Some New Classes of Orthogonal Polynomials and Special Functions

In dieser Dissertation präsentieren wir zunächst eine Verallgemeinerung der üblichen Sturm-Liouville-Probleme mit symmetrischen Lösungen und erklären eine umfassendere Klasse. Dann führen wir einige neue Klassen orthogonaler Polynome und spezieller Funktionen ein, welche sich aus dieser symmetrischen Verallgemeinerung ableiten lassen. Als eine spezielle Konsequenz dieser Verallgemeinerung führen wir ein Polynomsystem mit vier freien Parametern ein und zeigen, dass in diesem System fast alle klassischen symmetrischen orthogonalen Polynome wie die Legendrepolynome, die Chebyshevpolynome erster und zweiter Art, die Gegenbauerpolynome, die verallgemeinerten Gegenbauerpolynome, die Hermitepolynome, die verallgemeinerten Hermitepolynome und zwei weitere neue endliche Systeme orthogonaler Polynome enthalten sind. All diese Polynome können direkt durch das neu eingeführte System ausgedrückt werden. Ferner bestimmen wir alle Standardeigenschaften des neuen Systems, insbesondere eine explizite Darstellung, eine Differentialgleichung zweiter Ordnung, eine generische Orthogonalitätsbeziehung sowie eine generische Dreitermrekursion. Außerdem benutzen wir diese Erweiterung, um die assoziierten Legendrefunktionen, welche viele Anwendungen in Physik und Ingenieurwissenschaften haben, zu verallgemeinern, und wir zeigen, dass diese Verallgemeinerung Orthogonalitätseigenschaft und -intervall erhält. In einem weiteren Kapitel der Dissertation studieren wir detailliert die Standardeigenschaften endlicher orthogonaler Polynomsysteme, welche sich aus der üblichen Sturm-Liouville-Theorie ergeben und wir zeigen, dass sie orthogonal bezüglich der Fisherschen F-Verteilung, der inversen Gammaverteilung und der verallgemeinerten t-Verteilung sind. Im nächsten Abschnitt der Dissertation betrachten wir eine vierparametrige Verallgemeinerung der Studentschen t-Verteilung. Wir zeigen, dass diese Verteilung gegen die Normalverteilung konvergiert, wenn die Anzahl der Stichprobe gegen Unendlich strebt. Eine ähnliche Verallgemeinerung der Fisherschen F-Verteilung konvergiert gegen die chi-Quadrat-Verteilung. Ferner führen wir im letzten Abschnitt der Dissertation einige neue Folgen spezieller Funktionen ein, welche Anwendungen bei der Lösung in Kugelkoordinaten der klassischen Potentialgleichung, der Wärmeleitungsgleichung und der Wellengleichung haben. Schließlich erklären wir zwei neue Klassen rationaler orthogonaler hypergeometrischer Funktionen, und wir zeigen unter Benutzung der Fouriertransformation und der Parsevalschen Gleichung, dass es sich um endliche Orthogonalsysteme mit Gewichtsfunktionen vom Gammatyp handelt.

Hierarchical Object Recognition Using Libraries of Parameterized Model Sub-Parts

This thesis describes the development of a model-based vision system that exploits hierarchies of both object structure and object scale. The focus of the research is to use these hierarchies to achieve robust recognition based on effective organization and indexing schemes for model libraries. The goal of the system is to recognize parameterized instances of non-rigid model objects contained in a large knowledge base despite the presence of noise and occlusion. Robustness is achieved by developing a system that can recognize viewed objects that are scaled or mirror-image instances of the known models or that contain components sub-parts with different relative scaling, rotation, or translation than in models. The approach taken in this thesis is to develop an object shape representation that incorporates a component sub-part hierarchy- to allow for efficient and correct indexing into an automatically generated model library as well as for relative parameterization among sub-parts, and a scale hierarchy- to allow for a general to specific recognition procedure. After analysis of the issues and inherent tradeoffs in the recognition process, a system is implemented using a representation based on significant contour curvature changes and a recognition engine based on geometric constraints of feature properties. Examples of the system's performance are given, followed by an analysis of the results. In conclusion, the system's benefits and limitations are presented.

Special Functions

Exam questions and solutions in LaTex

Special Functions pdf

Exam questions and solutions in PDF

WAIS seminar: Linked Cultural Media

Wednesday 9th April 2014 Speaker(s): Guus Schreiber Time: 09/04/2014 11:00-11:50 Location: B32/3077 File size: 546Mb Abstract In this talk I will discuss linked data for museums, archives and libraries. This area is known for its knowledge-rich and heterogeneous data landscape. The objects in this field range from old manuscripts to recent TV programs. Challenges in this field include common metadata schema's, inter-linking of the omnipresent vocabularies, cross-collection search strategies, user-generated annotations and object-centric versus event-centric views of data. This work can be seen as part of the rapidly evolving field of digital humanities. Speaker Biography Guus Schreiber Guus is a professor of Intelligent Information Systems at the Department of Computer Science at VU University Amsterdam. Guus’ research interests are mainly in knowledge and ontology engineering with a special interest for applications in the field of cultural heritage. He was one of the key developers of the CommonKADS methodology. Guus acts as chair of W3C groups for Semantic Web standards such as RDF, OWL, SKOS and REFa. His research group is involved in a wide range of national and international research projects. He is now project coordinator of the EU Integrated project No Tube concerned with integration of Web and TV data with the help of semantics and was previously Scientific Director of the EU Network of Excellence “Knowledge Web”.

