Thesis (Ph.D.)--The University of Chicago, 2002. / Includes bibliographical references.

Thesis (Ph. D.)--University of Chicago, 2002. / Includes bibliographical references (leaves 384-397). Also available on the Internet.

We study bifurcations of periodic solutions with spatio-temporal symmetries of functional differential equations (FDEs). The two main results are: (1) a centre manifold reduction around a periodic solution of FDEs with spatio-temporal symmetries, and (2) symmetry-breaking bifurcations for symmetric rings of delay-coupled lasers. For the case of ODEs, symmetry-breaking bifurcations from periodic solutions has already been studied. We extend this result to the case of symmetric FDEs using a Centre Manifold Theorem for symmetric FDEs which reduces FDEs into ODEs on an integral manifold around a periodic solution. We show that the integral manifold is invariant under the spatio-temporal symmetries which guarantees that the symmetry structure of the system of FDEs is preserved by this reduction. We also consider a problem in rings of delay-coupled lasers modeled using the Lang-Kobayashi rate equations. We classify the symmetry of bifurcating branches of solutions from steady-state and Hopf bifurcations that occur in 3-laser systems. This involves finding isotropy subgroups of the symmetry group of the system, and then using the Equivariant Branching Lemma and the Equivariant Hopf Theorem. We then utilize this result to find the bifurcating branches of solutions in DDE-Biftool. Symmetry often causes eigenvalues to have multiplicity, and in some cases, this could lead DDE-Biftool to incorrectly predict the bifurcation points. We address this issue by developing a method of finding bifurcation points which can be used for the general case of n-laser systems with unidirectional and bidirectional coupling. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2012-04-30 11:25:01.011

Th.--Sci. phys.--Paris 6, 1978.

abstract: There has been a lot of work on the characterization of capacity and achievable rate regions, and rate region outer-bounds for various multi-user channels of interest. Parallel to the developed information theoretic results, practical codes have also been designed for some multi-user channels such as multiple access channels, broadcast channels and relay channels; however, interference channels have not received much attention and only a limited amount of work has been conducted on them. With this motivation, in this dissertation, design of practical and implementable channel codes is studied focusing on multi-user channels with special emphasis on interference channels; in particular, irregular low-density-parity-check codes are exploited for a variety of cases and trellis based codes for short block length designs are performed. Novel code design approaches are first studied for the two-user Gaussian multiple access channel. Exploiting Gaussian mixture approximation, new methods are proposed wherein the optimized codes are shown to improve upon the available designs and off-the-shelf point-to-point codes applied to the multiple access channel scenario. The code design is then examined for the two-user Gaussian interference channel implementing the Han-Kobayashi encoding and decoding strategy. Compared with the point-to-point codes, the newly designed codes consistently offer better performance. Parallel to this work, code design is explored for the discrete memoryless interference channels wherein the channel inputs and outputs are taken from a finite alphabet and it is demonstrated that the designed codes are superior to the single user codes used with time sharing. Finally, the code design principles are also investigated for the two-user Gaussian interference channel employing trellis-based codes with short block lengths for the case of strong and mixed interference levels. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2015

What do we mean by “seeing”? Although we may see the same object in front of us, we each consciously or unconsciously select what we wish to see, eliminating information we find unnecessary. An artist or poet can see in even a tiny flower, which others barely notice, a wealth of colors or countless words. How then do our own eyes and those of others differ? This thesis aims to explore how the act of seeing shapes one’s life and influences it through a consideration of the works of Kobayashi Hideo 小林秀雄 (1902-1983), a literary critic in modern Japan. In 1949 Kobayashi published a long essay entitled “Watakushi no jinseikan” 私の人生観(My View of Life), originally given as a speech in 1948 when he was forty-six years old. In this work Kobayashi analyzes the word kan 観 (vision) with reference to more than forty historical figures from both the West and the East. The thesis selects for discussion two of these in particular, namely Miyamoto Musashi 宮本武蔵(1584-1645), a Japanese warrior of the early Edo era, and Henri Bergson (1859-1941), a major French philosopher of the twentieth century upon whom Kobayashi places special significance. While the primary focus is on interpreting this speech of Kobayashi’s, the thesis also discusses his earlier and later works in order to show the various transitions his philosophy went through over the course of his long career. The strong belief to which Kobayashi held on throughout his life as a literary critic is that the only way to see the essence of any object is to reject all rational and analytical interpretation and instead to unite one’s self with the objects: this was the ultimate approach that Kobayashi adopted in order to understand the word kan. This thesis finally addresses the question of whether this vision enabled Kobayashi to achieve his potential as a critic and as an individual.

