Average growth-behavior and distribution properties of generalized weighted digit-block-counting functions

We introduce a generalized weighted digit-block-counting function on the nonnegative integers, which is a generalization of many digit-depending functions as, for example, the well known sum-of-digits function. A formula for the first moment of the sum-of-digits function has been given by Delange in 1972. In the first part of this paper we provide a compact formula for the first moment of the generalized weighted digit-block-counting function and show that a (weak) Delange type formula holds if the sequence of weights converges. The question, whether the converse is true as well, can only be answered partially at the moment. In the second part of this paper we study distribution properties of generalized weighted digit-block-counting sequences and their d-dimensional analogues. We give an if and only if condition under which such sequences are uniformly distributed modulo one.     

Determination of Testosterone Metabolites in Rat Hepatocytes with and without Cryopreservation by On-Line SPE Column-Switching LC and MS Detection

In a recently published paper development of a sensitive automated “on-line” solid-phase extraction (SPE)/RP-HPLC assay for 6β-hydroxytestosterone (6β-OHT) with corticosterone as the internal standard (IS) was reported and its potential for quantification of various testosterone metabolites in culture media reflecting metabolic activity of cultured human and animal hepatocytes demonstrated [1]. In this following contribution the technique has been extended to determination of another five testosterone metabolites in cultured rat hepatocytes using an identical “on-line” SPE/RP-HPLC procedure and detection by tandem MS-MS with an atmospheric pressure chemical ionization (APCI) source in the selected reaction monitoring (SRM) mode as that described in [1]. All six testosterone metabolites, namely 2α-OHT, 2β-OHT, 6α-OHT, 6β-OHT, 7α-OHT and 16α-OHT, could be sufficiently separated from each other and thus an unequivocal assignment to the individual structures was achieved. Validation data are presented specifying the limits of quantitation as well as the mean values of the coefficients of variation (CV) for the target analytes and the accuracy obtained at five different days. Regio- and stereoselective testosterone hydroxylation by rat hepatocytes was measured in a long-term culture system with and without exposure to rifampicin as an inducer of liver CYP 3A4 activity. In addition, testosterone hydroxylation was analyzed in cultures of cryopreserved hepatocytes that had been stored at −196 °C. The rat hepatocytes were cultured after thawing for up to 11 days and induction of testosterone hydroxylase activity could be demonstrated in cultures which underwent a new cryopreservation protocol. This paper is dedicated to Professor Hinrich Cramer on the occasion of his 75th birthday.     

Practice of thin-layer chromatography

Ohne Zusammenfassung

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Practice of thin-layer chromatography By J.C. Touchstone and M.F. Dobbins, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, 1978

     

Zur Theorie der endlichen Transformationsgruppen

Ohne Zusammenfassung     

Einen Apparat zur unmittelbaren Angabe des Gewichtes und Volumens von Gasen

Ohne Zusammenfassung