This thesis presents new numerical methods for solving differential equations with periodicity. Spectral methods for solving linear and nonlinear ODEs, linear ODE eigenvalue problems and linear time-dependent PDEs on a periodic interval are reviewed, and a novel approach for computing multiplication matrices is presented. Choreographies, periodic solutions of the n-body problem that share a common orbit, are computed for the first time to high accuracy using an algorithm based on approximation by trigonometric polynomials and optimization techniques with exact gradient and exact Hessian matrix. New choreographies in spaces of constant curvature are found. Exponential integrators for solving periodic semilinear stiff PDEs in 1D, 2D and 3D periodic domains are reviewed, and 30 exponential integrators are compared on 11 PDEs. It is shown that the complicated fifth-, sixth- and seventh-order methods do not really outperform one of the simplest exponential integrators, the fourth-order ETDRK4 scheme of Cox and Matthews. Finally, algorithms for solving semilinear stiff PDEs on the sphere with spectral accuracy in space and fourth-order accuracy in time are proposed. These are based on a new variant of the double Fourier sphere method in coefficient space and standard implicit-explicit time-stepping schemes. A comparison is made against exponential integrators and it is found that implicit-explicit schemes perform better. The algorithms described in each chapter of this thesis have been implemented in MATLAB and made available as part of Chebfun.

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詩經為我國最古之詩歌總集，其內容包括周代約六百年間的民間歌謠、士大夫作品以 及祭神之頌辭，生動且全面地反映了當時現實生活的種種情形與古代歷史文化脈動的 軌跡．既有經學與文學的價值，又蘊藏著豐富的政治 社會 經濟 宗教等各方面的 資料，是一部提供後人探索古代史實與社會情況的珍貴史料． 司馬遷撰史記，亦認為詩經具備豐富的史料價值，並且多所取材．然因二者體裁不同 ，寫作方式與目的亦異，因此在保存古史資料原貌與經過史識整理兩層系統的表現上 ，便各有短長．若能取之相互對照，比較二者所載史事之異同，並補以其他有關資料 ，定可窺見古史較信實可靠之面貌． 本論文即根據上述觀點，探求二書所敘古史之內容，考辨其異同．全文分六章完成． 第一章緒論，旨在說明本論文之研究動機、方法，並確定研究資料之範圍與時代．第 二章詩經與史記皆載之史事，羅列考辨二者皆述及之史事，分詩經略而史記詳者、詩 經本文可佐證史記者、詩經可與史記相對照者三節敘之．第三章史記所載引述詩經之 史事，將史記中引述詩經篇名、本文，或所謂詩人作刺之史事，分節敘述．第四章詩 經所載可補正史記缺失之史事，以詩經所載，補充矯正史記缺略或失誤之各項史事． 第五章詩經所反映之周代社會概況，分政治組織、教育設施、軍事戰備、農業情況、 禮樂制度、民情習俗六節敘述之，旨在說明詩經尚有豐富的社會史資料，以補充前三 章具體史實的考辨．第六章結論，根據前所論述，比較詩經與史記所載史事異同之處 ，並勾勒周代社會之概況．

Title: A traffic flow with a bottelneck Author: Adam Kovařík Department: Department of Numerical Mathematics Supervisor: prof. RNDr. Vladimír Janovský, DrSc. Supervisor's e-mail address: janovsky@karlin.mff.cuni.cz Abstract: In this paper we study a microscopic follow-the-leader traffic model on a circu- lar road with a bottleneck. We assume that all drivers are identical and overtaking is not permitted. We sketch a small part of the rich dynamics of the model including Hopf and Neimark-Sacker bifurcations. We introduce so called POM and quasi-POM solutions and an algorithm how to search them. The main goal of this work is to investigate how the optimal velocity model with a bottleneck deals with so called aggressive behavior of dri- vers. The effect of variable reaction time and a combination of both named factors is also tested. Using numerical simulations we'll find out that aggressiveness and faster reactions have positive effect on traffic flow. In the end we discuss models with two bottlenecks and with one extraordinary driver. Keywords: dynamical systems, ODEs, traffic flow, bottleneck, aggressiveness. 1

O objetivo deste trabalho é apresentar uma tradução e um comentário textual à 13ª Olímpica de Píndaro, com base nas mais recentes edições e trabalhos críticos acerca do poeta e do gênero desse poema, o epinício. Também foi composto um ensaio interpretativo que tenta abarcar os temas mais importantes da ode e relacioná-los com o todo da obra de Píndaro. As imagens do poema desenvolvem a contraposição entre medida e excesso, representada tanto nas referências mitológicas (Têmis e as Horas contra a Soberba e Insolência; Belerofonte encilhando Pégaso) quanto nas reflexões da primeira pessoa (que não deve exceder-se no elogio para não errar o alvo, assim como um arqueiro disparando suas flechas; nem deve tentar relatar todas as vitórias da família, pois são tão numerosas quanto os grãos de areia etc.). Em anexo, há a tradução dos escólios relativos a essa ode para permitir a consulta direta a essa fonte, que não se acha traduzida. / The objective of this study is to present a translation and a textual commentary of Pindar\'s Olympian 13, based on the most recent editions and critical works about the poet and the genre of this poem, the epinician. An interpretative essay was composed in order to cover the most important themes of this ode and articulate them with Pindar\'s other works. The poetical imagens of the poem develop the central theme, the opposition between measure and excess, represented by the mithological references (Themis and the Hours against the Excess and the Satiety; Bellerophon taming Pegasus etc.) and by the first-person\'s reflections on the laudatory art (the first-person should not exceed in praise in order to not miss the target, as an archer with his arrows; nor should try to enumerate all the victories of this family, for they are greater than the grains of sand from the sea). There is a translation of the scholia to this ode attached, allowing direct consultation, once there is no other version of this text.

