WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

MORE ON INDUCED MAPS ON N-FOLD SYMMETRIC PRODUCT SUSPENSIONS

We continue the work initiated by the first named author in Induced maps on n-fold symmetric product suspensions, Topology Appl. 158 (2011), 1192-1205. We consider classes of maps not included in the mentioned paper, namely: almost monotone, atriodic, freely decomposable, joining, monotonically refinable, refinable, semi-confluent, semi-open, simple and strongly freely decomposable maps

Mediacion intercultural en sociedades multiculturales : hacia una nueva conceptualización

La mediación intercultural se ha definido en los últimos años en España a partir de una práctica especializada de atención e intervención con población inmigrante extranjera en las sociedades occidentales, lo que ha dado origen a la conocida "nueva" necesidad de mediadores interculturales en estos contextos sociales. En este texto queremos dar un paso atrás analizando algunas definiciones del término mediación, para a partir de ahí reconceptualizar la práctica de la mediación intercultural no como una herramienta únicamente necesaria ante la presencia de inmigrantes extranjeros en la sociedad española, sino como el instrumento que permite la convivencia de múltiples culturas en el ámbito social. Para esto desvinculamos la mediación de la inmigración, abriéndola al campo de la diversidad cultural y permitiendo por tanto una mejor comprensión de los procesos de construcción social que están teniendo lugar en nuestros tiempos en todo el planeta.During the last decade, in Spain there has been a specialized practice and intervention with foreign immigrant population that has fostered the definition of intercultural mediation as a “new” necessity in occidental societies. In this text we want to go one step backward analyzing some of the definitions of mediation to be able to reconceptualize the practice of intercultural mediation not only as a necessary tool to face the increasing presence of foreign immigrants in Spanish society, but as the instrument that allows the cohabitation of multiple cultures in the social arena. To do this, we separate mediation from immigration, so allowing mediation to be open to any kind of cultural diversity and thus implying a better understanding of the social construction processes that are currently taking place all over the worl

Dynamic properties of the dynamical system SFnm(X), SFnm(f))

