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arXiv 2017年

作者： Jahanshahi, S. Babolian, E. Torres, D.F.M. Vahidi, A. Department of Mathematics Science and Research Branch Islamic Azad University Tehran Iran Center for Research Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

We introduce an efficient algorithm for computing fractional integrals and derivatives and apply it for solving problems of the calculus of variations of fractional order. The proposed approximations are particularly useful for solving fractional boundary value problems. As an application, we solve a special class of fractional Euler-Lagrange equations. The method is based on Hale and Townsend algorithm for finding the roots and weights of the fractional Gauss-Jacobi quadrature rule and the predictor-corrector method introduced by Diethelm for solving fractional differential equations. Illustrative examples show that the given method is more accurate than the one introduced in [Comput. Math. Appl. 66 (2013), no. 5, 597-607], which uses the Golub-Welsch algorithm for evaluating fractional directional *** Codes 26A33, 49K05 Copyright © 2017, The Authors. All rights reserved.

关键词： Variational techniques

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-rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels

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Integral Equations and Operator Theory 2024年第4期96卷 1-37页

作者： Alpay, Daniel Cerejeiras, Paula Kaehler, Uwe Schneider, Baruch Faculty of Mathematics Physics and Computation Schmid College of Science and Technology Chapman University Orange USA Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal Department of Mathematics University of Ostrava Ostrava Czech Republic

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

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Quantitative Hennessy-Milner Theorems via Notions of Density

arXiv

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arXiv 2022年

作者： Forster, Jonas Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul Friedrich-Alexander-Universität Erlangen-Nürnberg Germany Center for Research and Development in Mathematics and Applications University of Aveiro Portugal

The classical Hennessy-Milner theorem is an important tool in the analysis of concurrent processes;it guarantees that any two non-bisimilar states in finitely branching labelled transition systems can be distinguished by a modal formula. Numerous variants of this theorem have since been established for a wide range of logics and system types, including quantitative versions where lower bounds on behavioural distance (e.g. in weighted, metric, or probabilistic transition systems) are witnessed by quantitative modal formulas. Both the qualitative and the quantitative versions have been accommodated within the framework of coalgebraic logic, with distances taking values in quantales, subject to certain restrictions, such as being so-called value quantales. While previous quantitative coalgebraic Hennessy-Milner theorems apply only to liftings of set functors to (pseudo-)metric spaces, in the present work we provide a quantitative coalgebraic Hennessy-Milner theorem that applies more widely to functors native to metric spaces;notably, we thus cover, for the first time, the well-known Hennessy-Milner theorem for continuous probabilistic transition systems, where transitions are given by Borel measures on metric spaces, as an instance. In the process, we also relax the restrictions imposed on the quantale, and additionally parametrize the technical account over notions of closure and, hence, density, providing associated variants of the Stone-Weierstraß theorem;this allows us to cover, for instance, behavioural ultrametrics. © 2022, CC BY.

关键词： Topology

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Kantorovich Functors and Characteristic Logics for Behavioural Distances

arXiv

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arXiv 2022年

作者： Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul Friedrich-Alexander-Universität Erlangen-Nürnberg Germany Center for Research and Development in Mathematics and Applications University of Aveiro Portugal

Behavioural distances measure the deviation between states in quantitative systems, such as probabilistic or weighted systems. There is growing interest in generic approaches to behavioural distances. In particular, coalgebraic methods capture variations in the system type (non-deterministic, probabilistic, game-based etc.), and the notion of quantale abstracts over the actual values distances take, thus covering, e.g., two-valued equivalences, (pseudo)metrics, and probabilistic (pseudo)metrics. Coalgebraic behavioural distances have been based either on liftings of Set-functors to categories of metric spaces, or on lax extensions of Set-functors to categories of quantitative relations. Every lax extension induces a functor lifting but not every lifting comes from a lax extension. It was shown recently that every lax extension is Kantorovich, i.e. induced by a suitable choice of monotone predicate liftings, implying via a quantitative coalgebraic Hennessy-Milner theorem that behavioural distances induced by lax extensions can be characterized by quantitative modal logics. Here, we essentially show the same in the more general setting of behavioural distances induced by functor liftings. In particular, we show that every functor lifting, and indeed every functor on (quantale-valued) metric spaces, that preserves isometries is Kantorovich, so that the induced behavioural distance (on systems of suitably restricted branching degree) can be characterized by a quantitative modal logic. © 2022, CC BY.

