Fuzzy Quasi-Metric Spaces: Bicompletion, Contractions on Product Spaces, and Applications to Access Predictions

Desde que L.A. Zadeh presentó la teoría de conjuntos difusos en 1965, esta se ha usado en una amplia serie de áreas de las matemáticas y se ha aplicado en una gran variedad de escenarios de la vida real. Estos escenarios cubren procesos complejos sin modelo matemático sencillo tales como dispositivos de control industrial, reconocimiento de patrones o sistemas que gestionen información imprecisa o altamente impredecible. La topología difusa es un importante ejemplo de uso de la teoría de L.A. Zadeh. Durante años, los autores de este campo han buscado obtener la definición de un espacio métrico difuso para medir la distancia entre elementos según grados de proximidad. El presente trabajo trata acerca de la bicompletación de espacios casi-métricos difusos en el sentido de Kramosil y Michalek. Sherwood probó que todo espacio métrico difuso admite completación que es única excepto por isometría basándose en propiedades de la métrica de Lévy. Probamos aquí que todo espacio casi-métrico difuso tiene bicompletación usando directamente el supremo de conjuntos en [0,1] y límites inferiores de secuencias en [0,1] en lugar de usar la métrica de Lévy. Aprovechamos tanto la bicompletitud y bicompletación de espacios casi-métricos difusos como las propiedades de los espacios métricos difusos y difusos intuicionistas para presentar varias aplicaciones a problemas del campo de la informática. Así estudiamos la existencia y unicidad de solución para las ecuaciones de recurrencia asociadas a ciertos algoritmos formados por dos procedimientos recursivos. Para analizar su complejidad aplicamos el principio de contracción de Banach tanto en un producto de casi-métricas no-Arquimedianas en el dominio de las palabras como en la casi-métrica producto de dos espacios de complejidad casi-métricos de Schellekens. Estudiamos también una aplicación de espacios métricos difusos a sistemas de información basados en localidad de accesos.Castro Company, F. (2010). Fuzzy Quasi-Metric Spaces: Bicompletion, Contractions on Product Spaces, and Applications to Access Predictions [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8420Palanci

The bicompletion of fuzzy quasi-metric spaces

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced by its bicompletion. © 2010 Elsevier B.V.Supported by the Spanish Ministry of Science and Innovation, under Grant MTM2009-12872-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2011). The bicompletion of fuzzy quasi-metric spaces. Fuzzy Sets and Systems. 166(1):56-64. https://doi.org/10.1016/j.fss.2010.12.004S5664166

The deconstruction of the female character in Galdós: the case of Marianela and «La Peri»

El novelista canario Benito Pérez Galdós trazó en varias de sus obras un perfil canónico de la mujer española claramente diferenciado del atribuido, hasta el siglo XIX, por la tradición literaria en España. Esa construcción estética del personaje femenino implicó para el autor aportar la propuesta de un modelo literario y social nuevo, coincidente además con los postulados del republicanismo español de inicios del siglo XX, en el que militó. Para el escritor, la protagonista literaria debía trascender el papel convencional de esposa y madre hogareña hasta aportar estéticamente una proyección de futuro totalmente ajena al canon social vigente. Además, en toda su obra exploró y reinterpretó el papel de la mujer, tanto en la ficción narrativa y teatral como en el ensayo y el periodismo, hasta aportar modelos concretos como Marianela o «La Peri». En este trabajo se traza una lectura particular a partir de propuestas críticas contemporáneas, y se analiza la deconstrucción del personaje femenino galdosiano desde dos modelos singulares como las protagonistas de Marianela (1878) y Realidad (1889); asimismo se desarrolla un análisis de ambas obras a partir de las dimensiones física, psicológica y sociológica de sus protagonistas principales. La propuesta crítica de este trabajo se complementa con la contextualización del vínculo personal de Pérez Galdós con el transcurso político y social de su época, y con la relación del punto de vista aportado por el autor sobre la sociedad del momento como materia literaria y la pertenencia de la mujer a aquella.The Canarian novelist Benito Pérez Galdós depicted in several of his works a canonical profile of the Spanish woman unmistakably well differentiated from the one attributed, until the 19th century, by the literary tradition in Spain. This aesthetic construction of the female character implied for the author to contribute the proposal of a new literary and social model, also coinciding with the postulates of Spanish republicanism at the beginning of the 20th century, in which he militated. For the Canarian author, the female literary protagonist had to transcend the conventional role of the wife and homely mother to aesthetically provide a projection of the future totally alien to the current social canon. Furthermore, through all his literary work, he explored and reinterpreted the role of women both in narrative and theatrical fiction as well as in essays and journalism, to the point of providing specific models such as Marianela or «La Peri». In this work, the authors delineate a specific reading from contemporary critical proposals; as well as analyze the deconstruction of the Galdosian female character from two singular models such as the protagonists of Marianela (1878) and Realidad (1889); alongside the analysis of both works from the physical, psychological and sociological dimensions of their main protagonists. The critical proposal of this work is complemented by the contextualization of the personal bond of the writer of his studied works with the political and social course of his time, accompanied by the point of view provided by him on the society of the moment as a literary matter and the weight of women’s voice in it

