Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

International Institutions as Solutions to Underlying Games of Cooperation

This Working Paper was presented at the international workshop "Game Theory in International Relations at 50", organized and coordinated by Professor Jacint Jordana and Dr. Yannis Karagiannis at the Institut Barcelona d'Estudis Internacionals on May 22, 2009. The day-long Workshop was inspired by the desire to honour the ground-breaking work of Professor Thomas Schelling in 1959-1960, and to understand where the discipline International Relations lies today vis-à-vis game theory.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Resurgence of inner solutions for perturbations of the McMillan map

A sequence of “inner equations” attached to certain perturbations of the McMillan map was considered in [MSS09], their solutions were used in that article to measure an exponentially small separatrix splitting. We prove here all the results relative to these equations which are necessary to complete the proof of the main result of [MSS09]. The present work relies on ideas from resurgence theory: we describe the formal solutions, study the analyticity of their Borel transforms and use ´Ecalle’s alien derivations to measure the discrepancy between different Borel-Laplace sums.

On Cooperative solutions of a generalized assignment game: limit theorems to the set of competitive equilibria

We study two cooperative solutions of a market with indivisible goods modeled as a generalized assignment game: Set-wise stability and Core. We first establish that the Set-wise stable set is contained in the Core and it contains the non-empty set of competitive equilibrium payoffs. We then state and prove three limit results for replicated markets. First, the sequence of Cores of replicated markets converges to the set of competitive equilibrium payoffs when the number of replicas tends to infinity. Second, the Set-wise stable set of a two-fold replicated market already coincides with the set of competitive equilibrium payoffs. Third, for any number of replicas there is a market with a Core payoff that is not a competitive equilibrium payoff.

On stability of solutions to systems of convex inequalities

"Vegeu el resum a l'inici del document del fitxer adjunt."

Some solutions to obtain very efficient separations in isocratic and gradient modes using small particles size and ultra-high pressure.

The UHPLC strategy which combines sub-2 microm porous particles and ultra-high pressure (>1000 bar) was investigated considering very high resolution criteria in both isocratic and gradient modes, with mobile phase temperatures between 30 and 90 degrees C. In isocratic mode, experimental conditions to reach the maximal efficiency were determined using the kinetic plot representation for DeltaP(max)=1000 bar. It has been first confirmed that the molecular weight of the compounds (MW) was a critical parameter which should be considered in the construction of such curves. With a MW around 1000 g mol(-1), efficiencies as high as 300,000 plates could be theoretically attained using UHPLC at 30 degrees C. By limiting the column length to 450 mm, the maximal plate count was around 100,000. In gradient mode, the longest column does not provide the maximal peak capacity for a given analysis time in UHPLC. This was attributed to the fact that peak capacity is not only related to the plate number but also to column dead time. Therefore, a compromise should be found and a 150 mm column should be preferentially selected for gradient lengths up to 60 min at 30 degrees C, while the columns coupled in series (3x 150 mm) were attractive only for t(grad)>250 min. Compared to 30 degrees C, peak capacities were increased by about 20-30% for a constant gradient length at 90 degrees C and gradient time decreased by 2-fold for an identical peak capacity.

Use-dependent block of the voltage-gated Na+ channel by tetrodotoxin and saxitoxin: Effect of pore mutations that change ionic selectivity.

Voltage-gated Na(+) channels (NaV channels) are specifically blocked by guanidinium toxins such as tetrodotoxin (TTX) and saxitoxin (STX) with nanomolar to micromolar affinity depending on key amino acid substitutions in the outer vestibule of the channel that vary with NaV gene isoforms. All NaV channels that have been studied exhibit a use-dependent enhancement of TTX/STX affinity when the channel is stimulated with brief repetitive voltage depolarizations from a hyperpolarized starting voltage. Two models have been proposed to explain the mechanism of TTX/STX use dependence: a conformational mechanism and a trapped ion mechanism. In this study, we used selectivity filter mutations (K1237R, K1237A, and K1237H) of the rat muscle NaV1.4 channel that are known to alter ionic selectivity and Ca(2+) permeability to test the trapped ion mechanism, which attributes use-dependent enhancement of toxin affinity to electrostatic repulsion between the bound toxin and Ca(2+) or Na(+) ions trapped inside the channel vestibule in the closed state. Our results indicate that TTX/STX use dependence is not relieved by mutations that enhance Ca(2+) permeability, suggesting that ion-toxin repulsion is not the primary factor that determines use dependence. Evidence now favors the idea that TTX/STX use dependence arises from conformational coupling of the voltage sensor domain or domains with residues in the toxin-binding site that are also involved in slow inactivation.

Compositional data analysis of archaeological glass: problems and possible solutions

Presentation in CODAWORK'03, session 4: Applications to archeometry