Soit $M$ une variété projective lisse. Soit $\mathscr{F}$ une filtration holomorphe sur $M$, c'est à dire une filtration d'un fibré vectoriel holomorphe $\mathcal{F}$ induite par des sous-fibrés. Nous introduisons une notion de Gieseker stabilité pour de tels objets puis donnons une condition analytique équivalente en terme de métriques sur $\mathcal{F}$, dites équilibrées au sens de S.K. Donaldson, provenant d'une construction de la Théorie des Invariants Géométriques. Si le fibré $\mathcal{F}$ peut être muni d'une métrique $h$ solution de l'équation $\boldsymbol{\tau}$-Hermite-Einstein étudiée par \'lvarez-C\'{o}nsul et Garc\'a-Prada:<br />$$\sqrt\Lambda F_h = \sum_i \widetilde_i\pi^_$$<br />alors nous prouvons que la suite de métriques équilibrées existe, converge et sa limite est, à un changement conforme, solution de l'équation précédente. De ce résultat nous déduisons, par réduction dimensionnelle, un théorème d'approximation dans le cas des équations Vortex de Bradlow ainsi que leurs généralisations aux équations couplées Vortex.

Dans le chapitre 1, nous développons le “corps d’Okounkov” pour une (1,1)-classe pseudo-effective sur une variété kählerienne compacte. Nous démontrons la formule de différentiabilité des volumes de classes grosses pour les varétés kähleriennes sur lesquelles les cônes nef modifiés et les cônes nef coı̈ncident. Par conséquent, nous démontrons l’inégalité de Morse transcendante de Demailly pour ces variétés kähleriennes particulières, y compris les surfaces kähleriennes. Ensuite, nous construisons le corps d’Okounkov généralisé pour toute (1,1)-classe grosse, et nous donnons une caractérisation complète des corps d’Okounkov généralisés sur les surfaces. Nous démontrons que cela se rapporte le volume euclidien standard du corps au volume de la classe grosse correspondant défini par Boucksom, ce qui permet de résoudre un problème proposé par Lazarsfeld et Mustaţă dans le cas des surfaces. Nous étudions aussi le comportement des corps d’Okounkov généralisé sur le bord du cône gros.Dans le chapitre 2, nous étudions la dégénérescence des courbes entières qui sont les feuilles de feuilletages sur des variétés projectives. Nous généralisons l’approximation diophantienne de McQuillan pour les feuilletages de dimension 1 avec des singularités absolument isolées. Comme une application, nous donnons une nouvelle preuve du théorème de Brunella, c’est-à-dire, toutes les feuilles d’un feuilletage générique de degré superieur à 2 dans CP^n est hyperbolique. Ensuite, nous introduisons la notion singularités faiblement réduites pour les feuilletages de dimension 1. L’hypothèse de singularités faiblement réduites est moins exigeante que celle de singularités réduites, mais joue le même rôle dans l’étude de la conjecture de Green-Griffiths-Lang. Finalement, nous discutons d’une stratégie pour démontrer cette conjecture pour les surfaces complexes.Dans le chapitre 3, nous démontrons la non-dégénérescence de la mesure de volume au sens de Kobayashi-Eisenman pour une variété dirigée singulière, c’est-à-dire l’hyperbolicité de la mesure au sens de Kobayashi, lorsque le faisceau canonique est gros au sens de Demailly.Dans le chapitre 4, notre premier objectif est de traiter des questions d’effitivité liées aux conjectures de Kobayashi et Debarre, reliant sur le travail de Brotbek et celui en collaboration avec Darondeau. Ensuite, nous combinons ces techniques pour étudier la conjecture sur l’amplitude des fibrés de Demailly-Semple proposés par Diverio et Trapani, et nous obtenons des estimations effectives liées à ce problème. Notre résultat contient à la fois les conjectures de Kobayashi et Debarre, avec certaines estimations effectives.Le but du chapitre 5 est double: d’une part, nous étudions une conjecture du type Fujita proposée par Popa et Schnell, et nous donnons une borne effective linéaire sur la génération globale générique de l’image directe du faisceau pluricanonique tordu. Nous signalons également la relation entre la constante de Seshadri et la borne optimale. D’autre part, nous donnons une réponse affirmative à une question de Demailly-Peternell-Schneider dans un cadre plus général. Comme des applications, nous généralisons les théorèmes de Fujino et Gongyo sur les images des variétés de Fano faibles aux cas KLT, et nous raffinons un résultat de Broustet et Pacienza sur la connexité rationnelle de l’image.Dans le chapitre 6, nous donnons une preuve concrète et constructive de l’équivalence entre la catégorie de fibrés de Higgs semistables de classes de Chern nulles, et celle des représentations linéaires du groupe fondamental d’une variété kählerienne compacte lisse. / In Part 1 of this thesis, we construct “Okounkov bodies” for an arbitrary pseudo-effective (1,1-class on a Kähler manifold. We prove the differentiability formula of volumes of big classes for Kähler manifolds on which modified nef cones and nef cones coincide. As a consequence we prove Demailly’s transcendental Morse inequality for these particular Kähler manifolds; this includes Kähler surfaces. Then we construct the generalized Okounkov body for any big (1,1)-class, and give a complete characterization of generalized Okounkov bodies on surfaces. We show that this relates the standard Euclidean volume of the body to the volume of the corresponding big class as defined by Boucksom; this solves a problem raised by Lazarsfeld and Mustaţă in the case of surfaces. We also study the behavior of the generalized Okounkov bodies on theboundary of the big cone.Part 2 deals with Kobayashi hyperbolicity-related problems. Chapter 2’s goal is to study the degeneracy of leaves of the one-dimensional foliations on higher dimensional manifolds. The first part of Chapter 2 generalizes McQuillan’s Diophantine approximations for one-dimensional foliations with absolutely isolated singularities, on higher dimensional manifolds. As an application, we give a new proof of Brunella’s hyperbolicity theorem, that is, all the leaves of a generic foliation of degree larger than 2 in CP 6n is hyperbolic. In the second part of Chapter 2 we introduce the so-called weakly reduced singularities for one-dimensional foliations on higher dimensional manifolds. The “weakly reduced singularities” assumption is less demanding than the one required for “reduced singularities”, but play the same role in studying the Green-Griffiths-Lang conjecture. Finally we discuss a strategy to prove the Green-Griffiths-Lang conjecture for complex surfaces.In Chapter 3, assuming that the canonical sheaf is big in the sense of Demailly, we prove theKobayashi volume-hyperbolicity for any (possibly singular) directed variety.In Chapter 4, our first goal is to deal with effective questions related to the Kobayashi and Debarre conjectures, relying on the work of Brotbek and his joint work with Darondeau. We then combine these techniques to study the conjecture on the ampleness of the Demailly-Semple bundles raised by Diverio and Trapani, and also obtain some effective estimates related to this problem. Our result integrates both the Kobayashi and Debarre conjectures, with some effective estimates.The purpose of Chapter 5 is twofold: on the one hand we study a Fujita-type conjecture by Popa and Schnell, and give an effective (linear) bound on the generic global generation of the direct image of the twisted pluricanonical bundle. We also point out the relation between the Seshadri constant and the optimal bound. On the other hand, we give an affirmative answer to a question by Demailly-Peternell-Schneider in a more general setting. As applications, we generalize the theorems by Fujino and Gongyo on images of weak Fano manifolds to the Kawamata log terminal cases, and refine a result by Broustet and Pacienza on the rational connectedness of the image.In Chapter 6, we give a concrete and constructive proof of the equivalence between the category of semistable Higgs bundles with vanishing Chern classes and the category of all representations of the fundamental groups on smooth Kähler manifolds. This chapter is written for the complex geometers who are not familiar with the language of differential graded category used by Simpson to prove the above equivalence on smooth projective manifolds, and for those who would like to see an elementary proof of Corlette-Simpson correspondence for semistable Higgs bundles.

