Quasi Exactly Solvable NxN-Matrix Schroedinger Operators

New examples of matrix quasi exactly solvable Schroedinger operators are constructed. One of them constitutes a matrix generalization of the quasi exactly solvable anharmonic oscillator, the corresponding invariant vector space is constructed explicitely. Also investigated are matrix generalizations of the Lame equation.Comment: 16 latex pages, new results adde

Quasi-exactly Solvable Lie Superalgebras of Differential Operators

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

Rotura cuadricipital en edad pediátrica

La rotura del tendón del cuádriceps es una patología característica de la edad adulta, siendo excepcional en la infancia. Se presenta el caso de un niño de 9 años con una gonalgia izquierda de 2 meses de evolución sin claro antecedente traumático. Se realiza Resonancia Magnética, que establece el diagnóstico de rotura parcial del tendón del cuádriceps. Se decide reanclaje del mismo en el polo superior de la rótula, seguido de rehabilitación. Después del tratamiento quirúrgico realizado el paciente recupera el balance articular y muscular. La rotura del tendón del cuádriceps es excepcional en la edad pediátrica. La realización de una buena exploración, tanto clínica como radiológica es fundamental. El tratamiento viene determinado por el tipo de rotura y la clínica asociada. Hemos realizado una revisión bibliográfica de la literatura con el fin de dar a conocer este tipo de patología y su manejo.Rupture of the quadriceps tendon is a common pathology in adults, but exceptionally rare in children. The case reported is that of a 9-year old boy with a 2-month history of pain in the left knee without any clear history of trauma. Magnetic Resonance Imaging study was carried out, leading to the diagnosis of partial tear of the left quadricipital tendon. The tendon was re-anchored at the upper pole of the patella, followed by rehabilitation. The patient recovered joint and muscular balance after the surgery. Rupture of the quadriceps tendon is exceptionally rare at pediatric ages. A thorough examination, both clinical as well as radiological, is of fundamental importance. Treatment is determined by the kind of rupture and associated clinical symptoms. We have carried out a bibliographical review of the literature in order to offer a better understanding of this pathology and its treatment

On the generalised Chaplygin gas: worse than a big rip or quieter than a sudden singularity?

Although it has been believed that the models with generalised Chaplygin gas do not contain singularities, in a previous work we have studied how a big freeze could take place in some kinds of phantom generalised Chaplygin gas. In the present work, we study some types of generalised Chaplygin gas in order to show how different sorts of singularities could appears in such models, in the future or in the past. We point out that: (i) singularities may not be originated from the phantom nature of the fluid, and (ii) if initially the tension of the brane in a brane-world Chaplygin model is large enough then an infrared cut off appears in the past.Comment: 19 pages, 6 figures. Discussion expanded and references added. Version to appear in the International Journal of Modern Physics

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

Snap beans: Present status in the developing world and bibliography of research (1919-1987)

The present status of snap beans in the developing world is reviewed in the leading paper accompanying this publication. Socioeconomic aspects are mainly discussed. Production, marketing, and consumption features are described and the future potential for the crop is outlined. Constraints to production increases are discussed and the opportunities for research and development of the crop are defined. The bibliography contains 922 references to research on snap beans. Most of the documents (761) are available at CIAT. References are organized by disciplines and are complemented with author and subject indexes. The institutions identified by the Bean Information Center as carrying out research on snap beans are listed in the enclosed preliminary directory, which also includes the names of the snap bean researchers recorded in the CIAT database and the participants in the workshop on snap bean breeding held at CIAT in 1987. (CIAT)Se revisa la situacion actual de la habichuela en el mundo en desarrollo en el articulo principal que acompana esta bibliografia. Se discuten principalmente los aspectos socioeconomicos. Se describen los aspectos de produccion, mercadeo y consumo y se esboza el potencial futuro para el cultivo. Se discuten las limitaciones para el incremento de la produccion y se definen las oportunidades de investigacion y desarrollo del cultivo. La bibliografia contiene 922 referencias de investigacion sobre habichuela. La mayoria de los documentos (761) se encuentran disponibles en el CIAT. Las referencias estan organizadas por disciplinas y complementadas con indices de autores y materias. En el directorio preliminar adjunto se enumeran las instituciones identificadas por el Centro de Informacion sobre Frijol que estan realizando investigacion en habichuela. Tambien se incluyen los nombres de los investigadores de habichuela registrados en la base de datos del CIAT y los participantes en la reunion sobre mejoramiento de habichuela realizado en CIAT en 1987. (CIAT