Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen

Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________

Adaptive integral assessment package for the A2UN@ project

This paper presents a first approach of Evaluation Engine Architecture (EEA) as proposal to support adaptive integral assessment, in the context of a virtual learning environment. The goal of our research is design an evaluation engine tool to assist in the whole assessment process within the A2UN@ project, linking that tool with the other key elements of a learning design (learning task, learning resources and learning support). The teachers would define the relation between knowledge, competencies, activities, resources and type of assessment. Providing this relation is possible obtain more accurate estimations of student's knowledge for adaptive evaluations and future recommendations. The process is supported by usage of educational standards and specifications and for an integral user modelling

MA160exam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA160exam01pdf

Exam questions and solutions in PDF

MA160exam00pdf

Exam questions and solutions in PDF

La intuición en la toma de decisiones estratégicas de la dirección empresarial

Las organizaciones han sido percibidas y descritas por los académicos como un producto de la racionalidad, por lo tanto su gestión debe realizarse de manera racional. En el presente trabajo se reivindica el rol de la intuición en los procesos de toma de decisiones estratégicas en las organizaciones; para ello, una vez descrita la “organización racional” y sus implicaciones, con ayuda de la psicología y de la sociología se desvirtúa la separación entre racionalidad e intuición. Mediante el trabajo de campo realizado y utilizando como herramientas de análisis los modelos duales de cognición y comportamiento desarrollados en la última década, se evidencia que la intuición juega un papel importante y relevante en los procesos de toma de decisiones estratégicas en las organizaciones, papel que ha sido deliberadamente olvidado por la academia y que debe ser estudiado, con el fin de poder tener una comprensión integral de las organizaciones.

Estrategias para el funcionamiento integral de los servicios de salud para la comunidad indígena Nükak del Guaviare

Los Nükák son un pueblo indígena nómada del nordeste amazónico, ubicados en el departamento del Guaviare que basa su supervivencia en prácticas de caza y recolección principalmente. Desde su contacto con la sociedad mayoritaria, esta población se ha encontrado amenazada en su pervivencia como pueblo, en especial por las características de la población de colonos que ingresó a su territorio, el conflicto armado que los impacta provocando muertes y desplazamientos, y un nuevo departamento como lo es el Guaviare (1991) con grandes dificultades sociales, políticas y económicas; siendo la salud de los Nükák una de las más afectadas en medio de este complejo contexto. Ante esta necesidad, se hace imperativo generar una estrategia para el funcionamiento integral de los servicios de salud específica para esta comunidad, que reconozca por un lado la realidad local y su influencia en el citado pueblo y por otro, la percepción que tiene dicho pueblo sobre su salud, analizando el contexto de los Nükák a partir de un estado del arte y su sentir a partir de encuestas aplicadas a mujeres casadas de dicho pueblo. Este estudio es una expresión novedosa e intercultural de la Atención primaria desde la promoción de la salud y prevención de la enfermedad, de la operatividad del primer y segundo nivel de atención, del diagnóstico, la rehabilitación, las redes integradas e integrales, la participación, la intersectorialidad, entre otros elementos adaptados a la cultura Nükák que articulados son la estrategia para el funcionamiento integral del servicio de salud para el pueblo Nükák de San José del Guaviare.

PPP, UIP and Fisher parity: speculation or rational expectations? Evidence for four Latin American countries

This work aims to test the equilibrium relations of two international macroeconomics models for Colombia, Chile, Mexico and Brazil. The first model is the rational expectation hypothesis (REH) where three key relations will be tested: Purchasing Power Parity (PPP), Uncovered Interest Rate Parity (UIP) and the Fisher Parity condition. The second model follows the line of though of Imperfect Knowledge Economics (IKE) where two equilibrium relations will be tested. According to IKE, even under the assumption that agents are rational, the presence of speculative behavior in financial markets helps explain the long swings often observed in the behavior of exchange rates. The results support the view that the predictions of the IKE model hold for Colombia, while those of the REH hold for both Brazil and Mexico. Mixed findings are obtained for Chile.

3D Analysis of the TCR/pMHCII Complex Formation in Monkeys Vaccinated with the First Peptide Inducing Sterilizing Immunity against Human Malaria

T-cell receptor gene rearrangements were studied in Aotus monkeys developing high antibody titers and sterilizing immunity against the Plasmodium falciparum malaria parasite upon vaccination with the modified synthetic peptide 24112, which was identified in the Merozoite Surface Protein 2 (MSP-2) and is known to bind to HLA-DR beta 1*0403 molecules with high capacity. Spectratyping analysis showed a preferential usage of V beta 12 and V beta 6 TCR gene families in 67% of HLA-DR beta 1*0403-like genotyped monkeys. Docking of peptide 24112 into the HLA-DR beta 1*0401-HA peptide-HA1.7TCR complex containing the VDJ rearrangements identified in fully protected monkeys showed a different structural signature compared to nonprotected monkeys. These striking results show the exquisite specificity of the TCR/pMHCII complex formation needed for inducing sterilizing immunity and provide important hints for a logical and rational methodology to develop multiepitopic, minimal subunit-based synthetic vaccines against infectious diseases, among them malaria.

