Filter products of C0-semigroups and ultraproduct representations for Lie groups

We provide a new approach to filter products of C₀-semigroups and prove a spectral theorem for the generator and its filter product. In a similar fashion, we construct ultraproducts of strongly continuous unitary representations of locally compact groups and study spectral theoretic connections between the representations and their ultraproducts. In the case of Lie groups, our investigations are extended to the infinitesimal representation.     

Intrinsic and Intramolecular Lipophilicity Effects in O-Glucuronides

In this study, we compared the lipophilicity of O-glucuronides and their aglycones. Distribution coefficients (log D) and P values of neutral species (log P) were determined by centrifugal partition chromatography (CPC) in octanol/buffer systems. Two-phase potentiometry was also used to measure the log P value of some lipophilic solutes. The experimentally determined global influence of glucuronidation on lipophilicity, obtained as the difference (decrement) log P_{(glucuronide)} ? log P_(aglycone), was found to be ?1.30 ± 0.16 (n = 4) for glucuronides of alcohols (methyl, menthyl, neomenthyl, and chloramphenicol O-glucuronide). The mean decrement was ?2.06 ± 0.31 (n = 9) for glucuronides of phenols (phenyl, p-nitrophenyl, 1-naphthyl, 6-bromo-2-naphthyl, 4-methylumbelliferyl, 3-coumarinyl, phenolphthalein, 4′-benzophenonyl O-glucuronide, and diflunisal phenolic glucuronide). For the acylglucuronide of diflunisal and its rearrangement isomers, the mean decrement was ?1.80 ± 0.08 (n = 4; range ?1.7 to ?1.9). Differences in through-bond proximity effects as parametrized in the CLOGP algorithm seem to account for much of this difference. Conformational factors may also play a role, although it appears modest and unassessable for the glucuronides investigated here. The results imply that in vivo glucuronidation should have a stronger influence on the excretion of phenols than on that of alcohols.     

Novel RPLC stationary phases for lipophilicity measurement: solvatochromic analysis of retention mechanisms for neutral and basic compounds

An RPLC was developed to rapidly determine lipophilicity of neutral and basic compounds using three base deactivated RPLC stationary phases particularly designed for the analysis of basic compounds, namely, Supelcosil ABZ(+)Plus, Discovery RP Amide C16, and Zorbax Extend C18. The work consisted of three sets of experiments. In the first log kw values of neutral compounds were extrapolated using hydroorganic mobile phases at different compositions. Good correlation between log kw and log Poct indicated that the method was appropriate for these supports, without adding a silanol masking agent. In the second set of experiments, isocratic log k values of neutral and basic compounds were measured with three different mobile phases. The best estimation of lipophilicity was obtained for neutral and basic compounds when the secondary interactions were strongly reduced (i. e., when basic compounds were under their neutral form). In the third set of experiments, isocratic retention factors of basic compounds (in their neutral form) were measured with a high-pH mobile phase, on a chemically stable support (Zorbax Extend C18). Under these chromatographic conditions, correlation between the isocratic retention factors and log Poct (log D10.5) for basic compounds was similar to that for neutral compounds.     

A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach

In this paper, we construct a general theory of a priori error estimates for scalar conservation laws by suitably modifying the original Kuznetsov approximation theory. As a first application of this general technique, we show that error estimates for conservation laws can be obtained without having to use explicitly any regularity properties of the approximate solution. Thus, we obtain optimal error estimates for the Engquist-Osher scheme without using the fact (i) that the solution is uniformly bounded, (ii) that the scheme is total variation diminishing, and (iii) that the discrete semigroup associated with the scheme has the -contraction property, which guarantees an upper bound for the modulus of continuity in time of the approximate solution.

     

Electron impact induced intramolecular hydrogen transfer reactions in polymethylene glycol di-p-toluenesulfonates

The mechanisms of formation of the ionized acid and the protonated acid fragments in the electron impact induced fragmentation of the title compounds were investigated. The well known mechanisms of hydrogen transfer through mono- and bicyclic transition states that occur in the molecular ions of carboxylic esters are not the main pathways giving rise to these fragments. The major component of the m/z 172 peak corresponding formally to ionized p-toluenesulfonic acid in fact has a different structure; its formation involves a complex mechanism including a double hydrogen transfer reaction.     

