In order to deliver statistical and qualitative backing to latent fingerprint evidence, algorithms are proposed (1) to perform fingerprint matching to aid in quality assessment, and (2) to discover statistically rare features or patterns in fingerprints. These features would help establish an objective minimum-quality baseline for latent prints as well as aid in the latent examination process in making a matching comparison. The proposed methodologies use minutiae triplet-based features in a hierarchical fashion, where not only minutia points are used, but ridge information is used to help establish relations between minutiae. Results show (1) that our triplet-based descriptor is useful in eliminating false matches in the matching algorithm, and (2) that a set of distinctive features can be found that have sufficient discriminatory power to aid in quality assessment. / Master of Science

La présente thèse vise à explorer différents types de modèles log-bilinéaires dans le domaine des sciences actuarielles. Le point de départ consiste en le modèle de Lee-Carter, utilisé pour les problèmes de projection de la mortalité. Différentes variantes sont développées, et notamment le modèle de Poisson log-bilinéaire. L'introduction de variables explicatives est également analysée. Enfin, une tentative de d'exportation de ces modèles au cas des triangles IBNR est effectuée.

La présente thèse vise à explorer différents types de modèles log-bilinéaires dans le domaine des sciences actuarielles. Le point de départ consiste en le modèle de Lee-Carter, utilisé pour les problèmes de projection de la mortalité. Différentes variantes sont développées, et notamment le modèle de Poisson log-bilinéaire. L'introduction de variables explicatives est également analysée. Enfin, une tentative de d'exportation de ces modèles au cas des triangles IBNR est effectuée.

This thesis describes the synthesis of a host of polynuclear iron complexes synthesised with phenolic oxime ligands, fundamentally developing the coordination chemistry of iron with these ligands. The metallic cores that occur within iron phenolic oxime clusters were found to contain almost exclusively oxo-centred triangles and oxo-centred tetrahedra. We found that we could alter the reaction conditions or derivatise the ligands and develop these basic building blocks into more elaborate arrays, exerting a degree of control over creating larger or smaller clusters. Chapter one describes the syntheses, structures and magnetic properties of new iron complexes alongside previously synthesised related complexes (4, 5, 8, 9 and 15) containing salicylaldoxime (saoH2) or derivatised salicylaldoximes (RsaoH2). These are [Fe3O(OMe)(Ph-sao)2Cl2(py)3]·2MeOH (1·2MeOH), [Fe3O(OMe)(Ph-sao)2Br2(py)3]·Et2O (2·Et2O), [Fe4(Ph-sao)4F4(py)4]·1.5MeOH (3·1.5MeOH), [Fe6O2(OH)2(Et-sao)2(Et-saoH)2(O2CPh)6] (4), [HNEt3]2[Fe6O2(OH)2(Et-sao)4(O2CPh(Me)2)6]·2MeCN (5·2MeCN), [Fe6O2(O2CPh)10(3-tBut-5-NO2-sao)2(H2O)2]·2MeCN (6·2MeCN), [Fe6O2(O2CCH2Ph)10(3-tBut-sao)2(H2O)2]·5MeCN (7·5MeCN), {[Fe6Na3O(OH)4(Me-sao)6(OMe)3(H2O)3(MeOH)6]·MeOH}n (8·MeOH) and [HNEt3]2[Fe12Na4O2(OH)8(sao)12(OMe)6(MeOH)10] (9). The predominant building block appears to be the triangular [Fe3O(R-sao)3]+ species which can self-assemble into more elaborate arrays depending on reaction conditions. The four hexanuclear and two octanuclear complexes of formulae [Fe8O2(OMe)4(Mesao) 6Br4(py)4]·2Et2O·MeOH (10·2Et2O·MeOH), [Fe8O2(OMe)3.85(N3)4.15(Mesao) 6(py)2] (11), [Fe6O2(O2CPh-4-NO2)4(Me-sao)2(OMe)4Cl2(py)2] (12), [Fe6O2(O2CPh-4-NO2)4(Et-sao)2(OMe)4Cl2(py)2]·2Et2O·MeOH (13·2Et2O·MeOH), [HNEt3]2[Fe6O2(Me-sao)4(SO4)2(OMe)4(MeOH)2] (14) and [HNEt3]2[Fe6O2(Etsao) 4(SO4)2(OMe)4(MeOH)2] (15) all are built from series of edge-sharing [Fe4( μ4- O)]10+ tetrahedra. Complexes 10 and 11 display a new μ4-coordination mode of the oxime ligand and join a small group of Fe-phenolic oxime complexes with nuclearity greater than six. Chapter three then introduces co-ligands to the reaction scheme to compete with the salicylaldoxime ligands for metal coordination