关键词： Topology

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Impact of rescuer position, arm angle, and anthropometric variables on muscle fatigue during cardiopulmonary resuscitation: an international multicentric randomized crossover simulation study

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Resuscitation Plus 2025年 24卷 100971-100971页

作者： Sa-Couto, Carla Sa-Couto, Pedro Nicolau, Abel Lazarovici, Marc Ericsson, Christoffer Vieira-Marques, Pedro Bispo, Ingrid RISE-Health Community Medicine Information and Decision Sciences Department (MEDCIDS) Faculty of Medicine University of Porto (FMUP) Porto Portugal Center for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics (DMAT) University of Aveiro Portugal RISE-Health Faculty of Medicine University of Porto Porto Portugal Institut für Notfallmedizin und Medizinmanagement (INM) LMU Klinikum LMU München München Germany Arcada University of Applied Sciences School of Business and Healthcare Helsinki Finland Community Medicine Information and Decision Sciences Department (MEDCIDS) Faculty of Medicine University of Porto (FMUP) Porto Portugal

Background: There is a lack of studies using surface electromyography (sEMG) to objectively assess the impact of rescuer position and arm angle on muscle fatigue during CPR. Additionally, the relationship between anthropometric variables (height and weight) and muscle fatigue remains underexplored. Aim: This study aims to objectively assess muscle fatigue during CPR by analyzing triceps brachii sEMG activation during continuous chest compressions (CCs) across different rescuer positions and arm angles. A secondary objective is to examine correlations between anthropometric variables and muscle fatigue, while also evaluating the impact of CCs quality on fatigue levels. Methods: This international, multicentric, randomized crossover simulation trial included healthcare professionals assigned to one of four rescuer positions: kneeling on the floor, standing, standing on a step stool, and kneeling on a bed. Participants performed two 3-minute trials of continuous CCs at 90° and 105° arm angles. Muscle fatigue was assessed via sEMG, while compression quality was evaluated using manikin-derived data. Results: A total of 72 participants were included. The 105° arm angle significantly increased muscle fatigue compared to 90° (p < 0.001) across all rescuer positions. Taller and heavier rescuers exhibited lower fatigue for both arm angles (p < 0.05);however, fatigue levels were consistently higher at 105° than at 90°. Conclusion: Arm angle is a key determinant of rescuer muscle fatigue, with 105° increasing fatigue compared to 90°. Rescuer position alone was not significant, though fatigue was more pronounced in kneeling and elevated positions. Taller and heavier rescuers demonstrated greater endurance but remained affected by suboptimal arm angles. © 2025 The Authors

关键词： Anthropometric variables Arm angle Cardiopulmonary resuscitation Chest compressions quality Rescuer fatigue Rescuer position Surface electromyography

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Kerr black holes with synchronized axionic hair

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Physical Review D 2021年第10期103卷 104029-104029页

作者： Jorge F. M. Delgado Carlos A. R. Herdeiro Eugen Radu Departamento de Matemática Universidade de Aveiro Center for Research and Development in Mathematics and Applications - CIDMA Campus de Santiago Aveiro 3810-183 Portugal

We construct and analyze Kerr black holes (BHs) with synchronized axionic hair. These are the BH generalizations of the recently constructed rotating axion boson stars [J. F. Delgado, C. A. Herdeiro, and E. Radu, Rotating axion boson stars, J. Cosmol. Astropart. Phys. 06 (2020) 037]. Such BHs are stationary, axially symmetric, asymptotically flat solutions of the complex Einstein-Klein-Gordon theory with a QCD axionlike potential. They are regular everywhere on and outside the event horizon. The potential is characterized by two parameters: the mass of the axionlike particle, ma, and the decay constant, fa˜. The limit fa˜→∞ recovers the original example of Kerr BHs with synchronized scalar hair [C. A. R. Herdeiro and E. Radu, Kerr Black Holes with Scalar Hair, Phys. Rev. Lett. 112, 221101 (2014)]. The effects of the nonlinearities in the potential become important for fa˜≲1. We present an overview of the parameter space of the solutions together with a study of their basic geometric and phenomenological properties, for an illustrative value of the coupling that yields a non-negligible impact of the self-interactions.

