A timelike extension of Fermat's principle in general relativity and applications

We define a variational problem based on the arrival time functional for timelike curves on a Lorentzian manifold parameterized by a fixed constant multiple of their proper time. Under a causality assumption for the manifold , we prove that the stationary points of our problem are geodesics, obtaining an extension of the Fermat's Principle for light rays proven in [14] (see also [2]). Moreover, we study the compactness pr operties of the arrival time functional by global variational techniques. Under intrinsic assumptions on the metric of we get results of existence and multiplicity for geodesics with a given energy between an event and an observer of .     

Bayesian Analysis of Extreme Values by Mixture Modeling

Modeling of extreme values in the presence of heterogeneity is still a relatively unexplored area. We consider losses pertaining to several related categories. For each category, we view exceedances over a given threshold as generated by a Poisson process whose intensity is regulated by a specific location, shape and scale parameter. Using a Bayesian approach, we develop a hierarchical mixture prior, with an unknown number of components, for each of the above parameters. Computations are performed using Reversible Jump MCMC. Our model accounts for possible grouping effects and takes advantage of the similarity across categories, both for estimation and prediction purposes. Some guidance on the specification of the prior distribution is provided, together with an assessment of inferential robustness. The method is illustrated throughout using a data set on large claims against a well-known insurance company over a 15-year period.     

Influence of organotin compounds on phosphatidylserine membranes

Organotin compounds are widely distributed toxicants. They are membrane‐active molecules with broad biological toxicity. We have studied the interaction of tributyltin and triphenyltin with phosphatidylserine model membranes using differential scanning calorimetry, infrared spectroscopy and X‐ray diffraction techniques. Organotin compounds produced a broadening of the gel to the liquid‐crystalline phase transition of the phospholipid and a shifting of the phase transition temperature to lower values. Infrared spectroscopy experiments showed that tributyltin exerted a fluidizing effect on the apolar part of the bilayer, and that both tributyl‐ and triphenyltin interact with the interfacial region of the bilayer, making the carbonyl groups less accessible to water. As seen by X‐ray diffraction experiments, organotin compounds were unable to change the bilayer macroscopic organization of the phospholipid, but they were able to reduce the long‐range order of the multibilayer system and to disorder the packing of the phospholipid molecules. The observed interaction between organotin compounds and phosphatidylserine membranes promotes physical perturbations that could affect membrane function and may mediate some of their toxic effects. Copyright © 2004 John Wiley & Sons, Ltd.     

Synthesis, characterization and optical response of polyene-cored stilbenoid dendrimers

The synthesis of first- and second-generation dendrimers bearing phenylenevinylene chromophores within the dendritic branches (stilbenoid dendrimers) and polyenes (3 and 5 double bonds) as cores is described. A preliminary study of the optical properties of the resulting compounds was conducted by UV/vis and fluorescence spectroscopy.     

On the equipartitions of finite groups

Summary It is proved that the p- groups of submaximal class do not admit equipartitions other than the atomic (Theorem 3.2). This result is then wed to give a complete classification of the groups of order p⁶ admitting nonatomic equipartitions (Theorem 5.1).     

A model of interim information sharing under incomplete information

We propose a two-person game-theoretical model to study information sharing decisions at an interim stage when information is incomplete. The two agents have pieces of private information about the state of nature, and that information is improved by combining the pieces. Agents are both senders and receivers of information. There is an institutional arrangement that fixes a transfer of wealth from an agent who lies about her private information. In our model, we show that (1) there is a positive relation between information revelation and the amount of the transfers, and (2) information revelation has a collective action structure, in particular, the incentives of an agent to reveal decrease with respect to the amount of information disclosed by the other.     

Schauder Bases under Uniform Renormings

Let X be a separable superreflexive Banach space with a Schauder basis. We prove the existence of an equivalent uniformly smooth (resp. uniformly rotund) renorming under which the given basis is monotone. First author supported by the grants MTM2005-08379 of MECD (Spain), 00690/PI/04 of Fundación Séneca (CARM, Spain) and AP2003-4453 of MECD (Spain), Second author supported by AV0Z10190503 and A100190502.     

Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.