A fixed point theorem for preordered complete fuzzy quasi-metric spaces and an application

We obtain a fixed point theorem for a type of generalized contractions on preordered complete fuzzy quasi-metric spaces which is applied to deduce, among other results, a procedure to show in a direct and easy fashion the existence of solution for the recurrence equations that are typically associated to Quicksort and Divide and Conquer algorithms, respectively.The second and third named authors thank the supports of the Universitat Politecnica de Valencia, grant PAID-06-12-SP20120471, and the Ministry of Economy and Competitiveness of Spain, grant MTM2012-37894-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2014). A fixed point theorem for preordered complete fuzzy quasi-metric spaces and an application. Journal of Inequalities and Applications. 2014(122):1-11. doi:10.1186/1029-242X-2014-122S111201412

On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings

[EN] We present a procedure to construct a compatible metric from a given fuzzy metric space. We use this approach to obtain a characterization of a large class of complete fuzzy metric spaces by means of a fuzzy version of Caristi’s fixed point theorem, obtaining, in this way, partial solutions to a recent question posed in the literature. Some illustrative examples are also given.The authors thank the referees for several useful suggestions. Salvador Romaguera and Pedro Tirado acknowledge the support of the Ministry of Economy and Competitiveness of Spain, grant MTM2012-37894-C02-01.Castro Company, F.; Romaguera Bonilla, S.; Tirado Peláez, P. (2015). On the construction of metrics from fuzzy metrics and its application to the fixed point theory of multivalued mappings. Fixed Point Theory and Applications. 2015:226. https://doi.org/10.1186/s13663-015-0476-1S2015:226Kelley, JL: General Topology. Springer, New York (1955)Schweizer, B, Sklar, A: Statistical metric spaces. Pac. J. Math. 10, 314-334 (1960)Klement, E, Mesiar, R, Pap, E: Triangular Norms. Kluwer Academic, Dordrecht (2000)Hamacher, H: Über logische Verknüpfungen unscharfer Aussagen und deren zugehörige Bewertungsfunktionen. In: Progress in Cybernetics and Systems Research, pp. 276-287. Hemisphere, New York (1975)Kramosil, I, Michalek, J: Fuzzy metrics and statistical metric spaces. Kybernetika 11, 326-334 (1975)George, A, Veeramani, P: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395-399 (1994)Gregori, V, Romaguera, S: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485-489 (2000)Radu, V: On the triangle inequality in PM-spaces. STPA, West University of Timişoara 39 (1978)Abbas, M, Ali, B, Romaguera, S: Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness. Filomat 29(6), 1217-1222 (2015)Cho, YJ, Grabiec, M, Radu, V: On Nonsymmetric Topological and Probabilistic Structures. Nova Science Publishers, New York (2006)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Mihet, D: A note on Hicks type contractions on generalized Menger spaces. STPA, West University of Timişoara 133 (2002)Mihet, D: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431-439 (2004)Radu, V: Some fixed point theorems in PM spaces. In: Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol. 1233, pp. 125-133. Springer, Berlin (1985)Radu, V: Some remarks on the probabilistic contractions on fuzzy Menger spaces (The Eighth Intern. Conf. on Applied Mathematics and Computer Science, Cluj-Napoca, 2001). Autom. Comput. Appl. Math. 11(1), 125-131 (2002)Chauhan, S, Shatanawi, W, Kumar, S, Radenović, S: Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces. J. Nonlinear Sci. Appl. 7, 28-41 (2014)Hussain, N, Salimi, P, Parvaneh, V: Fixed point results for various contractions in parametric and fuzzy b-metric spaces. J. Nonlinear Sci. Appl. 8, 719-739 (2015)Mihet, D: Common coupled fixed point theorems for contractive mappings in fuzzy metric spaces. J. Nonlinear Sci. Appl. 6, 35-40 (2013)Hicks, TL: Fixed point theory in probabilistic metric spaces. Zb. Rad. Prir.-Mat. Fak. (Novi Sad) 13, 63-72 (1983)Radu, V: Some suitable metrics on fuzzy metric spaces. Fixed Point Theory 5, 323-347 (2004)O’Regan, D, Saadati, R: Nonlinear contraction theorems in probabilistic spaces. Appl. Math. Comput. 195, 86-93 (2008)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed-point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Ansari, QH: Metric Spaces: Including Fixed Point Theory and Set-Valued Maps. Alpha Science, Oxford (2010