sites. Five tetranuclear and two nononuclear complexes are stabilised with salicylaldoxime (saoH2) or derivatised salicylaldoximes (R-saoH2) in conjunction with either 1,4,7- triazocyclononane (tacn), 2-hydroxymethyl pyridine (hmpH) or 2,6-pyridine dimethanol (pdmH2), [Fe4O2(sao)4(tacn)2]·2MeOH (16·MeOH), [Fe4O2(Mesao) 4(tacn)2]·2MeCN (17·2MeCN), [Fe4O2(Et-sao)4(tacn)2]·MeOH (18·MeOH), [Fe9NaO4(Et-sao)6(hmp)8]·3MeCN·Et2O (19·3MeCN·Et2O), [Fe4 (Etsao) 4(hmp)4]·Et-saoH2 (20·Et-saoH2), [Fe4(Ph-sao)4(hmp)4]·2MeCN (21·2MeCN) [Fe9O3(sao)(pdm)6(N3)7(H2O)] (22). Chapter four straps two salicylaldoxime units together in the 3-position, using ligands with aliphatic a,W-aminomethyl links, allowing the assembly of the polynuclear complexes [Fe7O2(OH)6(H2L1)3(py)6](BF4)5·6H2O·14MeOH (23·6H2O·14MeOH), [Fe6O(OH)7(H2L2)3][(BF4)3]·4H2O·9MeOH (24·4H2O·9MeOH) and [Mn6O2(OH)2(H2L1)3(py)4(MeCN)2](BF4)5(NO3)·3MeCN·H2O·5py (25·3MeCN·H2O·5py). In each case the metallic skeleton of the cluster is based on a trigonal prism in which two [MIII 3O] triangles are tethered together via three helically twisted double-headed oximes. The latter are present as H2L2- in which the oximic and phenolic O-atoms are deprotonated and the amino N-atoms protonated, with the oxime moieties bridging across the edges of the metal triangles. Both the identity of the metal ion and the length of the straps connecting the salicylaldoxime units have a major impact on the nuclearity and topology of the resultant cage, with, perhaps counter-intuitively, the longer straps producing the “smallest” clusters.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal

O ensino de Matemática é, de modo geral, orientado pelos processos contidos nos livros didáticos. Sendo assim, a organização dos conceitos matemáticos nesses livros deveria ser capaz de permitir ao leitor interpretar a Matemática em sua essência, admitindo o estabelecimento de relações entre os conteúdos. No entanto, o que geralmente se observa nos materiais é um aglomerado de definições e conceitos desconexos que conduzem o leitor a dificuldades de aprendizado na área. Por essa razão, a presente dissertação teve o objetivo principal de localizar, além de caracterizar, os pontos notáveis do triângulo: o centróide ou baricentro (G), o ortocentro (H), o circuncentro (O), o centro (N) da circunferência de nove pontos, os três ex-centros das circunferências ex-inscritas, as projeções ortogonais dos vértices sobre os lados opostos e os pontos de tangência da circunferência inscrita e ex-inscrita. Quatro abordagens são apresentadas em busca de tal objetivo: a-) apresentar a geometria do triângulo segundo técnicas de percepção visual; b-) caracterizar alguns pontos notáveis do triângulo, como pontos de máximo ou de mínimo de funções com as demonstrações utilizando desigualdade de Cauchy-Schwarz e entre média aritmética e geométrica; c-) utilizar um sistema cartesiano adequado para o cálculo das abscissas e ordenadas do centróide (G), do ortocentro (H) e do circuncentro (O) de um triângulo; d-) utilizar os números complexos para a completa localização de todos os pontos notáveis do triângulo além de apresentar a equação da reta de Euler, o incentro (I) e os três excentros IA, IB e IC localizados em fórmulas simples. A dissertação finaliza com o Teorema de Feuerbach, apresentado com uma prova elementar, mostrando que a circunferência de nove pontos e a circunferência inscrita são tangentes internamente e que a circunferência dos nove pontos é tangente exteriormente a cada uma das três ex circunferências e o Teorema de Napoleão, no qual os baricentros de triângulos equiláteros, construídos a partir dos lados de um triângulo qualquer, formam um outro triângulo equilátero. Comparando as várias abordagens da dissertação, a conclusão é a de que a compreensão dos números complexos paradoxalmente simplifica a resolução de problemas de geometria plana e a solução de equações polinomiais. Assim, acredita-se que uma maior exploração desse conteúdo no ensino da Matemática poderia tornar o aprendizado mais atraente e simplificado / The teaching of Mathematics is generally guided by the procedures contained in the textbooks. Thus, the organization of the mathematical concepts in these books should be able to allow the reader to interpret the Mathematics in its essence, admitting the establishment of relationships between the contents. However, what is observed in the materials is a conglomeration of disparate definitions and concepts that lead the reader to learning difficulties in the area. For this reason, this work aimed to locate and characterize the notable points of the triangle: the centroid or barycenter (G), the orthocenter (H), the circumcenter (O), the center (N) of circumference of nine points, three former centers of the ex-inscribed circles, orthogonal projections of the vertices on the opposite sides and the points of tangency of the inscribed and the ex-inscribed circumference. Four approaches are presented to achieve these goals: a-) to introduce the geometry of the triangle using visual perception techniques, b-) to characterize some notable points of the triangle, as points of maximum or minimum of functions with the demonstrations using the Cauchy-Schwarz inequality and between the arithmetic and geometric mean;-c) to use a suitable Cartesian system for calculating the abscissas and ordinates of the centroid (G), of orthocenter (H) and of the circumcenter (O) of a triangle;-d) to use complex numbers for the complete location of all notable points of the triangle, beyond depicting the Euler equation of the line, the incenter (I) and the three former centers IA, IB and IC located in simple formulas. The work is concluded with the Feuerbach\'s Theorem, presented with an elementary proof, showing that the nine-point circle and the incircle is tangent internally and that the circumference of the nine points is externally tangent to each of the three ex-inscribed circles and the Napoleons Theorem, in which the barycenters of equilateral triangles, constructed from the sides of any triangle, form another equilateral triangle. Comparing the approaches detached hitherto, the conclusion is that the understanding of complex numbers paradoxically simplifies troubleshooting of plane geometry and the solution of polynomial equations. Thus, it is believed that further exploration of this content in mathematics education could make learning more attractive and simplified

La première partie de la thèse porte sur les graphes de Steinhaus réguliers. On commence par obtenir une nouvelle preuve du théorème de Dymacek, selon lequel toute matrice de Steinhaus associée à un graphe pair est bisymétrique, en exhibant une relation entre les éléments de l'antidiagonale d'une matrice de Steinhaus et les degrés des sommets du graphe associé. Ce théorème est ensuite utilisé pour montrer que toute matrice de Steinhaus associée à un graphe régulier de degré impair admet une grande sous-matrice multisymétrique. On étudie alors les matrices de Steinhaus multisymétriques, en particulier celles dont le graphe associé admet une certaine régularité. Cette étude permet enfin de vérifier jusqu'à 1500 sommets une conjecture de Dymacek, qui annonce que le graphe complet à deux sommets K2 est le seul graphe de Steinhaus régulier de degré impair, améliorant ainsi d'un facteur 12 la borne précédemment connue (117 sommets).<br />La seconde partie porte sur les triangles de Steinhaus dans Z/nZ. En 1978 Molluzzo pose le problème de savoir si, pour tout n≥1 et pour toute longueur admissible m, il existe une suite balancée de longueur m dans Z/nZ, c'est-à-dire une suite dont le triangle de Steinhaus associé contienne chaque élément de Z/nZ avec la même multiplicité. On donne ici une réponse complète et positive au Problème de Molluzzo dans tout groupe cyclique d'ordre une puissance de 3. Plus généralement, on construit une infinité de suites balancées dans tout groupe cyclique d'ordre impair. Ces résultats, qui sont les premiers obtenus sur ce problème dans Z/nZ avec n>3, proviennent de l'étude des triangles de Steinhaus des suites arithmétiques dans les groupes cycliques.

