A bar cell in the shape of an isosceles trapezoid is devised for use in flexure problems of circular plates. The cell members are endowed with elastic properties such that it deforms in the same manner as a piece of plate in condition of arbitrary uniform bending about any axis in the plane of a plate. The stiffness matrix of the cell is derived explicitly. Two methods of computation of stresses are described, one by the nodal forces and the other by the nodal displacements. The validity of the cell is tested on two examples whose exact solutions are known. One involves a semicircular clamped plate under uniform load, and the other a simply-supported circular plate under an eccentric concentrated load. The results compared favourably with the theory of elasticity solutions and the no-bar finite element solutions. Good trend of convergence of solutions is indicated on reduction of the element size. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

A t-spanner of a graph G is a subgraph H of G, which the distance between any two vertices in H is at most t times their distance in G. A tree t-spanner of G is a t-spanner which is a tree. In this dissertation, we discuss the t-spanners on trapezoid, permutation, and interval graphs. We first introduce an O(n) algorithm for finding a tree 4-spanner on trapezoid graphs. Then, give an O(n)algorithm for finding a tree 3-spanner on permutation graphs, improving the existed O(n + m) algorithm. Since the class of permutation graphs is a subclass of trapezoid graphs, we can apply the algorithm on permutation graphs to find the approximation of a tree 3-spanner on trapezoid graphs in O(n) time with edge bound 2n. Finally, we show that not all interval graphs have a tree 2-spanner.

Bayesian modelling is a widely used, powerful approach for reducing absolute dating uncertainties in archaeological research. It is important that the methods used in chronology building are robust and reflect substantial prior knowledge. This thesis focuses on the development and evaluation of two novel, prior models: the trapezoidal phase model; and the Poisson process deposition model. Firstly, the limitations of the trapezoidal phase model were investigated by testing the model assumptions using simulations. It was found that a simple trapezoidal phase model does not reflect substantial prior knowledge and the addition of a non-informative element to the prior was proposed. An alternative parameterisation was also presented, to extend its use to a contiguous phase scenario. This method transforms the commonly-used abrupt transition model to allow for gradual changes. The second phase of this research evaluates the use of Bayesian model averaging in the Poisson process deposition model. The use of model averaging extends the application of the Poisson process model to remove the subjectivity involved in model selection. The last part of this thesis applies these models to different case studies, including attempts at resolving the Iron Age chronological debate in Israel, at determining the age of an important Quaternary tephra, at refining a cave chronology, and at more accurately modelling the mid-Holocene elm decline in the British Isles. The Bayesian methods discussed in this thesis are widely applicable in modelling situations where the associated prior assumptions are appropriate. Therefore, they are not limited to the case studies addressed in this thesis, nor are they limited to analysing radiocarbon chronologies.

Title: Understanding Area and Volume Formulae of Geometric Figures in the History of Mathematics and by Pupils Author: Bc. Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, DSc. The aim of this thesis is to describe the nature and possible causes of problematic areas in pupils' understanding of area and volume of geometric shapes and solids and treat this issue from the point of view of its ontogeny and phylogeny. Modern theories of gradual formation of the concepts of area and volume in pupils' minds will be characterized, together with the historical development of these concepts (from ancient Egypt and Greece to modern day). Complex analysis of the current Mathematics course books for primary and lower-secondary level is offered in the second part of the thesis. The analysis is based on the criteria following from the study of academic literature and on the historic research in this area. The aim of the analysis is to describe the way in which the course books treat geometric formulae and to what extent they respect their gradual development. In the final discussion, general aspects leading from the analysis will be summarized and offered as possible inspiration for pupils, teachers and future teachers of Mathematics. Key Words: formula, area, volume, algebraic language, hypothetical...

