Uniqueness of the polar factorisation and projection of a vector-valued mapping

G.R. BURTON and R.J. DOUGLAS, Uniqueness of the polar factorisation and projection of a vector-valued mapping. Ann. I.H. Poincare ? A.N. 20 (2003), 405-418.

Control circuits for avalanche photodiodes

Avalanche Photodiodes (APDs) have been used in a wide range of low light sensing applications such as DNA sequencing, quantum key distribution, LIDAR and medical imaging. To operate the APDs, control circuits are required to achieve the desired performance characteristics. This thesis presents the work on development of three control circuits including a bias circuit, an active quench and reset circuit and a gain control circuit all of which are used for control and performance enhancement of the APDs. The bias circuit designed is used to bias planar APDs for operation in both linear and Geiger modes. The circuit is based on a dual charge pumps configuration and operates from a 5 V supply. It is capable of providing milliamp load currents for shallow-junction planar APDs that operate up to 40 V. With novel voltage regulators, the bias voltage provided by the circuit can be accurately controlled and easily adjusted by the end user. The circuit is highly integrable and provides an attractive solution for applications requiring a compact integrated APD device. The active quench and reset circuit is designed for APDs that operate in Geiger-mode and are required for photon counting. The circuit enables linear changes in the hold-off time of the Geiger-mode APD (GM-APD) from several nanoseconds to microseconds with a stable setting step of 6.5 ns. This facilitates setting the optimal `afterpulse-free' hold-off time for any GM-APD via user-controlled digital inputs. In addition this circuit doesn’t require an additional monostable or pulse generator to reset the detector, thus simplifying the circuit. Compared to existing solutions, this circuit provides more accurate and simpler control of the hold-off time while maintaining a comparable maximum count-rate of 35.2 Mcounts/s. The third circuit designed is a gain control circuit. This circuit is based on the idea of using two matched APDs to set and stabilize the gain. The circuit can provide high bias voltage for operating the planar APD, precisely set the APD’s gain (with the errors of less than 3%) and compensate for the changes in the temperature to maintain a more stable gain. The circuit operates without the need for external temperature sensing and control electronics thus lowering the system cost and complexity. It also provides a simpler and more compact solution compared to previous designs. The three circuits designed in this project were developed independently of each other and are used for improving different performance characteristics of the APD. Further research on the combination of the three circuits will produce a more compact APD-based solution for a wide range of applications.

Estimación de la temperatura mínima mensual media para estudios agroclimáticos

p.77-83

Integral completeness of locally convex spaces

A locally convex space X is said to be integrally complete if each continuous mapping f: [0, 1] --> X is Riemann integrable. A criterion for integral completeness is established. Readily verifiable sufficient conditions of integral completeness are proved.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Scaling of the entanglement spectrum near quantum phase transitions

The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to nonintegrable quantum phase transitions in one-dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest nondegenerate Schmidt eigenvalues yields with good accuracy critical points and mass scaling exponents.

An Eigenfunction Approach for Volatility Modeling.

In this paper, we introduce a new approach for volatility modeling in discrete and continuous time. We follow the stochastic volatility literature by assuming that the variance is a function of a state variable. However, instead of assuming that the loading function is ad hoc (e.g., exponential or affine), we assume that it is a linear combination of the eigenfunctions of the conditional expectation (resp. infinitesimal generator) operator associated to the state variable in discrete (resp. continuous) time. Special examples are the popular log-normal and square-root models where the eigenfunctions are the Hermite and Laguerre polynomials respectively. The eigenfunction approach has at least six advantages: i) it is general since any square integrable function may be written as a linear combination of the eigenfunctions; ii) the orthogonality of the eigenfunctions leads to the traditional interpretations of the linear principal components analysis; iii) the implied dynamics of the variance and squared return processes are ARMA and, hence, simple for forecasting and inference purposes; (iv) more importantly, this generates fat tails for the variance and returns processes; v) in contrast to popular models, the variance of the variance is a flexible function of the variance; vi) these models are closed under temporal aggregation.

Superintégrabilité avec séparation de variables en coordonnées polaires et intégrales du mouvement d’ordre supérieur à deux