Visi mokiniai, nepriklausomai nuo jų gabumų, polinkių ar mokymosi ypatumų turėtų pajusti matematikos praktinę naudą. Pagrindinėje mokykloje kiekvienas mokinys turi patirti sėkmę mokydamasis matematikos, o matematikos ugdymo turinys, jo perteikimo būdai ir tam naudojami metodai turi padėti mokiniui susiformuoti į mokymosi sėkmę. Atlikus tyrimą apie moksleivių ir mokytojų požiūrį į esamų mokomųjų kompiuterinių priemonių panaudojimą mokantis skaičiuoti įvairų trikampių plotus 7-oje klasėje, buvo kuriama interaktyvi mokymo priemonė „Trikampių plotai“. Šiame darbe pristatoma mokymo priemonė „Trikampių plotai“, kuri padeda mokyti(s) įvairių gebėjimų mokiniams matematikos pagrindų. Mokomoji priemonė sukurta Imagine Logo pagalba (Logo programavimo kalba). Mokomosios kompiuterinės programos „Trikampių plotai“ interaktyvi ir teorinė, ir praktinė dalis. Produktas buvo pristatytas Ukmergės Dukstynos pagrindinės mokyklos 7-os klasės moksleiviams ir matematikos mokytojams. Pagal atliktą matematikos mokytojų ir mokinių apklausą (tyrimą), mokomoji kompiuterinė priemonė yra patraukli, lengvai valdoma, suprantama, padedanti interaktyviai mokyti(s) skaičiuoti trikampio plotą įvairių gebėjimų mokinimas. / All pupils independent of their learning skills, abilities and peculiarity have to notice the practical advantage of mathematics. In Basic school every pupil has to delight in learning mathematics. The training content, its means of impart and used methods have to help pupil to form its attitude to learn successfully. The development of interactive learning tool “The Area of Triangles” was based on the results of the of research the attitude of pupils and teachers towards the use of exiting educational teaching computer courses in learning how to calculate the area of triangles in the 7th classes. In this work you can find the attractive visual, simple in use teaching aid “The Area of Triangles” which helps to teach/ learn the essentials of mathematics for pupils with different abilities. Teaching aid was created with the help of Image Logo (Logo computerese). Teaching computer aid “The Area of Triangles” include interactive theoretical and practical parts. The course was introduced to the pupils of 7th classes and teachers of mathematics. According to the results of the research the teaching aid is attractive and easy to use, comprehensible and instrumental to teach/learn interactively to calculate the area of triangles for pupils with different abilities.

