A computationally efficient finite element model with perfectly matched layers applied to scattering from axially symmetric objects

A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.     

Determination of Picoxystrobin and Pyraclostrobin by MEKC with On-Line Analyte Concentration

Micellar electrokinetic capillary chromatography was used for the determination of picoxystrobin and pyraclostrobin. The background electrolyte consisted of borate buffer (40 mmol L⁻¹ pH 8.5), SDS (30 mmol L⁻¹) and acetonitrile (15% in volume). Runs were made at 25 °C with 25 kV applied potential. The developed method was applied to analyte fortified urine samples. On-line analyte concentration, combined with a capillary of a longer optical path length, allowed limits of quantification of 8.6 × 10⁻⁸ mol L⁻¹ for picoxystrobin and 1.8 × 10⁻⁷ mol L⁻¹ for pyraclostrobin.

     

Logical structures and genus of proofs

Any arbitrarily complicated non-oriented graph, that is a graph of arbitrarily large genus, can be encoded in a cut-free proof. This unpublished result of Statman was shown in the early seventies. We provide a proof of it, and of a number of other related facts.     

Enzymatic resolution of (±)-5-phenyl-4,5-dihydroisoxazole-3-carboxylic acid ethyl ester and its transformations into polyfunctionalised amino acids and dipeptides

Enantiomerically pure (5R)-(?)-5-phenyl-4,5-dihydroisoxazole-3-carboxylic acid ethyl ester was obtained via enzymatic resolution of the corresponding racemic mixture using a lipase from hog pancreas (PPL). The following reduction of the ester group to the corresponding alcohol and the oxidation of the latter led to (5R)-(?)-5-phenyl-4,5-dihydroisoxazole-3-carbaldehyde, and the reaction between this and Schöllkopf’s reagent, (2R)-(+)-2,5-dihydro-3,6-dimethoxy-2-isopropylpyrazine, gave mixtures of adducts with a good syn/anti ratio. The steric configurations of the major diastereoisomer were assigned on the basis of spectroscopic data and X-ray analysis. The subsequent controlled hydrolysis of the pyrazine ring led to β-(5-phenyl-4,5-dihydroisoxazol-3-yl)-serine methyl esters and the corresponding dipeptides with (R)-valine. Finally, reductive cleavage of the 4,5-dihydroisoxazole ring under hydrolytic conditions made it possible to obtain the corresponding polyfunctionalised dipeptides.     

Comments on selected fundamental aspects of microarray analysis

Microarrays are becoming a ubiquitous tool of research in life sciences. However, the working principles of microarray-based methodologies are often misunderstood or apparently ignored by the researchers who actually perform and interpret experiments. This in turn seems to lead to a common over-expectation regarding the explanatory and/or knowledge-generating power of microarray analyses. In this note we intend to explain basic principles of five (5) major groups of analytical techniques used in studies of microarray data and their interpretation: the principal component analysis (PCA), the independent component analysis (ICA), the t-test, the analysis of variance (ANOVA), and self organizing maps (SOM). We discuss answers to selected practical questions related to the analysis of microarray data. We also take a closer look at the experimental setup and the rules, which have to be observed in order to exploit microarrays efficiently. Finally, we discuss in detail the scope and limitations of microarray-based methods. We emphasize the fact that no amount of statistical analysis can compensate for (or replace) a well thought through experimental setup. We conclude that microarrays are indeed useful tools in life sciences but by no means should they be expected to generate complete answers to complex biological questions. We argue that even well posed questions, formulated within a microarray-specific terminology, cannot be completely answered with the use of microarray analyses alone.     

Oxidative coupling of 17beta-estradiol: inventory of oligomer products and configuration assignment of atropoisomeric c4-linked biphenyl-type dimers and trimers

The oxidation chemistry of 17beta-estradiol (1) is of central relevance to the nongenomic effects of estrogens and offers valuable prospects in the search for novel steroidal scaffolds of academic and industrial interest. Herein, we report the results of a detailed investigation into the nature of the oligomer products formed by phenolic oxidation of 1. Of the oxidants tested, the peroxidase/H2O2 system proved to be the most effective in inducing conversion of 1 to a complex mixture of oligomer species. Repeated chromatographic fractionation followed by extensive 2D NMR and mass spectrometric analysis allowed identification of a series of phenolic coupling products comprising, besides the C2-symmetric dimers 2 and 3, a 2,4' dimer (4), two O-linked dimers (5, 6), and the novel trimers 7-9. All 4-linked biphenyl-type oligomers, i.e., 3 and 7-9, occurred as couples of atropoisomers, reflecting steric hindrance at biphenyl linkages. For all atropoisomers, absolute configuration was established by the exciton chirality method and the interconversion energy was determined by dynamic NMR. These results provide the first systematic inventory of oxidative coupling products of 1 and lay the foundation for future studies aimed to develop novel estrogen derivatives based on oligomeric scaffolds.     

Cover Picture

The cover picture shows the metalloporphyrin heterodimer [(tpp)Mo$\rm{\mathop{-}^{4}}$Re(oep)](+) with the novel [Mo$\rm{\mathop{-}^{4}}$Re](5+) core. The core represents the first example of a quadruple bond between elements of different triads, thus proving that heterometallic quadruple bonds are not limited to the Group 6 metals. From the space-filling model it is clear that there is no interaction between the stabilizing porphyrin ligands. The ORTEP plot in a projection along the Re-Mo axis emphasizes the perfectly eclipsed geometry of the porphyrins, which is unambiguous proof of the existence of the quadruple bond in the solid state. The diamagnetism and large magnetic anisotropy of the cation, as determined by (1)H NMR spectroscopy, indicate that the quadruple bond is retained in solution. A logical and well-defined synthetic route was used to synthesize the dimer, and can be extended to other metalloporphyrins to generate further novel quadruple bonds (the picture was generated by Marina Boulan, St. Petersburg, Russia), full details are reported by J. P. Collman et al. on p. 1271 ff.     

Smooth solutions to a class of free boundary parabolic problems

We establish existence, uniqueness, and regularity results for solutions to a class of free boundary parabolic problems, including the free boundary heat equation which arises in the so-called ``focusing problem' in the mathematical theory of combustion. Such solutions are proved to be smooth with respect to time for positive , if the data are smooth.

     

Ionization and Partitioning Profiles of Zwitterions: The case of the anti-inflammatory drug azapropazone

Azapropazone ( 1 ) is a non-steroidal anti-inflammatory drug (NSAID) whose chemical structure is markedly different from that of other agents in this class and challenges our understanding of structure-activity and structure-permeation relationships. Using a variety of experimental and computational techniques, we studied 1 for its molecular structure in the gas phase and non-protic polar solvents, protonation/deprotonation equilibra, tautomerism, and pH-lipophilicity profiles (octan-1-ol/H₂O and dodecane/H₂O). Other NSAIDs and model compounds were also examined for comparison. Due to its very low acidic pK_a1, 1 exists in the physiological pH range as a zwitterion and as an anion. Some pharmacological implications of these findings are discussed.