Many problems in fluid mechanics and material sciences deal with liquid-vapour flows. In these flows, the ideal gas assumption is not accurate and the van der Waals equation of state is usually used. This equation of state is non-convex and causes the solution domain to have two hyperbolic regions separated by an elliptic region. Therefore, the governing equations of these flows have a mixed elliptic-hyperbolic nature. Numerical oscillations usually appear with standard finite-difference space discretization schemes, and they persist when the order of accuracy of the semi-discrete scheme is increased. In this study, we propose to use a Chebyshev pseudospectral method for solving the governing equations. A comparison of the results of this method with very high-order (up to tenth-order accurate) finite difference schemes is presented, which shows that the proposed method leads to a lower level of numerical oscillations than other high-order finite difference schemes, and also does not exhibit fast-traveling packages of short waves which are usually observed in high-order finite difference methods. The proposed method can thus successfully capture various complex regimes of waves and phase transitions in both elliptic and hyperbolic regimes

One-way and two-way classification models in experimental design for both balanced and unbalanced cases are considered when the errors have Generalized Secant Hyperbolic distribution. Efficient and robust estimators for main and interaction effects are obtained by using the modified maximum likelihood estimation (MML) technique. The test statistics analogous to the normal-theory F statistics are defined to test main and interaction effects and a test statistic for testing linear contrasts is defined. It is shown that test statistics based on MML estimators are efficient and robust. The methodogy obtained is also generalized to situations where the error distributions from block to block are non-identical.

Naive Bayes classifier and maximum likelihood hypotheses in Bayesian learning are considered when the errors have non-normal distribution. For location and scale parameters, efficient and robust estimators that are obtained by using the modified maximum likelihood estimation (MML) technique are used. In naive Bayes classifier, the error distributions from class to class and from feature to feature are assumed to be non-identical and Generalized Secant Hyperbolic (GSH) and Generalized Logistic (GL) distribution families have been used instead of normal distribution. It is shown that the non-normal naive Bayes classifier obtained in this way classifies the data more accurately than the one based on the normality assumption. Furthermore, the maximum likelihood (ML) hypotheses are obtained under the assumption of non-normality, which also produce better results compared to the conventional ML approach.

This thesis analyzes procedure of generation of hyperbolic grids formulated by two constraints, which specify grid orthogonality and cell volume. The procedure was applied on a wide range of geometries and high quality two and three dimensional hyperbolic grids were generated by using grid control and smoothing procedures, which supply grid clustering in all directions and prevent grid deformation (grid shock), respectively.

We obtain explicit formulae for Lagrangian representations of the (p, q, r)-triangle group into the group of direct isometries of the complex hyperbolic plane in the case where p=q=r. Numerically approximated matrix generators of representations of the (p, p, p)-triangle group are obtained using a special basis. The numerical approximations are then used to guess the exact generators by a process utilizing the LLL algorithm. The matrices are proved rigorously to generate Lagrangian representations of the (p, p, p)-triangle group and are applied to the problem of deciding whether or not an interval contains representations of the (p, p, p)-triangle group which are not discrete.

