Cauchyness and convergence in fuzzy metric spaces

[EN] In this paper we survey some concepts of convergence and Cauchyness appeared separately in the context of fuzzy metric spaces in the sense of George and Veeramani. For each convergence (Cauchyness) concept we find a compatible Cauchyness (convergence) concept. We also study the relationship among them and the relationship with compactness and completeness (defined in a natural sense for each one of the Cauchy concepts). In particular, we prove that compactness implies p-completeness.Almanzor Sapena acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant TEC2013-45492-R. Valentín Gregori acknowledges the support of Ministry of Economy and Competitiveness of Spain under grant MTM 2012-37894-C02-01.Gregori Gregori, V.; Miñana, J.; Morillas, S.; Sapena Piera, A. (2017). Cauchyness and convergence in fuzzy metric spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 111(1):25-37. https://doi.org/10.1007/s13398-015-0272-0S25371111Alaca, C., Turkoglu, D., Yildiz, C.: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons Fractals 29, 1073–1078 (2006)Edalat, A., Heckmann, R.: A computational model for metric spaces. Theor. Comput. Sci. 193, 53–73 (1998)Engelking, R.: General topology. PWN-Polish Sci. Publ, Warsawa (1977)Fang, J.X.: On fixed point theorems in fuzzy metric spaces. Fuzzy Sets Syst. 46(1), 107–113 (1992)George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64, 395–399 (1994)George, A., Veeramani, P.: Some theorems in fuzzy metric spaces. J. Fuzzy Math. 3, 933–940 (1995)George, A., Veeramani, P.: On some results of analysis for fuzzy metric spaces. Fuzzy Sets Syst. 90, 365–368 (1997)Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27, 385–389 (1989)Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces. Fuzzy Sets Syst. 115, 485–489 (2000)Gregori, V., Romaguera, S.: On completion of fuzzy metric spaces. Fuzzy Sets Syst. 130, 399–404 (2002)Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces. Fuzzy Sets Syst. 144, 411–420 (2004)Gregori, V., López-Crevillén, A., Morillas, S., Sapena, A.: On convergence in fuzzy metric spaces. Topol. Appl. 156, 3002–3006 (2009)Gregori, V., Miñana, J.J.: Some concepts realted to continuity in fuzzy metric spaces. In: Proceedings of the conference in applied topology WiAT’13, pp. 85–91 (2013)Gregori, V., Miñana, J.-J., Sapena, A.: On Banach contraction principles in fuzzy metric spaces (2015, submitted)Gregori, V., Miñana, J.-J.: std-Convergence in fuzzy metric spaces. Fuzzy Sets Syst. 267, 140–143 (2015)Gregori, V., Miñana, J.-J.: Strong convergence in fuzzy metric spaces Filomat (2015, accepted)Gregori, V., Miñana, J.-J., Morillas, S.: Some questions in fuzzy metric spaces. Fuzzy Sets Syst. 204, 71–85 (2012)Gregori, V., Miñana, J.-J., Morillas, S.: A note on convergence in fuzzy metric spaces. Iran. J. Fuzzy Syst. 11(4), 75–85 (2014)Gregori, V., Morillas, S., Sapena, A.: On a class of completable fuzzy metric spaces. Fuzzy Sets Syst. 161, 2193–2205 (2010)Gregori, V., Morillas, S., Sapena, A.: Examples of fuzzy metric spaces and applications. Fuzzy Sets Syst. 170, 95–111 (2011)Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetika 11, 326–334 (1975)Mihet, D.: On fuzzy contractive mappings in fuzzy metric spaces. Fuzzy Sets Syst. 158, 915–921 (2007)Mihet, D.: Fuzzy $$\varphi$$ φ -contractive mappings in non-Archimedean fuzzy metric spaces. Fuzzy Sets Syst. 159, 739–744 (2008)Mihet, D.: A Banach contraction theorem in fuzzy metric spaces. Fuzzy Sets Syst. 144, 431–439 (2004)Mishra, S.N., Sharma, N., Singh, S.L.: Common fixed points of maps on fuzzy metric spaces Internat. J. Math. Math. Sci. 17(2), 253–258 (1994)Morillas, S., Sapena, A.: On Cauchy sequences in fuzzy metric spaces. In: Proceedings of the conference in applied topology (WiAT’13), pp. 101–108 (2013)Ricarte, L.A., Romaguera, S.: A domain-theoretic approach to fuzzy metric spaces. Topol. Appl. 163, 149–159 (2014)Sherwood, H.: On the completion of probabilistic metric spaces. Z.Wahrschein-lichkeitstheorie verw. Geb. 6, 62–64 (1966)Sherwood, H.: Complete Probabilistic Metric Spaces. Z. Wahrschein-lichkeitstheorie verw. Geb. 20, 117–128 (1971)Tirado, P.: On compactness and G-completeness in fuzzy metric spaces. Iran. J. Fuzzy Syst. 9(4), 151–158 (2012)Tirado, P.: Contraction mappings in fuzzy quasi-metric spaces and [0,1]-fuzzy posets. Fixed Point Theory 13(1), 273–283 (2012)Vasuki, R., Veeramani, P.: Fixed point theorems and Cauchy sequences in fuzzy metric spaces. Fuzzy Sets Syst. 135(3), 415–417 (2003)Veeramani, P.: Best approximation in fuzzy metric spaces. J. Fuzzy Math. 9, 75–80 (2001

