On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

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

A Novel Multi-parameter Family of Quantum Systems with Partially Broken N-fold Supersymmetry

We develop a systematic algorithm for constructing an N-fold supersymmetric system from a given vector space invariant under one of the supercharges. Applying this algorithm to spaces of monomials, we construct a new multi-parameter family of N-fold supersymmetric models, which shall be referred to as "type C". We investigate various aspects of these type C models in detail. It turns out that in certain cases these systems exhibit a novel phenomenon, namely, partial breaking of N-fold supersymmetry.Comment: RevTeX 4, 28 pages, no figure

Proximal, Microbiological and Nutritional Characterization in Chinese Potato Flour of the White Variety Colocasia Esculenta for Application in Functional Foods

The study presents a qualitative-quantitative scope through descriptive statistics for the variables studied with its analyses, with the objective of performing physical, proximal, microbiological and contained characterization of amino acids in Chinese potato flour of the white variety Colocasia esculenta for its application in functional foods. By obtaining the flour, the proximal percentages are evaluated; moisture 9.01%, ash 2.24 ± 0.15% protein 2.02 ± 0.02% fiber 4.25 ± 0.26% and fat 0.43 ± 0.15%. Additionally, the physical-chemical analyses carried out on the flour obtain a pH of 6.66 ± 0.10% acidity (oxalic) 2.24 ± 0.00% Brix degrees 2 ± 0.50%. The nutritional values reported in the Chinese potato flour of the white variety lies mainly in its content of Methionine with a value of 21.15%, Alanine with 10.43%, Isoleucine with 8.08%, Threonine with 7.41%, Histidine with 3.65% and lysine with 3.10%. Finally, the microbiological analysis of the product is determined, concluding that they are within the parameters established in wheat flours with the INEN 616: 2006 standard; thus it is considered of good quality, suitable for human consumption and consequently, for use in the food industry. Therefore, it can be used as functional food or be transformed through the use of different techniques, thus being an important plant genetic resource to improve the nutritional quality of food, productivity, food health, as well as the protection and prevention of diseases in areas of the equator with high levels of malnutrition. Keywords: characterization, nutritional food, Chinese potato, industrialization, flour. Resumen El estudio presenta un alcance cualitativo-cuantitativo mediante la estadística descriptiva para las variables estudiadas con sus respectivos análisis y el objetivo de realizar la caracterización física, proximal, microbiológica y contenida de aminoácidos en harina de papa China de la variedad blanca Colocasia esculenta para su aplicación en alimentos funcionales. Mediante la obtención de la harina se evalúa los porcentajes proximales; humedad 9,01%, cenizas 2,24 ± 0,15% proteína 2,02 ± 0,02% fibra 4,25 ± 0,26% y grasa 0,43 ± 0.15%. Además, los análisis físico-químicos realizados en la harina se obtiene un pH de 6,66 ± 0,10% acidez (oxálico) 2,24 ± 0,00% grados Brix 2 ± 0,50%. Los valores nutricionales reportados en la harina de papa China de la variedad blanca radica principalmente en su contenido de Metionina con un valor de 21,15%, Alanina 10,43%, Isoleucina 8,08%, Treonina 7,41%, Histidina 3,65% y lisina con el 3,10%. Finalmente, se determina el análisis microbiológico del producto concluyendo que se encuentran dentro de los parámetros establecidos en harinas de trigo con la norma INEN 616:2006 de este modo se considera de buena calidad, apta para el consumo humano y consecutivamente empleada en industria alimentaria. Por lo que, puede ser utilizado como alimento funcional o ser trasformado mediante la utilización de distintas técnicas siendo así un importante recurso fitogenético para mejorar la calidad nutricional de los alimentos, la productividad, la 171 sanidad alimentaria, así como la protección y prevención de enfermedades en zonas del ecuador con altos niveles de desnutrición. Palabras clave: caracterización, alimento nutricional, papa China, industrialización, harina

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

On the families of orthogonal polynomials associated to the Razavy potential

We show that there are two different families of (weakly) orthogonal polynomials associated to the quasi-exactly solvable Razavy potential V(x)=(\z \cosh 2x-M)^2 (\z>0, $M\in\mathbf N$). One of these families encompasses the four sets of orthogonal polynomials recently found by Khare and Mandal, while the other one is new. These results are extended to the related periodic potential U(x)=-(\z \cos 2x -M)^2, for which we also construct two different families of weakly orthogonal polynomials. We prove that either of these two families yields the ground state (when $M$ is odd) and the lowest lying gaps in the energy spectrum of the latter periodic potential up to and including the $(M-1)^{\rm th}$ gap and having the same parity as $M-1$. Moreover, we show that the algebraic eigenfunctions obtained in this way are the well-known finite solutions of the Whittaker--Hill (or Hill's three-term) periodic differential equation. Thus, the foregoing results provide a Lie-algebraic justification of the fact that the Whittaker--Hill equation (unlike, for instance, Mathieu's equation) admits finite solutions.Comment: Typeset in LaTeX2e using amsmath, amssymb, epic, epsfig, float (24 pages, 1 figure

Action-Research, Professional Development of the Physical Education Teachers in Rural Schools

La finalidad de este estudio es analizar la influencia de un grupo de trabajo de Investigación-Acción en el desarrollo profesional de maestros de Educación Física (EF) que ejercen su labor docente en la Escuela Rural. El diseño es un estudio multicaso. Para la recogida de datos se utilizaron: historias de vida, entrevistas en profundidad, análisis de documentos y diario de investigación. El análisis de datos se realizó a través de un proceso de categorización. Los resultados muestran que: (a)-los maestros de EF que ejercen su labor docente en la escuela rural pasan por situaciones difíciles y complicadas los primeros años, y que la pertenencia a grupos de Investigación-Acción les ayuda a que la adaptación a este contexto educativo sea más rápida y fácil; (b)-la metodología de Investigación-Acción genera procesos de reflexión que ayudan a mejorar su práctica docente, influye positivamente en su desarrollo profesional y supone un apoyo.The purpose of this paper is to analyze the influence of a Action Research group on professional development of physical education (PE) teachers in rural school. The research methodology used was case study. Data collection was conducted through interviews, life stories, document analysis and research notebook. Data analysis was performed through a categorization process. The results show that: (a)-PEF teachers in rural school engaged in difficult situations at early years, and to be a membership of Action Research group helps them adapt to this context educational faster and easier, (b)-the Action Research methodology generates reflective processes that help improve their teaching, has a positive influence on their professional development and represent a suppor

¿Qué está haciendo el científico? : análisis de la actividad científica descrita por alumnos secundarios chilenos de 11° y 12° grado de distintos tipos de establecimientos educacionales

Con el objetivo de conocer la representación de estudiantes secundarios chilenos de distintos tipos de establecimientos acerca de los científicos y la actividad que estos realizan, se aplicó a una muestra de 438 estudiantes de 11° y 12° grado el Draw-a-Scientist-Test, en la versión de Türkmen (2008). En ella, los alumnos son invitados a describir de manera escrita la actividad que realiza el científico que dibujaron. Dichas narraciones fueron analizadas en función de los procesos científicos relatados, propósitos y consecuencia de la actividad descrita. Los procesos científicos más frecuentemente mencionados fueron “experimentar” y “observar”. “Formular modelos”, proceso fundamental en la actividad científica, prácticamente no fue mencionado. En relación a propósitos y consecuencias la mayoría de los alumnos tiene una imagen positiva de la actividad científica

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