Abstract:
We have studied the fossil Rhinocerotidae from Bu ol (Valencia, Spain). It is realized as stratigraphic synthesis of the deposit and dated as Orleanium Mammal Age (lower-middle Aragonium), which is equivalent to the 4b Neogene MammaL Unit (zonation of Mein, 1976). We conclude that the fossil association is a thanatocoenosis, with strongly rounded elements. The paleoenvironment, in which this association was accumulated, was a marsh zone in the distal part of an alluvial fan. Two species of Rhinocerotidae have been determined, one of the ,genus Acerotherium and another of the genus Dicerorhinus. The second is more abundant than the former and probably it would be adapted to a marshy habitat. We describe and figure the more representative material of both species. Se han estudiado los Rinoceróntidos fósiles de Bu ol (Valencia). Se realiza una síntesis estratigráfica del yacimiento, estableciéndose su edad orleaniense (Aragoniense inferior-medio), equivalente a la zona 4b de la zonación de Mein (1975). Se concluye que el yacimiento corresponde a una tanatocenosis, con elementos fuertemente rodados, acumulada en una zona palustre situada en la parte distal de un abanico aluvial. Se han determinado dos especies de Rinoceróntidos: una, correspondiente al género Aceratherium, está poco representada y otra, asignable al género Dicerorhinus, es más abundante y probablemente estaba adaptada a un hábitat pantanoso. Se describe y figura el material más representativo de ambas especies.

Abstract:
In this work we present a numerical study, based on molecular dynamics simulations, to estimate the freezing point of hard spheres and hypersphere systems in dimension D = 4, 5, 6 and 7. We have studied the changes of the Radial Distribution Function (RDF) as a function of density in the coexistence region. We started our simulations from crystalline states with densities above the melting point, and moved down to densities in the liquid state below the freezing point. For all the examined dimensions (including D = 3) it was observed that the height of the first minimum of the RDF changes in an almost continuous way around the freezing density and resembles a second order phase transition. With these results we propose a numerical method to estimate the freezing point as a function of the dimension D using numerical fits and semiempirical approaches. We find that the estimated values of the freezing point are very close to previously reported values from simulations and theoretical approaches up to D = 6 reinforcing the validity of the proposed method. This was also applied to numerical simulations for D = 7 giving new estimations of the freezing point for this dimensionality.

Abstract:
We prove a general extrinsic rigidity theorem for homogeneous varieties in $\mathbb{CP}^N$. The theorem is used to show that the adjoint variety of a complex simple Lie algebra $\mathfrak{g}$ (the unique minimal G orbit in $\mathbb{P}\mathfrak{g}$) is extrinsically rigid to third order. In contrast, we show that the adjoint variety of $SL_3\mathbb{C}$, and the Segre product $\mathit{Seg}(\mathbb{P}^1\times \mathbb{P}^n)$, both varieties with osculating sequences of length two, are flexible at order two. In the $SL_3\mathbb{C}$ example we discuss the relationship between the extrinsic projective geometry and the intrinsic path geometry. We extend machinery developed by Hwang and Yamaguchi, Se-ashi, Tanaka and others to reduce the proof of the general theorem to a Lie algebra cohomology calculation. The proofs of the flexibility statements use exterior differential systems techniques.

Abstract:
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe explicitly.

Abstract:
We classify codimension two analytic submanifolds X of projective space having the property that any line through a general point p having contact to order two with X at p automatically has contact to order three. We give applications to the study of the Debarre--de Jong conjecture, and of n-dimensional varieties whose Fano variety of lines has dimension 2n-4.

Abstract:
Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.

Abstract:
Crampes and Moreaux [1] provide a two period model of competition between a hydrostation and a thermal station for the generation of electricity. We modify this model to make it more directly comparable with an infinite horizon model. The closed loop equilibrium is characterized.

Abstract:
A thermodynamic approach to derive the liquid-glass transition line in the reduced temperature vs reduced density plane for a monatomic Lennard-Jones fluid is presented. The approach makes use of a recent reformulation of the classical perturbation theory of liquids [M. Robles and M. L\'opez de Haro, Phys. Chem. Chem. Phys. {\bf 3}, 5528 (2001)] which is at grips with a rational function approximation for the Laplace transform of the radial distribution function of the hard-sphere fluid. The only input required is an equation of state for the hard-sphere system. Within the Mansoori-Canfield/Rasaiah-Stell variational perturbation theory, two choices for such an equation of state, leading to a glass transition for the hard-sphere fluid, are considered. Good agreement with the liquid-glass transition line derived from recent molecular dynamic simulations [Di Leonardo et al., Phys. Rev. Lett. {\bf 84}, 6054(2000)] is obtained.

Abstract:
We show that a microscopic definition of crystal defect, based on the effective mean single-particle potential energy, makes it possible to detect and visualize various types of local and extended crystal defects and develop an effective algorithm for tracking their time evolution.

Abstract:
The phase diagram of the attractive hard-core Yukawa fluid derived previously [M. Robles and M. L\'opez de Haro, J. Phys. Chem. C 111, 15957 (2007)] is used to obtain the liquid-vapor coexistence curve of real water. To this end, the value of the inverse range parameter of the intermolecular potential in the Yukawa fluid is fixed so that the ratio of the density at the critical point to the liquid density at the triple point in this model coincides with the same ratio in water. Subsequently, a (relatively simple) nonlinear rescaling of the temperature is performed which allows one to obtain the full liquid vapor coexistence curve of real water in the temperature-density plane with good accuracy, except close to the triple point. Such rescaling may be physically interpreted in terms of an effective temperature-dependent attractive hard-core Yukawa interaction potential which in turn introduces an extra temperature dependence in the equation of state. With the addi- tion of a multiplicative factor to obtain from the model the critical pressure of real water, the corrected equation of state yields reasonably accurate isotherms in the liquid phase region except in the vicinity of the critical isotherm and in the vicinity of the triple point isotherm. The liquid-vapor coexistence curves in the pressure-temperature and pressure-density planes are also computed and a possible way to improve the quantitative agreement with the real data is pointed out.