No description available.

Further investigations intending illucidate the mechanism of a newly discovered redox-alkylation reaction of azo dyes are presented. Preliminary results indicate that this reaction most probably proceeds via initial N-alkylation of the anion derived from an alpha-ketohydrazone. An investigation is continued to study the synthesis of macrocycle-carbohydrate-dye hybrids. The development of a modular approach to macrocycle assembly has enabled the synthesis of a library of pyridine-based macrocycles possessing multiple donor sites. A central dye scaffold, prepared from the SNAr reaction between halo-substituted azo dye and a disubstituted phenol, was decorated with a representative carbohydrate or macrocycle using Sharpless click chemistry. Also an "S3N-ligand azo-dye" conjugate has been synthesised with a view to the development of a sensor for heavy metal ions. Complexation of this system with Ag(I), Hg(II) and Cu(II) salts has been investigated. Complexation of the dye to metals results in a bathochromic shift in the absorption maximum of the azo dye, an effect which is most pronounced for Cu(II).The Kobayashi fragmentation has transformed the area of benzyne chemistry as it enables its generation from readily available precursors under mild reaction conditions. The controlled generation of benzyne in this manner has been utilised by many groups, allowing readily access to a variety of functionalised aromatic and heteroaromatic from simple precursors. During the course of a synthetic project, which was to utilise the Kobayashi fragmentation in a key intramolecular Diels-Alder reaction, we noticed that alternate modes of fragmentation/rearrangement accompanied the desired elimination reaction leading to benzyne generation. In particular, competing Fries or Smiles rearrangements became the major routes of fragmentation in appropriately functionalised substrates. The results of an investigation into the factors affecting the course of the Kobayashi fragmentation, together with the development of a novel bi-aryl synthesis are presented in this thesis.