Topological and Computational Models for Fuzzy Metric Spaces via Domain Theory

This doctoral thesis is devoted to investigate the problem of establishing connections between Domain Theory and the theory of fuzzy metric spaces, in the sense of Kramosil and Michalek, by means of the notion of a formal ball, and then constructing topological and computational models for (complete) fuzzy metric spaces. The antecedents of this research are mainly the well-known articles of A. Edalat and R. Heckmann [A computational model for metric spaces, Theoret- ical Computer Science 193 (1998), 53-73], and R. Heckmann [Approximation of metric spaces by partial metric spaces, Applied Categorical Structures 7 (1999), 71-83], where the authors obtained nice and direct links between Do- main Theory and the theory of metric spaces - two crucial tools in the study of denotational semantics - by using formal balls. Since every metric induces a fuzzy metric (the so-called standard fuzzy metric), the problem of extending Edalat and Heckmann's works to the fuzzy framework arises in a natural way. In our study we essentially propose two di erent approaches. For the rst one, valid for those fuzzy metric spaces whose continuous t-norm is the minimum, we introduce a new notion of fuzzy metric completeness (the so-called standard completeness) that allows us to construct a (topological) model that includes the classical theory as a special case. The second one, valid for those fuzzy metric spaces whose continuous t-norm is greater or equal than the Lukasiewicz t-norm, allows us to construct, among other satisfactory results, a fuzzy quasi-metric on the continuous domain of formal balls whose restriction to the set of maximal elements is isometric to the given fuzzy metric. Thus we obtain a computational model for complete fuzzy metric spaces. We also prove some new xed point theorems in complete fuzzy metric spaces with versions to the intuitionistic case and the ordered case, respec- tively. Finally, we discuss the problem of extending the obtained results to the asymmetric framework.Ricarte Moreno, L. (2013). Topological and Computational Models for Fuzzy Metric Spaces via Domain Theory [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/34670TESI

On phi-contractions in fuzzy metric spaces with application to the intuitionistic setting

[EN] We obtain two fixed point theorems for a kind of phi-contractions in complete fuzzy metric spaces, which are applied to easily deduce intuitionistic versions that improve and simplify the recent results of X. Huang, C. Zhu and X. Wen.The second named author thanks the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Ricarte Moreno, LA.; Romaguera Bonilla, S. (2013). On phi-contractions in fuzzy metric spaces with application to the intuitionistic setting. Iranian Journal of Fuzzy Systems. 10(6):63-72. http://hdl.handle.net/10251/57003S637210

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 $\gamma$ 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 $\gamma$-ray instruments