Non-simple blow-up solutions for the Neumann two-dimensional sinh-Gordon equation

For the Neumann sinh-Gordon equation on the unit ball

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.     

Lipid phase transition in saccharide-coated cholate-containing liposomes: coupling to the surrounding matrix

We performed FTIR measurements on cholate-containing liposomes (CCL) embedded in saccharide (trehalose or sucrose) matrixes with different contents of residual water. We obtained information on the CCL phase transition following the thermal evolution (310-70 K) of the IR spectrum of the carbonyl moieties of phospholipids in the frequency range 4225-4550 cm(-1). Furthermore, we simultaneously followed the thermal evolution of the water association band, which gave information on the behavior of the surrounding water-saccharide matrix. The analysis revealed a small sub-band of the water association band present in CCL but not in cholate-free liposomes, the thermal evolution of which is tightly coupled to that of the spectrum of the carbonyl moieties of phospholipids. We suggest that this band arises from water molecules, which are inserted within the lipidic structure, in the region located at the border between the hydrophilic and the hydrophobic moieties of phospholipids in the presence of cholic acid. Such water molecules could be responsible for the peculiar flexibility and hydrophilicity of CCL. Following Giuffrida et al. (J. Phys. Chem. B 2003, 107, 13211-13217), we also performed a Spectra Distance analysis, which enabled us to detect an overall liposomes-matrix structural coupling.     

Sopra un problema fondamentale della teoria delle frazioni continue algebriche generalizzate

Rendiconti del Circolo Matematico di Palermo Series 1 -     

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.