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[ES] El modelo matemático utilizado en el estudio del oleaje es REEF3D::FNPF, un modelo de resolución en fase (Phase-resolving) basado en la resolución de la equación de Laplace. Para llevar a cabo dicho estudio se han realizado diversas simulaciones. Primero se realizaron dos estudios de convergencia, bidimensional y tridimensional. Una vez establecido el tamaño de celda a usar para una simulación eficiente del oleaje se llevaron a cabo diversas simulaciones para el estudio del oleaje. Estas simulaciones a parte de proporcionar la altura de ola significante, el periodo pico y el espectro de energía en los puntos deseados también nos proporcionó una reconstrucción del oleaje a lo largo del espacio y tiempo. Mediante esta reconstrucción fenómenos como la difracción, refracción y reflexión han sido estudiados conjuntamente con la altura de ola significante, los periodos predominantes y la energía del oleaje (densidad espectral) en el exterior e interior del puerto, especialmente en la zona entre el Muelle de la Energía y el Muelle Prat, donde el nuevo pantalán ha sido proyectado., [EN] The numerical wave model chosen for this thesis is the phase-resolving model REEF3D ::FNPF. Several simulations were carried out to ensure a proper representation of the wave transformation phenomena. Convergence studies were made in order to select an effective and efficient cell size for the numerical domain. After determining the cell size, three simulations were made with different significant wave heights and peak periods to ensure concurrent results. To select the most unfavorable scenario, the maximum annual significant wave height was selected in the most unfavorable direction for the area regarding the new dock, the southeastern incident waves. The analysis of wave conditions at the harbor show that strong wave transformation phenomena take place. Thanks to the visual representation of the wave field these phenomena can be observed and studied. This together with the speed and accuracy obtained in the results, make REEF3D::FNPF a great tool for harbor modeling. The strong diffraction and energy dissipation in the southern entrance of the Barcelona harbor make possible the introduction of a new dock, as they significantly reduce the significant wave height and the spectral energy density.

[ES] El modelo matemático utilizado en el estudio del oleaje es REEF3D::FNPF, un modelo de resolución en fase (Phase-resolving) basado en la resolución de la equación de Laplace. Para llevar a cabo dicho estudio se han realizado diversas simulaciones. Primero se realizaron dos estudios de convergencia, bidimensional y tridimensional. Una vez establecido el tamaño de celda a usar para una simulación eficiente del oleaje se llevaron a cabo diversas simulaciones para el estudio del oleaje. Estas simulaciones a parte de proporcionar la altura de ola significante, el periodo pico y el espectro de energía en los puntos deseados también nos proporcionó una reconstrucción del oleaje a lo largo del espacio y tiempo. Mediante esta reconstrucción fenómenos como la difracción, refracción y reflexión han sido estudiados conjuntamente con la altura de ola significante, los periodos predominantes y la energía del oleaje (densidad espectral) en el exterior e interior del puerto, especialmente en la zona entre el Muelle de la Energía y el Muelle Prat, donde el nuevo pantalán ha sido proyectado., [EN] The numerical wave model chosen for this thesis is the phase-resolving model REEF3D ::FNPF. Several simulations were carried out to ensure a proper representation of the wave transformation phenomena. Convergence studies were made in order to select an effective and efficient cell size for the numerical domain. After determining the cell size, three simulations were made with different significant wave heights and peak periods to ensure concurrent results. To select the most unfavorable scenario, the maximum annual significant wave height was selected in the most unfavorable direction for the area regarding the new dock, the southeastern incident waves. The analysis of wave conditions at the harbor show that strong wave transformation phenomena take place. Thanks to the visual representation of the wave field these phenomena can be observed and studied. This together with the speed and accuracy obtained in the results, make REEF3D::FNPF a great tool for harbor modeling. The strong diffraction and energy dissipation in the southern entrance of the Barcelona harbor make possible the introduction of a new dock, as they significantly reduce the significant wave height and the spectral energy density.

[ES] El modelo matemático utilizado en el estudio del oleaje es REEF3D::FNPF, un modelo de resolución en fase (Phase-resolving) basado en la resolución de la equación de Laplace. Para llevar a cabo dicho estudio se han realizado diversas simulaciones. Primero se realizaron dos estudios de convergencia, bidimensional y tridimensional. Una vez establecido el tamaño de celda a usar para una simulación eficiente del oleaje se llevaron a cabo diversas simulaciones para el estudio del oleaje. Estas simulaciones a parte de proporcionar la altura de ola significante, el periodo pico y el espectro de energía en los puntos deseados también nos proporcionó una reconstrucción del oleaje a lo largo del espacio y tiempo. Mediante esta reconstrucción fenómenos como la difracción, refracción y reflexión han sido estudiados conjuntamente con la altura de ola significante, los periodos predominantes y la energía del oleaje (densidad espectral) en el exterior e interior del puerto, especialmente en la zona entre el Muelle de la Energía y el Muelle Prat, donde el nuevo pantalán ha sido proyectado., [EN] The numerical wave model chosen for this thesis is the phase-resolving model REEF3D ::FNPF. Several simulations were carried out to ensure a proper representation of the wave transformation phenomena. Convergence studies were made in order to select an effective and efficient cell size for the numerical domain. After determining the cell size, three simulations were made with different significant wave heights and peak periods to ensure concurrent results. To select the most unfavorable scenario, the maximum annual significant wave height was selected in the most unfavorable direction for the area regarding the new dock, the southeastern incident waves. The analysis of wave conditions at the harbor show that strong wave transformation phenomena take place. Thanks to the visual representation of the wave field these phenomena can be observed and studied. This together with the speed and accuracy obtained in the results, make REEF3D::FNPF a great tool for harbor modeling. The strong diffraction and energy dissipation in the southern entrance of the Barcelona harbor make possible the introduction of a new dock, as they significantly reduce the significant wave height and the spectral energy density.

