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

Propuesta de modelización: Reflexión de ondas por una superficie rugosa

[EN] Within the framework of the new curriculum, where active learning is the student, we propose a practice of modelling in science education to work with basics of mathematics and physics. The practice involves the modelling of wave reflection by rough surfaces. In a first stage, the reflection is analysed by a completely flat surface using geometric and physical concepts. The wave reflected from the surface is calculated from the waves emitted by a virtual source placed at the position symmetrical to the source position with respect to the mirror surface. To calculate the reflected wave, probability concepts are introduced. The wave reflection by a rough surface is obtained from the waves emitted by different sources for virtually every point of reflection. Courses in architecture and basic engineering, or even a master of acoustics are exceptional framework for the implementation of this practice.[ES] Dentro del marco de los nuevos planes de estudio, donde el activo del aprendizaje es el alumno, se propone una práctica de modelización para trabajar conceptos básicos de matemáticas y física en los primeros cursos Universitarios. La práctica consiste en la modelización de la reflexión de ondas por superficies rugosas. En un primer estadio de la práctica se analiza la reflexión por una superficie totalmente plana usando conceptos geométricos y físicos. La onda reflejada por la superficie plana se calcula a partir de las ondas emitidas por una fuente virtual colocada en la posición totalmente simétrica a la posición de la fuente respecto a la superficie especular. Para el cálculo de la onda reflejada se introducen conceptos de probabilidad. La reflexión de la onda por una superficie rugosa se obtiene a partir de las ondas emitidas por diferentes fuentes virtuales para cada punto de reflexión. Cursos de arquitectura y de ingeniería básica, o incluso algún máster de acústica, son marcos excepcionales para la aplicación de esta práctica.Garcia-Raffi, L.; Romero-García, V. (2011). Propuesta de modelización: Reflexión de ondas por una superficie rugosa. Modelling in Science Education and Learning. 4:195-205. doi:10.4995/msel.2011.3072SWORD1952054Sánchez-Pérez, E.A., Garcia-Raffi, L. M., Sánchez-Pérez, J. V. Introducción a las Técnicas de Modelización para la ense-anza de la Física y las Matemáticas en los primeros cursos de Ingeniería. Ense-anza de las Ciencias 17(1) (1999), pp. 119-129.E. Osborn, and Garrett J. Stuck, A guide to MatlabQc : for beginners and experienced users. Cambridge University Press. Cambridge (2001)

Pattern Formation by Traveling Localized Modes in Two-Dimensional Dissipative Media with Lattice Potentials

We analyze pattern-formation scenarios in the two-dimensional (2D) complex Ginzburg-Landau (GL) equation with the cubic-quintic nonlinearity and a cellular potential. The equation models laser cavities with built-in gratings, which stabilize 2D patterns. The pattern-building process is initiated by kicking a compound mode, in the form of a dipole, quadrupole, or vortex which is composed of four local peaks. The hopping motion of the kicked mode through the cellular structure leads to the generation of various extended patterns pinned by the structure. In the ring-shaped system, the persisting freely moving dipole hits the stationary pattern from the opposite side, giving rise to several dynamical regimes, including periodic elastic collisions, i.e., persistent cycles of elastic collisions between the moving and quiescent dissipative solitons, and transient regimes featuring several collisions which end up by absorption of one soliton by the other. Another noteworthy result is transformation of a strongly kicked unstable vortex into a stably moving four-peaked cluster

An application of bilinear integration to quantum scattering

Scattering theory has its origin in Quantum Mechanics. From the mathematical point of view it can be considered as a part of perturbation theory of self-adjoint operators on the absolutely continuous spectrum. In this work we deal with the passage from the time-dependent formalism to the stationary state scattering theory. This problem involves applying Fubini's Theorem to a spectral measure integral and a Lebesgue integral of functions that take values in spaces of operators. In our approach, we use bilinear integration in a tensor product of spaces of operators with suitable topologies and generalize the results previously stated in the literature. (C) 2014 Elsevier Inc. All rights reserved.Supported by the Spanish Ministry of Education and Science and FEDER, under Grant #MTM2012-36740-c02-02.García-Raffi, LM.; Jefferies, B. (2014). An application of bilinear integration to quantum scattering. Journal of Mathematical Analysis and Applications. 415(1):394-421. https://doi.org/10.1016/j.jmaa.2014.01.055S394421415

Nuclear structure of Ac-231

The low-energy structure of 231Ac has been investigated by means of gamma ray spectroscopy following the beta-decay of 231Ra. Multipolarities of 28 transitions have been established by measuring conversion electrons with a mini-orange electron spectrometer. The decay scheme of 231Ra --> 231Ac has been constructed for the first time. The Advanced Time Delayed beta-gamma-gamma(t) method has been used to measure the half-lives of five levels. The moderately fast B(E1) transition rates derived suggest that the octupole effects, albeit weak, are still present in this exotic nucleus

Compactness and finite dimension in asymmetric normed linear spaces

AbstractWe describe the compact sets of any asymmetric normed linear space. After that, we focus our attention in finite dimensional asymmetric normed linear spaces. In this case we establish the equivalence between T1 separation axiom and normable spaces. It is proved an asymmetric version of the Riesz Theorem about the compactness of the unit ball. We also prove that the Heine–Borel Theorem characterizes finite dimensional asymmetric normed linear spaces that satisfies the T2 separation axiom. Finally we focus our attention on the T0 separation axiom and results that are related to the dual p-complexity spaces

Introducción de las técnicas de modelización para el estudio de la física y de las matemáticas en los primeros cursos de las carreras técnicas

In this article we present a program of interdisciplinary practices for a first engineering course. We followed this program during the course 1996-1997, and we give several examples of the kind of exercises that we used. We also present some remarks and conclusions that we have achieved in our experience. Our purpose is to introduce a teaching strategy for Mathematics and Physics at the University level