Rate of convergence of a particle method to the solution of the Mc Kean-Vlasov's equation

This paper studies the rate of convergence of an appropriatediscretization scheme of the solution of the Mc Kean-Vlasovequation introduced by Bossy and Talay. More specifically,we consider approximations of the distribution and of thedensity of the solution of the stochastic differentialequation associated to the Mc Kean - Vlasov equation. Thescheme adopted here is a mixed one: Euler/weakly interactingparticle system. If $n$ is the number of weakly interactingparticles and $h$ is the uniform step in the timediscretization, we prove that the rate of convergence of thedistribution functions of the approximating sequence in the $L^1(\Omega\times \Bbb R)$ norm and in the sup norm is of theorder of $\frac 1{\sqrt n} + h $, while for the densities is ofthe order $ h +\frac 1 {\sqrt {nh}}$. This result is obtainedby carefully employing techniques of Malliavin Calculus.

The struggle against creative accounting: Is "true and fair view" part of the problem or part of the solution?

Creative accounting is a growing issue of interest in Spain. In this article we argue that the concept true and fair view can limit or promote the use of creative accounting depending upon its interpretation. We review the range of meanings that true and fair view can take at an international level and compare the experience of the United Kingdom with the Australian one by analysing the use of true and fair view to limit creative accounting. Finally, we suggest lines of action to be considered by the Spanish accounting standards-setting institutions.

Pitfalls in the modeling of forward-looking price setting and investment decisions

The present paper makes progress in explaining the role of capital for inflation and output dynamics. We followWoodford (2003, Ch. 5) in assuming Calvo pricing combined with a convex capital adjustment cost at the firm level. Our main result is that capital accumulation affects inflation dynamics primarily through its impact on the marginal cost. This mechanism is much simpler than the one implied by the analysis in Woodford's text. The reason is that his analysis suffers from a conceptual mistake, as we show. The latter obscures the economic mechanism through which capital affects inflation and output dynamics in the Calvo model, as discussed in Woodford (2004).

Forward induction and the excess capacity puzzle: An experimental investigation

While the theoretical industrial organization literature has long arguedthat excess capacity can be used to deter entry into markets, there islittle empirical evidence that incumbent firms effectively behave in thisway. Bagwell and Ramey (1996) propose a game with a specific sequence ofmoves and partially-recoverable capacity costs in which forward inductionprovides a theoretical rationalization for firm behavior in the field. Weconduct an experiment with a game inspired by their work. In our data theincumbent tends to keep the market, in contrast to what the forwardinduction argument of Bagwell and Ramey would suggest. The results indicatethat players perceive that the first mover has an advantage without havingto pre-commit capacity. In our game, evolution and learning do not driveout this perception. We back these claims with data analysis, atheoretical framework for dynamics, and simulation results.

Generalized Multiobjective Multitree model solution using MOEA

In a previous paper a novel Generalized Multiobjective Multitree model (GMM-model) was proposed. This model considers for the first time multitree-multicast load balancing with splitting in a multiobjective context, whose mathematical solution is a whole Pareto optimal set that can include several results than it has been possible to find in the publications surveyed. To solve the GMM-model, in this paper a multi-objective evolutionary algorithm (MOEA) inspired by the Strength Pareto Evolutionary Algorithm (SPEA) is proposed. Experimental results considering up to 11 different objectives are presented for the well-known NSF network, with two simultaneous data flows

Reduction of symmetry in grandite solid solution

The results of a crystal structure refinement of an anisotropic grandite garnet specimen with composition Gro36-4 And63-6 are given. The structure obtained has orthorrombic symmetry (space group Fddd) and is compared with similar results obtained by other authors. In all cases the reduction of symmetry is due to the ordering of Fe3+ and Al in octahedral sites. Non cubic structures of grandites are discussed in connection with optical, morphological an grou-th features of these minerals.

Von Neumann-Morgenstern solution and convex descompositions of TU games

We study under which conditions the core of a game involved in a convex decomposition of another game turns out to be a stable set of the decomposed game. Some applications and numerical examples, including the remarkable Lucas¿ five player game with a unique stable set different from the core, are reckoning and analyzed.

SIMSAFADIM-CLASTIC: A new approach to mathematical 3D forward simulation modelling for terrigenous and carbonate marine sedimentation

Most sedimentary modelling programs developed in recent years focus on either terrigenous or carbonate marine sedimentation. Nevertheless, only a few programs have attempted to consider mixed terrigenous-carbonate sedimentation, and most of these are two-dimensional, which is a major restriction since geological processes take place in 3D. This paper presents the basic concepts of a new 3D mathematical forward simulation model for clastic sediments, which was developed from SIMSAFADIM, a previous 3D carbonate sedimentation model. The new extended model, SIMSAFADIM-CLASTIC, simulates processes of autochthonous marine carbonate production and accumulation, together with clastic transport and sedimentation in three dimensions of both carbonate and terrigenous sediments. Other models and modelling strategies may also provide realistic and efficient tools for prediction of stratigraphic architecture and facies distribution of sedimentary deposits. However, SIMSAFADIM-CLASTIC becomes an innovative model that attempts to simulate different sediment types using a process-based approach, therefore being a useful tool for 3D prediction of stratigraphic architecture and facies distribution in sedimentary basins. This model is applied to the neogene Vallès-Penedès half-graben (western Mediterranean, NE Spain) to show the capacity of the program when applied to a realistic geologic situation involving interactions between terrigenous clastics and carbonate sediments.