[ES] El modelo matemático utilizado en el estudio del oleaje es REEF3D::FNPF, un modelo de resolución en fase (Phase-resolving) basado en la resolución de la equación de Laplace. Para llevar a cabo dicho estudio se han realizado diversas simulaciones. Primero se realizaron dos estudios de convergencia, bidimensional y tridimensional. Una vez establecido el tamaño de celda a usar para una simulación eficiente del oleaje se llevaron a cabo diversas simulaciones para el estudio del oleaje. Estas simulaciones a parte de proporcionar la altura de ola significante, el periodo pico y el espectro de energía en los puntos deseados también nos proporcionó una reconstrucción del oleaje a lo largo del espacio y tiempo. Mediante esta reconstrucción fenómenos como la difracción, refracción y reflexión han sido estudiados conjuntamente con la altura de ola significante, los periodos predominantes y la energía del oleaje (densidad espectral) en el exterior e interior del puerto, especialmente en la zona entre el Muelle de la Energía y el Muelle Prat, donde el nuevo pantalán ha sido proyectado., [EN] The numerical wave model chosen for this thesis is the phase-resolving model REEF3D ::FNPF. Several simulations were carried out to ensure a proper representation of the wave transformation phenomena. Convergence studies were made in order to select an effective and efficient cell size for the numerical domain. After determining the cell size, three simulations were made with different significant wave heights and peak periods to ensure concurrent results. To select the most unfavorable scenario, the maximum annual significant wave height was selected in the most unfavorable direction for the area regarding the new dock, the southeastern incident waves. The analysis of wave conditions at the harbor show that strong wave transformation phenomena take place. Thanks to the visual representation of the wave field these phenomena can be observed and studied. This together with the speed and accuracy obtained in the results, make REEF3D::FNPF a great tool for harbor modeling. The strong diffraction and energy dissipation in the southern entrance of the Barcelona harbor make possible the introduction of a new dock, as they significantly reduce the significant wave height and the spectral energy density.

[ES] El modelo matemático utilizado en el estudio del oleaje es REEF3D::FNPF, un modelo de resolución en fase (Phase-resolving) basado en la resolución de la equación de Laplace. Para llevar a cabo dicho estudio se han realizado diversas simulaciones. Primero se realizaron dos estudios de convergencia, bidimensional y tridimensional. Una vez establecido el tamaño de celda a usar para una simulación eficiente del oleaje se llevaron a cabo diversas simulaciones para el estudio del oleaje. Estas simulaciones a parte de proporcionar la altura de ola significante, el periodo pico y el espectro de energía en los puntos deseados también nos proporcionó una reconstrucción del oleaje a lo largo del espacio y tiempo. Mediante esta reconstrucción fenómenos como la difracción, refracción y reflexión han sido estudiados conjuntamente con la altura de ola significante, los periodos predominantes y la energía del oleaje (densidad espectral) en el exterior e interior del puerto, especialmente en la zona entre el Muelle de la Energía y el Muelle Prat, donde el nuevo pantalán ha sido proyectado., [EN] The numerical wave model chosen for this thesis is the phase-resolving model REEF3D ::FNPF. Several simulations were carried out to ensure a proper representation of the wave transformation phenomena. Convergence studies were made in order to select an effective and efficient cell size for the numerical domain. After determining the cell size, three simulations were made with different significant wave heights and peak periods to ensure concurrent results. To select the most unfavorable scenario, the maximum annual significant wave height was selected in the most unfavorable direction for the area regarding the new dock, the southeastern incident waves. The analysis of wave conditions at the harbor show that strong wave transformation phenomena take place. Thanks to the visual representation of the wave field these phenomena can be observed and studied. This together with the speed and accuracy obtained in the results, make REEF3D::FNPF a great tool for harbor modeling. The strong diffraction and energy dissipation in the southern entrance of the Barcelona harbor make possible the introduction of a new dock, as they significantly reduce the significant wave height and the spectral energy density.

