On generalized Dedekind sums

In this paper we give a simple proof for the reciprocity formula for the generalized Dedekind sums and derive an explicit expression for these sums.     

Air-breathing laminar flow-based microfluidic fuel cell

This communication reports the design and characterization of an air-breathing laminar flow-based microfluidic fuel cell (LFFC). The performance of previous LFFC designs was cathode-limited due to the poor solubility and slow transport of oxygen in aqueous media. Introduction of an air-breathing gas diffusion electrode as the cathode addresses these mass transfer issues. With this design change, the cathode is exposed to a higher oxygen concentration, and more importantly, the rate of oxygen replenishment in the depletion boundary layer on the cathode is greatly enhanced as a result of the 4 orders of magnitude higher diffusion coefficient of oxygen in air as opposed to that in aqueous media. The power densities of the present air-breathing LFFCs are 5 times higher (26 mW/cm2) than those for LFFCs operated using formic acid solutions as the fuel stream and an oxygen-saturated aqueous stream at the cathode ( approximately 5 mW/cm2). With the performance-limiting issues at the cathode mitigated, these air-breathing LFFCs can now be further developed to fully exploit their advantages of direct control over fuel crossover and the ability to individually tailor the chemical composition of the cathode and anode media to enhance electrode performance and fuel utilization, thus increasing the potential of laminar flow-based fuel cells.     

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.     

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.