Isoperimetric inequalities in Riemann surfaces of infinite type

75 pages, 1 figure.-- MSC2000 code: 30F45.MR#: MR1715412 (2000j:30075)Zbl#: Zbl 0935.30028Research partially supported by a grant from Dirección General de Enseñanza Superior (Ministerio de Educación y Ciencia), Spain.Publicad

Approximation theory for weighted Sobolev spaces on curves

17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.Research of V. Álvarez, D. Pestana and J.M. Rodríguez partially supported by a grant from DGI, BFM2000-0206-C04-01, Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II

32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.Research partially supported by a grant from DGES (MEC), Spain.Publicad

Weighted Sobolev spaces on curves

45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.Research of second (D.P.), third (J.M.R.) and fourth (E.R.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Estructura de superficies de Riemann, desigualdades isoperimétricas y medida p-armónica en grafos

Se estructura el trabajo en torno a un capítulo introductorio y cinco capítulos temáticos que desarrollan teorías referidas a la descomposición de superficies, a la desigualdad isopemétrica en superficies de Riemann con punturas, a la desigualdad isoperimétrica en superficies de Denjoy, a la desigualdad isoperimétrica en superficies de Riemann generales y a la medida p-armónica en Arboles. En el capítulo introductorio se tratan conceptos importantes para poder exponer los resultados obtenidos y se describe, de forma breve cuáles son esos resultados

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey

6 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2219917 (2006k:42051)Zbl#: Zbl 1146.42005In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first author (J.M.R.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain. Research by second author (V.A.) was partially supported by grants from MCYT (MTM 2004-00078) and Junta de Andalucía (FQM-210), Spain. Research by third author (E.R.) was partially supported by a grant from DGI (BFM 2003-06335-C03-02), Spain. Research by fourth author (D.P.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain.Publicad

Gromov hyperbolicity of Denjoy domains

25 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2276245 (2007i:30069)Zbl#: Zbl 1115.53030In this paper we characterize the Gromov hyperbolicity of the double of a metric space. This result allows to give a characterization of the hyperbolic Denjoy domains, in terms of the distance to $\Bbb{R}$ of the points in some geodesics. In the particular case of trains (a kind of Riemann surfaces which includes the flute surfaces), we obtain more explicit criteria which depend just on the lengths of what we have called fundamental geodesics.Research partially supported by three grants from M.E.C. (MTM 2006-11976, MTM 2006-13000-C03-02 and MTM 2004-21420-E), Spain.Publicad

El catear de la montaña minera: Una propuesta del quehacer diario sobre un grupo de mineros en el municipio de La Llanada Nariño

En la actualidad las obras de arte, y en especial aquellas que se incluyen entre las llamadas Artes Visuales investigan una forma de vida, un estilo de vida en conexión con el conocimiento; haciendo posible la visualización del otro en este caso el minero. La hermenéutica permite el ejercicio de interpretación del lenguaje artístico y la práctica del minero, entonces el Catear de la montaña se puede entender como un fenómeno reflexivo que se presenta cuando la montaña catea al minero, cuando ejerce la actividad de cateo sobre éste. Porque el minero no es solo quien catea la montaña sino también quien es cateado por la montaña. Cateo = purificación

Aplicación de la química analítica en el estudio de metales en alimentos

En la actualidad ha surgido interés en la calidad de los alimentos que consume el hombre, por lo que, es importante determinar contaminantes en alimentos. En este trabajo se analiza la presencia de metales en vegetales que son cultivados en las Chinampas de Xochimilco; estos son regados con aguas tratadas y residuales procedentes de descargas industriales y municipales. Es probable que exista contaminación por metales tóxicos (Galán y Romero 2008) para el hombre, como son: Cr, Pb y Cu. La Unión Europea propone como límite máximo de plomo en hortalizas de 0.1 a 0.3 ppm, el cromo con un límite de 0.1 ppm para cualquier alimento y el cobre de 10 ppm. En este trabajo se analizaron hojas de espinaca, betabel y brócoli, los cuales tiene un contenido de plomo de 0.5, 0.291 y 0.258 ppm respectivamente; cromo en hoja de espinaca 0.365 ppm, en betabel 0.249 ppm, en brócoli no se detectan cantidades apreciables de este metal; el cobre para estas hortalizas está dentro del límite permitido por la Unión Europea (Unión Europea 2014). Para respaldar los resultados obtenidos se realizó un análisis estadístico para la determinación de sensibilidad, límite de detección, límite de cuantificación para cada uno de los metales analizados por espectroscopía de absorción atómica.Nowadays there is a great concern about the quality of the food consumed by man. Hence the importance of identifying the contaminants in food. In this investigation project the presence of metals in vegetables that are cultivated in the chinampas of Xochimilco is analyzed. These crops are irrigated with treated water that comes from industrial and municipal discharges. It is likely that there might be contamination of toxic metals such as Cr, Pb and Cu. The European Union proposes 0.1 to 0.3 ppm as the maximum limit of Lead in crops. Chromium has a limit of 0.1 ppm for any food, whereas Copper limit is 10 ppm. In this investigation spinach, beetroot and broccoli leaves were analyzed. The Lead content of the samples was 0.5, 0.291 and 0.258 ppm respectively. Chromium in spinach leaves was 0.365 ppm, while in beetroot was 0.249 ppm. However, in broccoli no appreciable amounts of this metal were detected. Copper in these crops is within the limit allowed by the European Union. In order to support the results obtained, a statistical analysis for the determination of sensibility, detection limit and quantification limit was carried out for every metal that was analyzed using atomic absorption spectroscopy