Diversidad de razas caprinas criollas en Argentina

Se estima que el 90% de los casi cinco millones de caprinos en Argentina se pueden asignar a poblaciones locales tradicionalmente llamadas Criollos. Se denomina así a un colectivo indefinido, menospreciado en sus atributos fenotípicos y productivos característicos, originados a partir de selección por diferentes etnias y en general adaptados a ambientes disímiles y hostiles de crianza. Con el objetivo de determinar las características diferenciales de razas locales o biotipos dentro de las Criollas contribuyendo a su valoración como recurso genético, se recuperaron trabajos de caracterización fenotípica realizados desde el año 2000 hasta el 2013. Se construyó una base datos a partir de las originales, con 19 variables cualitativas y cuantitativas de 2170 hembras de 6 poblaciones locales: Criollas de Formosa (FOR), Córdoba (CBA), La Rioja (LRI), San Luis (SLU), Neuquén (NQN) y Colorada Pampeana (LPA). Se analizó en forma descriptiva y multivariada para detectar diferencias y similitudes entre ellas. Los resultados mostraron rasgos compartidos (perfil recto; orejas horizontales) y divergentes (tipo de pelaje, perímetro de la caña). Los conglomerados formados en base al análisis factorial de datos mixtos muestran una clara diferenciación para FOR, LPA y NQN. CBA muestra rasgos de cruzamientos con Anglo Nubian, LRI y SLU se muestran dispersas. Se formaron 4 clústeres con buena definición para FOR, LPA, CBA y NQN. Se concluye que las razas Criolla Formoseña, Neuquina y Colorada Pampeana alcanzan un grado de diferenciación fenotípico significativo. LRI y SLU no muestran clara diferenciación y la CBA evidencia signos de cruzamientos con razas comerciales y riesgo de erosión genética.It is estimated that 90% of the almost five million goats in Argentina are local populations traditionally called Criollo. This designation refers to goats whose phenotypic and productive attributes are neglected. These populations have different origins and were selected by diverse rural communities; however, they share some common characteristics, such as being adapted to harsh environmental conditions and being bred in arid areas. In order to determine the differential traits of local breeds within Criollo and contribute to their assessment as a local genetic resource, phenotypic characterization research carried out in the last decades were recovered. A database was built, with 19 qualitative and quantitative variables of 2170 females from 6 local populations: Criolla de Formosa (FOR), Córdoba (CBA), La Rioja (LRI), San Luis (SLU), Neuquén (NQN) and Colorada Pampeana (LPA). They were analysed descriptively and by multivariate analysis in order to define differences and similarities among them. The results showed shared (straight profile, horizontal ears) and divergent (type of coat, shin circumference) features. The conglomerates formed on the basis of the mixed data factor analysis showed a clear differentiation for FOR, LPA and NQN. CBA showed evidence of crossing with Anglo Nubian, while LRI and SLU were scattered. Four Clusters with good definition were formed for FOR, LPA, CBA and NQN. It is concluded that FOR, NQN and LPA populations have achieved a significant degree of phenotypic differentiation. The LRI and SLU did not show a clear differentiation and the CBA showed signs of crossing with commercial breeds and risk of genetic erosion.Estación Experimental Agropecuaria BarilocheFil: Lanari, María Rosa. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche; ArgentinaFil: Giovannini, Nicolas. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Bariloche; ArgentinaFil: Maizon, Daniel Omar. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Anguil; ArgentinaFil: Deza, Maria C.V. Universidad Nacional de Cordoba. Facultad de Ciencias Agropecuarias; ArgentinaFil: Bedotti, Daniel Osvaldo. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Anguil; ArgentinaFil: de la Rosa-Carbajal, Sebastian Arnoldo. Centro de Validacion Laguna Yema; ArgentinaFil: Vera, Tomas Anibal. Instituto Nacional de Tecnología Agropecuaria (INTA). Instituto de Investigación y Desarrollo Tecnológico para la Agricultura Familiar. Región NOA; ArgentinaFil: Ricarte, Ramon Armando. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria La Rioja; ArgentinaFil: Mezzadra, Carlos Alberto. Instituto Nacional de Tecnología Agropecuaria (INTA). Estación Experimental Agropecuaria Balcarce; Argentin

