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

Starburst-Driven Galactic Winds: Filament Formation and Emission Processes

We have performed a series of three-dimensional simulations of the interaction of a supersonic wind with a non-spherical radiative cloud. These simulations are motivated by our recent three-dimensional model of a starburst-driven galactic wind interacting with an inhomogeneous disk, which show that an optically emitting filament can be formed by the break-up and acceleration of a cloud into a supersonic wind. In this study we consider the evolution of a cloud with two different geometries (fractal and spherical) and investigate the importance of radiative cooling on the cloud's survival. We have also undertaken a comprehensive resolution study in order to ascertain the effect of the assumed numerical resolution on the results. We find that the ability of the cloud to radiate heat is crucial for its survival. While an adiabatic cloud is destroyed over a short period of time, a radiative cloud is broken up via the Kelvin-Helmholtz instability into numerous small, dense cloudlets, which are drawn into the flow to form a filamentary structure. The degree of fragmentation is highly dependent on the resolution of the simulation, with the number of cloudlets formed increasing as the Kelvin-Helmholtz instability is better resolved. Nevertheless, there is a clear qualitative trend, with the filamentary structure still persistent at high resolution. We confirm the mechanism behind the formation of the H-alpha emitting filaments found in our global simulations of a starburst-driven wind. Based on our resolution study, we conclude that bow shocks around accelerated gas clouds, and their interaction, are the main source of the soft X-ray emission observed in these galactic-scale winds. [ABRIDGED]Comment: Accepted to ApJ, 39 pages, 21 figures, movie file can obtained at http://www.mso.anu.edu.au/~jcooper/movie/halpha.mo

Anatomical distribution of spontaneous iron pigment overload in the liver of han wistar and sprague-dawley rats

The authors performed a retrospective study to determine and describe the incidence of spontaneous pigment overload in the liver of control Han Wistar and Sprague-Dawley rats. Data was collected from 1170 control animals (550 Han-Wistar and 620 Sprague-Dawley) from control dose groups from long term regulatory studies (104-week carcinogenicity studies). Further 628 control animals (300 Han-Wistar and 328 Sprague-Dawley) from control dose groups from short term regulatory studies (13-week and 4 weeks studies) evaluated at the authors’ laboratory between 2009 and 2011. Livers from Han Wistar and Sprague-Dawley rats were re-evaluated using special stains to identify the nature of the pigments. In the periportal hepatocytes and in scattered sinusoidal Kupffer cells, the predominant pigment was identified as haemosiderin and a diagnosis of spontaneous iron overload was made. A comparison between the two strains revealed higher incidences of iron overload in Han Wistar rats than Sprague-Dawley rats. A significant sex difference was observed in both strains but was greater in Han Wistar rats. An age-related increase in the incidence and severity of pigment deposition was also apparent. Since there is little compiled data on spontaneous pigment overload in the liver the aim of this report was to summarize and discuss the incidence, distribution and factors affecting the occurrence of this background finding in control rats on toxicity studies

Rapid TeV variability in Blazars as result of Jet-Star Interaction

We propose a new model for the description of ultra-short flares from TeV blazars by compact magnetized condensations (blobs), produced when red giant stars cross the jet close to the central black hole. Our study includes a simple dynamical model for the evolution of the envelope lost by the star in the jet, and its high energy nonthermal emission through different leptonic and hadronic radiation mechanisms. We show that the fragmented envelope of the star can be accelerated to Lorentz factors up to 100 and radiate effectively the available energy in gamma-rays predominantly through proton synchrotron radiation or external inverse Compton scattering of electrons. The model can readily explain the minute-scale TeV flares on top of longer (typical time-scales of days) gamma-ray variability as observed from the blazar PKS 2155-304. In the framework of the proposed scenario, the key parameters of the source are robustly constrained. In the case of proton synchrotron origin of the emission a mass of the central black hole of $M_{\rm BH}\approx 10^8 M_{\odot}$, a total jet power of $L_{\rm j} \approx 2\times 10^{47} \, \rm erg\,s^{-1}$ and a Doppler factor, of the gamma-ray emitting blobs, of $\delta\geq 40$ are required. Whilst for the external inverse Compton model, parameters of $M_{\rm BH}\approx 10^8 M_{\odot}$, $L_{\rm j} \approx 10^{46} \, \rm erg\,s^{-1}$ and the $\delta\geq 150$ are required.Comment: 25 pages, 11 figures, Submitted to Ap

A Single-centre, Before-After Study of the Short- and Long-term Efficacy of Narivent® in the Treatment of Nasal Congestion

Objective:Nasal congestion is a common symptom in allergic and nonallergic rhinitis, rhinosinusitis and nasal polyposis. The present study evaluated the clinical effectiveness of Narivent®, an osmo..

