On a combinatorial theorem related to a theorem of G. Szegö

In 1954, M. Kac discovered a probabilistic interpretation of a theorem of G. Szegö of Toeplitz matrices and demonstrated that this theorem can be provedin an elementary way by using a combinatorial identify of G. A. Hunt. In this paper Hunt's combinatorial identity is derived from a more general combinatorial result.     

Nachweis und volumetrische Bestimmung von Nitrosoderivaten im Mikromaßstab

Zusammenfassung Nitrosoverbindungen lassen sich in Gegenwart von Rhodanidionen durch Eisen(II)-sulfat quantitativ reduzieren. Auf dieser Reaktion beruht ein neuer Nachweis der Nitrosogruppe auf Grund der Farbe des Eisen(III)-rhodanidkomplexes, sowie ihre Bestimmung durch Titration des Eisen(III) mit Quecksilber(I)-nitrat-Maßlösung. Diese Methode ermöglicht die Analyse auch in Gegenwart von Nitroverbindungen.

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Detection and volumetric microdetermination of nitroso compounds

Summary Nitroso compounds can be quantitatively reduced by iron(II) sulphate in the presence of thiocyanate ions. The reaction provides a new method for the detection of the nitroso group, based on the colour developed by the iron(III) thiocyanate complex. The determination of nitroso group can also be carried out by titrating the iron(III) with mercury(I) nitrate, even if nitro compounds are present.

     

A fundamental identity in the theory of queues

Summary The main result of this paper is a fundamental identity for single-server queueing processes. By using the fundamental identity it is possible to find the mathematical laws describing the behavior of a queue in continuous time if we know the mathematical laws describing the behavior of the same queue in discrete time. The case of single-server queues with recurrent input and general service times is discussed in detail. This research was supported by the National Science Foundation under Contract No. GP-7847.     

Non-central limit theorems for random selections

Selection from finite sets is a basic procedure of statistics and the partial sum behavior of selected elements is completely known under the “uniform asymptotic negligibility” condition of central limit theory. The purpose of the present paper is to determine the asymptotic behavior of partial sums when the central limit theorem fails. As an application, we describe the limiting properties of permutation and bootstrap statistics in case of infinite variance.     

Chiral separation of lansoprazole and rabeprazole by capillary electrophoresis using dual cyclodextrin systems

Novel capillary electrophoresis methods using CDs as chiral selectors were developed and validated for the chiral separation of lansoprazole and rabeprazole, two proton pump inhibitors. Fourteen different neutral and anionic CDs were screened at pH 4 and 7 in the preliminary analysis. Sulfobutyl‐ether‐β‐CD with a degree of substitution of 6.5 and 10 at neutral pH proved to be the most suitable chiral selector for both compounds. Various dual CD systems were also compared, and the possible mechanisms of enantiomer separation were investigated. A dual selector system containing sulfobutyl‐ether‐β‐CD degree of substitution 6.5 and native γ‐CD proved to be the most adequate system for the separations. Method optimization was carried out using an experimental design approach, performing an initial fractional factorial screening design, followed by a central composite design to establish the optimal analytical conditions. The optimized methods (25 mM phosphate buffer, pH 7, 10 mM sulfobutyl‐ether‐β‐CD/20 mM γ‐CD, +20 kV voltage; 17°C temperature; 50 mbar/3 s injection, detection at 210 nm for lansoprazole; 25 mM phosphate buffer, pH 7, 15 mM sulfobutyl‐ether‐β‐CD/30 mM γ‐CD, +20 kV voltage; 18°C temperature; 50 mbar/3 s injection, detection at 210 nm for rabeprazole) provided baseline separation for lansoprazole (R_s = 2.91) and rabeprazole (R_s = 2.53) enantiomers with favorable migration order (in both cases the S‐enantiomers migrates first). The optimized methods were validated according to current guidelines and proved to be reliable, linear, precise, and accurate for the determination of 0.15% distomer as chiral impurity in dexlansoprazole and dexrabeprazole samples.     

Gravity-Related Wave Function Collapse

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.     

Synthesis of 4-thiaharmalan analogue 4-aryl-1,3-thiazino[5,6-b]indole derivatives by prevention of rearrangements to position two of the indole moiety

An efficient and selective non-acidic protocol has been developed for the synthesis of derivatives of a new ring system: 4-aryl-1,3-thiazino[5,6-b]indole, a 4-thiaharmalan analogue. The convenient amidomethylation of indole-3-thiol (5) afforded 3-benzoylaminomethylthio-1H-indole (7a), with ortho-amidomethylated 2-benzoylamino-methyl-3-benzoylaminomethylthio-1H-indole (8) as side product. Following the Bischler-Napieralski reaction of 7a the rearranged 2-benzoylaminomethylthio-1H-indole 11 could be isolated. In order to prevent such rearrangements the target thiazinoindoles were prepared via 3-thiobenzoylaminomethylthioindole (13) via a modified Bischler-Napieralski reaction.     

Nanophase separation in segmented polyurethane elastomers: Effect of specific interactions on structure and properties

Polyurethanes were prepared from 4,4′-methylenebis (phenyl isocyanate) (MDI), 1,4-butanediol (BD) and poly (tetrahydrofurane) polyether polyol (PTHF). The -OH functional group ratio of polyol/total diol was kept constant at 0.4 in all experiments, while the ratio of the isocianate and hydroxyl groups (NCO/OH) changed between 0.940 and 1.150. Melt polymerization was carried out in an internal mixer. The polymers were characterized with a number of methods including GPC, FTIR, WAXS, DSC, DMA and tensile testing. Changing stoichiometry modifies molecular weight as expected, but the relative concentration of end-groups also changes at the same time. The respective end-groups preferentially associate with each other leading to phase separation. -OH end-groups enter into weaker interactions with each other than urethane and amine groups. The extent of phase separation, as well as the size and properties of the dispersed phase depend on composition. Each property of the polymer is affected differently by molecular weight and phase separation. Melt viscosity depends mostly on the length of the molecules, ultimate tensile properties are influenced also by interactions, while stiffness is determined almost exclusively by phase structure.