Submitted by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:36:54Z No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-11-27T11:48:24Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) / Made available in DSpace on 2015-11-27T11:48:24Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1442870 bytes, checksum: 1ffe2705b4478d0321349b2c4248fdd5 (MD5) Previous issue date: 2014-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study some applications of the Poncelet's Theorem for teaching geometry. One of our main motivations for this work is that in some the high school leved math courses the study of geometry is slightly used and in certain circunstances the theorems are not demonstrated to the knowledge of the theories discussed. Finally, a list of exercises is proposed. / Neste trabalho estudaremos algumas aplicações do Teorema de Poncelet à geometria do Ensino Médio. Uma das nossas principais motivações é que nos cursos de Matemática a nível de Ensino Médio a Geometria é pouco utilizada e em algumas circunstâncias os teoremas não são demonstrados para o conhecimento das teorias abordadas. Finalmente, uma lista de exercícios é proposta.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-04T15:52:34Z No. of bitstreams: 1 arquivototal.pdf: 2481244 bytes, checksum: 2b4b148ac44f9e7f5aa5ab44424db75c (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2017-09-04T15:55:02Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 2481244 bytes, checksum: 2b4b148ac44f9e7f5aa5ab44424db75c (MD5) / Made available in DSpace on 2017-09-04T15:55:02Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2481244 bytes, checksum: 2b4b148ac44f9e7f5aa5ab44424db75c (MD5) Previous issue date: 2014-08-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We have developed this work to contribute positively to teaching of geometry in basic education form, because although this branch of mathematics is very important in the training of students is very underprivileged in this phase of education. Through him, we mentioned some factors that can in uence in the context in which it is teaching geometry, aiming to serve as a re ection and a possible repositioning apposite situation. We also made a simple approach to deductive and reasoning and the axiomatic method primary education, taking into account the importance of this method in the study of geometry that stage. To develop skills in geometry while giving consistency to certain content in basic education, and more precisely on cevianas associated with a triangle, we have created an axiomatic model, through we approach simply some classic de nitions and theorems of Euclidean Geometry, some of them being common in primary education, and others, not so much. So they are: Menelaus's Theorem, Ceva's Theorem, Stewars's Theorem, the four notable points of the triangle (orthocenter, circumcenter, incenter and the centroid), Euler Line, Nine - Point circle, Euler Point, Gergonne Point, Nagel Point, Feuerbach Point, as well as introduce the de nition of isotomic points, isotomic straights and reciprocal points. In the theorems, we use only elementary methods of Synthetic Geometry, becoming a subject easy to understand that can be exploited in basic education. We believe the focus of the structure of this work can serve as a motivation for students and primary school teachers seeking to improve their knowledge of geometry. / Desenvolvemos esse trabalho no sentido de contribuir de forma positiva para o ensino de geometria na educação básica, pois embora esse ramo da matemática seja muito importante na formação dos alunos ele é muito desprivilegiado nessa fase de ensino. Por meio dele, mencionamos alguns fatores que podem in uenciar o quadro em que se encontra o ensino de geometria, visando servir de re exão e um possível reposicionamento frente à situação. Fizemos também uma singela abordagem sobre o raciocínio dedutivo e o método axiomático no ensino básico, levando em consideração a importância desse método no estudo de geometria nessa fase. No sentido de desenvolver habilidade em geometria e ao mesmo tempo dar consistência a determinados conteúdos no ensino básico, mais precisamente sobre cevianas e pontos associados a um triângulo, criamos um modelo axiomático, através do qual, abordamos de maneira simples alguns teoremas e de nições clássicas da Geometria Euclidiana Plana, sendo uns deles comuns no ensino básico, e outros, nem tanto. São eles: Teorema de Menelaus, Teorema de Ceva, Teorema de Stewart, os quatro pontos notáveis do triângulo (ortocentro, circuncentro, incentro e o baricentro), Reta de Euler, Circunferência dos Nove Pontos, Pontos de Euler, Ponto de Gergonne, Ponto de Nagel, os Pontos de Feuerbach, bem como introduziremos a de nição de pontos isotômicos, retas isotômicas e pontos recíprocos. Nos teoremas, utilizamos apenas métodos elementares da Geometria Sintética, constituindo-se um assunto de fácil compreensão que pode ser bem explorado no ensino básico. Acreditamos que os enfoques da estrutura do trabalho possam servir de motivação para alunos e professores do ensino básico que busquem aprimorar seus conhecimentos em geometria.