Extreme points and geometric aspects of compact convex sets in asymmetric normed spaces

[EN] The Krein-Milman theorem states that every compact convex subset in a locally compact convex space is the closure of the convex hull of its extreme points. Inspired by this result, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite dimensional case, giving a geometric description of all compact convex subsets of a finite dimensional asymmetric normed space.Jonard-Perez, N.; Sánchez Pérez, EA. (2016). Extreme points and geometric aspects of compact convex sets in asymmetric normed spaces. Topology and its Applications. 203:12-21. https://doi.org/10.1016/j.topol.2015.12.071S122120

Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers

[EN] In this paper, a new methodology for the determination of the boundaries between oscillatory and non-oscillatory motion for nonviscously damped nonproportional systems is proposed. It is assumed that the damping forces are expressed as convolution integrals of the velocities via hereditary exponential kernels. Oscillatory motion is directly related to the complex nature of eigensolutions in a frequency domain and, in turn, on the value of the damping parameters. New theoretical results are derived on critical eigenmodes for viscoelastic systems with multiple degrees of freedom, with no restrictions on the number of hereditary kernels. Furthermore, these outcomes enable the construction of a numerical approach to draw the critical curves as solutions of certain parameter-dependent eigenvalue problems. The method is illustrated and validated through two numerical examples, covering discrete and continuous systems.This research was partially supported by the Grant PID2020-112759GB-I00, funded by MCIN/AEI/10.13039/501100011033, and by "ERDF A way of making Europe".Lázaro, M.; García-Raffi, LM. (2022). Boundaries of Oscillatory Motion in Structures with Nonviscous Dampers. Applied Sciences. 12(5):1-23. https://doi.org/10.3390/app1205247812312

Applications of the complexity space to the General Probabilistic Divide and Conquer Algorithms

AbstractSchellekens [M. Schellekens, The Smyth completion: A common foundation for denotational semantics and complexity analysis, in: Proc. MFPS 11, in: Electron. Notes Theor. Comput. Sci., vol. 1, 1995, pp. 535–556], and Romaguera and Schellekens [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999) 311–322] introduced a topological foundation to obtain complexity results through the application of Semantic techniques to Divide and Conquer Algorithms. This involved the fact that the complexity (quasi-metric) space is Smyth complete and the use of a version of the Banach fixed point theorem and improver functionals. To further bridge the gap between Semantics and Complexity, we show here that these techniques of analysis, based on the theory of complexity spaces, extend to General Probabilistic Divide and Conquer schema discussed by Flajolet [P. Flajolet, Analytic analysis of algorithms, in: W. Kuich (Ed.), 19th Internat. Colloq. ICALP'92, Vienna, July 1992; Automata, Languages and Programming, in: Lecture Notes in Comput. Sci., vol. 623, 1992, pp. 186–210]. In particular, we obtain a general method which is useful to show that for several recurrence equations based on the recursive structure of General Probabilistic Divide and Conquer Algorithms, the associated functionals have a unique fixed point which is the solution for the corresponding recurrence equation

Manual bibliogràfic per a l'ensenyament de la filosofia

Manual bibliogràfic per a l'ensenyament de la filosofia, amb llibres de text, llibres, revistes i articles sobre didàctica de la filosofia i recursos didàctics en general

Cinema i coneixement

L’article exposa les línies fonamentals de l’àrea en emergència de cine i coneixement mostrant els elements essencials que la conformen. S’examina el paper del cine en el modelatge de conductes, el coneixement de la realitat, la construcció de la memòria social, l’educació sentimental, l’autobiografia, l’inconscient i els arquetips culturals. S’exposa igualment la capacitat d’anàlisi sociològic del cine sobre la pobresa i les seues causes a partir de pel•lícules canòniques, en especial del film Ciutat de Déu.The chapter presents the fundamental lines of the emerging fild of film and knowledge and shows its essential elements. The chapter examines the role of cinema in shaping behavior, knowledge of reality, the construction of social memory, the sentimental education, autobiography, unconscious and cultural archetypes. Also exhibits the ability of sociological analysis of film about poverty and its causes from canonical films, especially "City of God"

Nonlinear self-collimated sound beams in sonic crystals

We report the propagation of high-intensity sound beams in a sonic crystal, under self-collimation or reduced-divergence conditions. The medium is a fluid with elastic quadratic nonlinearity, where the dominating nonlinear effect is harmonic generation. The conditions for the efficient generation of narrow, non-diverging beam of second harmonic are discussed. Numerical simulations are in agreement with the analytical predictions made, based on the linear dispersion characteristics in modulated media and the nonlinear interaction in a quadratic medium under phase matching conditions.Comment: Sent to PR