Eutectic phase polymerization of activated ribonucleotide mixtures yields quasi-equimolar incorporation of purine and pyrimidine nucleobases

The RNA world hypothesis requires a plausible mechanism by which RNA itself (or precursor RNA-like polymers) can be synthesized nonenzymatically from the corresponding building blocks. Simulation experiments have exploited chemically reactive mononucleotides as monomers. Solutions of such monomers in the prebiotic environment were likely to be very dilute, but in experimental simulations of polymerization reactions dilute solutions of activated mononucleotides in the millimolar range hydrolyze extensively, and only trace amounts of dimers and trimers are formed. We report here that random medium-size RNA analogues with mixed sequences (5- to 17-mers with traces of longer products) can be synthesized in ice eutectic phases that are produced when dilute solutions of activated monomers and catalysts (Mg(II) and Pb(II)) are frozen and maintained at -18 degrees C for periods up to 38 days. Under these conditions, the monomers are concentrated as eutectics in an ice matrix. Hydrolysis of the activated mononucleotides was suppressed at low-temperature ranges, and polymerization was enhanced with yields up to 90%. Analysis of the mixed oligomers established that incorporation of both purine and pyrimidine bases proceeded at comparable rates and yields. These results suggest that ice deposits on the early Earth could have facilitated the synthesis of short- and medium-size random sequence RNA analogues and thereby provided a microenvironment suitable for the formation of biopolymers or their precursors.     

Oxygen-17 nuclear magnetic resonance: The effects of remote unsaturation on 17o-chemical shifts in polycyclic ethers

Natural-abundance ¹⁷O-NMR spectra of 7-oxanorbornane exo-3-oxatricyclo [3.2.1.0^2.4]octane and their unsaturated derivatives (endo cyclic and exocyclic double bonds) have been measured. Linear correlation laws were observed for $\text{δ}{}_{\mathrm{o}}\text{δ}{}_{\mathrm{c}}$ of these ethers/corresponding hydrocarbons. The “cyclization shifts” for δ_o in ethers were not correlated by the “cyclization shifts” for δ_c of the corresponding hydrocarbons.     

Cyclic voltammetry of highly hydrophilic ions at a supported liquid membrane

Cyclic voltammetry has been used to study the coupling of ion transfer reactions at a liquid membrane. The liquids are either supported by a porous hydrophobic membrane (polyvinylidene difluoride, PVDF) when the organic solvent is non-volatile (o-nitrophenyloctylether) or are merely a free standing organic solvent layer such as 1,2-dichloroethane comprised between two hydrophilic dialysis membranes supporting the adjacent aqueous phases. The passage of current across the liquid membrane is associated with two ion transfer reactions across the two polarised liquid liquid interfaces in series. It is shown that it is possible to study the transfer of highly hydrophilic ions at one interface by limiting the mass transfer of the other ion transfer reaction at the other interface. Indeed, for systems comprising an ion M in one aqueous phase and a reference ion R partitioned between the membrane and the other aqueous phase, the observed and simulated cyclic voltammograms have a half-wave potential determined by the Gibbs energy of transfer of M transferring at one interface and by the limiting mass transfer of R at the other interface. This new methodology opens a way to measure the Gibbs energy of transfer of highly hydrophilic or hydrophobic ions, which usually limits the potential window at single liquid liquid interfaces (ITIES).     

MS-Express: data-extracting and -processing software for high-throughput experimentation with mass spectrometry

High-throughput experiments (HTE) result in large amounts of raw data that have to be evaluated for sample classification. Especially mass spectrometry, a widely used detection method in catalytic HTE applications, produces enormous amounts of data. In the past few years, in catalysts research, several test rigs based on mass spectrometric detection have been independently reported by different groups. In a typical HTE, the catalysts are tested sequentially; the recording of the scans, however, occurs continuously. For this reason, the scans of interest have to be extracted from the raw data, and scans belonging to the same sample have to be averaged in a tedious procedure before further processing. In this publication, we present our custom-designed software MS-Express (mass spectrometry data-extracting and -processing software), an efficient tool for HTE MS data evaluation. MS-Express not only sorts the data, it also establishes statistical significance with the help of reference and blank data and provides concise information about abundance and intensity distributions of expected peaks. A special feature is that the program also reports unexpected MS signals, which potentially lead to unexpected discoveries.