Hankel and Loewner matrices

Mutual relations between the Hankel, Toeplitz, Bézout, and Loewner matrices as well as further connections to rational interpolation and projective geometry are investigated.     

Contributions to the Gaussian Line Broadening of the Proxyl Spin Probe EPR Spectrum Due to Magnetic-Field Modulation and Unresolved Proton Hyperfine Structure

A simple expression is derived to compute the total Gaussian linewidth of a Voigt line that is broadened by sinusoidal magnetic-field modulation as follows: ΔH^G_pp(H_m)²= ΔH^G_pp(0)²+ κ²H²_m, where ΔH^G_pp(H_m) is the Gaussian linewidth observed with an modulation amplitudeH_m/2 and ΔH^G_pp(0) is the Gaussian linewidth in the limit of zero modulation. The field modulation contributes an additional Gaussian broadening of κH_m, where κ is a constant, which adds in quadrature to ΔH^G_pp(0) to give the total Gaussian linewidth. Denoting the overall linewidth of the Voigt line in the absence of modulation broadening by ΔH⁰_pp(0), it is shown, both by analytical means and by spectral simulation, that the constant κ is equal to 1/2 in the limit ofH_m ΔH⁰_pp(0); however, using values ofH_mas large as ΔH⁰_pp(0) leads to only minor departures from κ = 1/2. The formulation is valid both for Lorentzian and Voigt lines and is tested for 2,2,5,5-tetramethylpyrrolidin-1-oxyl-3-carboxylic acid (3-carboxy proxyl) in CCl₄and in aqueous buffer. This spin probe was studied because the proxyl group is the only major spin-probe moiety whose Gaussian linewidth had not been characterized in the literature. For 3-carboxy proxyl, it is found that ΔH^G_pp(0) = 1.04 ± 0.01 G independent of solvent polarity. Precision values of the¹⁴N hyperfine coupling constant for 3-carboxy proxyl at 9.5°C are as follows: 14.128 ± 0.001 G in CCl₄and 16.230 ± 0.002 G in aqueous buffer. The temperature dependence of ΔH^G_pp(0) and the¹⁴N hyperfine coupling constant are reported as empirical equations. Results of the present work taken together with previously published data permits accurate correction for the effects of inhomogeneous broadening due to unresolved hyperfine structure and modulation broadening for the majority of spin probes in common use.     

On the general form of the Beltrami equation and Papkovich's solution of the axially symmetrical problem of the classical theory of elasticity

The paper shows the connection between the general form of the Beltrami equation of compatibility, which had already been derived by the author, and the form given for it in orthogonal curvilinear coordinates by Lurye (para 2, 3).Some of the properties of Papkovich's general solution of the axially symmetrical problem (without body forces) of the theory of elasticity and its relation to the Finzi-Krutkov solution are discussed so as to supplement to a certain extent the paper of Trenin (para 4, 5, 6).     

Charakterisierung der in der Fett- und Seifenindustrie verwendeten Carbons?uren durch Oxydation mit Chroms?ure

Zusammenfassung Es wird eine Methode zur Charakterisierung der in der Fett- und Seifenindustrie verwendeten organischen Säuren ausgearbeitet. Das Verfahren beruht auf der oxydativen Spaltung der Substanz mit Chromsäure und Schwefelsäure unter den Bedingungen der C-Methyl-gruppenbestimmung und auf der alkalimetrischen Titration der gebildeten, mit Wasserdampf flüchtigen Säuren. Das Ergebnis der Bestimmung, ausgedrückt in Milligrammen KOH, die zur Neutralisation der aus 1 g Substanz gebildeten flüchtigen Säuren erforderlich sind, wird als Kuhn-Rothsche Zahl bezeichnet. Das Verhältnis der Kuhn-Rothschen Zahl und der Säurezahl ist für den Typus der Säure charakteristisch, und es ist möglich, mittels dieses Verhältnisses die Naphthensäuren von den Fettsäuren und Harzsäuren zu unterscheiden.Wir danken dem Akademiker R. Luke herzlich für anregende Diskussionen und für die Besorgung der Naphthensäureproben. Dem Betrieb der Severoeské tukové závody n.p., Ústí n. L., sind wir für dieÜbergabe der übrigen Rohstoffe und Fabrikate zu Dank verpflichtet.     

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The magnetic and hyperthermia studies of bare and silica-coated La<Subscript>0.75</Subscript>Sr<Subscript>0.25</Subscript>MnO<Subscript>3</Subscript> nanoparticles

The magnetic nanoparticles of La_0.75Sr_0.25MnO₃ perovskite manganite with a controlled size were prepared via sol–gel procedure, followed by thermal treatment and subsequent mechanical processing of the resulting raw product. The prepared materials were structurally studied by the XRD and TEM methods and probed by DC magnetic measurements. The nanoparticles of the mean crystallite sizes 11–40 nm exhibit T _C in the range of ≈310–347 K and the sample possessing 20-nm crystallites was identified as the most suitable for hyperthermia experiments. In order to obtain a colloidally stable suspension and prevent toxic effects, the selected magnetic cores were further encapsulated into silica shell using tetraethoxysilane. The detailed magnetic studies were focused on the comparison of the raw product, the bare nanoparticles after mechanical processing and the silica-coated nanoparticles, dealing also with effects of size distribution and magnetic interactions. The heating experiments were carried out in an AC field of frequencies 100 kHz–1 MHz and amplitude 3.0–8.9 kA m⁻¹ on water dispersions of the samples, and the generated heat was deduced from their warming rate taking into account experimentally determined thermal losses into surroundings. The experiments demonstrate that the heating efficiency of the coated nanoparticles is generally higher than that of the bare magnetic cores. It is also shown that the aggregation of the bare nanoparticles increases heating efficiency at least in a certain concentration range.     

Branching on general disjunctions

This paper considers a modification of the branch-and-cut algorithm for Mixed Integer Linear Programming where branching is performed on general disjunctions rather than on variables. We select promising branching disjunctions based on a heuristic measure of disjunction quality. This measure exploits the relation between branching disjunctions and intersection cuts. In this work, we focus on disjunctions defining the mixed integer Gomory cuts at an optimal basis of the linear programming relaxation. The procedure is tested on instances from the literature. Experiments show that, for a majority of the instances, the enumeration tree obtained by branching on these general disjunctions has a smaller size than the tree obtained by branching on variables, even when variable branching is performed using full strong branching.