La thèse a pour corpus le Canon des Poèmes (Shijing 詩經). S’appuyant sur l’étude de diverses interprétations des Poèmes, elle propose une application numérique pour interpréter le procédé incitatif (Xing 興) qui, jusque-là, n’a pas été clairement défini au plan rythmique. On y considère le sinogramme à la manière d’une note musicale, ou plus précisément d’une sino-syllabe (hanzi -yinjie 漢字-音節). La thèse peut alors se baser sur trois principes d’analyse :1. le contraste d’effectifs des sino-syllabes ;2. le calcul combinatoire des sino-syllabes ;3. l’échelle de perception des sino-syllabes.En suivant ces trois principes d’analyse, la thèse expose une méthode de lecture expérimentale qui distingue deux aspects dans les sino-syllabes aperçues pendant la lecture : les composants fondamentaux (qui créent le rythme dominant) et les idées principales (qui constituent le sujet thématique). La collaboration harmonieuse du rythme dominant avec le sujet thématique, révèle un système de figuration qui transforme les propos en langage poétique sur le plan rythmique. Ce système sert de référence interne au corpus pour objectiver le rapport rythmique entre le motif initial (= premier groupe de vers) et le motif final (= deuxième groupe de vers), dans la strophe créée par le procédé de Xing. On propose de nommer ce système « figure rythmique » (jielü xiuci 節律修辭). / The present thesis has chosen to center its attention on The Book of Odes. After the study of diverse interpretations of these poems, the thesis is brought to suggest using numeric humanities in the analysis of what Xing calls “the incentive process” whose rhythmic figure has not yet been clearly defined. At the condition that a sinogram could be considered a musical note, it would be more accurate to call it a “sino-syllable” (hanzi-yinjie 漢字-音節). The results are relayed by these three principles: 1. The contrast of occurrences between sino-syllables 2. The sino-syllables’ combinatorial calculation 3. The scale of perception in comprehending sino-syllablesApplying these principles of analysis, the thesis then reveals an experimental method of reading which sets forth two aspects: the basic components that create the dominant rhythm and the mean ideas that constitute the thematic subject.The harmonious relationship of the dominant rhythm with the thematic subject reveals a system that rhythmically transforms words to poetic language. This metaphorical system, called “rhythmic figure” (jiulü xiuci 節律修辭) for the purpose of this research, serves as an internal reference to the corpus to manifest the rhythmic relationship between the first and final patterns in verses produced with Xing’s method.

This work is to give an overview over the research that I've done up to now. The overall idea behind my interests has been that of understanding analytical and geometrical properties of non smooth spaces both from both a theoretical and a practical point of view. The two main classes of spaces on which I focussed are: the Wasserstein space (P2(M),W2) built over a Riemannian manifold, and abstract metric and metric-measure spaces, in particular those with Ricci curvature bounded below.

Thesis (Ph. D.)--Königl. Universität Breslau, 1910. / Cover title. Vita. Includes bibliographical references.

The application of persona theory to the poetry of Horace is a well-established method of critical analysis, but in Horace’s love poems we can also distinguish various erotic voices. The Odes and Epodes of Horace feature several distinct sexual personae as the speakers of the poems. Horace the Lothario is a witty, didactic, slightly detached expert on love and erotic behavior. Horace the Excluded Lover is a gloomy failure at love who desires someone he cannot have. Horace the Ephebophile seeks as the object of his erotic desire a young man generally older than traditional Roman pederasty would suggest, but this desire is coded and suppressed. Horace the Moralist, possibly in ironic relation to the other three, attacks loose sexual morals and praises Augustus for returning chastity and monogamy to Rome. Finally, the sexual personae of some of Horace’s poems defy simple categorization and must be analyzed more closely in order to explain the nature of the speaker. This methodology, the division into sexual personae, allows us to give a fresh critical appraisal to Horace’s erotic poetry. / text

Since Suetonius, Odes 4 has been the focus of much criticism and apology. Some explanation seems required for Odes 4’s apparent disunity and eclectic mixture of encomium with occasional pieces. My dissertation offers an interpretation of Book 4 by considering it in the light of the Mausoleum of Augustus. By considering the ways in which Horace builds evocations of the Mausoleum into book 4, I argue that there is sustained connection between the two works, which points towards a unified purpose for Odes 4: Horace is building a literary Mausoleum of Augustus. The first chapter establishes the justification for viewing Odes 4 through the lens of the material world by considering the functions of architecture and topography in Horace's models and contemporaries. After studying the ways the city of Rome is used by the Augustan poets and by Horace, the chapter concludes by making a case for understanding Odes 4 as a poetic monument. The second chapter studies the interrelationship between C.3.30 and the Mausoleum. First, I parse out a preliminary list of the Mausoleum's evocations. I then show how Horace evokes the Mausoleum in C.3.30 and recreates it in the poetic sphere. In chapter 3, I revisit Horace's autobiography and Suetonius's statements regarding the origin of Odes 4. I argue that the impetus of Odes 4 is not imperial compulsion but rather Horace's understanding of his own role as poet in the years following his selection by Augustus to compose the Carmen Saeculare. In chapter 4, I make the case for Odes 4 being a literary Mausoleum of Augustus. I first discuss the ways Horace builds his new poetic work upon the foundation of his earlier lyric successes. I then show how Horace uses the themes of time, death and the power of poetry as the brick and mortar of his literary mausoleum. I conclude by showing how Horace praises Augustus in ways that engage specifically with the Mausoleum by incorporating many of its evocations into this book. / text