MEDIDAS PARA LA CONSERVACIÓN DE LA BIODIVERSIDAD DE LOS POLINIZADORES SILVESTRES EN LA PENÍNSULA IBÉRICA

Los científicos y científicas abajo firmantes consideramos muy importante hacer llegar a instituciones, agricultores/as y a la sociedad en general, la necesidad urgente de implementar conjuntamente medidas y cambios que consigan frenar el declive de los polinizadores silvestres ocasionado por la actividad humana. Durante la última década, son múltiples los estudios que alertan de la creciente desaparición de los polinizadores por todo el mundo, en concreto de las abejas silvestres, (Biesmeijer et al. 2006; Potts et al. 2010; Burkle et al. 2013), y de las graves consecuencias que su déficit podría provocar sobre la biodiversidad global (Biesmeijer et al. 2006; Burkle et al. 2013; Lundgren et al. 2016) y sobre la producción agrícola (Aizen y Harder 2009; Garibaldi et al. 2013). No debemos olvidar que la península Ibérica es, por su condición mediterránea y su proximidad al continente africano, uno de los lugares con mayor diversidad de polinizadores de la Unión Europea y, en concreto, una de las zonas con mayor diversidad de abejas del mundo (Michener 2007; Nieto et al. 2014). Hasta el momento, el número de especies de abejas en España presentes en la zona íbero-balear es algo superior a 1.100, cifra a la que cabe añadir algunas especies exclusivas de Portugal más los nuevos hallazgos de los últimos años (Ortiz-Sánchez 2011). Esta gran diversidad de abejas y polinizadores en general está asociada al gran número de especies de plantas con flor presentes en la península Ibérica, alrededor de las 7.000 especies (Aguado Martín et al. 2015). En cuanto al número de mariposas y polillas (lepidópteros) se estima que existen en la península Ibérica unas 5.000 especies (Stefanescu et al. 2018). Más difícil es estimar el número exacto de especies de escarabajos florícolas (coleópteros polinizadores), pero atendiendo a la riqueza de los principales géneros podemos estimar su número en más de 750 (Stefanescu et al. 2018). Somos conscientes de que, a pesar del desarrollo explosivo de los últimos 10 años de la investigación en ecología y gestión de la polinización de los cultivos por insectos silvestres, hoy en día son numerosas las lagunas de conocimiento básico y aplicado sobre el estado de conservación de los insectos polinizadores silvestres. Y es, bajo esta premisa, que presentamos este trabajo de revisión de la literatura científica sobre insectos polinizadores desde principios del siglo XX hasta ahora, cuyo resultado ha quedado plasmado en una lista, no exhaustiva, de los aspectos que consideramos fundamentales para el desarrollo y debate de esta relevante cuestió

A Universal Power-law Prescription for Variability from Synthetic Images of Black Hole Accretion Flows

We present a framework for characterizing the spatiotemporal power spectrum of the variability expected from the horizon-scale emission structure around supermassive black holes, and we apply this framework to a library of general relativistic magnetohydrodynamic (GRMHD) simulations and associated general relativistic ray-traced images relevant for Event Horizon Telescope (EHT) observations of Sgr A*. We find that the variability power spectrum is generically a red-noise process in both the temporal and spatial dimensions, with the peak in power occurring on the longest timescales and largest spatial scales. When both the time-averaged source structure and the spatially integrated light-curve variability are removed, the residual power spectrum exhibits a universal broken power-law behavior. On small spatial frequencies, the residual power spectrum rises as the square of the spatial frequency and is proportional to the variance in the centroid of emission. Beyond some peak in variability power, the residual power spectrum falls as that of the time-averaged source structure, which is similar across simulations; this behavior can be naturally explained if the variability arises from a multiplicative random field that has a steeper high-frequency power-law index than that of the time-averaged source structure. We briefly explore the ability of power spectral variability studies to constrain physical parameters relevant for the GRMHD simulations, which can be scaled to provide predictions for black holes in a range of systems in the optically thin regime. We present specific expectations for the behavior of the M87* and Sgr A* accretion flows as observed by the EHT