Conceptual Rapprochement and the Analysis of the Historical, Normative and Jurisprudential Treatment of the Rural Workers, as Regards the Need for Special Protection

This article aims to present an approach to the issue of farm or rural zone workers, including a labour law study of agrarian legal decisions, so as to demonstrate their importance in respect to social, economic and cultural rights in Colombia. The study will serve to illustrate through the history, the applicable law and the jurisprudence, the different ways in which farmers have been treated from the time of the origin until the arrival of modern systems of industrialization. It calls into question the effectiveness of existing laws and the role of the courts, in spite of globalization, to maintain the minimum rights and guarantees of farm workers who are considered to be a vulnerable population. In conclusion, this study seeks to illustrate the current role of the Labor law and the National Health Service in the area of demonstrating of the existence or absence of mechanisms to protect workers in rural areas and the need to create some mechanisms that involve social justice given its prime importance in the Constitution of 1991.

The three systems for the protection of fundamental human rights in the European Union and exceptional measures against terrorism: the case of extraordinary extraditions (the CIA flights) with special reference to the Spanish case

This document is aimed first of all, make a small introductory reference on the three levels of protection of fundamental rights in Europe with the idea of helping to clarify and understand mainly to non-European systems that we are not talking. For that, based on this, going on to assess the impact generated in these systems suggest that the complaints alleged involvement of European countries in secret CIA flights to combat international terrorism, as well as investigate the responses that have given each protection of these areas to try to clarify them. 

Introduction to the Special Issue

  

Academic libraries and learning support in the eectronic enviroment. 'Bibliotecas universitarias y apoyo al aprendizaje en el entorno electrónico'.

Resumen basado en el del autor

Liaison between librarians and lecturers regarding information literacy: a case study of some academic libraries. 'Vinculación entre bibliotecarios y profesores universitarios en cuanto a competencias en información : estudio de algunas bibliotecas universitarias'.

Resumen tomado del autor

Social skills activities for special children.

Incluye actividades prácticas y hojas de ejercicios para ayudar a los niños con trastornos emocionales a llevar un aceptable comportamiento social y a adquirir destrezas sociales básicas. Cada lección presenta el desarrollo de una habilidad específica en el contexto de situaciones de la vida real, que guiada por el profesor permite a los alumnos trabajar, pensar, discutir y practicar sobre ella, tanto dentro como fuera del aula.

Fun with messy play : ideas and activities for children with special needs.

Colores vivos, sonidos suaves, texturas extrañas, sabores y olores, forman parte de cómo los niños desarrollan la conciencia sensorial. Las actividades propuestas en este manual aumentan la percepción sensorial de los niños con necesidades especiales, mediante el uso imaginativo de la vida cotidiana, que les ayuda a mejorar su coordinación, habilidades comunicativas y cognitivas, así como su autoestima y habilidades sociales. Al permitir a los niños explorar sus sentidos mientras se divierten, proporciona una terapia relajante que fomenta la capacidad de respuesta sensorial sin crearles estrés.

What really works in special and inclusive education : using evidence-based teaching strategies.

En este manual se presentan una serie de estrategias que los educadores pueden implementar en el aula con alumnos con necesidades educativas especiales, con el objetivo de ayudarles a tener un aprendizaje de calidad y buenos resultados sociales. Cada una de las veinticuatro estrategias incluidas en el manual tiene una base sustancial de investigación, una justificación teórica, directrices prácticas sobre cómo puede emplearse, así como consejos sobre su uso. Si bien el libro se centra en alumnos con necesidades educativas especiales, la mayor parte de las estrategias son aplicables a todos los alumnos.

Meeting special needs in mainstream schools : a practical guide for teachers.

Se ofrece información sobre la identificación de los tipos de necesidades educativas especiales, ya que la mayoría de los niños con estas necesidades se encuentran en las escuelas ordinarias, y sugiere estrategias para facilitar a los profesores el desarrollo de las habilidades requeridas para que puedan: identificar a los alumnos con necesidades educativas especiales; saben donde conseguir ayuda; proporcionar un apoyo positivo y objetivo; estar familiarizados con el código de prácticas para NEE; aplicar registros y seguir los planes de enseñanza individualizada.

Play for children with special needs : supporting children with learning differences, 3-9.

El objetivo de este manual es mostrar la importancia del juego en el aprendizaje de los niños, con necesidades especiales o no. Destaca lo esencial de crear un entorno seguro, de observar a los niños mientras juegan con el fin de identificar sus dificultades, de analizar distintas zonas de juegos diferentes para apreciar las diversas clases de aprendizaje (intelectual, creativo, motor, social y emocional), y así encontrar las formas mas adecuadas para mejorar su aprendizaje.