Über Rhoeadin und Rhoeagenin

Ohne Zusammenfassung     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

Existence and Uniqueness of Fixed Points for Markov Operators and Markov Processes

This paper concerns a Markov operator T on a space L₁, and aMarkov process P which defines a Markov operator on a spaceM of finite signed measures. For T, the paper presents necessaryand sufficient conditions for:

a the existence of invariant probabilitydensities (IPDs)

b the existence of strictly positive IPDs,and

c the existence and uniqueness of IPDs.

Similar resultson invariant probability measures for P are presented. The basicapproach is to pose a fixed-point problem as the problem ofsolving a certain linear equation in a suitable Banach space,and then obtain necessary and sufficient conditions for thisequation to have a solution. 1991 Mathematics Subject Classification:60J05, 47B65, 47N30.     

Formation and decomposition of N,N,N-trimethylanilinium cations on zeolite H-Y investigated by in situ stopped-flow MAS NMR spectroscopy

Methylation of aniline by methanol on zeolite H-Y has been investigated by in situ (13)C MAS NMR spectroscopy under flow conditions. The in situ (13)C continuous-flow (CF) MAS NMR experiments were performed at reaction temperatures between 473 and 523 K, molar methanol-to-aniline ratios of 1:1 to 4:1, and modified residence times of (13)CH(3)OH between 20 and 100 (g x h)/mol. The methylation reaction was shown to start at 473 K. N,N,N-Trimethylanilinium cations causing a (13)C NMR signal at 58 ppm constitute the major product on the catalyst surface. Small amounts of protonated N-methylaniline ([PhNH(2)CH(3)](+)) and N,N-dimethylaniline ([PhNH(CH(3))(2)](+)) were also observed at ca. 39 and 48 ppm, respectively. After increase of the temperature to 523 K, the contents of N,N-dimethylanilinium cations and ring-alkylated reaction products strongly increased, accompanied by a decrease of the amount of N,N,N-trimethylanilinium cations. With application of the in situ stopped-flow (SF) MAS NMR technique, the decomposition of N,N,N-trimethylanilinium cations on zeolite H-Y to N,N-dimethylanilinium and N-methylanilinium cations was investigated to gain a deeper insight into the reaction mechanism. The results obtained allow the proposal of a mechanism consisting of three steps: (i) the conversion of methanol to surface methoxy groups and dimethyl ether (DME); (ii) the alkylation of aniline with methanol, methoxy groups, or DME leading to an equilibrium mixture of N,N,N-trimethylanilinium, N,N-dimethylanilinium, and N-methylanilinium cations attached to the zeolite surface; (iii) the deprotonation of N,N-dimethylanilinium and N-methylanilinium cations causing the formation of N,N-dimethylaniline (NNDMA) and N-methylaniline (NMA) in the gas phase, respectively. The chemical equilibrium between the anilinium cations carrying different numbers of methyl groups is suggested to play a key role for the products distribution in the gas phase.     

Quantitative structure-activity relationships by neural networks and inductive logic programming. I. The inhibition of dihydrofolate reductase by pyrimidines

Summary Neural networks and inductive logic programming (ILP) have been compared to linear regression for modelling the QSAR of the inhibition of E. coli dihydrofolate reductase (DHFR) by 2,4-diamino-5-(substitured benzyl)pyrimidines, and, in the subsequent paper [Hirst, J.D., King, R.D. and Sternberg, M.J.E., J. Comput.-Aided Mol. Design, 8 (1994) 421], the inhibition of rodent DHFR by 2,4-diamino-6,6-dimethyl-5-phenyl-dihydrotriazines. Cross-validation trials provide a statistically rigorous assessment of the predictive capabilities of the methods, with training and testing data selected randomly and all the methods developed using identical training data. For the ILP analysis, molecules are represented by attributes other than Hansch parameters. Neural networks and ILP perform better than linear regression using the attribute representation, but the difference is not statistically significant. The major benefit from the ILP analysis is the formulation of understandable rules relating the activity of the inhibitors to their chemical structure.     

Synthesis of silylated methylenecyclopropanes

2-Trimethylsilylmethylenecyclopropane (=3) was synthesized by reaction of lithio methylenecyclopropane with TMSCl. The lithium salt of (=3) reacts with some electrophiles by α- or γ-attack depending on the nature of the electrophile. Whereas alkenylbromides $\text{8}$ and $\text{9}$ or alkinylbromide $\text{10}$ give exclusively α-attack, benzaldehyde reacts with γ-alkylation.     

In vitro EVALUATION OF PHOTOTOXIC PROPERTIES OF FOUR STRUCTURALLY RELATED BENZOPORPHYRIN DERIVATIVES

Four structural analogs of benzoporphyrin derivative (BPD) have been studied and compared for photosensitizing activity in vitro. All analogs have an identical reduced tetrapyrrol porphyrin ring, and differ by the position of a cyclohexadiene ring (fused at either ring A or ring B of the porphyrin) and the presence of either two acid groups or one acid and one ester group at rings C and D of the porphyrin. Photosensitizer activity was tested with the M1 tumor cell line using an assay (the MTT assay) which detects mitochondrial hydrogenases as a measure of cell viability. This assay was shown to be equivalent to the standard clonogenicity or [3H]thymidine uptake assay. Comparative studies with the BPD analogs showed that the monoacid derivatives had equivalent cytotoxicity and were about five-fold more active than the diacid forms. This was the case whether the assays were performed in the presence or absence of fetal calf serum.     

Chemical derivatization of amino acids for in situ analysis of Martian samples by gas chromatography

Three different methods of derivatization are tested in order to select and optimize one for the in situ analysis of amino acids in Martian samples. The silylation procedure can easily be automated with a high yield and a linear response in a large range of concentrations. The alkylation method is simple and easily automated, but irreproducible data are obtained for the reaction in the GC liner at quite a high temperature (300 degrees C). Moreover by-products of the reaction interfere in the GC chromatograms and mass spectrometry detection is needed for product identification. The chloroformate derivatization has several advantages such as one-step reaction and short time analysis. The main problem of this procedure is the shaking step which difficult to develop in space application.     

Mikro-Elementaranalyse

Ohne Zusammenfassung