This research studies the interaction among the following contexts: natural language, geometrical language and musical language and it can provide new instruments to accord didactical situations and for a deeper understanding of communication processes. It springs from the consideration that the geometrical transformations are usually used in the compositional processes and the “role of the music to learn geometrical transformations” is actually a new study. In the field of the theory of situations by G. Brousseau (1986) we can assume to be in front of a learning teaching-situation including non-teaching situation as the teacher of musical instruments, while transmitting the knowledge of musical language (theoretical-practical) didn’t have the intention to transmit the geometrical transformation.

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The aim of the submitted diploma thesis is to complete a series of graded tasks from the manipulative environment of Parquet. Then apply these tasks to preschool and school children in the 1st year of elementary school. Not only observe how they cope with these activities, but also how they think, explain their actions, and how they communicate with each other. Observe myself, as a researcher, how do I work with children, how do I communicate with them and how do I submit them the tasks. Record my knowledge and learn from it. The theoretical part defines the individual stages for the preschool and pupils in terms of the development of psychology, they are constructive concepts of teaching mathematics with reference to the RVP ZV and RVP PV. Studied textbooks for the 1st and 2nd year of elementary school searched for activities from the environment of Parquet. Activities are selected that illustrate the typology of tasks. The relevant didactic games related to the Parquet environment are also described. For the practical part is chosen method of qualitative research on the basis of experiments in two research groups. The experiments are composed of individual activities, which are graded from the very basic creation of the parquet, specifying the rules of laying them down on the floor, to the final...

Indiana University-Purdue University Indianapolis (IUPUI) / A crucial task in computer vision and biomedical image applications is to represent images in a numerically compact form for understanding, evaluating and/or mining their content. The fundamental step of this task is the segmentation of images into regions, given some homogeneity criteria, prior appearance and/or shape information criteria. Specifically, segmentation of cells in microscopic images is the first step in analyzing many biomedical applications. This thesis is a part of the project entitled "Construction and profiling of biodegradable cardiac patches for the co-delivery of bFGF and G-CSF growth factors" funded by National Institutes of Health (NIH). We present a method that simultaneously segments the population of cells while partitioning the cell regions into cytoplasm and nucleus in order to evaluate the spatial coordination on the image plane, density and orientation of cells. Having static microscopic images, with no edge information of a cytoplasm boundary and no time sequence constraints, traditional cell segmentation methods would not perform well. The proposed method combines deformable models with a probabilistic framework in a simple graphical model such that it would capture the shape, structure and appearance of a cell. The process aims at the simultaneous cell partitioning into nucleus and cytoplasm. We considered the relative topology of the two distinct cell compartments to derive a better segmentation and compensate for the lack of edge information. The framework is applied to static fluorescent microscopy, where the cultured cells are stained with calcein AM.

This thesis makes an original contribution to knowledge in the fi eld of data objects' comparison where the objects are described by attributes of fuzzy or heterogeneous (numeric and symbolic) data types. Many real world database systems and applications require information management components that provide support for managing such imperfect and heterogeneous data objects. For example, with new online information made available from various sources, in semi-structured, structured or unstructured representations, new information usage and search algorithms must consider where such data collections may contain objects/records with di fferent types of data: fuzzy, numerical and categorical for the same attributes. New approaches of similarity have been presented in this research to support such data comparison. A generalisation of both geometric and set theoretical similarity models has enabled propose new similarity measures presented in this thesis, to handle the vagueness (fuzzy data type) within data objects. A framework of new and unif ied similarity measures for comparing heterogeneous objects described by numerical, categorical and fuzzy attributes has also been introduced. Examples are used to illustrate, compare and discuss the applications and e fficiency of the proposed approaches to heterogeneous data comparison. / Libyan Embassy