An examination of the logical relationships between attitude statements suggests that attitudes can be ordered according to favourability, and can also stand in relationships of implication to one another. The traditional representation of attitudes, as points on a single dimension, is inadequate for representing both these relations but representing attitudes as intervals on a single dimension can incorporate both favourability and implication. An interval can be parameterised using its two endpoints or alternatively by its midpoint and latitude. Using this latter representation, the midpoint can be understood as the �favourability� of the attitude, while the latitude can be understood as its �generality�. It is argued that the generality of an attitude statement is akin to its latitude of acceptance, since a greater semantic range increases the likelihood of agreement. When Coombs� Theory of Unidimensional Unfolding is reformulated using the interval representation, the key question is how to measure the distance between two intervals on the dimension. There are innumerable ways to answer this question, but the present study restricts attention to eighteen possible �distance� measures. These measures are based on nine basic distances between intervals on a dimension, as well as two families of models, the Minkowski r-metric and the Generalised Hyperbolic Cosine Model (GHCM). Not all of these measures are distances in the strict sense as some of them fail to satisfy all the metric axioms. To distinguish between these eighteen �distance� measures two empirical tests, the triangle inequality test, and the aligned stimuli test, were developed and tested using two sets of attitude statements. The subject matter of the sets of statements differed but the underlying structure was the same. It is argued that this structure can be known a priori using the logical relationships between the statement�s predicates, and empirical tests confirm the underlying structure and the unidimensionality of the statements used in this study. Consequently, predictions of preference could be ascertained from each model and either confirmed or falsified by subjects� judgements. The results indicated that the triangle inequality failed in both stimulus sets. This suggests that the judgement space is not metric, contradicting a common assumption of attitude measurement. This result also falsified eleven of the eighteen �distance� measures because they predicted the satisfaction of the triangle inequality. The aligned stimuli test used stimuli that were aligned at the endpoint nearest to the ideal interval. The results indicated that subjects preferred the narrower of the two stimuli, contrary to the predictions of six of the measures. Since these six measures all passed the triangle inequality test, only one measure, the GHCM (item), satisfied both tests. However, the GHCM (item) only passes the aligned stimuli tests with additional constraints on its operational function. If it incorporates a strictly log-convex function, such as cosh, the GHCM (item) makes predictions that are satisfied in both tests. This is also evidence that the latitude of acceptance is an item rather than a subject or combined parameter.

Thesis (Ph. D.)--University of Texas at Austin, 2007. / Vita. Includes bibliographical references.

Τα ασύρματα δίκτυα μικρής εμβέλειας (short-range wireless networks) γνωρίζουν σήμερα μεγάλη ανάπτυξη. Ένα βασικό δομικό στοιχείο των ασύρματων δικτύων είναι οι δέκτες (receivers), οι οποίοι περιλαμβάνουν μεταξύ των άλλων συστήματα για τον υποβιβασμό της συχνότητας του σήματος (down conversion) σε χαμηλότερες ενδιάμεσες συχνότητες (Intermediate Frequencies-IF). Κατά τη διαδικασία αυτή δημιουργείται το πρόβλημα της εμφάνισης ενός ειδώλου συχνότητας (image frequency), το οποίο συνυπάρχει με το σήμα προς επεξεργασία και θα πρέπει να απομακρυνθεί με χρήση κατάλληλων ηλεκτρονικών μιγαδικών φίλτρων (complex filters). Στόχος της Μεταπτυχιακής Διπλωματικής Εργασίας είναι η ανάπτυξη νέων δομών μιγαδικών φίλτρων τα οποία χρησιμοποιούνται σε δέκτες που λειτουργούν με τα πρότυπα Bluetooth/Zigbee. Κύρια πλεονεκτήματα αποτελούν η δυνατότητα λειτουργίας σε χαμηλή τάση τροφοδοσίας (1.2V), η ρύθμιση των χαρακτηριστικών τους με το ρεύμα πόλωσης, καθώς και η απουσία αντιστατών. Η εξομοίωση της λειτουργίας καθώς και η φυσική τους σχεδίαση έγιναν με χρήση του λογισμικού Cadence, σε τεχνολογία AMS 0.35μm. / Short-range wireless networks nowadays find great development. A basic structural component of wireless networks is the receivers, which include among others systems for down conversion of the signal into lower Intermediate Frequencies (IF). The problem of image frequency is created due to this procedure, which coexists with the under process signal and it should be removed through suitable electronic complex filters. The objective of this diploma Thesis is the development of new complex filters structures which are compatible with the Bluetooth/ZigBee standards. The main advantages are the operation availability in low-voltage supply (1.2V) environment, the adjustment of its characteristics through the dc bias current, and also the absence of resistors. The simulation of the filter and, also, the physical layout design were performed through the utilization of the Cadence with AMS BiCMOS 0.35um design kit.

