Tez (Yüksek Lisans) - Süleyman Demirel Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, 2009. / Kaynakça var.

Ramsey Theorem, in the most simple form, states that if we are given a positive integer l, there exists a minimal integer r(l), called the Ramsey number, such any partition of the edges of K_r(l) into two sets, i.e. a 2-coloring, yields a copy of K_l contained entirely in one of the partitioned sets, i.e. a monochromatic copy of Kl. We prove an extension of Ramsey's Theorem, in the more general form, by replacing complete graphs by multipartite graphs in both senses, as the partitioned set and as the desired monochromatic graph. More formally, given integers l and k, there exists an integer p(m) such that any 2-coloring of the edges of the complete multipartite graph K_p(m);r(k) yields a monochromatic copy of K_m;k . The tools that are used to prove this result are the Szemeredi Regularity Lemma and the Blow Up Lemma. A full proof of the Regularity Lemma is given. The Blow-Up Lemma is merely stated, but other graph embedding results are given. It is also shown that certain embedding conditions on classes of graphs, namely (f , ?) -embeddability, provides a method to bound the order of the multipartite Ramsey numbers on the graphs. This provides a method to prove that a large class of graphs, including trees, graphs of bounded degree, and planar graphs, has a linear bound, in terms of the number of vertices, on the multipartite Ramsey number.

The system of the four partial fluxions of the primary row of differential equations the row of which dwindles at the points of plane has been analysed. The systems of the expressions of families of the detached solutions have been derived by converging degree rows at the environment of malformation rows through the technique of summation of degree rows. The solutions at the malformation points are particular for having degree particularities. Still, the particularities depend on the other to variables, in conformity to which there are no system malformation weigh. The effect is not evident in the analytical theory of malformed vulgar differential equation.

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

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Made available in DSpace on 2016-03-15T19:42:13Z (GMT). No. of bitstreams: 1 Eduardo de Campos Garcia.pdf: 4355839 bytes, checksum: d7931e9f63f1a4de4ab0adace65dab1f (MD5) Previous issue date: 2011-12-09 / This Master's thesis work aims to uncover the power and knowledge involved in the formation of the concept, which is on the scene of disability. Investigate the word disability, considering it as a fossilized object, and its use in history by the ideological apparatus of the state as school and cinema. Describe and analyze how people relate to the word disability in contemporary society. Therefore, its theoretical framework, among others, Michel Foucault, Flusser and George Canguilhem. To conclude this dissertation shows that the concept of disability as a negative value and synonymous deficit is rooted in knowledge and clinical and judicial powers and that some ideological apparatus of the state, such as school and film, produce and reinforce the disability as something negative. About how some people relate to the concept of disability, the research shows that the blind, wheelchair, hydrocephalus, and do not consider themselves deaf or disabled person would call themselves, although this brand, person with disabilities has been placed on the scene by the school. The paper also points out that in contemporary times, some teachers in the state of São Paulo, but bring with them a certain doubt about what disability is and what it means, still consider it a negative state of life and behavior, a specialty to be resolved by medicine. / Esta dissertação de Mestrado tem como objetivo de trabalho desvelar os poderes e saberes envolvidos na formação do conceito, que está em cena, da deficiência. Investigar a palavra deficiência, considerando-a como um objeto fossilizado, e seu uso na história pelos aparelhos ideológicos do estado como escola e cinema. Descrever e analisar como as pessoas relacionam-se com a palavra deficiência na contemporaneidade. Para tanto, toma como referencial teórico, entre outros, Michel Foucault, Vilém Flusser e George Canguilhem. Como conclusão esta dissertação de mestrado aponta que o conceito de deficiência como um valor negativo e sinônimo de déficit tem sua raiz nos saberes e poderes clínicos e judiciário e que alguns aparelhos ideológicos do estado, tais como a escola e o cinema, produzem e reforçam a deficiência como algo negativo. Sobre o modo como algumas pessoas se relacionam com o conceito de deficiência, a pesquisa aponta que cegos, cadeirantes, hidrocefálicos, surdos não se consideram e nem se autodeclaram pessoa com deficiência, muito embora essa marca, pessoa com deficiência, tenha sido colocada em cena pela escola. A dissertação aponta também que na contemporaneidade, alguns professores do estado de São Paulo, embora tragam consigo uma certa dúvida sobre o que é a deficiência e o que ela significa, ainda a consideram um estado negativo de vida e comportamento, uma especialidade a ser resolvida pela medicina.