[EN] Let X be a continuum and let n be a positive integer. We consider the hyperspaces Fn(X) and SFn(X). If m is an integer such that n > m ≥ 1, we consider the quotient space SFnm(X). For a given map f : X → X, we consider the induced maps Fn(f) : Fn(X) → Fn(X), SFn(f) : SFn(X) → SFn(X) and SFnm(f) : SFnm(X) → SFnm(X). In this paper, we introduce the dynamical system (SFnm(X), SFnm (f)) and we investigate some relationships between the dynamical systems (X, f), (Fn(X), Fn(f)), (SFn(X), SFn(f)) and (SFnm(X), SFnm(f)) when these systems are: exact, mixing, weakly mixing, transitive, totally transitive, strongly transitive, chaotic, irreducible, feebly open and turbulent.This paper was partially supported by the project: “Propiedades din´amicas y topol´ogicas sobre sistemas din´amicos inducidos”, (UTMIX-PTC-064) of PRODEP, 2017.Barragán, F.; Santiago-Santos, A.; Tenorio, JF. (2020). Dynamic properties of the dynamical system SFnm(X), SFnm(f)). Applied General Topology. 21(1):17-34. https://doi.org/10.4995/agt.2020.11807OJS1734211G. Acosta, A. Illanes and H. Méndez-Lango, The transitivity of induced maps, Topology Appl. 156, no. 5 (2009), 1013-1033. https://doi.org/10.1016/j.topol.2008.12.025E. Akin, The General Topology of Dynamical Systems, Grad. Stud. Math., vol. 1, Amer. Math. Soc., Providence, 1993.J. Banks, Chaos for induced hyperspace maps, Chaos Solitons Fractals 25, no. 3 (2005), 681-685. https://doi.org/10.1016/j.chaos.2004.11.089F. Barragán, On the n-fold symmetric product suspensions of a continuum, Topology Appl. 157, no. 3 (2010), 597-604. https://doi.org/10.1016/j.topol.2009.10.017F. Barragán, Induced maps on n-fold symmetric product suspensions, Topology Appl. 158, no. 10 (2011), 1192-1205. https://doi.org/10.1016/j.topol.2011.04.006F. Barragán, Aposyndetic properties of the n-fold symmetric product suspensions of a continuum, Glas. Mat. Ser. III 49(69), no. 1 (2014), 179-193. https://doi.org/10.3336/gm.49.1.13F. Barragán, S. Macías and J. F. Tenorio, More on induced maps on n-fold symmetric product suspensions, Glas. Mat. Ser. III 50(70), no. 2 (2015), 489-512. https://doi.org/10.3336/gm.50.2.15F. Barragán, A. Santiago-Santos and J. F. Tenorio, Dynamic properties for the induced maps on n-fold symmetric product suspensions, Glas. Mat. Ser. III 51(71), no. 2 (2016), 453-474.W. Bauer and K. Sigmund, Topological dynamics of transformations induced on the space of probability measures, Monatsh. Math. 79 (1975), 81-92. https://doi.org/10.1007/BF01585664G. D. Birkhoff, Dynamical Systems, American Math. Soc., Colloquium Publication., Vol. IX, Amer. Math. Soc. Providence, R. I., 1927.K. Borsuk and S. Ulam, On symmetric products of topological space, Bull. Amer. Math. Soc. 37, no. 12 (1931), 875-882. https://doi.org/10.1090/S0002-9904-1931-05290-3J. Camargo, C. García and A. Ramírez, Transitivity of the Induced Map $C_n(f)$, Rev. Colombiana Mat. 48, no. 2 (2014), 235-245. https://doi.org/10.15446/recolma.v48n2.54131J. S. Cánovas-Peña and G. Soler-López, Topological entropy for induced hyperspace maps, Chaos Solitons Fractals 28, no. 4 (2006), 979-982. https://doi.org/10.1016/j.chaos.2005.08.173E. Castañeda-Alvarado and J. Sánchez-Martínez, On the unicoherence of $F_n(X)$ and $SF^n_m(X)$ of continua, Topology Proc. 42 (2013), 309-326.E. Castañeda-Alvarado, F. Orozco-Zitli and J. Sánchez-Martínez, Induced mappings between quotient spaces of symmetric products of continua, Topology Appl. 163 (2014), 66-76. https://doi.org/10.1016/j.topol.2013.10.007J. Dugundji, Topology, Boston, London, Sydney, Toronto: Allyn and Bacon, Inc, 1966.L. Fernández and C. Good, Shadowing for induced maps of hyperspaces, Fund. Math. 235, no. 3 (2016), 277-286. https://doi.org/10.4064/fm136-2-2016J. L. Gómez-Rueda, A. Illanes and H. Méndez-Lango, Dynamic properties for the induced maps in the symmetric products, Chaos Solitons Fractals 45, no. 9-10 (2012), 1180-1187. https://doi.org/10.1016/j.chaos.2012.05.003G. Higuera and A. Illanes, Induced mappings on symmetric products, Topolology Proc. 37 (2011), 367-401.A. Illanes and S. B. Nadler, Jr., Hyperspaces: fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Math., Vol. 216, Marcel Dekker, New York, Basel, 1999.S. Kolyada, L. Snoha and S. Trofimchuk, Noninvertible minimal maps, Fund. Math. 168, no. 2 (2001), 141-163. https://doi.org/10.4064/fm168-2-5D. Kwietniak, Exact Devaney chaos and entropy, Qual. Theory Dyn. Syst. 6, no. 1 (2005), 169-179. https://doi.org/10.1007/BF02972670D. Kwietniak and P. Oprocha, Topological entropy and chaos for maps induced on hyperspaces, Chaos Solitons Fractals 33, no. 1 (2007), 76-86. https://doi.org/10.1016/j.chaos.2005.12.033G. Liao, L. Wang and Y. Zhang, Transitivity, mixing and chaos for a class of set-valued mappings, Sci. China Ser. A 49, no. 1 (2006), 1-8. https://doi.org/10.1007/s11425-004-5234-5X. Ma, B. Hou and G. Liao, Chaos in hyperspace system, Chaos Solitons Fractals 40, no. 2 (2009), 653-660. https://doi.org/10.1016/j.chaos.2007.08.009J. C. Macías, On n-fold pseudo-hyperspace suspensions of continua, Glas. Mat. Ser. III 43(63), no. 2 (2008), 439-449. https://doi.org/10.3336/gm.43.2.14S. Macías, On the n-fold hyperspaces suspension of continua, Topology Appl. 138, no. 1-3 (2004), 125-138. https://doi.org/10.1016/j.topol.2003.08.023S. Macías, Topics on Continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca Raton, London, New York, Singapore, 2005.S. B. Nadler, Jr., A fixed point theorem for hyperspaces suspensions, Houston J. Math. 5, no. 1 (1979), 125-132.S. B. Nadler, Jr., Hyperspaces of sets, Monographs and Textbooks in Pure and Applied Math., Vol. 49, Marcel Dekker, New York, Basel, 1978. Reprinted in: Aportaciones Matemáticas de la Sociedad Matemática Mexicana, Serie Textos #33, 2006.A. Peris, Set-valued discrete chaos, Chaos Solitons Fractals 26, no. 1 (2005), 19-23. https://doi.org/10.1016/j.chaos.2004.12.039H. Román-Flores, A note on transitivity in set-valued discrete systems, Chaos Solitons Fractals 17, no. 1 (2003), 99-104. https://doi.org/10.1016/S0960-0779(02)00406-XM. Sabbaghan and H. Damerchiloo, A note on periodic points and transitive maps, Math. Sci. Q. J. 5, no. 3 (2011), 259-266.Y. Wang and G. Wei, Characterizing mixing, weak mixing and transitivity on induced hyperspace dynamical systems, Topology Appl. 155, no. 1 (2007), 56-68. https://doi.org/10.1016/j.topol.2007.09.00

