P-regularity and weights for operators between Lp-spaces

We explore the connection between p-regular operators on Banach function spaces and weighted p-estimates. In particular, our results focus on the following problem. Given finite measure spaces µ and ν, let T be an operator defined from a Banach function space X(ν) and taking values on L(vdµ) for v in certain family of weights V ⊂ L(µ) we analyze the existence of a bounded family of weights W ⊂ L(ν) such that for every v ∈ V there is w ∈ W in such a way that T: L(wdν) → L(vdµ) is continuous uniformly on V. A condition for the existence of such a family is given in terms of p-regularity of the integration map associated to a certain vector measure induced by the operator T.E. A. S´anchez P´erez gratefully acknowledges support of Spanish Ministerio de Econom´ıa, Industria y Competitividad through grant MTM2016-77054-C2-1-P. P. Tradacete gratefully acknowledges support of Spanish Ministerio de Econom´ıa, Industria y Competitividad through grants MTM2016-76808-P, MTM2016-75196-P and the “Severo Ochoa Programme for Centres of Excellence in R&D” (SEV-2015-0554

Una aplicación didáctica de la modelización matemática: control de velocidad de vehículos en vías rurales

[EN] In this paper a didactic model for the control of the speed of the vehicles in a road is presented. Based on empirical assumptions, the model provides an answer to the problem of finding the best road from the point of view of the time that is needed for going from the top of a hill to a certain point in the valley under the assumption that certain restrictions for the speed are imposed. Thus, we construct a simple model for representing the time dependence of the traffic in a road as an exercise of mathematical modelling adequate for a basic level of a civil engineering career.[ES] En este artículo presentamos un modelo didáctico para el control de la velocidad de los vehículos en una carretera. Basado en supuestos empíricos, el modelo da una respuesta al problema de encontrar el mejor trazado de carretera desde el punto de vista del tiempo que se necesita para ir desde la cima de una colina a un cierto punto en el valle, respetando las limitaciones de velocidad necesarias. Así, construimos un modelo simple para representar la dependencia temporal del tráfico en una carretera como un ejercicio de modelización matemático para un nivel básico de una carrera de ingeniería civil.Juan, M.; Sánchez-Pérez, E. (2012). Una aplicación didáctica de la modelización matemática: control de velocidad de vehículos en vías rurales. Modelling in Science Education and Learning. 5:65-75. doi:10.4995/msel.2012.2134SWORD65755M. P. Do Carmo, "Geometría diferencial de curvas y super cies". Alianza Universidad Textos, Madrid, 1990. L. M. García Raffi, M. Figueres Moreno, M. J. Pérez Pe-alver y E. A. Sánchez Pérez, "Métodos numéricos con Mathematica". Alfaomega Grupo Editor Argentino, México, 2003.Garcia-Raffi, L. M., Sánchez-Pérez, E. A., & Sopena Novales, M. (2008). Realidad y educación: un modelo didáctico para la catástrofe del Prestige. Modelling in Science Education and Learning, 1, 29. doi:10.4995/msel.2008.3131E. A. Sánchez Pérez, J. V. Sánchez Pérez y L. M. García Raffi, "Introducción de las técnicas de modelización para el estudio de la Física y de las Matemáticas en los primeros cursos de las carreras técnicas". Ense-anza de las Ciencias, 17 (1999), 119-13

The pp-Daugavet property for function spaces

A natural extension of the Daugavet property for $p$-convex Banach function spaces and related classes is analysed. As an application, we extend the arguments given in the setting of the Daugavet property to show that no reflexive space falls into this class

Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators

[EN] Using compactness properties of bounded subsets of spaces of vector measure integrable functions and a representation theorem for q-convex Banach lattices, we prove a domination theorem for operators between Banach lattices. We generalize in this way several classical factorization results for operators between these spaces, as psumming operators.The authors acknowledge the support of the Generalitat Valenciana, Spain, grant GV04B-371, the Spanish Ministry of Science and Technology, Plan Nacional I+D+I , grant BFM2003-02302; and the support of the Universidad Polit´ecnica de Valencia, under grant 2003-4114 for Interdisciplinary Research Projects.Garcia-Raffi, LM.; Sánchez-Pérez, E. (2005). Compactness properties of bounded subsets of spaces of vector measure integrable functions and factorization of operators. Applied General Topology. 6(2):135-142. https://doi.org/10.4995/agt.2005.19521351426