The aim of this work is to derive mathematical descriptions of gravitation. Postulating gravitation as a force field, Newton's law of gravitation is heuristically derived by considering linear differential operators invariant under euclidean isometries and by finding the fundamental solution to Helmholtz equation in three dimensions. Thereafter, the theory of differential geometry is introduced, providing a framework for the subsequent review of gravitation as curvature. Lastly, in the light of Einstein's postulates and equivalence principle, Lovelock's proof of uniqueness of Einstein's field equations is presented.

The aim of this work is to derive mathematical descriptions of gravitation. Postulating gravitation as a force field, Newton's law of gravitation is heuristically derived by considering linear differential operators invariant under euclidean isometries and by finding the fundamental solution to Helmholtz equation in three dimensions. Thereafter, the theory of differential geometry is introduced, providing a framework for the subsequent review of gravitation as curvature. Lastly, in the light of Einstein's postulates and equivalence principle, Lovelock's proof of uniqueness of Einstein's field equations is presented.

State estimators are developed for discrete linear systems with scalar additive Laplace process and measurement noises and their properties are analyzed. For the scalar case, an analytic recursive estimator is presented, along with detailed analysis of its behavior with respect to noise parameters. In addition, a one-step model predictive controller is developed. Using an objective function with 1-norm control and terminal state costs, the expectation of the objective function with respect to the conditional probability density function is determined by using the computational structure developed for the estimator. Numerical simulations for both the estimator and one-step controller are presented to demonstrate their unique behavior, including robustness to noise spikes in the measurements. For the general vector system, update and propagation algorithms as well as a method for computing moments in closed form using characteristic functions are presented. An explicit state estimator is developed for the two-state case, and a numerical example is presented to demonstrate the algorithms and the unique properties of Laplace estimators.

Business valuation is a set of procedures used by financial market participants to determine the price they are willing to pay or receive for businesses. Valuations play a crucial role in financial reporting, capital budgeting, and investment analysis. Current approaches to business valuation rely on professional expertise, causing the valuation to be as good as the analyst's assumptions. In this thesis, the entire valuation effort is translated into a systems and control problem. Economic engineering is used to formulate signal- and energy-based analogs for valuation concepts. A bond-graph model is developed to express general business dynamics as a set of differential equations. The model's analogy with the economic theory is shown by representing the model as a complex port-Hamiltonian system, and giving all elements and signals economic interpretations. A theory is developed to perform valuations in the frequency domain. This theory extends both the existing economic-engineering framework, and the existing valuation effort. Business valuation is performed by using this theory, by using the bond-graph model for business dynamics. The developed theory goes beyond the field of business valuations, as frequency-domain valuation can be applied to any type of financial instrument., Mechanical Engineering | Systems and Control

State estimators are developed for discrete linear systems with scalar additive Laplace process and measurement noises and their properties are analyzed. For the scalar case, an analytic recursive estimator is presented, along with detailed analysis of its behavior with respect to noise parameters. In addition, a one-step model predictive controller is developed. Using an objective function with 1-norm control and terminal state costs, the expectation of the objective function with respect to the conditional probability density function is determined by using the computational structure developed for the estimator. Numerical simulations for both the estimator and one-step controller are presented to demonstrate their unique behavior, including robustness to noise spikes in the measurements. For the general vector system, update and propagation algorithms as well as a method for computing moments in closed form using characteristic functions are presented. An explicit state estimator is developed for the two-state case, and a numerical example is presented to demonstrate the algorithms and the unique properties of Laplace estimators.

Business valuation is a set of procedures used by financial market participants to determine the price they are willing to pay or receive for businesses. Valuations play a crucial role in financial reporting, capital budgeting, and investment analysis. Current approaches to business valuation rely on professional expertise, causing the valuation to be as good as the analyst's assumptions. In this thesis, the entire valuation effort is translated into a systems and control problem. Economic engineering is used to formulate signal- and energy-based analogs for valuation concepts. A bond-graph model is developed to express general business dynamics as a set of differential equations. The model's analogy with the economic theory is shown by representing the model as a complex port-Hamiltonian system, and giving all elements and signals economic interpretations. A theory is developed to perform valuations in the frequency domain. This theory extends both the existing economic-engineering framework, and the existing valuation effort. Business valuation is performed by using this theory, by using the bond-graph model for business dynamics. The developed theory goes beyond the field of business valuations, as frequency-domain valuation can be applied to any type of financial instrument., Mechanical Engineering | Systems and Control

A regular-grid volume-integration algorithm has been previously developed for solving non-homogeneous versions of the Laplace and the elasticity equations. This note demonstrates that the same approach can be successfully adapted to the case of non-homogeneous, incompressible Stokes flow. The key observation is that the Stokeslet (Green’s function) can be written as U= μ∇ 2 ℋ, where ℋ has a simple analytical expression. As a consequence, the volume integral can be reformulated as an easily evaluated boundary integral, together with a remainder domain integral that can be computed using a regular cuboid grid covering the domain. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

