Heat problems for a starlike shaped plate

The Fourier solution of the heat problem for a circular plate is generalized to a starlike shaped plate. We show that the classical solution can be used even in this more general case, provided that a suitable change of variables in the polar co-ordinate system is performed.     

Drawing parameters optimization for birefringence reduction in optical fibers

The impact of the drawing process on the stress-induced birefringence in optical fiber is experimentally analyzed. By means of the photoelastic tomographic technique, residual internal stresses are measured in fiber samples drawn under different conditions of temperature, drawing tension and speed. From measured residual stress distributions, the stress-induced birefringence and beatlength are mathematically derived and compared, proving that an effective birefringence reduction can be obtained by a proper choice of drawing parameters.     

A quasi-Newton method for solving fixed point problems in Hilbert spaces

Summary We study the convergence properties of a projective variant of Newton's method for the approximation of fixed points of completely continuous operators in Hilbert spaces. We then discuss applications to nonlinear integral equations and we produce some numerical examples.     

Non-steroidal antiinflammatory agents. VI. Synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic Acid,a conformationally restricted analogue of tolmetin

The synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic acid 4 , a tricyclic analogue of tolmetin which might show significant analgesic-antiinflammatory activity, has been accomplished in four steps. Alkylation of ethyl 2-pyrrolylglyoxylate ( 15 ) with 2-cyanobenzyl bromide afforded derivative 16 , which was transformed by the Huang-Minion reaction into the dicarboxylic acid 6 . Cyclization of this key intermediate to 17 , followed by alkaline hydrolysis, afforded 10-oxo-5H-pyrrolo[1,2–6]isoquinoline-3-acetic acid ( 4 ). Various attempted syntheses of 6 are also discussed.     

Determination of the enantiomeric purity of 2-(2′-carboxy-3′-phenylcyclopropyl)glycines by chiral capillary electrophoresis

Summary A fast and practical chiral capillary electrophoretic method has been developed for determination of the enantiomeric purity of 2-(2′-carboxy-3′-phenylcyclopropyl)glycine (PCCG) compounds. In particular, the isomer PCCG-13, a potent selective and competitive antagonist at phospholipaseD-coupled metabotropic glutamate receptors (mGluRs), was completely resolved from its enantiomer PCCG-15 by use of dimethyl-β-cyclodextrin (DMCD) as chiral selector. pH 9.0 running buffer containing 2-amino-2-methyl-1,3-propanediol (AMPD; 100mM) was a suitable medium enabling resolution of the enantiomers in a short (32.5 cm total length) poly(vinyl alcohol) (PVA)-coated capillary. Because of the suppression of the electroosmotic flow and the good peak shape, baseline resolution of the enantiomers was obtained by use of the optimum concentration of chiral selector. For quantitative purposes at impurity levels, high sample loading was required and adequate separation was obtained in the presence of 80 mM DMCD. This CE method enabled quantification of 0.3% m/m of undesired enantiomer in PCCG-13; the samples analyzed, obtained from enantioselective synthesis, proved to be of high enantiomeric purity.     

Equilibrium strategy and population-size effects in lowest unique bid auctions

In lowest unique bid auctions, N players bid for an item. The winner is whoever places the lowest bid, provided that it is also unique. We use a grand canonical approach to derive an analytical expression for the equilibrium distribution of strategies. We then study the properties of the solution as a function of the mean number of players, and compare them with a large data set of internet auctions. The theory agrees with the data with striking accuracy for small population-size N, while for larger N a qualitatively different distribution is observed. We interpret this result as the emergence of two different regimes, one in which adaptation is feasible and one in which it is not. Our results question the actual possibility of a large population to adapt and find the optimal strategy when participating in a collective game.     

Interior estimates for some semilinear elliptic problem with critical nonlinearity

We study compactness properties for solutions of a semilinear elliptic equation with critical nonlinearity. For high dimensions, we are able to show that any solutions sequence with uniformly bounded energy is uniformly bounded in the interior of the domain. In particular, singularly perturbed Neumann equations admit pointwise concentration phenomena only at the boundary.     

A coherence-based approach for the pattern recognition of time series

A pattern recognition approach based on the frequency domain measure of squared coherence is a useful approach to identify linearly related groupings of time series over different periods of time. It is considered in an application to identify similar patterns of the yearly rates of change in the Gross Domestic Product (GDP) of twenty two highly developed countries in an econophysics context. The approach is also tested in simulation studies using linearly related time series, and it is shown to have a very good success rate of correct pattern matching.