Factorization of strongly (p,sigma)-continuous multilinear operators

We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.D. Achour acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under project PNR 8-U28-181. E. Dahia acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) [grant number 10/PG-FMI/2013] and the Universite de M'Sila (2013) for short term stage. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) under project MTM2012-36740-C02-02.Achour, D.; Dahia, E.; Rueda, P.; Sánchez Pérez, EA. (2014). Factorization of strongly (p,sigma)-continuous multilinear operators. Linear and Multilinear Algebra. 62(12):1649-1670. doi:10.1080/03081087.2013.839677S164916706212Matter, U. (1987). Absolutely Continuous Operators and Super-Reflexivity. Mathematische Nachrichten, 130(1), 193-216. doi:10.1002/mana.19871300118Diestel, J., Jarchow, H., & Tonge, A. (1995). Absolutely Summing Operators. doi:10.1017/cbo9780511526138Pietsch, A. (1967). Absolut p-summierende Abbildungen in normierten Räumen. Studia Mathematica, 28(3), 333-353. doi:10.4064/sm-28-3-333-353Achour, D., & Mezrag, L. (2007). On the Cohen strongly p-summing multilinear operators. Journal of Mathematical Analysis and Applications, 327(1), 550-563. doi:10.1016/j.jmaa.2006.04.065Apiola, H. (1976). Duality between spaces ofp-summable sequences, (p, q)-summing operators and characterizations of nuclearity. Mathematische Annalen, 219(1), 53-64. doi:10.1007/bf01360858Sánchez PérezEA. Ideales de operadores absolutamente continuos y normas tensoriales asociadas [PhD Thesis]. Spain: Universidad Politécnica de Valencia; 1997.López Molina, J. A., & Sánchez Pérez, E. A. (2000). On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, 138(1), 25-40. doi:10.4064/sm-138-1-25-40Cohen, J. S. (1973). Absolutelyp-summing,p-nuclear operators and their conjugates. Mathematische Annalen, 201(3), 177-200. doi:10.1007/bf01427941Mezrag, L., & Saadi, K. (2012). Inclusion and coincidence properties for Cohen strongly summing multilinear operators. Collectanea Mathematica, 64(3), 395-408. doi:10.1007/s13348-012-0071-2Achour, D., & Alouani, A. (2010). On multilinear generalizations of the concept of nuclear operators. Colloquium Mathematicum, 120(1), 85-102. doi:10.4064/cm120-1-7Mujica, X. (2008). τ(p;q)-summing mappings and the domination theorem. Portugaliae Mathematica, 211-226. doi:10.4171/pm/1806Campos, J. R. (2013). Cohen and multiple Cohen strongly summing multilinear operators. Linear and Multilinear Algebra, 62(3), 322-346. doi:10.1080/03081087.2013.779270Bu, Q., & Shi, Z. (2013). On Cohen almost summing multilinear operators. Journal of Mathematical Analysis and Applications, 401(1), 174-181. doi:10.1016/j.jmaa.2012.12.005Ryan, R. A. (2002). Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics. doi:10.1007/978-1-4471-3903-4Achour, D., & Belaib, M. T. (2011). Tensor norms related to the space of Cohen $p$-nuclear‎ ‎multilinear mappings. Annals of Functional Analysis, 2(1), 128-138. doi:10.15352/afa/1399900268Achour, D. (2011). Multilinear extensions of absolutely (p;q;r)-summing operators. Rendiconti del Circolo Matematico di Palermo, 60(3), 337-350. doi:10.1007/s12215-011-0054-2Dahia, E., Achour, D., & Sánchez Pérez, E. A. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications, 397(1), 205-224. doi:10.1016/j.jmaa.2012.07.034Botelho, G., Pellegrino, D., & Rueda, P. (2007). On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials. Publications of the Research Institute for Mathematical Sciences, 43(4), 1139-1155. doi:10.2977/prims/1201012383Pellegrino, D., Santos, J., & Seoane-Sepúlveda, J. B. (2012). Some techniques on nonlinear analysis and applications. Advances in Mathematics, 229(2), 1235-1265. doi:10.1016/j.aim.2011.09.014Ramanujan, M. S., & Schock, E. (1985). Operator ideals and spaces of bilinear operators. Linear and Multilinear Algebra, 18(4), 307-318. doi:10.1080/03081088508817695Floret, K., & Hunfeld, S. (2002). Proceedings of the American Mathematical Society, 130(05), 1425-1436. doi:10.1090/s0002-9939-01-06228-

Absolutely continuous multilinear operators

We introduce the new class of the (p;p1,...,pm; s)-absolutely continuous operators, that is defined using a summability property that provides the multilinear version of the (p, s)-absolutely continuous operators. We give an analogue of the Pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for (p, s)-absolutely continuous operators, obtaining in this way a rich factorization theory. We present also a tensor norm which represents this multi-ideal by trace duality. As an application, we show that (p; p1, . . . , pm; s)-absolutely continuous multilinear operators are compact under some requirements. Applications to factorization of linear maps on Banach function spaces through interpolation spaces are also given.EL-Hadj Dahia acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under grant 555/PGRS/C.U.K.M. (2011) for a short term stage. D. Achour acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under project PNR 8-U28-6543. E.A. Sanchez acknowledges with thanks the support of the Ministerio de Economia y Connpetitividad (Spain) under project #MTM2009-14483-C02-02.Dahia, E.; Achour, D.; Sánchez Pérez, EA. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications. 397:205-224. https://doi.org/10.1016/j.jmaa.2012.07.034S20522439