The locations of a significant number of industrial facilities, landfills and almost all mineral ore bodies are characterised by high in situ stresses and fractures and fissures act as flow paths for fluids underground. Regional scale fracture systems that transport pollution from spatially isolated source locations can cause mixing of chemical pollutants from different source origins due to fracture- fracture flux across two or more intersecting fractures, hence reactive transport. Alerts of groundwater contamination in response to multicomponent pollution transport have been investigated using a mathematical model of the hydrodynamic response of incompressible fluids such as groundwater flow. Fundamental to the model is the conservation of mass associated with the applied source strength and the concentration velocity field redistributions after source has released pollution, assuming the formation is homogenous. Solute distribution depends on the formation porosity and generally, fluids travel faster in fractures than in sedimentary formations. Different variations of the deterministic advection dispersion equation have been employed to predict coupled transport/reactive processes by substitution of a reaction term (retardation factor, etc..) which accounts for the changing concentration of the solid face components through time due to chemical reaction. However, fractured aquifers are inherently heterogeneous due to interconnecting fractures. The results in a non-homogenous mathematical formulation which difficult to solve analytically. As a result, most research endeavours have tended to depend on numerical solutions, increasingly made possible through advanced computational power. Even though it is questionable to what extend numerical models of groundwater reactive transport can be useful in making accurate quantitative predictions, it is still possible for a reactive model to predict the outcome of a particular chemical representation in an aquifer. Neverthe

The French cartoonist Jean Laplace (1934-2018) has been, unintentionally, one of the most representative artists of contemporary art in the context of mass culture. From his collaborations in several newspapers of various nationalities,for more than half a century, Laplace popularized a hobby known as "The Eight Mistakes" in which the reader was invited to take a pencil and concentrate on finding the eightdifferences between two scenes. The discretion marked the biography of Jean Laplace, an artist whose studies have barely been published, but few artists have presented a work so recognizable by the public, so authentic and so continued in time with a very extensive production, close to twenty thousand works.Laplace's characters are simple people with big bulging eyes, drawn in a linear style that tendstoward the geometric, who live absurd and surreal situations, El dibujante francés Jean Laplace (1934-2018) ha sido, sin pretenderlo, uno de los artistas más representativos del arte actual en el contexto de la cultura de masas. Desde sus colaboraciones en varios periódicos de varias nacionalidades, durante más de medio siglo, Laplace popularizó un pasatiempo conocido como «Los ocho errores»en el cual el lector era invitado a coger un lápiz y a concentrarse en encontrar las ocho diferencias que había entre dos escenas humorísticas casi idénticas. La discreción marcóla biografía de Jean Laplace, un artista del que apenas se han publicado estudios, pero pocos dibujantes han presentado un trabajo tan reconocible por el público, tan auténtico y tan continuado en el tiempo con una producción muy extensa, próximo a las veinte mil obras. Los personajes de Laplace son gentes sencillas con grandes ojos saltones, dibujados en un estilo lineal que tiende hacia lo geométrico, que viven humorísticas situaciones absurdas y surrealistas.

We present in this work two schemes of approximation for numerical solutions of PDEs. The first one is the maximum entropy method (max-ent) and the second one is the b-spline method. These methods let us impose a special kind of boundary conditions: periodic boundary conditions for unbounded domains. Some experiments need a large domain (or unbounded domain), however, this domain is divdided into some periodic cells. We develop a technique that let us simulate in the whole domain only doing a simulation in one cell. We apply this method for the resolution of second and fourth order problems (with periodic boundary conditions) like: Laplace, Kirchhoff plate and flexoelectricity.

Esta publicación intenta facilitar el aprendizaje de los métodos fundamentales de resolución de ecuaciones diferenciales ordinarias de primer orden, superior y sistemas. Además se exponen dos herramientas específicas para la búsqueda de solución en los procesos en los que se conocen condiciones iniciales de partida: la transformada de Laplace y por métodos numéricos. La exposición de ejemplos resueltos es extensa e incluye el modelizado de situaciones físicas, el cálculo de la transformada inversa por diversos métodos y su aplicación al estudio de la estabilidad de sistemas dinámicos. Junto con los fundamentos teóricos se incluyen las demostraciones que se consideran formativas. La exposición se complementa con aplicaciones y ejemplos seleccionados con el fin de ayudar a entender y asimilar los resultados presentados. Cada capítulo finaliza con una lista de ejercicios propuestos cuya resolución consolida los conocimientos adquiridos. Capítulos: Ecuaciones diferenciales, Ecuaciones no lineales en y', Ecuaciones de orden superior, Sistemas de ecuaciones diferenciales, La transformada de Laplace, La transformada inversa de Laplace y Aplicaciones, Interpolación, Resolución numérica de problemas de valor inicial.