DESCRIPTIVE ANALYSIS OF THE SMALL RUMINANT MEAT OFFERING IN PUERTO RICO

DESCRIPTIVE ANALYSIS OF THE SMALL RUMINANT MEAT OFFERING IN PUERTO RIC

Classification of red grapes according to their state of ripeness using a low-cost multispectral device

[ES] El objetivo del presente trabajo fue evaluar la idoneidad de un sensor multiespectral de bajo costo para la determinación del estado de maduración de uvas tintas. El dispositivo propuesto se basa en un sensor multiespectral, con 18 bandas de detección en el rango entre los 410 y los 940 nm. La recogida de muestras se llevó a cabo en un viñedo comercial situado en Rociana del Condado, Huelva. El dispositivo propuesto se utilizó para adquirir la respuesta espectral de 80 racimos de uva en condiciones de laboratorio. Tras esto, cada una de las muestras fue analizada mediante métodos estándar de laboratorio para obtener indicadores objetivos de su estado de maduración (sólidos solubles totales y acidez). Los 18 valores de reflectancia ofrecidos por el sensor fueron usados como datos de entrada para entrenar redes neuronales artificiales para la clasificación de las muestras de uva en función de los parámetros objetivo. Los resultados obtenidos fueron prometedores, lo cual allana el camino hacia la implementación de un sistema para la monitorización del estado de maduración de uvas asequible para los vinicultores.[EN] The present work aims to evaluate a low-cost multispectral device for non-destructive grape ripening status assessment. The proposed device is based on a multispectral sensor, with a spectral response of 18 channels in a range from 410 to 940 nm. The experimental validation was carried out in a commercial vineyard in Rociana del Condado, Huelva. The proposed device was used to analyze 80 grape samples under laboratory conditions. After being processed with the proposed device the grape samples were analyzed with standard chemical methods to generate ground truth values of ripening status indicators (solid soluble content, and acidity). The 18-reflectance data corresponding to the spectral channels of the employed sensor, were used as input variables for developing artificial neural network models to classify the berries samples based on the mentioned ripeness indicators. The obtained results were promising, which paves the way for the implementation of a portable grape ripening appraisal system affordable for grape growers

Continuos y el producto simétrico suspensión

En este artículo presentamos una breve introducción a la teoría de los continuos y sus hiperespacios. Nos enfocamos en algunos modelos geométricos del producto simétrico suspensión de un continuo y mostramos resultados acerca de conexidad local y arcoconexidad de este espacio.In this paper we present a short introduction to continuum theory and its hyperspaces. We focus our attention on some geometric models of the symmetric product suspensions of a continuum and we show results on local connectedness and arcwise connectedness of this space

Continuos y el producto simétrico suspensión

In this paper we present a short introduction to continuum theory and its hyperspaces. We focus our attention on some geometric models of the symmetric product suspensions of a continuum and we show results on local connectedness and arcwise connectedness of this space.En este artículo presentamos una breve introducción a la teoría de los continuos y sus hiperespacios. Nos enfocamos en algunos modelos geométricos del producto simétrico suspensión de un continuo y mostramos resultados acerca de conexidad local y arcoconexidad de este espacio

Drop-in analysis of an internal heat exchanger in a vapour compression system using R1234ze(E) and R450A as alternatives for R134a

The IHX (internal heat exchanger) is introduced in some refrigeration systems in order to achieve higher energy performances. Results obtained vary greatly depending on the refrigerant used and working conditions. This paper describes a drop-in analysis of IHX effects on the performance of a vapour compression system using R1234ze(E) and R450A (R134a/R1234ze(E) commercial mixture) as R134a low-GWP replacements. The tests were carried out in a completely monitored vapour compression system varying the condensing and evaporating temperature, with and without a counter-current flow tube-in-tube IHX. Because the cooling capacity rises and the power consumption remains similar, the conclusion is that the IHX has a positive influence on the energy efficiency for all refrigerants tested. The COP (coefficient of performance) gain using R1234ze(E) is the highest observed (overcomes the R134a COP for the same conditions). The R1234ze(E) and R450A discharge temperature increments are lower than those of R134a so does not reach dangerous values and the IHX pressure drops are also below than that of R134a.The authors thankfully acknowledge "Ministerio de Educacion, Cultura y Deporte - Gobierno de Espana" (Grant number FPU12/02841) for supporting this work through "Becas y Contratos de Formacion de Profesorado Universitario del Programa Nacional de Formacion de Recursos Humanos de Investigacion del ejercicio 2012".Mota Babiloni, A.; Navarro Esbrí, J.; Barragán Cervera, Á.; Moles, F.; Peris, B. (2015). Drop-in analysis of an internal heat exchanger in a vapour compression system using R1234ze(E) and R450A as alternatives for R134a. Energy. 90:1636-1644. https://doi.org/10.1016/j.energy.2015.06.133S163616449