Systems of quasilinear partial differential equations of the first order, known as hydrodynamic type systems, are one of the most important classes of nonlinear partial differential equations in the modern theory of integrable systems. They naturally arise in continuum mechanics and in a wide range of applications, both in pure and applied mathematics. Deep connections between the mathematical theory of hydrodynamic type systems with differential geometry, firstly revealed by Riemann in the nineteenth century, have been thoroughly investigated in the eighties by Dubrovin and Novikov. They introduced and studied a class of Poisson structures generated by a flat pseudo-Riemannian metric, called first-order Poisson brackets of hydrodynamic type. Subsequently, these structures have been generalised in a whole variety of different ways: degenerate, non-homogeneous, higher order, multi-dimensional, and non-local. The first part of this thesis is devoted to the classification of such structures in two dimensions, both non-degenerate and degenerate. Complete lists of such structures are provided for a small number of components, as well as partial results in the multi-component non-degenerate case. In the second part of the thesis we deal with deformations of Poisson structures of hydrodynamic type. The deformation theory of Poisson structures is of great interest in the theory of integrable systems, and also plays a key role in the theory of Frobenius manifolds. In particular, we investigate deformations of two classes of structures of hydrodynamic type: degenerate one-dimensional Poisson brackets and non-semisimple bi-Hamiltonian structures associated with Balinskii-Novikov algebras. Complete classification of second-order deformations are presented for two-component structures.

This dissertation presents experimental and theoretical studies of transient degenerate four wave mixing (DFWM) in organic dyes. Chapter 1 is an introduction to DFWM. Chapter 2 describes DFWM experiments that were performed in the gain medium of a dye laser. Chapter 3 presents the theory of DFWM of short pulses in three level saturable media. Chapter 4 presents DFWM experiments of femtosecond pulses in the saturable absorber of a passively modelocked ring dye laser. Chapter 5 presents the theory of DFWM of ultrashort pulses in resonant media.

The present thesis is divided into two parts. Part I is devoted to the study of Gribov ambiguity in gauge systems and its relation with the appearance of degeneracies in the symplectic structure of the corresponding reduced phase space after gauge fixation. Part II is concerned with classical dual field theories for three-dimensional Einstein gravity and the symplectic structure on coadjoint orbits of the corresponding asymptotic symmetry group.In Part I, the Gribov problem is studied in the context of finite temperature QCD and the structure of the gluon propagator is analyzed. The standard confined scenario is found for low temperatures, while for high enough temperatures deconfinement takes place and a free gluon propagator is obtained. Subsequently, the relation between Gribov ambiguity and degeneracies in the symplectic structure of gauge systems is analyzed. It is shown that, in finite-dimensional systems, the presence of Gribov ambiguities in regular constrained systems always leads to a degenerate symplectic form upon Dirac reduction. The implications for the Gribov-Zwanziger approach to QCD and the symplectic structure of the theory are discussed. In Part II, geometrical actions for three-dimensional Einstein gravity are constructed by studying the symplectic structure on coadjoint orbits of the asymptotic symmetry group. The geometrical action coming from the Kirillov-Kostant symplectic form on coadjoint orbits is analyzed thought Dirac's algorithm for constrained systems. By studying the case of centrally extended groups and semi-direct products, the symplectic structure on coadjoint orbits of the Virasoro and the BMS3 group are analyzed. This allows one to associate separate geometric actions to each coadjoint orbit of the solution space, leading to two-dimensional dual fiel theories for asymptotically AdS and asymptotically flat three-dimensional gravity respectively. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20161号 / 理博第4246号 / 新制||理||1611(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 高橋 義朗, 教授 田中 耕一郎, 教授 川上 則雄 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM