Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions

In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as “quasi-parabolic.” This is the class of composition operators on <em>H</em><sup>2</sup> with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form <em>φ</em>(<em>z</em>)=<em>z</em>+<em>ψ</em>(<em>z</em>), where <em>ψ</em>∈<em>H</em><sup>∞</sup>(<em>H</em>) and ℑ(<em>ψ</em>(<em>z</em>))><em>?</em>>0. We especially examine the case where <em>ψ</em> is discontinuous at infinity. A new method is devised to show that this type of composition operator fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra.     

The generalized trust region subproblem: solution complexity and convex hull results

Mathematical Programming - We consider the generalized trust region subproblem (GTRS) of minimizing a nonconvex quadratic objective over a nonconvex quadratic constraint. A lifting of this...     

A methodology to select suppliers to increase sustainability within supply chains

Central European Journal of Operations Research - Sustainability practice within supply chains remains in an early development phase. Enterprises still need tools that support the integration of...     

Random walk on a disordered directed Bethe lattice

The random walk of a particle on a directed Bethe lattice of constant coordinance<i>Z</i> is examined in the case of random hopping rates. As a result, the higher the coordinance, the narrower the regions of anomalous drift and diffusion. The annealed and quenched mean square dispersions are calculated in all dynamical phases. In opposition to the one-dimensional (<i>Z</i>=2) case, the annealed and quenched mean quadratic dispersions are shown to be identical in all phases.We shall employ indifferently the expressions Bethe lattice or infinite Cayley tree to denote an infinite ramified lattice of constant coordinance<i>Z</i>.<sup>(4, 5)</sup>     

Quantum-confined electronic states in atomically well-defined graphene nanostructures

Despite the enormous interest in the properties of graphene and the potential of graphene nanostructures in electronic applications, the study of quantum-confined states in atomically well-defined graphene nanostructures remains an experimental challenge. Here, we study graphene quantum dots (GQDs) with well-defined edges in the zigzag direction, grown by chemical vapor deposition on an Ir(111) substrate by low-temperature scanning tunneling microscopy and spectroscopy. We measure the atomic structure and local density of states of individual GQDs as a function of their size and shape in the range from a couple of nanometers up to ca. 20 nm. The results can be quantitatively modeled by a relativistic wave equation and atomistic tight-binding calculations. The observed states are analogous to the solutions of the textbook "particle-in-a-box" problem applied to relativistic massless fermions.     

Equilibrium studies of mercury(II) complexes with penicillamine

A solid-phase microextraction method coupled with a flame photometric detector was developed for the analysis of organophosphorus pesticides in water. Two kinds of fiber (100 mum polydimethyl siloxane (PDMS) and 85 mum polyacrylate (PA) fibers) were used and compared. Parameters that may affect the extraction, such as the duration of absorption and desorption, temperature of absorption, ionic strength, elutropic strength, and concentration of humic acid were investigated. Higher sensitivity and lower detection limits were achieved using a PA fiber than using a PDMS fiber. The detection limit is less than 0.3 mug l(-1) for most of the analytes, except for mevinphos (420 mug l(-1)). The precision is better than 9%.     

A Counterexample on Sample-Path Optimality in Stable Markov Decision Chains with the Average Reward Criterion

This note deals with Markov decision chains evolving on a denumerable state space. Under standard continuity-compactness requirements, an explicit example is provided to show that, with respect to a strong sample-path average reward criterion, the Lyapunov function condition does not ensure the existence of an optimal stationary policy.     

A Lyusternik–Graves theorem for the proximal point method

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion <em>y</em>∈<em>T</em>(<em>x</em>), where <em>y</em> is a perturbation element near 0 and <em>T</em> is a set-valued mapping acting from a Banach space <em>X</em> to a Banach space <em>Y</em> which is metrically regular around some point <span class="a-plus-plus inline-equation id-i-eq1"> <span class="a-plus-plus equation-source format-t-e-x">$({\bar{x}},0)$</span> </span> in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove that they inherit the regularity properties of <em>T</em>, and vice versa. We analyze the cases when the mapping <em>T</em> is metrically regular and strongly regular.     

Biamperometric neutralisation titrations in non-aqueous solvents applying tin electrode pair for the end-point detection

Summary Tertiary amines and salts of organic acids in acetic anhydride with 5% of acetic acid were titrated applying a biamperometric indicating system consisting of a polarised or unpolarised pair of tin electrodes by means of 0.1 N perchloric acid in glacial acetic acid. Amounts of 15.4–29.8 mg were analysed with average deviations of <0.6%, the results obtained being in a good agreement with those of potentiometry. The biamperometric end-point detection using an indicating system of polarised pair of tin electrodes can be applied for coulometric determinations of these bases with satisfying accuracy. By means of anodic generation of hydrogen ions in the presence of hydroquinone amounts of 0.5–1.0 mg were titrated with average deviations of < 1.3%. The results obtained were compared with those obtained of catalytic thermometric and photometric titrations.<hr><blockquote>Biamperometrische Neutralisationstitrationen in nichtwä<img src="/content/g8j55175j018654q/xhuge946.gif" alt="beta" align="MIDDLE" BORDER="0">rigen Lösungsmitteln unter Anwendung eines Zinn-Elektrodenpaares als Indicatorsystem</blockquote><blockquote>Zusammenfassung Tertiäre Amine und Salze organischer Säuren werden in Acetanhydrid mit 5% Essigsäure durch Titration mit einer 0,1 N Lösung von Perchlorsäure in Essigsäure bestimmt. Das verwendete biamperometrische Indicatorsystem besteht aus einem Paar polarisierter oder nichtpolarisierter Zinnelektroden. Mengen von 15,4–29,8 mg wurden mit einer mittleren Abweichung von <0,6% analysiert. Die Ergebnisse stimmen gut mit denen von potentiometrischen Titrationen überein. Die biamperometrische Endpunkttechnik mit polarisierten Zinnelektroden kann für coulometrische Bestimmungen dieser Basen mit zufriedenstellender Genauigkeit benutzt werden. Durch anodische Erzeugung von Wasserstoffionen in Gegenwart von Hydrochinon wurden Mengen von 0,5–1,0 mg mit einer mittleren Abweichung von < 1,3% titriert. Die Ergebnisse wurden mit denen von katalytisch-thermometrischen und photometrischen Titrationen verglichen.</blockquote><blockquote></blockquote>