[pt] Um procedimento simples, para a avaliação do aumento ou diminuição (sensibilidade) das cargas de flambagem estática ou dinâmica (flutter) de estruturas na presença de pequenas imperfeições geométricas, é apresentado. O modelo computacional considera estruturas planas elásticas modeladas por elementos de viga retos. Os sistemas de carregamento podem ser conservativos ou não- conservativos. A formulação matricial inclui as matrizes de rigidez elástica, de massa e geométrica usuais. O algoritmo implementado avalia a carga crítica clássica. Adicionalmente, as imperfeições são levadas em conta a partir de uma matriz de imperfeição, resultante da mudança na rigidez elástica decorrente de pequenos desvios na geometria (pequenas rotações nos elementos). São apresentados exemplos para ilustrar a técnica desenvolvida e investigar as cargas de flambagem de algumas estruturas básicas: pórtico de Roorda, coluna de Euler, coluna de Beck, arco circular e viga sobre base elástica (análogo à deformação axissimétrica de uma casca cilíndrica). Conclui-se que o uso da matriz de imperfeição proposta pode fornecer valiosa informação qualitativa sobre a sensibilidade da carga de flambagem em relação às imperfeições. / [en] A simple procedure for the evaluation of the increase or decrease (sensitivity) of static and dynamic (flutter) buckling loads of structures in the presence of small geometrical imperfections is presented. The computational model considers plane elastic structures modelled by straight beam elements. The loading systems cam be conservative or non-conservative. The matrix formulation includes the usual elastic stiffness, mass, and geometric matrices. The algorithm implemented herein evaluates the classical critical load. In addition, the imperfections are taken into account by an imperfection matrix, which results from the change in the elastic stiffness due to small deviations of geometry (small rotations of the elements). Examples are presented to illustrate the technique developed herein and to investigate the buckling loads of some basic structures: Roorda´s frame, Euler´s column, Beck´s column, circular arch, and beam on elastic foundation (analogous to axissimetric deformation of cylindrical shell). It is concluded that the use of the proposed imperfection matrix can provide valuable qualitative information on the sensitivity of the buckling load to imperfections. / [es] En este trabajo se presenta un procedimento simple para la evaluación del aumento o disminución (sensibilidad) de las cargas de flameo estática o dinámica (flutter) de extructuras en presencia de pequeñas imperfecciones geométricas. El modelo computacional considera extructuras planas elásticas modeladas por elementos de viga rectos. Los sistemasde carga pueden ser conservativos o no- conservativos. La formulación matricial incluye las matrices de rígidez elástica, de masa y geométrica usuales. El algoritmo implementado evalúa la carga crítica clásica. Adicionalmente, las imperfecciones se consideran a partir de una matriz de imperfección, resultante de la mudanza en la rígidez elástica consecuencia de pequeños desvios en la geometría (pequeñas rotaciones en los elementos). Se presentan ejemplos para ilustrar la técnica desarrollada e investigar las cargas de flameo de algumas extructuras básicas: pórtico de Roorda, columna de Euler, columna de Beck, arco circular y viga sobre base elástica (análogo a la deformación axisimétrica de una cáscara cilíndrica). Se concluye que el uso de la matriz de imperfección propuesta puede ofrecer una valiosa información cualitativa sobre la sensibilidad de la carga de flameo en relación a las imperfecciones.

[pt] Este trabalho tem como objetivo aplicar uma técnica de síntese ótica de lentes dielétricas circularmente simétricas, que são iluminadas por uma fonte pontual com diagrama circularmente simétrico. A interface da lente (interface do dielétrico-ar) será modelada utilizando as aproximações da Ótica Geométrica e da Física Ótica. Da Ótica Geométrica, o controle da densidade de potência em campo distante é obtido pela aplicação de conservação de energia no interior dos tubos de raios que emergem do centro de fase da fonte e a determinação da direção dos raios que emergem da superfície do dielétrico é obtida através da aplicação da Lei de Snell para os raios incidentes na interface. Da Física Ótica, é possível obter as correntes elétrica e magnética na superfície externa da lente para determinar o campo radiado na integração dessas correntes pela superfície a partir da suposição de que as dimensões da lente e da curvatura da interface sejam muito maiores que um comprimento de onda no espaço livre. Devido a simetria circular, simplificações na formulação e nos esquemas numéricos para a solução serão apresentadas, resultando em técnica de projeto mais eficientes. A descrição da superfície da interface da lente é obtida através de técnica numérica. / [en] This work aims to apply a technique of optical synthesis of symmetrically circular dielectric lenses, which are illuminated by a point source with a symmetrically circular diagram. The lens interface (dielectric-air interface) will be modeled using the approximations of Geometric Optics and Physical Optics. From Geometric Optics, control of the power density in the far field is obtained by applying energy conservation inside the ray tubes that emerge from the phase center of the source and the determination of the direction of the rays emerging from the dielectric surface is obtained through the application of Snell’s law for the incident rays at the interface. From Physical Optics, it is possible to obtain the electric and magnetic currents on the external surface of the lens to determine the radiated field in the integration of these currents along the surface assuming that the lens dimensions and interface curvature are much larger than a wavelength in free space. Due to circular symmetry, simplifications in formulation and numerical schemes for the solution will be presented, resulting in a more efficient design technique. The description of the lens interface surface is obtained through numerical technique.

Modeling the free surface flows is important in order to estimate the total drag of the sea Vessels. It is also necessary to study the effects of various maritime maneuvers. In this work, different ways of approximating an unstructured free surface grid with a B-spline surface are investigated. The Least squares and Galerkin approaches are studied in this regard. B-spline nite element method (BSPFEM) is studied for the solution of the steady-state kinematic free surface equation. The volume grid has to be moved in order to match the free boundary when the surface-tracking approach is adopted for the solution of free surface problem. Inherent smoothness of the B-spline representation of the free surface aids this process. B-spline representation of the free surface aids in building viscous volume grids hose boundaries closely match the steady state free surface. The B-spline approximation algorithm and BSPFEM solution of free surface equation have been tested with hypothetical algebraic testcases and real cases such as Gbody, Wigley hull and David Taylor Model Basin(DTMB) 5415 hull series.

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