Orthosymplectic Jordan superalgebras and the Wedderburn principal theorem (WPT)

An analogue of the Wedderbur principal theorem (WPT) is considered for finite dimensional Jordan superalgebras A with solvable radical N, such that N^2=0 and A/N is isomorphic to Josp_n|2m(F), where F is an algebraicallly closed field of characteristic zero. Let's we prove that the WPT is valid under some restrictions over the irreducible Josp_n|2m(F)-bimodules contained in N, and it is shown with counter-examples that these restrictions can not be weakened.Comment: 13 page

Quasi-exact solvability beyond the SL(2) algebraization

We present evidence to suggest that the study of one dimensional quasi-exactly solvable (QES) models in quantum mechanics should be extended beyond the usual \sla(2) approach. The motivation is twofold: We first show that certain quasi-exactly solvable potentials constructed with the \sla(2) Lie algebraic method allow for a new larger portion of the spectrum to be obtained algebraically. This is done via another algebraization in which the algebraic hamiltonian cannot be expressed as a polynomial in the generators of \sla(2). We then show an example of a new quasi-exactly solvable potential which cannot be obtained within the Lie-algebraic approach.Comment: Submitted to the proceedings of the 2005 Dubna workshop on superintegrabilit

Exchange operator formalism for N-body spin models with near-neighbors interactions

We present a detailed analysis of the spin models with near-neighbors interactions constructed in our previous paper [Phys. Lett. B 605 (2005) 214] by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials.Comment: RevTeX, 31 pages, no figures; important additional conten

Forecasting characteristic earthquakes in a minimalist model

International audienceUsing error diagrams, we quantify the forecasting of characteristic-earthquake occurrence in a recently introduced minimalist model. Initially we connect the earthquake alarm at a fixed time after the ocurrence of a characteristic event. The evaluation of this strategy leads to a one-dimensional numerical exploration of the loss function. This first strategy is then refined by considering a classification of the seismic cycles of the model according to the presence, or not, of some factors related to the seismicity observed in the cycle. These factors, statistically speaking, enlarge or shorten the length of the cycles. The independent evaluation of the impact of these factors in the forecast process leads to two-dimensional numerical explorations. Finally, and as a third gradual step in the process of refinement, we combine these factors leading to a three-dimensional exploration. The final improvement in the loss function is about 8.5%

Petrophysical characterization of the Dolomitic Member of the Boñar Formation (Upper Cretaceous; Duero Basin, Spain) as a potential CO2 reservoir

La Formación Boñar (Cretácico Superior) es una sucesión carbonática que aflora al Norte de la Cuenca del Duero (España). Según datos previos, el Miembro Dolomítico de esta formación es el que muestra características petrográficas más favorables para almacenamiento geológico de CO2. El principal objetivo de este trabajo es el aporte de elementos de juicio que apoyen, clarifiquen y concreten –a un nivel de estudio preliminar– la potencialidad del Miembro Dolomítico de la Formación Boñar como roca almacén. La Formación Boñar (Cretácico Superior) es una sucesión carbonática que aflora al Norte de la Cuenca del Duero (España). Según datos previos, el Miembro Dolomítico de esta formación es el que muestra características petrográficas más favorables para almacenamiento geológico de CO2. El principal objetivo de este trabajo es el aporte de elementos de juicio que apoyen, clarifiquen y concreten –a un nivel de estudio preliminar– la potencialidad del Miembro Dolomítico de la Formación Boñar como roca almacén.Boñar Formation (Upper Cretaceous) is a mainly carbonate succession, which outcrops in the North of Duero Basin (Spain). According to the existing data, the Dolomitic Member of this formation appears to be the most suitable for geological storage of CO2. The main objective of this study is to find evidence to support, clarify and specify –at an initial level– the potential of the Dolomitic Member of the Boñar Formation as a geological reservoir. The study covers density, porosity and permeability tests on samples obtained from the outcrop of the succession near the village of Boñar (León). According to the analysis and interpretation of the mentioned petrophysical properties, the porosity of the Dolomitic Member is within the acceptable range for CO2 geological storage, but the permeability values are far too low. This minimizes the possibilities of the Dolomitic Member –and probably of the whole Boñar Formation– to become an appropriate CO2 reservoir

New Algebraic Quantum Many-body Problems

We develop a systematic procedure for constructing quantum many-body problems whose spectrum can be partially or totally computed by purely algebraic means. The exactly-solvable models include rational and hyperbolic potentials related to root systems, in some cases with an additional external field. The quasi-exactly solvable models can be considered as deformations of the previous ones which share their algebraic character.Comment: LaTeX 2e with amstex package, 36 page