Realidad y educación: un modelo didáctico para la catástrofe del Prestige

[EN] In this work we present an easy didactic model for the description of the movement of a liquid less dense than the water on the sea. The problem has been designed from a multi-level point of view, in order to use it as a tool for the teaching of several fundamental concepts of physics and mathematics at the university, or even in the last course of the high school.[ES] En este trabajo presentamos un modelo didáctico sencillo para la descripción del movimiento de un vertido de un material líquido menos denso que el agua en el mar. El problema ha sido diseñado según un planteamiento en diferentes niveles, para permitir su uso como herramienta en la enseñanza de ciertos conceptos fundamentales de las matemáticas y la física en la universidad, o incluso en el segundo curso del bachillerato.Garcia-Raffi, LM.; Sánchez-Pérez, E.; Sopena Novales, M. (2008). Realidad y educación: un modelo didáctico para la catástrofe del Prestige. Modelling in Science Education and Learning. 1:29-37. doi:10.4995/msel.2008.3131SWORD29371L.M. García Raffi, S. Pueblas, E.A. Sánchez Pérez, J.V. Sánchez Pérez, O. Valero. "Un modelo estocástico de propagación de incendios forestales". Epsilon, 54, 457-468. 2002.L.M. García Raffi, S. Pueblas, E.A. Sánchez Pérez, J.V. Sánchez Pérez. "Un modelo simple de propagación de incendios forestales con ecuaciones diferenciales ordinarias". Epsilon, 51, 489-502. 2001.L.M. García Raffi, E.A. Sánchez Pérez, J.V. Sánchez Pérez. "Introducción de las técnicas de modelización para el estudio de la física y de las matemáticas en los primeros cursos de las carreras técnicas". Ense-anza de las Ciencias, 17(1), 119-129. 1999

Vector valued information measures and integration with respect to fuzzy vector capacities

[EN] Integration with respect to vector-valued fuzzy measures is used to define and study information measuring tools. Motivated by some current developments in Information Science, we apply the integration of scalar functions with respect to vector-valued fuzzy measures, also called vector capacities. Bartle-Dunford-Schwartz integration (for the additive case) and Choquet type integration (for the non-additive case) are considered, showing that these formalisms can be used to define and develop vector-valued impact measures. Examples related to existing bibliometric tools as well as to new measuring indices are given.The authors would like to thank both Prof. Dr. Olvido Delgado and the referee for their valuable comments and suggestions which helped to prepare the manuscript. The first author gratefully acknowledges the support of the Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2016-77054-C2-1-P.Sánchez Pérez, EA.; Szwedek, R. (2019). Vector valued information measures and integration with respect to fuzzy vector capacities. Fuzzy Sets and Systems. 355:1-25. https://doi.org/10.1016/j.fss.2018.05.004S12535

Charge disproportionation in YNiO3_{3} : ESR and susceptibility study

We present a study of the magnetic properties of YNiO$_{3}$ in the paramagnetic range, above and below the metal-insulator (MI) transition. The dc susceptibility, $\chi_{dc}$ (measured up to 1000 K) is a decreasing function of T for $T >$150 K (the N\'{e}el temperature) and we observe two different Curie-Weiss regimes corresponding to the metallic and insulator phases. In the metallic phase, this behaviour seems to be associated with the small ionic radius of Y% $^{3+}$. The value of the Curie constant for T$<$ T$_{MI}$ allows us to discard the possibility of Ni$^{3+}$ localization. An electron spin resonance (ESR) spectrum is visible in the insulator phase and only a fraction of the Ni ions contributes to this resonance. We explain the ESR and $\chi _{dc}$ behaviour for T $<$ T$_{MI}$ in terms of charge disproportionation of the type 2Ni$$ Ni$^{2+}$+Ni$^{4+},$ that is compatible with the previously observed structural transition across T$_{MI}$.Comment: 10 pages, 4 figures, submitted to Phys. Rev.

Evaluación de las condiciones experimentales básicas para la producción de biomasa a partir de la microalga Chlorella vulgaris

La utilización de las microalgas como fuente de energía para la obtención de aceite y biodiesel presenta muchas ventajas respecto a otras materias primas. Las microalgas tienen un alto rendimiento por superficie cultivada, diversifica el tipo de combustible a producir y no compite con la producción de alimentos, siendo clasificado como un biocombustible de tercera generación. En el presente trabajo se evalúa la influencia del rendimiento de biomasa microalgal bajo diferentes condiciones de cultivo. La microalga Chlorella vulgaris fue cultivada a escala de laboratorio utilizando 6 elermeyers de 250 mL siguiendo la metodología descrita en el medio decultivo Watanabe modificado. Las condiciones de cultivo fueron 28°C ± 1°C con un pH aproximado entre 6 y 7. A partir del recuento celular mediante microscopía fue posible determinar la velocidad de crecimiento de la microalga en estudio con una duración de diez días; alcanzándose la máxima concentración de células en el cultivo con vitaminas y suministro de aire de 450.5×104 células/mL. A los cinco días los cultivos con vitaminas mostraron 8 veces mayor rendimiento, mientras que sin estas 7 veces. El mayor incremento se registró para el cultivo con vitaminas y suministro permanentede aire el cual incrementó su producción de biomasa 20 veces. Los resultados obtenidos en esta investigación demuestran el potencial que tiene la microalga Chlorella vulgaris para su uso con fines energéticos, encaminados fundamentalmente a la obtención de biodiesel