Esta publicación intenta facilitar el aprendizaje de los métodos fundamentales de resolución de ecuaciones diferenciales ordinarias de primer orden, superior y sistemas. Además se exponen dos herramientas específicas para la búsqueda de solución en los procesos en los que se conocen condiciones iniciales de partida: la transformada de Laplace y por métodos numéricos. La exposición de ejemplos resueltos es extensa e incluye el modelizado de situaciones físicas, el cálculo de la transformada inversa por diversos métodos y su aplicación al estudio de la estabilidad de sistemas dinámicos. Junto con los fundamentos teóricos se incluyen las demostraciones que se consideran formativas. La exposición se complementa con aplicaciones y ejemplos seleccionados con el fin de ayudar a entender y asimilar los resultados presentados. Cada capítulo finaliza con una lista de ejercicios propuestos cuya resolución consolida los conocimientos adquiridos. Capítulos: Ecuaciones diferenciales, Ecuaciones no lineales en y', Ecuaciones de orden superior, Sistemas de ecuaciones diferenciales, La transformada de Laplace, La transformada inversa de Laplace y Aplicaciones, Interpolación, Resolución numérica de problemas de valor inicial.

Esta publicación intenta facilitar el aprendizaje de los métodos fundamentales de resolución de ecuaciones diferenciales ordinarias de primer orden, superior y sistemas. Además se exponen dos herramientas específicas para la búsqueda de solución en los procesos en los que se conocen condiciones iniciales de partida: la transformada de Laplace y por métodos numéricos. La exposición de ejemplos resueltos es extensa e incluye el modelizado de situaciones físicas, el cálculo de la transformada inversa por diversos métodos y su aplicación al estudio de la estabilidad de sistemas dinámicos. Junto con los fundamentos teóricos se incluyen las demostraciones que se consideran formativas. La exposición se complementa con aplicaciones y ejemplos seleccionados con el fin de ayudar a entender y asimilar los resultados presentados. Cada capítulo finaliza con una lista de ejercicios propuestos cuya resolución consolida los conocimientos adquiridos. Capítulos: Ecuaciones diferenciales, Ecuaciones no lineales en y', Ecuaciones de orden superior, Sistemas de ecuaciones diferenciales, La transformada de Laplace, La transformada inversa de Laplace y Aplicaciones, Interpolación, Resolución numérica de problemas de valor inicial.

Esta publicación intenta facilitar el aprendizaje de los métodos fundamentales de resolución de ecuaciones diferenciales ordinarias de primer orden, superior y sistemas. Además se exponen dos herramientas específicas para la búsqueda de solución en los procesos en los que se conocen condiciones iniciales de partida: la transformada de Laplace y por métodos numéricos. La exposición de ejemplos resueltos es extensa e incluye el modelizado de situaciones físicas, el cálculo de la transformada inversa por diversos métodos y su aplicación al estudio de la estabilidad de sistemas dinámicos. Junto con los fundamentos teóricos se incluyen las demostraciones que se consideran formativas. La exposición se complementa con aplicaciones y ejemplos seleccionados con el fin de ayudar a entender y asimilar los resultados presentados. Cada capítulo finaliza con una lista de ejercicios propuestos cuya resolución consolida los conocimientos adquiridos. Capítulos: Ecuaciones diferenciales, Ecuaciones no lineales en y', Ecuaciones de orden superior, Sistemas de ecuaciones diferenciales, La transformada de Laplace, La transformada inversa de Laplace y Aplicaciones, Interpolación, Resolución numérica de problemas de valor inicial.

Esta publicación intenta facilitar el aprendizaje de los métodos fundamentales de resolución de ecuaciones diferenciales ordinarias de primer orden, superior y sistemas. Además se exponen dos herramientas específicas para la búsqueda de solución en los procesos en los que se conocen condiciones iniciales de partida: la transformada de Laplace y por métodos numéricos. La exposición de ejemplos resueltos es extensa e incluye el modelizado de situaciones físicas, el cálculo de la transformada inversa por diversos métodos y su aplicación al estudio de la estabilidad de sistemas dinámicos. Junto con los fundamentos teóricos se incluyen las demostraciones que se consideran formativas. La exposición se complementa con aplicaciones y ejemplos seleccionados con el fin de ayudar a entender y asimilar los resultados presentados. Cada capítulo finaliza con una lista de ejercicios propuestos cuya resolución consolida los conocimientos adquiridos. Capítulos: Ecuaciones diferenciales, Ecuaciones no lineales en y', Ecuaciones de orden superior, Sistemas de ecuaciones diferenciales, La transformada de Laplace, La transformada inversa de Laplace y Aplicaciones, Interpolación, Resolución numérica de problemas de valor inicial.