Long span bridges are susceptible to wind. Hence it is important to study their wind-induced vibrations to avoid any probable structural failures. In this thesis, the results of an experimental and computational investigation of the aerodynamic characteristics of trapezoid bridge deck cross-sections with three different aspect ratios (10, 12 and 15) and four different side angles (75&ordm / , 60 &ordm / , 45 &ordm / and 30 &ordm / ) are analyzed and presented. The flow around rigid fixed bridge deck models is investigated to obtain the relevant aerodynamic coefficients and the vortex shedding frequency and Strouhal number. Two dimensional unsteady Reynolds Averaged Navier-Stokes equations are solved using commercial CFD software at different Reynolds numbers. The numerical results are compared with the experimental data obtained by testing the model bridge decks geometries in a low speed wind tunnel. The results of this study demonstrate that the models aerodynamic parameters except their lift coefficient are almost dependent on the aspect ratio. In addition, the influence of side angle on all aerodynamic parameters has to be taken in account.

在這篇論文中，我們探討了最近在有界雙容忍序中的一些成果。同時， 我們提供一些標準的簡短證明，包含有界雙容忍序的等價種類， 單位有界雙容忍序與適當有界雙容忍序的關係。 我們的目標是希望能在有界雙容忍序的現今地位上，去提供新的洞悉，並給未來學習者一個方向。 / In the paper、we study recent work on some classes of bounded bitolerance orders. Also, we provide the short proofs of some of classical results on bounded bitolerance orders, including the equivalent classes of bounded bitolerance orders、the relation of unit and proper bitolerance orders. Our goal is to provide the fresh insights into the current status of research in the area while suggesting directions for the future.