Este trabalho tem como objetivo colaborar na inserção do ensino das Geometrias Não Euclidianas no ensino médio. Para tanto, fizemos uma pesquisa bibliográfica sobre o surgimento de tais Geometrias, em seguida apresentamos uma sequência de conteúdos para o ensino das Geometrias Elíptica e Hiperbólica, abordando os principais tópicos elencados pelas Diretrizes Curriculares do Estado do Paraná, comparando-as sempre que possível com a Geometria Euclidiana. Esclarecemos que onde citamos Geometria Elíptica, estamos realmente tratando da Geometria da Superfície Esférica, para que este trabalho fique compatível com as Diretrizes Curriculares do Estado do Paraná. Apesar de haver algumas proposições e suas provas, em grande parte do trabalho não há teoria e demonstrações com o rigor exigido pela matemática, buscamos apenas apresentar os principais conceitos e usar uma linguagem que possa ser compreendida por qualquer profissional que esteja disposto a compreender e depois de estudar, ensinar estas geometrias. Em novembro de 2013, na XVII Semana da Matemática e III Encontro de Ensino de Matemática do Câmpus de Pato Branco – PR da UTFPR, aplicamos um minicurso com parte deste conteúdo. Ao final do minicurso aplicamos um questionário sobre o conhecimento inicial do tema e a atual situação de ensino destas geometrias. Tal questionário visou identificar o interesse sobre o tema e sobre a real possibilidade de inserção destas geometrias nas salas de aula, cujos resultados encontram-se no texto. / This work aims to contribute in including teaching of Non-Euclidean Geometry in high school. For this, a bibliographic research was made about the appearance of such geometries and introduce content for teaching of Elliptical and Hyperbolic Geometries, addressing the main topics listed by Curriculum Guidelines of Paraná, comparing them with Euclidean Geometry. Clarify that where quoted elliptic geometry, we are really dealing with Surface Spherical Geometry, for that this work be compatible with the Curriculum Guidelines of the State of Paraná. Although there are some propositions and their proofs, in most part of the work there aren´t theoretical studies and statements with all rigors mathematics requires, we seek to show the main concepts and use a language that can be understood by any person who is willing to understand and after studying, teach these geometries in school. In November 2013, during the XVII Semana de Matemática and III Encontro de Ensino de Matemática Câmpus de Pato Branco – PR of UTFPR, a mini-course was applied with part of this content to some participants. At the end of the mini-course a questionnaire was applied inquiring the basic knowledge, the current teaching situation of these geometries and aim to identify the interest in this issue and the real possibility of inclusion in the classrooms, the results can be found in the following work.

Submitted by Alison Vanceto (alison-vanceto@hotmail.com) on 2017-09-05T18:40:22Z No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T19:46:16Z (GMT) No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Approved for entry into archive by Ronildo Prado (ronisp@ufscar.br) on 2017-09-20T19:46:22Z (GMT) No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) / Made available in DSpace on 2017-09-20T19:50:58Z (GMT). No. of bitstreams: 1 DissMFM.pdf: 6937427 bytes, checksum: 9f27179bedfcfdb23587f5a9f3e35e8c (MD5) Previous issue date: 2017-03-28 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / The current study aims to elaborate a didactic sequence to study the catenary curve through the dynamic geometry perspective. In onder to highlight the importance of using software/application to better understand the function and its graphical representation, a study has been made on its historical development, notation, construction as well as its properties. Therefore, a lesson plan on the curve will be applied to High School students. Based on their reports, we intend to analyze and discuss these results. / O principal objetivo deste trabalho é elaborar uma sequência didática para estudo da curva catenária, utilizando geometria dinâmica. Para isso, foi feito um estudo sobre seu desenvolvimento histórico, notação, construção e propriedades. Destacar a importância do uso de software/aplicativo para melhor compreensão da função e sua representação gráfica. Por fim, aplicar um plano de aula sobre a curva com alunos do Ensino Médio, coletar, analisar e discutir os resultados baseando-se nos relatos dos alunos envolvidos.