On some computational problems in finite abelian groups

We present new algorithms for computing orders of elements, discrete logarithms, and structures of finite abelian groups. We estimate the computational complexity and storage requirements, and we explicitly determine the -constants and -constants. We implemented the algorithms for class groups of imaginary quadratic orders and present a selection of our experimental results. Our algorithms are based on a modification of Shanks' baby-step giant-step strategy, and have the advantage that their computational complexity and storage requirements are relative to the actual order, discrete logarithm, or size of the group, rather than relative to an upper bound on the group order.

     

Density functional theory studies on the mechanisms of regioselective allylic and cis-vinylic deprotonation of allyl amides and allylamines

A density functional theory (B3LYP/6-31+G) study was undertaken in an effort to learn more about the mechanisms controlling the regioselective deprotonations of the synthetically versatile N-lithio-N-(tert-butyl)allylamide 1 and N-lithio-N-(trimethylsilyl)allylamine 2 compounds. The calculations suggest that deprotonation of 1 occurs exclusively at the allylic position. This agrees with experimental results. The calculations also suggest that deprotonation of allylamine 2 exclusively at the cis-vinylic position is due to kinetic control.     

Comparison of methods for the determination of total selenium in plasma by magnetic sector inductively coupled plasma mass spectrometry

Three sample preparation methods (dilution, microwave digestion and ethanol addition) were evaluated for the determination of Se in human plasma using magnetic sector inductively coupled plasma mass spectrometry (ICP-MS). A number of instrumental parameters were also considered, namely the choice of internal standard (Sc, Rh, In) and pre-defined spectral resolution (m/Δm ∼300 (low resolution, LR) and ∼7500 (high resolution, HR)). The isotopes and were selected for analysis avoiding the major and unresolvable Ar dimer interferences associated with other Se isotopes.Ethanol addition was found to be the most suitable and reliable sample preparation method. The optimum ethanol concentration for a 1+9 dilution of the plasma sample was 0.5% (v/v). Indium or Sc were selected over Rh as internal standards as Seronorm™ Level 1 target values were achieved at lower concentrations of ethanol modifier. Representative ICP-MS detection limits for this method using (HR) and (HR), were 0.1 and 0.2 μg l⁻¹.Accurate analysis of Se in Seronorm™ Level 1 (MI0181) was found using either or and HR (86±5 and 83±5 μg l⁻¹ respectively, n=5, In internal standard, target value=83±6 μg l⁻¹). Although offering improved precision (e.g. LR: 0-3% versus HR: 1-6%), accurate results were only obtained with LR for the Seronorm™ Level 1 sample when using (86±1 μg l⁻¹). The major interference precluded accurate Se analysis using and LR for all samples considered. Reliable Se concentrations were only found for a “real” pooled sample when using (HR), in part a result of non-negligible and unresolved interference when using LR. Consistently elevated Se concentrations were found under all conditions when Seronorm™ Level 2 (NO0371) was analysed. These results were confirmed by independent GF-AAS analysis.Magnetic sector ICP-MS with (HR), in combination with the ethanol addition sample preparation method, was used for the analysis of Se in human plasma samples as part of a small pilot study. Average measured selenium concentrations were 102±18 μg l⁻¹ (n=18).     

Fast horizontal electrophoresis. II. Development of fast automated staining procedures using PhastSystem

The development of equipment for fast automated staining is described. It is possible to handle staining procedures with up to 20 steps and nine different solutions. To increase the reaction rate in the reaction chamber, the gels are rotated and high temperatures are used. The temperature in the reaction chamber is controlled between room temperature and 50 degrees C. Increased temperature, above 20 degrees C, generally results in faster staining and destaining. However, some reactions proceed better at a low temperature, including fixation of proteins with TCA, and the development step in silver staining, where increased temperatures cause a high background stain. Silver staining using acidic silver nitrate solution is preferred, due to easy preparation and good storage stability of the reagents. This method also causes little precipitation of silver on the walls of the reaction chamber. Silver staining is accomplished within one hour. Staining with PhastGel Blue is accomplished within 30 min.     

Structure-Activity Relationships of Oxygenated Morphinans. I. 4-Mono- and 3,4-dimethoxy-N-methylmorphinans and -N-methyl-morphinan-6-ones with unusually high antinociceptive potency. Preliminary communication

The antinociceptive potency and receptor affinity of several optically active aromatic mono- and di-oxygenated N-methylmorphinans and N-methylmorphinan-6-ones, prepared from natural morphine, were determined. Thus, in order of antinociceptive potency, 4-methoxy-N-methylmorphinan-6-one ≈ 3,4-dimethoxy-N-methylmorphinan-6-one ≈ 3,4-dimethoxy-N-methylmorphinan > 4-methoxy-N-methylmorphinan ≈ 4-acetoxy-N-methylmorphinan-6-one > 4-acetoxy-N-methylmorphinan ≈ 4-hydroxy-N-methylmorphinan-6-one ≈ 4-hydroxy-N-methylmorphinan. The 4-hydroxy compounds were slightly less potent than morphine, and the 4-methoxy and 3,4-dimethoxy compounds were found to have three times the potency of morphine. 4-Methoxy-N-methylmorphinan-6-one showed an opiate receptor affinity one-third that of morphine; this is a remarkably high affinity for a non-phenolic compound.     

Dianion aggregates derived from lithiation of N-silyl allylamine

[reaction: see text] Three different N-silyl-protected allylamines, i.e., N-TMS, N-TBDMS, and N-TIPS allylamine, were lihtiated by reaction with excess n-butyllithium. Crystallization of the resulting dianions and X-ray structure determination yields three uniquely different aggregates.     

A stochastic population projection system based on general age-dependent branching processes

"Algorithms for a stochastic population process, based on assumptions underlying general age-dependent branching processes in discrete time with time inhomogeneous laws of evolution, are developed through the use of a new representation of basic random functions involving birth cohorts and random sums of random variables. New algorithms provide a capability for computing the mean age structure of the process as well as variances and covariances, measuring variation about means. Four exploratory population projections, testing the implications of the algorithms for the case of time-homogeneous laws of evolution, are presented. Formulas extending mean and variance functions for unit population projections...are also presented. These formulas show that, in population processes with non-random laws of evolution, stochastic fluctuations about the mean function are negligible when initial population size is large. Further extensions of these formulas to the case of randomized laws of evolution suggest that stochastic fluctuations about the mean function can be significant even for large initial populations."