De Scheduled Relaxation Jacobi (SRJ) methode is een toepassing van de Jacobi methode met relaxatiegewichten. De relaxatiegewichten worden gebruikt in een iteratie cyclus. Daarnaast zijn de relaxatiegewichten zodanig gekozen, dat het optimaal werkt voor de Laplace vergelijking. Met de SRJ methode is het gelukt om de Jacobi methode 100x sneller te laten convergeren op de Laplace vergelijking. In dit verslag wordt de convergentie van de SRJ methode toegepast op de Helmholtz vergelijking onderzocht., Electrical Engineering, Mathematics and Computer Science, Applied Mathematics

De Scheduled Relaxation Jacobi (SRJ) methode is een toepassing van de Jacobi methode met relaxatiegewichten. De relaxatiegewichten worden gebruikt in een iteratie cyclus. Daarnaast zijn de relaxatiegewichten zodanig gekozen, dat het optimaal werkt voor de Laplace vergelijking. Met de SRJ methode is het gelukt om de Jacobi methode 100x sneller te laten convergeren op de Laplace vergelijking. In dit verslag wordt de convergentie van de SRJ methode toegepast op de Helmholtz vergelijking onderzocht., Electrical Engineering, Mathematics and Computer Science, Applied Mathematics

We prove that, given any knot γ in a compact 3-manifold M, there exists a Riemannian metric on M such that there is a complex-valued eigenfunction u of the Laplacian, corresponding to the first nontrivial eigenvalue, whose nodal set u^(-1)(0) has a connected component given by γ. Higher dimensional analogs of this result will also be considered.

Background: Alcohol consumption in very old age is increasing; yet, little is known about the personal and health-related characteristics associated with different levels of alcohol consumption and the association between alcohol consumption and survival among the oldest old. Methods: Nationally representative data from the Swedish Panel Study of Living Conditions of the Oldest Old (SWEOLD, ages 76-101; n=863) collected in 2010/2011 were used. Mortality was analyzed unti12014. Alcohol consumption was measured with questions about frequency and amount. Drinks per month were calculated and categorized as abstainer, light-to-moderate drinker (0.5-30 drinks/month) and heavy drinker (>30 drinks/month). Multinomial logistic regressions and Laplace regressions were performed. Results: Compared to light-to-moderate drinkers, abstainers had lower levels of education and more functional health problems, while heavy drinkers were more often men, had higher levels of education, and no serious health or functional problems. In models adjusted only for age and sex, abstainers died earlier than drinkers. Among light-to-moderate drinkers, each additional drink/month was associated with longer survival, while among heavy drinkers, each additional drink/month was associated with shorter survival. However, after adjusting for personal and health-related factors, estimates were lower and no longer statistically significant. Conclusions: The association between alcohol consumption and survival in very old age seems to have an inverse J-shape; abstention and heavy use is associated with shorter survival compared to light-to moderate drinking. To a large extent, differences in survival are due to differences in baseline health and physical function.

Today, there is a tendency to overlook the contributions of women such as Émilie du Châtelet and Mary Somerville; yet, despite numerous obstacles, they were able to make meaningful contributions to science. This review of Robyn Arianrhod’s book provides brief biographical summaries of the lives of these extraordinary women. It also considers some of the ramifications of Isaac Newton’s theory. Throughout history, various factors have impeded women from full participation in scientific research; nevertheless, Émilie du Châtelet and Mary Somerville found and took advantage of opportunities to engage in scientific activities. This raises the question: had these women been born during contemporary times, what original scientific discoveries might they have made?

The Laplace distribution and its generalizations found applications in a variety of disciplines that range from image and speech recognition (input distributions) and ocean engineering to finance. In the present paper, our major goal is to study the family of distribution called the double Lomax distribution which is the ratio of two independent and identically distributed classical Laplace distributions. Also the double Lomax distribution can be obtained by compounding classical Laplace distribution with exponential density. The important statistical properties of double Lomax distribution are explored. Also the relationships with other families of distributions are established. Maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. A simulation study is conducted to validate the algorithm. Finally, the application of our model is illustrated. We have used a microarray data set for illustration.

Purpose: Low-to-moderate alcohol consumption is associated with decreased mortality. However, many aspects of this association are still debated. Our aim was to complement available information by conducting a dose-response analysis of the association between alcohol consumption and survival time. Methods: In a Swedish population-based cohort of 67,706 middle-aged and elderly men and women, frequency and amount of drinking were assessed through a self-administrated questionnaire. During 15 years of follow-up, 13,323 participants died. Differences in survival (10th percentile differences, PDs) according to levels of alcohol consumption were estimated using Laplace regression. Results: We found evidence of nonlinearity between alcohol consumption and survival. Among women, we observed a rapid increase in survival up to 6 g/d of alcohol consumption (0.5 drinks/d) where survival was 17 months longer (PD = 17 months, 95% confidence interval, 10 to 24). After this peak, higher alcohol consumption was progressively associated with shorter survival. Among men, survival improved up to 15 g/d (1.5 drinks/d) where we observed a PD of 15 months (95% confidence interval, 8 to 22). Conclusions: Low alcohol consumption was associated with improved survival up to 1.5 years for women with an average consumption of 0.5 drinks per day and to 13 years for men with an average consumption of 1.5 drinks per day. (C) 2014 Elsevier Inc. All rights reserved.