La contribución del PNUD y la OACNUDH en la formulación de una política pública integral de DD.HH. y DIH durante la primera administración de Juan Manuel Santos (2010-2014)

El presente trabajo de investigación tiene como objetivo estudiar la influencia de las agencias de Naciones Unidas, PNUD y OACNUDH, en la formulación de una política pública de DD.HH. y DIH en Colombia entre 2010 y 2014. Se argumenta que la cooperación internacional brindada por el PNUD y la OACNUDH, a través de su asesoría técnica, influyó determinantemente en el proceso de formulación de una política pública en materia de DD.HH y DIH durante el primer gobierno de Juan Manuel Santos. Lo anterior, permitió no solo un cambio en la forma de construir políticas públicas, sino en la manera en que se aborda la situación de DD.HH. en el país, teniendo en cuenta la coyuntura de las negociaciones de paz con las FARC.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Effect of two opposing changes in photoperiod upon age at first egg in layer-hybrid pullets

An experiment was designed to test the response of growing pullets to two changes in photoperiod (an increase from 8 to 14 h followed 5 weeks later by the reverse change, or a decrease from 14 to 8 h followed by an increase). The first change was made either at 35 days or at 56 days of age, to test the influence of age on the responses observed. Control groups were kept oil constant 8-h and constant 14-h photoperiods and the responses to appropriate single changes were also tested. Mean age at first egg varied from 111 days for birds given a single increment at 56 days to 166 days for pullets given an increase in photoperiod at 35 days followed by a reduction at 70 days. Responses to the single changes confirmed earlier reports that sensitivity to change in photoperiod varies with age ill a manner that is quantitatively predictable. Responses to the double changes could be explained by Postulating that the initial change altered the 'physiological age' of the bird to all extent that was also quantitatively predictable. An early increase in photoperiod advances sexual development and makes the bird more sensitive to a subsequent decrease than would be expected by reference to its chronological age. An early decrease in photoperiod delays sexual development, which can have the effect of making the bird more or less sensitive to a subsequent increase since, ill layer-strain pullets, sensitivity to an increment in photoperiod normally increases Lip to about 9 weeks of age but decreases thereafter. Mean age at first egg predicted using these concepts was very highly correlated with observed age at first egg. The results provide a rational basis for constructing a model to predict age at first egg for any combination of increases and decreases in photoperiod applied to growing pullets.

Design of a minimum variance multiple input-multiple output neuro self-tuning proportional-integral-derivative controller for non-linear dynamic systems

In this study a minimum variance neuro self-tuning proportional-integral-derivative (PID) controller is designed for complex multiple input-multiple output (MIMO) dynamic systems. An approximation model is constructed, which consists of two functional blocks. The first block uses a linear submodel to approximate dominant system dynamics around a selected number of operating points. The second block is used as an error agent, implemented by a neural network, to accommodate the inaccuracy possibly introduced by the linear submodel approximation, various complexities/uncertainties, and complicated coupling effects frequently exhibited in non-linear MIMO dynamic systems. With the proposed model structure, controller design of an MIMO plant with n inputs and n outputs could be, for example, decomposed into n independent single input-single output (SISO) subsystem designs. The effectiveness of the controller design procedure is initially verified through simulations of industrial examples.

A new frequency-uniform coercive boundary integral equation for acoustic scattering

A new boundary integral operator is introduced for the solution of the soundsoft acoustic scattering problem, i.e., for the exterior problem for the Helmholtz equation with Dirichlet boundary conditions. We prove that this integral operator is coercive in L2(Γ) (where Γ is the surface of the scatterer) for all Lipschitz star-shaped domains. Moreover, the coercivity is uniform in the wavenumber k = ω/c, where ω is the frequency and c is the speed of sound. The new boundary integral operator, which we call the “star-combined” potential operator, is a slight modification of the standard combined potential operator, and is shown to be as easy to implement as the standard one. Additionally, to the authors' knowledge, it is the only second-kind integral operator for which convergence of the Galerkin method in L2(Γ) is proved without smoothness assumptions on Γ except that it is Lipschitz. The coercivity of the star-combined operator implies frequency-explicit error bounds for the Galerkin method for any approximation space. In particular, these error estimates apply to several hybrid asymptoticnumerical methods developed recently that provide robust approximations in the high-frequency case. The proof of coercivity of the star-combined operator critically relies on an identity first introduced by Morawetz and Ludwig in 1968, supplemented further by more recent harmonic analysis techniques for Lipschitz domains.