Dans cette thèse, nous proposons de nouveaux résultats de systèmes superintégrables séparables en coordonnées polaires. Dans un premier temps, nous présentons une classification complète de tous les systèmes superintégrables séparables en coordonnées polaires qui admettent une intégrale du mouvement d'ordre trois. Des potentiels s'exprimant en terme de la sixième transcendante de Painlevé et de la fonction elliptique de Weierstrass sont présentés. Ensuite, nous introduisons une famille infinie de systèmes classiques et quantiques intégrables et exactement résolubles en coordonnées polaires. Cette famille s'exprime en terme d'un paramètre k. Le spectre d'énergie et les fonctions d'onde des systèmes quantiques sont présentés. Une conjecture postulant la superintégrabilité de ces systèmes est formulée et est vérifiée pour k=1,2,3,4. L'ordre des intégrales du mouvement proposées est 2k où k ∈ ℕ. La structure algébrique de la famille de systèmes quantiques est formulée en terme d'une algèbre cachée où le nombre de générateurs dépend du paramètre k. Une généralisation quasi-exactement résoluble et intégrable de la famille de potentiels est proposée. Finalement, les trajectoires classiques de la famille de systèmes sont calculées pour tous les cas rationnels k ∈ ℚ. Celles-ci s'expriment en terme des polynômes de Chebyshev. Les courbes associées aux trajectoires sont présentées pour les premiers cas k=1, 2, 3, 4, 1/2, 1/3 et 3/2 et les trajectoires bornées sont fermées et périodiques dans l'espace des phases. Ainsi, les résultats obtenus viennent renforcer la possible véracité de la conjecture.

Aspects géométriques et intégrables des modèles de matrices aléatoires

Travail réalisé en cotutelle avec l'université Paris-Diderot et le Commissariat à l'Energie Atomique sous la direction de John Harnad et Bertrand Eynard.

Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

Exercise sheet 10 pdf

Exercises and solutions in PDF

Exercise sheet 10

Exercises and solutions in LaTex

Activisme i educació social a les Illes Balears en el trànsit al segle XX. 'Activismo y educación social en las Islas Baleares en el tránsito al siglo XX'.

Resumen tomado parcialmente de la publicación

Criterios para el an??lisis, selecci??n, secuenciaci??n y organizacion de los contenidos educativos en el curr??culo : aplicaci??n a la secuenciaci??n de contenidos de biolog??a en la educaci??n primaria

Elaborar una propuesta de criterios que sea ??til para la elaboraci??n y revisi??n de las secuencias de contenidos educativos en el curr??culum. Revisi??n cr??tica de las diferentes aportaciones al tema desde la psicolog??a, la epistemolog??a y la did??ctica.Estudio de un caso en el que un equipo docente de Educaci??n Primaria elabora una secuencia educativa para el estudio de los seres vivos y la experimentaci??n en el aula. Bas??ndose en la propuesta de criterios elaborada. El estudio de casos realizado ha cubierto un periodo de cuatro a??os de trabajo conjunto entre el investigador y el equipo docente.Considera la secuenciaci??n como un proceso de toma de decisiones respecto a la forma de presentar los contenidos educativos a los alumnos a lo largo del curr??culo de manera relacionadan y progresiva, bas??ndose en criterios expl??citos. Analiza este proceso desde un marco psicopedag??gico global y un modelo curricular fundamentados te??ricamente: la concepci??n constructivista de los procesos de ense??anza-aprendizaje. La metodolog??a utilizada por el estudio del caso, basada en la observaci??n participante se ha mostrado adecuada para abordar los problemas planteados.No obstante se han presentado dificultades derivadas de la complejidad del problema abordado, de poca tradici??n de este tipo de investigaci??n y de la escasez de modelos e instrumentos adecuados a la misma. Concluye que la propuesta realizada es coherente e integrable en el marco de la concepci??n constructivista de la ense??anza y el aprendizaje, y en el modelo de curr??culum desarrollado.Por ello es necesario que se presenten los criterios de secuenciaci??n utilizados de manera expl??cita que fundamentada, para que puedan ser comprensibles por el profesor comprensibles por el profesorado y el alumnado. Se constata la necesidad de proseguir la l??nea de investigacion estudiando de manera emp??rica la aplicaci??n de la propuesta de criterios a otras ??reas del curr??culo y etapas educativas.Desarrollando propuestas te??ricas para la secuenciaci??n de contenidos procedimentales y actitudinales que superen las limitaciones apuntadas en esta investigaci??n.Elaborando secuencias educativas basadas en los criterios propuestos y revisando los dise??os de formaci??n inicial y permanente del profesorado en relaci??n a las cuestiones planteadas.

Pro&Regula : un programa para aprender a regularse durante el aprendizaje.

Este programa aporta al profesorado una metodología secuencializada para favorecer la enseñanza de los procedimientos de regulación del aprendizaje, proponiendo una forma alternativa y reflexiva para la realización de las actividades de clase. Se pretende aportar una herramienta de trabajo integrable en los procesos de enseñanza-aprendizaje. A los alumnos les aporta diferentes actividades similares a las realizadas cotidianamente en las áreas de conocimiento, proponiéndoles una forma alternativa y reflexiva para su realización. Para ello se trabaja de forma sistemática los siguientes tipos de conocimientos: conocimiento reflexivo o conciencia del aprendizaje, control del proceso de aprendizaje y realización de la evaluación. La metodología consiste en una preparación y motivación, un apoyo a través de la interacción (promovida por el docente y conjunta con el resto de la clase), una atención a los procesos cualitativos del proceso de aprendizaje y una enseñanza y aprendizaje sistemáticos. La evaluación debe realizarse de forma continua, cualitativa y procesual.