On the bicompletion of intuitionistic fuzzy quasi-metric spaces

[EN] Based on previous results that study the completion of fuzzy metric spaces, we show that every intuitionistic fuzzy quasi-metric space, using the notion of fuzzy metric space in the sense of Kramosil and Michalek to obtain a generalization to the quasi-metric setting, has a bicompletion which is unique up to isometry.Pedro Tirado acknowledges the support of the Ministry of Economy and Comptetitiveness of Spain, gran MTM2012-37894-C02-01Castro Company, F.; Tirado Peláez, P. (2016). On the bicompletion of intuitionistic fuzzy quasi-metric spaces. Iranian Journal of Fuzzy Systems. 13(3):143-151. doi:10.22111/IJFS.2016.2435S14315113

FOBr: A Version-Based Recovery Protocol For Replicated Databases

Within the field of databases that are deployed in distributed environments there is a need to guarantee consistency among replicas and availability among nodes despite of network disconnections and node crashes

Madis: A slim middleware for database replication

Abstract. Data replication serves to improve the availability and performance of distributed systems. The price to be paid consists of costs caused by protocols by which a sufficient degree of consistency of replicated data is maintained. Different kinds of targeted applications require different kinds of replication protocols, each one requiring a different set of metadata. We discuss the middleware architecture used in the MADIS project for maintaining the consistency of replicated databases. Instead of reinventing wheels, MADIS makes use of basic resources provided by conventional database systems (e.g. triggers, views, etc) to achieve its purpose, to a large extent. So, the underlying databases can perform more efficiently many of the routines needed to support any consistency protocol, the implementation of which thus becomes much simpler and easier. MADIS enables the databases to simultaneously maintain different metadata needed for different replication protocols, so that the latter can be chosen, plugged in and exchanged on the fly as online-configurable modules, in order to fit the shifting needs of given applications best, at each moment.

Lazy Recovery in a Hybrid Database Replication

COLUP is a hybrid database replication protocol that may be configured to behave either as an eager or a lazy update protocol. When a faulty replica joins again the system, a recovery subprotocol is needed to update its database state. Independently of the chosen update strategy, these recovery tasks are lazy and introduce a minimal overhead in the non-recovering replicas

Webinar: Océanos, vida y medio de subsistencia

Datos técnicos: 79 minutos, color, español. Emitido en directo el 8 de junio de 2021. Ficha técnica: Gabinete de Presidencia CSIC y Departamento de ComunicaciónHoy, #DíaMundialOcéanos, cuatro expertos del CSIC debatirán sobre las claves para garantizar una gestión sostenible de los océanos. El 8 de junio se celebra el Día Mundial de los Océanos y el Instituto Español de Oceanografía organiza un webinar con algunos de los mayores expertos de investigación marina, el 8 de junio a las 18:00 horas. Entre ellos, está el investigador Jordi Dachs, del grupo Global Change and Genomic Biogeochemistry. En el webinar participan también Carmen G. Castro, del Instituto de Investigacións Mariñas (IIM-CSIC), Pablo Abaunza y Salud Deudero, del IEO-CSIC y está moderado por Pablo Rodríguez Ros, del Institut de Cièncias del Mar (ICM-CSIC).Peer reviewe