We consider the problem of converting offline estimators into an online predictor or estimator with small extra regret. Formally this is the problem of merging a collection of probability measures over strings of length 1,2,3,... into a single probability measure over infinite sequences. We describe various approaches and their pros and cons on various examples. As a side-result we give an elementary non-heuristic purely combinatoric derivation of Turing’s famous estimator. Our main technical contribution is to determine the computational complexity of online estimators with good guarantees in general.

El vídeo explica cómo analizar circuitos integradores y derivadores con amplificadores operacionales usando la transformada de Laplace

El vídeo explica cómo analizar circuitos integradores y derivadores con amplificadores operacionales usando la transformada de Laplace

El vídeo explica cómo analizar circuitos integradores y derivadores con amplificadores operacionales usando la transformada de Laplace

El vídeo explica cómo analizar circuitos integradores y derivadores con amplificadores operacionales usando la transformada de Laplace

Power harvesters that extract energy from vibrating systems via piezoelectric transduction show strong potential for powering smart wireless sensor devices in applications of health condition monitoring of rotating machinery and structures. This paper presents an analytical method for modelling an electromechanical piezoelectric bimorph beam with tip mass under two input base transverse and longitudinal excitations. The Euler–Bernoulli beam equations were used to model the piezoelectric bimorph beam. The polarity-electric field of the piezoelectric element is excited by the strain field caused by base input excitation, resulting in electrical charge. The governing electromechanical dynamic equations were derived analytically using the weak form of the Hamiltonian principle to obtain the constitutive equations. Three constitutive electromechanical dynamic equations based on independent coefficients of virtual displacement vectors were formulated and then further modelled using the normalised Ritz eigenfunction series. The electromechanical formulations include both the series and parallel connections of the piezoelectric bimorph. The multi-mode frequency response functions (FRFs) under varying electrical load resistance were formulated using Laplace transformation for the multi-input mechanical vibrations to provide the multi-output dynamic displacement, velocity, voltage, current and power. The experimental and theoretical validations reduced for the single mode system were shown to provide reasonable predictions. The model results from polar base excitation for off-axis input motions were validated with experimental results showing the change to the electrical power frequency response amplitude as a function of excitation angle, with relevance for practical implementation.

Estimation methods for nonlinear mixed-effects modelling have considerably improved over the last decades. Nowadays, several algorithms implemented in different software are used. The present study aimed at comparing their performance for dose–response models. Eight scenarios were considered using a sigmoid E max model, with varying sigmoidicity and residual error models. One hundred simulated datasets for each scenario were generated. One hundred individuals with observations at four doses constituted the rich design and at two doses, the sparse design. Nine parametric approaches for maximum likelihood estimation were studied: first-order conditional estimation (FOCE) in NONMEM and R, LAPLACE in NONMEM and SAS, adaptive Gaussian quadrature (AGQ) in SAS, and stochastic approximation expectation maximization (SAEM) in NONMEM and MONOLIX (both SAEM approaches with default and modified settings). All approaches started first from initial estimates set to the true values and second, using altered values. Results were examined through relative root mean squared error (RRMSE) of the estimates. With true initial conditions, full completion rate was obtained with all approaches except FOCE in R. Runtimes were shortest with FOCE and LAPLACE and longest with AGQ. Under the rich design, all approaches performed well except FOCE in R. When starting from altered initial conditions, AGQ, and then FOCE in NONMEM, LAPLACE in SAS, and SAEM in NONMEM and MONOLIX with tuned settings, consistently displayed lower RRMSE than the other approaches. For standard dose–response models analyzed through mixed-effects models, differences were identified in the performance of estimation methods available in current software, giving material to modellers to identify suitable approaches based on an accuracy-versus-runtime trade-off.

We consider sequences of linear systems of equations that follow from the differential equations that describe the acoustics of a car, where the solution to a single linear system corresponds to the pressure perturbations that are caused by acoustic waves of a certain frequency. We consider several iterative numerical methods which belong to the class of Krylov subspace methods and that solve these linear systems. In addition we investigate a particular type of so-called preconditioning, which is a specific procedure that rewrites the system into a form that is more suitable for the numerical methods., Numerical linear algebra, Applied mathematics, Electrical Engineering, Mathematics and Computer Science

Este artículo presenta el diseño de un software cuyo objetivo es realizar la comparación de dos algoritmos que sirven para determinar la transformada inversa de Laplace. Esta comparación se lleva a cabo mediante la evaluación dos modelos matemáticos de pozos muy comunes en la industria petrolera que están dados en el dominio de Laplace, para los cuales se realiza la inversión y se grafican los resultados para establecer comparación. La herramienta de software se desarrolla en Visual Basic 2008, y consta de una interfaz gráfica que permite visualizar las inversiones realizadas por cada algoritmo y también genera dos archivos de texto donde se encuentran los datos de tiempo, presión y derivada de presión. La interfaz gráfica brinda varias opciones como poder escoger el modelo de pozo deseado o introducir mediante teclado otro modelo o función que se quiera invertir, también ofrece la opción de suprimir o agregar la gráfica de la derivada y de realizar las gráficas en escala logarítmica.El estudio permitió establecer que el algoritmo de Iseger maneja más eficazmente las discontinuidades de una función y se observó que para casos de pruebas de presión que al cumplir las condiciones que relacionan el tiempo con el número de puntos muestreados, se garantizan unos resultados de inversión más estables. También se comprobó que entre más puntos de inversión se usen, se obtienen unos resultados más precisos. Se encontró, además, en el parámetro nrp de 3 genera inversiones más estables que el propuesto originalmente por Iseger con valor de 8.