The Event Horizon Telescope Image of the Quasar NRAO 530

We report on the observations of the quasar NRAO 530 with the Event Horizon Telescope (EHT) on 2017 April 5−7, when NRAO 530 was used as a calibrator for the EHT observations of Sagittarius A*. At z = 0.902, this is the most distant object imaged by the EHT so far. We reconstruct the first images of the source at 230 GHz, at an unprecedented angular resolution of ∼20 μas, both in total intensity and in linear polarization (LP). We do not detect source variability, allowing us to represent the whole data set with static images. The images reveal a bright feature located on the southern end of the jet, which we associate with the core. The feature is linearly polarized, with a fractional polarization of ∼5%-8%, and it has a substructure consisting of two components. Their observed brightness temperature suggests that the energy density of the jet is dominated by the magnetic field. The jet extends over 60 μas along a position angle ∼ −28°. It includes two features with orthogonal directions of polarization (electric vector position angle), parallel and perpendicular to the jet axis, consistent with a helical structure of the magnetic field in the jet. The outermost feature has a particularly high degree of LP, suggestive of a nearly uniform magnetic field. Future EHT observations will probe the variability of the jet structure on microarcsecond scales, while simultaneous multiwavelength monitoring will provide insight into the high-energy emission origin

Combined dark matter searches towards dwarf spheroidal galaxies with Fermi-LAT, HAWC, H.E.S.S., MAGIC, and VERITAS

Cosmological and astrophysical observations suggest that 85% of the total matter of the Universe is made of Dark Matter (DM). However, its nature remains one of the most challenging and fundamental open questions of particle physics. Assuming particle DM, this exotic form of matter cannot consist of Standard Model (SM) particles. Many models have been developed to attempt unraveling the nature of DM such as Weakly Interacting Massive Particles (WIMPs), the most favored particle candidates. WIMP annihilations and decay could produce SM particles which in turn hadronize and decay to give SM secondaries such as high energy \u1d6fe rays. In the framework of indirect DM search, observations of promising targets are used to search for signatures of DM annihilation. Among these, the dwarf spheroidal galaxies (dSphs) are commonly favored owing to their expected high DM content and negligible astrophysical background. In this work, we present the very first combination of 20 dSph observations, performed by the Fermi-LAT, HAWC, H.E.S.S., MAGIC, and VERITAS collaborations in order to maximize the sensitivity of DM searches and improve the current results. We use a joint maximum likelihood approach combining each experiment’s individual analysis to derive more constraining upper limits on the WIMP DM self-annihilation cross-section as a function of DM particle mass. We present new DM constraints over the widest mass range ever reported, extending from 5 GeV to 100 TeV thanks to the combination of these five different \u1d6fe-ray instruments

A universal power-law prescription for variability from synthetic images of black hole accretion flows

Instrumentatio

Resolving the Inner Parsec of the Blazar J1924-2914 with the Event Horizon Telescope

The blazar J1924-2914 is a primary Event Horizon Telescope (EHT) calibrator for the Galactic center's black hole Sagittarius A*. Here we present the first total and linearly polarized intensity images of this source obtained with the unprecedented 20 mu as resolution of the EHT. J1924-2914 is a very compact flat-spectrum radio source with strong optical variability and polarization. In April 2017 the source was observed quasi-simultaneously with the EHT (April 5-11), the Global Millimeter VLBI Array (April 3), and the Very Long Baseline Array (April 28), giving a novel view of the source at four observing frequencies, 230, 86, 8.7, and 2.3 GHz. These observations probe jet properties from the subparsec to 100 pc scales. We combine the multifrequency images of J1924-2914 to study the source morphology. We find that the jet exhibits a characteristic bending, with a gradual clockwise rotation of the jet projected position angle of about 90 degrees between 2.3 and 230 GHz. Linearly polarized intensity images of J1924-2914 with the extremely fine resolution of the EHT provide evidence for ordered toroidal magnetic fields in the blazar compact core