Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

A Study of Elementary Operators

Department of Mathematics, Cochin University of Science and Technology

Spectral Analysis of Bounded Self-adjoint operators - A Linear Algebraic Approach

This thesis Entitled Spectral theory of bounded self-adjoint operators -A linear algebraic approach.The main results of the thesis can be classified as three different approaches to the spectral approximation problems. The truncation method and its perturbed versions are part of the classical linear algebraic approach to the subject. The usage of block Toeplitz-Laurent operators and the matrix valued symbols is considered as a particular example where the linear algebraic techniques are effective in simplifying problems in inverse spectral theory. The abstract approach to the spectral approximation problems via pre-conditioners and Korovkin-type theorems is an attempt to make the computations involved, well conditioned. However, in all these approaches, linear algebra comes as the central object. The objective of this study is to discuss the linear algebraic techniques in the spectral theory of bounded self-adjoint operators on a separable Hilbert space. The usage of truncation method in approximating the bounds of essential spectrum and the discrete spectral values outside these bounds is well known. The spectral gap prediction and related results was proved in the second chapter. The discrete versions of Borg-type theorems, proved in the third chapter, partly overlap with some known results in operator theory. The pure linear algebraic approach is the main novelty of the results proved here.

A Study of Morphological Operators with Applications

The present work deals with the A study of morphological opertors with applications. Morphology is now a.necessary tool for engineers involved with imaging applications. Morphological operations have been viewed as filters the properties of which have been well studied (Heijmans, 1994). Another well-known class of non-linear filters is the class of rank order filters (Pitas and Venetsanopoulos, 1990). Soft morphological filters are a combination of morphological and weighted rank order filters (Koskinen, et al., 1991, Kuosmanen and Astola, 1995). They have been introduced to improve the behaviour of traditional morphological filters in noisy environments. The idea was to slightly relax the typical morphological definitions in such a way that a degree of robustness is achieved, while most of the desirable properties of typical morphological operations are maintained. Soft morphological filters are less sensitive to additive noise and to small variations in object shape than typical morphological filters. They can remove positive and negative impulse noise, preserving at the same time small details in images. Currently, Mathematical Morphology allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets.Fuzzy sets have proved to be strongly advantageous when representing in accuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods.

Effectiveness Of Feature Detection Operators On The Performance Of Iris Biometric Recognition System

Iris Recognition is a highly efficient biometric identification system with great possibilities for future in the security systems area.Its robustness and unobtrusiveness, as opposed tomost of the currently deployed systems, make it a good candidate to replace most of thesecurity systems around. By making use of the distinctiveness of iris patterns, iris recognition systems obtain a unique mapping for each person. Identification of this person is possible by applying appropriate matching algorithm.In this paper, Daugman’s Rubber Sheet model is employed for irisnormalization and unwrapping, descriptive statistical analysis of different feature detection operators is performed, features extracted is encoded using Haar wavelets and for classification hammingdistance as a matching algorithm is used. The system was tested on the UBIRIS database. The edge detection algorithm, Canny, is found to be the best one to extract most of the iris texture. The success rate of feature detection using canny is 81%, False Accept Rate is 9% and False Reject Rate is 10%.

Optimization-Based Robotic Manipulation for Safe Interaction with Human Operators

This thesis investigates a method for human-robot interaction (HRI) in order to uphold productivity of industrial robots like minimization of the shortest operation time, while ensuring human safety like collision avoidance. For solving such problems an online motion planning approach for robotic manipulators with HRI has been proposed. The approach is based on model predictive control (MPC) with embedded mixed integer programming. The planning strategies of the robotic manipulators mainly considered in the thesis are directly performed in the workspace for easy obstacle representation. The non-convex optimization problem is approximated by a mixed-integer program (MIP). It is further effectively reformulated such that the number of binary variables and the number of feasible integer solutions are drastically decreased. Safety-relevant regions, which are potentially occupied by the human operators, can be generated online by a proposed method based on hidden Markov models. In contrast to previous approaches, which derive predictions based on probability density functions in the form of single points, such as most likely or expected human positions, the proposed method computes safety-relevant subsets of the workspace as a region which is possibly occupied by the human at future instances of time. The method is further enhanced by combining reachability analysis to increase the prediction accuracy. These safety-relevant regions can subsequently serve as safety constraints when the motion is planned by optimization. This way one arrives at motion plans that are safe, i.e. plans that avoid collision with a probability not less than a predefined threshold. The developed methods have been successfully applied to a developed demonstrator, where an industrial robot works in the same space as a human operator. The task of the industrial robot is to drive its end-effector according to a nominal sequence of grippingmotion-releasing operations while no collision with a human arm occurs.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

Importancia y necesidad de regular las intervenciones educativas de la policía local en materia de tráfico.

