Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Predictive score for mortality in patients with COPD exacerbations attending hospital emergency departments

Background: Limited information is available about predictors of short-term outcomes in patients with exacerbation of chronic obstructive pulmonary disease (eCOPD) attending an emergency department (ED). Such information could help stratify these patients and guide medical decision-making. The aim of this study was to develop a clinical prediction rule for short-term mortality during hospital admission or within a week after the index ED visit. Methods: This was a prospective cohort study of patients with eCOPD attending the EDs of 16 participating hospitals. Recruitment started in June 2008 and ended in September 2010. Information on possible predictor variables was recorded during the time the patient was evaluated in the ED, at the time a decision was made to admit the patient to the hospital or discharge home, and during follow-up. Main short-term outcomes were death during hospital admission or within 1 week of discharge to home from the ED, as well as at death within 1 month of the index ED visit. Multivariate logistic regression models were developed in a derivation sample and validated in a validation sample. The score was compared with other published prediction rules for patients with stable COPD. Results: In total, 2,487 patients were included in the study. Predictors of death during hospital admission, or within 1 week of discharge to home from the ED were patient age, baseline dyspnea, previous need for long-term home oxygen therapy or non-invasive mechanical ventilation, altered mental status, and use of inspiratory accessory muscles or paradoxical breathing upon ED arrival (area under the curve (AUC) = 0.85). Addition of arterial blood gas parameters (oxygen and carbon dioxide partial pressures (PO2 and PCO2)) and pH) did not improve the model. The same variables were predictors of death at 1 month (AUC = 0.85). Compared with other commonly used tools for predicting the severity of COPD in stable patients, our rule was significantly better. Conclusions: Five clinical predictors easily available in the ED, and also in the primary care setting, can be used to create a simple and easily obtained score that allows clinicians to stratify patients with eCOPD upon ED arrival and guide the medical decision-making process.

An approach version of fuzzy metric spaces including an ad hoc fixed point theorem

In this paper, inspired by two very different, successful metric theories such us the real view-point of Lowen's approach spaces and the probabilistic field of Kramosil and Michalek's fuzzymetric spaces, we present a family of spaces, called fuzzy approach spaces, that are appropriate to handle, at the same time, both measure conceptions. To do that, we study the underlying metric interrelationships between the above mentioned theories, obtaining six postulates that allow us to consider such kind of spaces in a unique category. As a result, the natural way in which metric spaces can be embedded in both classes leads to a commutative categorical scheme. Each postulate is interpreted in the context of the study of the evolution of fuzzy systems. First properties of fuzzy approach spaces are introduced, including a topology. Finally, we describe a fixed point theorem in the setting of fuzzy approach spaces that can be particularized to the previous existing measure spaces.

Algorithm for identification in the v-gap metric

This paper suggests a method for identification in the v-gap metric. For a finite number of frequency response samples, a problem for identification in the v-gap metric is formulated and an approximate solution is described. It uses an iterative technique for obtaining an L2-gap approximation. Each stage of the iteration involves solving an LMI optimisation. Given a known stabilising controller and the L2-gap approximation, it is shown how to derive a v-gap approximation.