关键词： Classical black holes General relativity General relativity equations & solutions Gravitation

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Equatorial timelike circular orbits around generic ultracompact objects

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Physical Review D 2022年第6期105卷 064026-064026页

作者： Jorge F. M. Delgado Carlos A. R. Herdeiro Eugen Radu Departamento de Matemática Universidade de Aveiro Center for Research and Development in Mathematics and Applications CIDMA Campus de Santiago Aveiro 3810-183 Portugal

For a stationary, axisymmetric, asymptotically flat, ultracompact [i.e., containing light rings (LRs)] object, with a Z2 north-south symmetry fixing an equatorial plane, we establish that the structure of timelike circular orbits (TCOs) in the vicinity of the equatorial LRs, for either rotation direction, depends exclusively on the radial stability of the LRs. Thus, an unstable LR delimits a region of unstable TCOs (no TCOs) radially above (below) it; a stable LR delimits a region of stable TCOs (no TCOs) radially below (above) it. Corollaries are discussed for both horizonless ultracompact objects and black holes. We illustrate these results with a variety of exotic stars examples and non-Kerr black holes, for which we also compute the efficiency associated with converting gravitational energy into radiation by a material particle falling under an adiabatic sequence of TCOs. For most objects studied, it is possible to obtain efficiencies larger than the maximal efficiency of Kerr black holes, i.e., larger than 42%.

关键词： Alternative gravity theories General relativity General relativity equations & solutions Gravitation

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Variable order fractional variational calculus for double integrals

Variable order fractional variational calculus for double in...

引用

IEEE Conference on Decision and Control

作者： Tatiana Odzijewicz Agnieszka B. Malinowska Delfim F. M. Torres Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal Faculty of Computer Science Białystok Technical University Bialystok Poland

ISBN: (纸本)9781467320658

We introduce three types of partial fractional operators of variable order. An integration by parts formula for partial fractional integrals of variable order and an extension of Green's theorem are proved. These results allow us to obtain a fractional Euler-Lagrange necessary optimality condition for variable order two-dimensional fractional variational problems.

关键词： Fractional calculus Educational institutions Equations Integral equations Optimal control

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Implementation of behavioral systems

Lecture Notes in Control and Information Sciences

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Lecture Notes in Control and Information Sciences 2015年 462卷 151-168页

作者： Napp, Diego Rocha, Paula Department of Mathematics CIDMA – Center for Research and Development in Mathematics and Applications University of Aveiro Campus Universitario de Santiago Aveiro3810-193 Portugal Department of Electrical and Computer Engineering SYSTEC - Research Center for Systems and Technologies University of Porto Porto Portugal

In this chapter, we study control by interconnection of a given linear differential system (the plant behavior) with a suitable controller. The problem formulations and their solutions are completely representation free, and specified only in terms of the system dynamics. A controller is a system that constrains the plant behavior through a certain set of variables. In this context, there are two main situations to be considered: either all the system variables are available for control, i.e., are control variables (full control) or only some of the variables are control variables (partial control). For systems evolving over a time domain (1D) the problems of implementability by partial (regular) interconnection are well understood. In this chapter, we study why similar results are not valid in themultidimensional (nD) case. Finally, we study two important classes of controllers, namely, canonical controllers and regular controllers. © Springer International Publishing Switzerland 2015.

关键词： Controllers

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A point-free perspective on lax extensions and predicate liftings

arXiv

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arXiv 2021年

作者： Goncharov, Sergey Hofmann, Dirk Nora, Pedro Schröder, Lutz Wild, Paul Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen Germany Center for Research and Development in Mathematics and Applications University of Aveiro Portugal

In this paper we have a fresh look at the connection between lax extensions and predicate liftings of a functor from the point of view of quantale-enriched relations. Using this perspective, in particular we show that various fundamental concepts and results arise naturally and their proofs become very elementary. Ultimately, we prove that every lax extension is represented by a class of predicate liftings and discuss several implications of this result. © 2021, CC BY.

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