Discontinuous viscosity solutions to dirichlet problems for hamilton-jacob1 equations with

We introduce a new formulation of Dirichlet problem for a class of first order, nonlinear equations containing the minimum time problem, whose solution is expected to be discontinuous. We prove existence, uniqueness and representation formulas for the solution in the sense of viscosity solutions. Our method relies on a new way of prescribing the boundary condition, the use of recent ideas of Barron-Jensen [8] and Barles [5] , and the derivation of a "backwards" dynamic programming principle. We use the same ideas to prove uniqueness for the usual Dicchlet type formulation, following Ishii [13] and Bales-Perthame [6], under additional regularity conditions on the domain.     

Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes

We compute analytically the full distribution of Andreev conductance G(NS) of a metal-superconductor interface with a large number N(c) of transverse modes, using a random matrix approach. The probability distribution P(G(NS),N(c) in the limit of large N(c) displays a Gaussian behavior near the average value =(2-√2)N(c) and asymmetric power-law tails in the two limits of very small and very large G(NS). In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power-law tail for large G(NS). Weakly nonanalytic points separate these four regimes-these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.     

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.     

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.     

Structure-property interplay of proton conducting membranes based on PBI5N, SiO2-Im and H3PO4 for high temperature fuel cells

Polybenzimidazoles (PBIs) are among the polymers of choice to prepare membranes for high temperature polymer fuel cells. Poly-2,2'(2,6-pyridine)-5,5'-bibenzimidazole (PBI5N), doped with H(3)PO(4), and acid-doped PBI5N containing 10 wt% of imidazole-functionalized silica membranes were studied with thermogravimetric analysis, differential scanning calorimetry, dynamic-mechanical analysis, infrared spectroscopy, and broadband electric spectroscopy to examine the structure-property relationships. Key results show that: (1) doped PBI5N membranes show thermal decomposition starting at 120 °C, while pristine PBI5N is stable up to 300 °C; (2) the presence of filler increases the acid uptake and decreases the crystallinity of PBI5N; (3) the addition of phosphoric acid reduces the mechanical properties of the membrane, while the addition of filler has the opposite effect; (4) acid-doped membranes have conductivity values on the order of 10(-2)-10(-3) S cm(-1); and (5) membranes exhibit a Vogel-Tamman-Fulcher (VTF) type proton conduction mechanism, where proton hopping is coupled with the segmental motion of the polymer chain. Infrared spectroscopy combined with DFT quantum mechanical calculations was used to assign the experimental spectrum of PBI5N.     

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.