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Gauss y el polígono regular de 17 lados.

Se recoge uno de los concepto más destacados de Carl Friedrich Gauss como es el polígono regular de 17 lados. Se estudian los diferentes pasos que llevan a la construcción de este polígono con los diferentes cálculos aritméticos.

Les estrategies d'interacció del professor amb l'alumne sord a l'aula regular. Criteris per a la seva utilització. 'Las estrategias de interacción del profesor con el alumno sordo en el aula regular. Criterios para su utilización'.

Conocer la realidad comunicativa que se produce en el aula regular entre profesor y alumno sordo; identificar los patrones que gobiernan los diferentes estilos comunicativos del profesor y sus efectos sobre el habala del alumno; y, plantear una propuesta del modelo para el análisis y la optimización del estilo comunicativo del profesor en el aula integradora.. Primera fase: 20 profesores y 20 alumnos (16-18 años) de 20 aulas de escuelas de integración. Segunda fase: 6 profesors y 6 alumnos (3 grupo control, 3 grupo experimental) de diversos cursos de EGB, de 6 aulas de escuelas de integración. Elabora un marco teórico, expone los conceptos fundamentales de la integración del alumno sordo en nuestro pais, describe de forma global las particularidades comunicativas que suelen caracterizar a los sujetos con pérdidas auditivas, revisa las aportaciones teóricas, expone las investigaciones llevadas a cabo con anterioridad. El trabajo de investigación se divide en 2 fases: en la primera obtiene un perfil que muestra los principales parámetros de la interacción entre el profesor y el alumno sordo en el aula de integración, en la segunda fase aplica el programa de ciclo de aprendizaje al grupo experimental para modificar los parámetros observados en la anterior fase y observa las diferencias encontradas con respecto al grupo control. . Entrevistas. Cuestionario. Transcripción. Cámara de video. Prueba de la historia empleada por Rams-Pott. Cuaderno de registro. . Porcentajes. Análisis descriptivo. Análisis comparativo. Distribución de frecuencias. Sistema de codificación Clan. . Existe una relación entre las estrategias de trabajo utilizadas por el profesor con el alumno sordo y la actitud ideológica del profesor hacia la integración. El comportamiento docente observado en realción a las situaciones de reparación didáctica está vinculado a la experiencia del docente con el alumno. Ante errores de ejecución o producción las estrategias más empleadas son de tipo restrictivo y ante errores de comprensión las estrategias son más expansivas. Cualitativamente mejora el perfil interactivo de los profesores y alumnos del grupo experimental. . Es necesario poner en marcha nuevas investigaciones que respondan a las siguientes preguntas: +Cuáles son los mecanismos de adaptación del alumno a los diversos patrones interactivos mostrados por el profesor?, +Cómo influye el modelo comunicativo del profesor en el intercambio entre los compañeros oyentes y el propio sordo?.

Equivalencia entre cualquier polígono regular o irregular y un triángulo equilátero.

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Una revisión al diseño curricular nacional de educación básica regular del Perú en el nivel secundario y de Área de Matemáticas.

Resumen basado en el de la publicación. Resumen en inglés

Integraci??n en el aula regular de alumnos con S??ndrome de Asperger o autismo de alto funcionamiento : una mirada desde la actitud docente

En el estudio se desarrollan tres aspectos en torno a la integraci??n del alumnado con necesidades educativas especiales (n.e.e.) con S??ndrome de Asperger. Analiza la actitud docente hacia la integraci??n del estudiantado con n.e.e. en general y con s??ndrome de Asperger, en particular, en el aula ordinaria. El trabajo se realiza en municipios de Uribe Kosta (Vizcaya). Participan en la investigaci??n, realizada mediante cuestionarios y entrevistas semiestructuradas, s??lo profesores que ten??an integrados en sus respectivas aulas alumnos con s??ndrome de Asperger o autismo de Alto Funcionamiento. Se abordan, por una parte, los cinco factores del dato cuantitativo; y, por otra, los doce ??ndices Tem??ticos del Programa Nudist vinculados al antecedente cualitativo. Todo ello desemboca en la convergencia de las dos variables consideradas. De la reordenaci??n de ambas jerarqu??as, se extraen las respectivas conclusiones.

Planificación y cuantificación del entrenamiento en una temporada regular de fútbol sala.

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