may enhance prediction of conversion to secondary progressive multiple sclerosis (SPMS). Objectives: : To identify robust real-world predictors of MS progression in the literature. Methods: : A systematic review was conducted in EMBASE. A total of 20,338 MS patients from 64 eligible studies were included. A p