Avec plus de 1000 génomes complets disponibles (la grande majorité venant de bactéries), les analyses comparatives de génomes deviennent indispensables pour leurs annotations fonctionnelles, ainsi que pour la compréhension de leur structure et leur évolution, et s'appliquent par exemple en phylogénomique ou au design des vaccins. L'une des approches de plus utilisées pour comparer des génomes est l'alignement de leurs séquences d'ADN, i.e. alignement de génomes complets, c'est à dire identifier les régions de similarité en s'affranchissant de toute annotation. Malgré des améliorations significatives durant les dernières années, des outils performants pour cette approche ainsi que des méthodes pour l'estimation de la qualité des résultats qu'elle produit, en particulier sur les génomes bactériens, restent encore à développer. Outre leurs grandes tailles qui rendent les solutions classiques basées sur la programmation dynamique inutilisables, l'alignement de génomes complets posent des difficultés supplémentaires dues à leur évolution particulière, comprenant: la divergence, qui estompe les similarités entre les séquences, le réordonnancent des portions génomiques (réarrangements), ou l'acquisition de matériel génétique extérieur, qui produit des régions non alignables entres les séquences, e.g. transfert horizontal des gènes, phages. En conséquence, les solutions pour l'alignement de génomes sont des heuristiques, dont la plus commune est appelée stratégie basée sur des ancres. Cette stratégie commence par identifier un ensemble initial de régions de similarité (phase 1). Ensuite une phase de chaînage sélectionne un sous-ensemble (non-chevauchantes et généralement colinéaires) de ces similarités de poids maximal, nommées ancres (phase 2). Les phases 1 et 2 sont appliquées de manière récursive sur les régions encore non-alignées (phase 3). La dernière phase consiste en l'application systématique des outils d'alignement classiques sur toutes les régions courtes qui n'ont pas encore été alignées. Cette thèse adresse plusieurs problèmes liés à l'alignement de génomes complets dont: l'évaluation de la qualité des résultats produits par les outils d'alignement et l'amélioration de la stratégie basée sur des ancres. Premièrement, nous avons créé un protocole pour évaluer la qualité des résultats d'alignement, contenant des mesures de calcul quantitatives et qualitatives, dont certaines basées sur des connaissances biologiques. Une analyse de la qualité des alignements produits par deux des principaux outils existants sur des paires de génomes bactériens intra-espèces révèle leurs limitations: des similarités non détectées et des portions d'alignement incorrectes. À partir de ces résultats, qui suggèrent un manque de sensibilité et spécificité, nous proposons un nouvel outil pour l'alignement deux à deux de génomes complets, YOC, qui implémente une version simplifiée de la stratégie basée sur des ancres, contenant seulement deux phases. Dans la phase 1, YOC améliore la sensibilité en utilisant comme ancres, pour la première fois dans cette stratégie, des similarités locales basées sur des graines espacées, capables de détecter des similarités plus longues dans des régions plus divergentes. Cette phase est suivie par une méthode de chainage adaptée aux similarités locales, un nouveau type de chaînage colinéaire, permettant des chevauchements proportionnels. Nous avons donné une formulation de ce nouveau problème et réalisé un premier algorithme. L'algorithme, qui adopte une approche de programmation dynamique basée sur le paradigme de la ``sweep-line'', donne une solution optimale, i.e. est exacte, et s'exécute en temps quadratique. Nous avons montré que cet algorithme, comparé au chainage colinéaire classique, améliore les résultats sur des génomes bactériens, tout en restant aussi efficace en pratique. / With more than 1000 complete genomes available (among which, the vast majority come from bacteria), comparative genomic analysis become essential for the functional annotation of genomes, the understanding of their structure and evolution and have applications in phylogenomics or vaccine design. One of the main approaches for comparing genomes is by aligning their DNA sequences, i.e. whole genome alignment (WGA), which means identifying the similarity regions without any prior annotation knowledge. Despite the significant improvements during the last years, reliable tools for WGA and methodology for estimating its quality, in particular for bacterial genomes, still need to be designed. Besides their extremely large lengths that make classical dynamic programming alignment methods unsuitable, aligning whole genomes involves several additional difficulties, due to the mechanisms through which genomes evolve: the divergence, which let sequence sim ilarity vanish over time, the reordering of genomic segments (rearrangements), or the acquisition of external genetic material generating regions that are unalignable between sequences, e.g. horizontal gene transfer, phages. Therefore, whole genome alignment tools implement heuristics, among which the most common is the anchor based strategy. It starts by detecting an initial set of similarity regions (phase 1), and, through a chaining phase (phase 2), selects a non-overlapping maximum-weighted, usually collinear, subset of those similarities, called anchors. Phases 1 and 2 are recursively applied on yet unaligned regions (phase 3). The last phase (phase 4) consists in systematically applying classical alignment tools to all short regions still left unaligned.This thesis addresses several problems related to whole genome alignment: the evaluation of the quality of results given by WGA tools and the improvement of the classical anchor based strategy. We first designed a protocol for evaluating the quality of alignment results, based on both computational and biological measures. An evaluation of the results given by two state of the art WGA tools on pairs of intra-species bacterial genomes revealed their shortcomings: the failure of detecting some of the similarities between sequences and the misalignment of some regions. Based on these results, which imply a lack in both sensitivity and specificity, we propose a novel, pairwise whole genome alignment tool, YOC, implementing a simplified two-phase version of the anchor strategy. In phase 1, YOC improves sensitivity by using as anchors, for the first time, local similarities based on spaced seeds that are capable of detecting larger similarity regions in divergent sequences. This ph ase is followed by a chaining method adapted to local similarities, a novel type of collinear chaining, allowing for proportional overlaps. We give a formulation for this novel problem and provide the first algorithm for it. The algorithm, implementing a dynamic programming approach based on the sweep-line paradigm, is exact and runs in quadratic time. We show that, compared to classical collinear chaining, chaining with overlaps improves on real bacterial data, while remaining almost as efficient in practice. Our novel tool, YOC, is evaluated together with other four WGA tools on a dataset composed of 694 pairs of intra-species bacterial genomes. The results show that YOC improves on divergent cases by detecting more distant similarities and by avoiding misaligned regions. In conclusion, YOC should be easier to apply automatically and systematically to incoming genomes, for it does not require a post-filtering step to detect misalignment and is less complex to calibrate.

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