COVID-19 Vaccination Status among Adults Admitted to Intensive Care Units in Veneto, Italy

: This cohort study examines admissions to intensive care units for COVID-19–associated acute respiratory distress syndrome by COVID-19 vaccination status among adults in the Veneto region of Italy from May to December 2021

Second-look turbt: Evaluation of anatomopatological and oncologic results in a single center

Introduction: T1 bladder cancer is associated with a high risk of recurrence and progression; concomitant carcinoma in situ and/or multifocality are negative prognostic factors. Persistent disease after resection of T1 tumours has been observed in 33-55% of patients, and after resection of High-grade (HG) Ta tumour in 41,4%. It has been demonstrated that a second TURB can increase recurrence-free survival and it can make a restaging of the cancer. Patients and methods: From January 2011 to December 2016, 87 patients with superficial bladder tumor (Ta-T1), undergoing TURB and routine repeat TURB (Re-TURB) 4-6 weeks after the initial resection, were included in the study. Re-TURB was applied to the scar of the first resection and other suspicious lesions in the bladder. After the second-look, we studied the follow-up of each patient. Results: Specimens obtained during the second TURBT showed no tumor in 47 (54,02%) patients; 40 (45,98%) patients had residual cancer: 34 of them had cancer of the same stage, 6 patients of pT1 had a lower stage, and 3 had a higher stage. 5 patient underwent radical cistectomy immediatly after re-TURBT. During the first year of follow up, 15 patients had a recurrent bladder cancer; 2 of them underwent radical cistectomy. Conclusions: T1 bladder cancer is an high risk tumor, so that second-look TURBT is a valuable procedure for accurate staging of nonmuscle-invasive bladder cancer and it can guarantee a better eradicationof the neoplasm

Effect of preoperative pulmonary hemodynamic and cardiopulmonary bypass on lung function in children with congenital heart disease

In children with congenital heart disease (CHD), pulmonary blood flow (Qp) contributes to alterations of pulmonary mechanics and gas exchange, while cardiopulmonary bypass (CPB) induces lung edema. We aimed to determine the effect of hemodynamics on lung function and lung epithelial lining fluid (ELF) biomarkers in biventricular CHD children undergoing CPB. CHD children were classified as high Qp (n = 43) and low Qp (n = 17), according to preoperative cardiac morphology and arterial oxygen saturation. We measured ELF surfactant protein B (SP-B) and myeloperoxidase activity (MPO) as indexes of lung inflammation and ELF albumin as index of alveolar capillary leak in tracheal aspirate (TA) samples collected before surgery and in 6 hourly intervals within 24 h after surgery. At the same time points, we recorded dynamic compliance and oxygenation index (OI). The same biomarkers were measured in TA samples collected from 16 infants with no cardiorespiratory diseases at the time of endotracheal intubation for elective surgery. Preoperative ELF biomarkers in CHD children were significantly increased than those found in controls. In the high Qp, ELF MPO and SP-B peaked 6 h after surgery and tended to decrease afterward, while they tended to increase within the first 24 h in the low Qp. ELF albumin peaked 6 h after surgery and decreased afterwards in both CHD groups. Dynamic compliance/kg and OI significantly improved after surgery only in the High Qp. Conclusion: In CHD children, lung mechanics, OI, and ELF biomarkers were significantly affected by CPB, according to the preoperative pulmonary hemodynamics.What is Known:• Congenital heart disease children, before cardiopulmonary run, exhibit changes in respiratory mechanics, gas exchange, and lung inflammatory biomarkers that are related to the preoperative pulmonary hemodynamics.• Cardiopulmonary bypass induces alteration of lung function and epithelial lining fluid biomarkers according to preoperative hemodynamics.What is New:• Our findings can help to identify children with congenital heart disease at high risk of postoperative lung injury who may benefit of tailored intensive care strategies, such as non-invasive ventilation techniques, fluid management, and anti-inflammatory drugs that can improve cardiopulmonary interaction in the perioperative period