Binding energy and momentum distribution of nuclear matter using Green's functions methods

The influence of hole-hole (h-h) propagation in addition to the conventional particle-particle (p-p) propagation, on the energy per particle and the momentum distribution is investigated for the v2 central interaction which is derived from Reid¿s soft-core potential. The results are compared to Brueckner-Hartree-Fock calculations with a continuous choice for the single-particle (SP) spectrum. Calculation of the energy from a self-consistently determined SP spectrum leads to a lower saturation density. This result is not corroborated by calculating the energy from the hole spectral function, which is, however, not self-consistent. A generalization of previous calculations of the momentum distribution, based on a Goldstone diagram expansion, is introduced that allows the inclusion of h-h contributions to all orders. From this result an alternative calculation of the kinetic energy is obtained. In addition, a direct calculation of the potential energy is presented which is obtained from a solution of the ladder equation containing p-p and h-h propagation to all orders. These results can be considered as the contributions of selected Goldstone diagrams (including p-p and h-h terms on the same footing) to the kinetic and potential energy in which the SP energy is given by the quasiparticle energy. The results for the summation of Goldstone diagrams leads to a different momentum distribution than the one obtained from integrating the hole spectral function which in general gives less depletion of the Fermi sea. Various arguments, based partly on the results that are obtained, are put forward that a self-consistent determination of the spectral functions including the p-p and h-h ladder contributions (using a realistic interaction) will shed light on the question of nuclear saturation at a nonrelativistic level that is consistent with the observed depletion of SP orbitals in finite nuclei.

Zenith angle distributions at Super-Kamiokande and SNO and the solution of the solar neutrino problem

We have performed a detailed study of the zenith angle dependence of the regeneration factor and distributions of events at SNO and SK for different solutions of the solar neutrino problem. In particular, we discuss the oscillatory behavior and the synchronization effect in the distribution for the LMA solution, the parametric peak for the LOW solution, etc. A physical interpretation of the effects is given. We suggest a new binning of events which emphasizes the distinctive features of the zenith angle distributions for the different solutions. We also find the correlations between the integrated day-night asymmetry and the rates of events in different zenith angle bins. The study of these correlations strengthens the identification power of the analysis.

Film-free laser forward printing of transparent and weakly absorbing liquids

A laser-based technique for printing transparent and weakly absorbing liquids is developed. Its principle of operation relies in the tight focusing of short laser pulses inside the liquid and close to its free surface, in such a way that the laser radiation is absorbed in a tiny volume around the beam waist, with practically no absorption in any other location along the beam path. If the absorbed energy overcomes the optical breakdown threshold, a cavitation bubble is generated, and its expansion results in the propulsion of a small fraction of liquid which can be collected on a substrate, leading to the printing of a microdroplet for each laser pulse. The technique does not require the preparation of the liquid in thin film form, and its forward mode of operation imposes no restriction concerning the optical properties of the substrate. These characteristics make it well suited for printing a wide variety of materials of interest in diverse applications. We demonstrate that the film-free laser forward printing technique is capable of printing microdroplets with good resolution, reproducibility and control, and analyze the influence of the main process parameter, laser pulse energy. The mechanisms of liquid printing are also investigated: time-resolved imaging provides a clear picture of the dynamics of liquid transfer which allows understanding the main features observed in the printed droplets.

Exact gravitational shockwaves and Planckian scattering on branes

We obtain a solution describing a gravitational shock wave propagating along a Randall-Sundrum brane. The interest of such a solution is twofold: on the one hand, it is the first exact solution for a localized source on a Randall-Sundrum three-brane. On the other hand, one can use it to study forward scattering at Planckian energies, including the effects of the continuum of Kaluza-Klein modes. We map out the different regimes for the scattering obtained by varying the center-of-mass energy and the impact parameter. We also discuss exact shock waves in ADD scenarios with compact extra dimensions.

A Rotating black ring solution in five dimensions

The vacuum Einstein equations in five dimensions are shown to admit a solution describing a stationary asymptotically flat spacetime regular on and outside an event horizon of topology S1S2. It describes a rotating black ring. This is the first example of a stationary asymptotically flat vacuum solution with an event horizon of nonspherical topology. The existence of this solution implies that the uniqueness theorems valid in four dimensions do not have simple five-dimensional generalizations. It is suggested that increasing the spin of a spherical black hole beyond a critical value results in a transition to a black ring, which can have an arbitrarily large angular momentum for a given mass.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.