Este artículo presenta el diseño de un software cuyo objetivo es realizar la comparación de dos algoritmos que sirven para determinar la transformada inversa de Laplace. Esta comparación se lleva a cabo mediante la evaluación dos modelos matemáticos de pozos muy comunes en la industria petrolera que están dados en el dominio de Laplace, para los cuales se realiza la inversión y se grafican los resultados para establecer comparación. La herramienta de software se desarrolla en Visual Basic 2008, y consta de una interfaz gráfica que permite visualizar las inversiones realizadas por cada algoritmo y también genera dos archivos de texto donde se encuentran los datos de tiempo, presión y derivada de presión. La interfaz gráfica brinda varias opciones como poder escoger el modelo de pozo deseado o introducir mediante teclado otro modelo o función que se quiera invertir, también ofrece la opción de suprimir o agregar la gráfica de la derivada y de realizar las gráficas en escala logarítmica.El estudio permitió establecer que el algoritmo de Iseger maneja más eficazmente las discontinuidades de una función y se observó que para casos de pruebas de presión que al cumplir las condiciones que relacionan el tiempo con el número de puntos muestreados, se garantizan unos resultados de inversión más estables. También se comprobó que entre más puntos de inversión se usen, se obtienen unos resultados más precisos. Se encontró, además, en el parámetro nrp de 3 genera inversiones más estables que el propuesto originalmente por Iseger con valor de 8.

La asignatura obligatoria de sistemas electrónicos impartida en los grados de ingeniería, relacionados con la electricidad y la electrónica, del campus de Vilanova de la Universitat Politècnica de Catalunya nos abre paso hacia una propuesta para el aprendizaje, prevista fuera de clases, en la que será el propio estudiante el responsable de su aprendizaje. La técnica docente propuesta corresponde al Aprendizaje Basado en Problemas y el material de aprendizaje es la herramienta informática Matlab 7. La aplicación de la técnica en ingeniería sobre el programa matemático está focalizada a su uso en el análisis de circuitos, por tanto hay que ofrecer por una parte el diseño de la estrategia de aprendizaje y, por el otro, el material necesario para llevar a buen puerto la práctica. Este proyecto aboga por el aprendizaje basado en problemas, como evaluarlo, sugiere una propuesta docente para el conocimiento y aplicación de Matlab en el análisis de circuitos electrónicos. Plantea la forma y el material necesario para llevar a cabo este método docente propuesto para habilitar al alumno es el dominio de la aplicación del software Matlab para la solución circuital.

We consider sequences of linear systems of equations that follow from the differential equations that describe the acoustics of a car, where the solution to a single linear system corresponds to the pressure perturbations that are caused by acoustic waves of a certain frequency. We consider several iterative numerical methods which belong to the class of Krylov subspace methods and that solve these linear systems. In addition we investigate a particular type of so-called preconditioning, which is a specific procedure that rewrites the system into a form that is more suitable for the numerical methods., Numerical linear algebra, Applied mathematics, Electrical Engineering, Mathematics and Computer Science

Pharmacodynamic processes and disease progression are increasingly characterized with pharmacometric models. However, modelling options for discrete-type responses remain limited, although these response variables are commonly encountered clinical endpoints. Types of data defined as discrete data are generally ordinal, e.g. symptom severity, count, i.e. event frequency, and time-to-event, i.e. event occurrence. Underlying assumptions accompanying discrete data models need investigation and possibly adaptations in order to expand their use. Moreover, because these models are highly non-linear, estimation with linearization-based maximum likelihood methods may be biased. The aim of this thesis was to explore pharmacometric methods and novel models for discrete data through (i) the investigation of benefits of treating discrete data with different modelling approaches, (ii) evaluations of the performance of several estimation methods for discrete models, and (iii) the development of novel models for the handling of complex discrete data recorded during (pre-)clinical studies. A simulation study indicated that approaches such as a truncated Poisson model and a logit-transformed continuous model were adequate for treating ordinal data ranked on a 0-10 scale. Features that handled serial correlation and underdispersion were developed for the models to subsequently fit real pain scores. The performance of nine estimation methods was studied for dose-response continuous models. Other types of serially correlated count models were studied for the analysis of overdispersed data represented by the number of epilepsy seizures per day. For these types of models, the commonly used Laplace estimation method presented a bias, whereas the adaptive Gaussian quadrature method did not. Count models were also compared to repeated time-to-event models when the exact time of gastroesophageal symptom occurrence was known. Two new model structures handling repeated time-to-categorical event