Submitted by Maike Costa (maiksebas@gmail.com) on 2016-03-29T13:02:55Z No. of bitstreams: 1 arquivo total.pdf: 683890 bytes, checksum: 0a793cef55b22424f093f0e99992e623 (MD5) / Made available in DSpace on 2016-03-29T13:02:55Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 683890 bytes, checksum: 0a793cef55b22424f093f0e99992e623 (MD5) Previous issue date: 2015-05-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The Dissertation study the relations between control theory, stochastic calculus and parabolic partial di erential equations. The aim is to study representations of viscosity solutions for parabolic equations via the Feynman-Kac nonlinear formulas. To this end, the control theory plays an important role in the connection between the stochastic and deterministic approaches. / A Disserta c~ao aborda algumas rela c~oes existentes entre teoria de controle, c alculo estoc astico e equa c~oes diferenciais parciais parab olicas. O interesse e estudar representa c~oes de solu c~oes de viscosidade para equa c~oes parab olicas via f ormulas de Feynman-Kac n~ao lineares. Para isso, o ferramental de teoria de controle tem papel importante na conex~ao entre a abordagem estoc astica e determin stica.

_I The theory of impulsive di&reg / erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di&reg / erential equations. In this work, higher order linear impulsive equations at &macr / xed moments of impulses together with certain boundary conditions are investigated by making use of a Green&#039 / s formula, constructed for piecewise di&reg / erentiable functions. Existence and uniqueness of solutions of such boundary value problems are also addressed. Properties of Green&#039 / s functions for higher order impulsive boundary value prob- lems are introduced, showing a striking di&reg / erence when compared to classical bound- ary value problems of ordinary di&reg / erential equations. Necessarily, instead of an or- dinary Green&#039 / s function there corresponds a sequence of Green&#039 / s functions due to impulses. Finally, as a by-product of boundary value problems, eigenvalue problems for higher order linear impulsive di&reg / erential equations are studied. The conditions for the existence of eigenvalues of linear impulsive operators are presented. Basic properties of eigensolutions of self-adjoint operators are also investigated. In particular, a necessary and su&plusmn / cient condition for the self-adjointness of Sturm-Liouville opera- tors is given. The corresponding integral equations for boundary value and eigenvalue problems are also demonstrated in the present work.

Um anel noetheriano S satisfaz a propriedade ( ) se todas as extens~oes essenciais c clicas de S-m odulos simples s~ao artinianas. An eis noetherianos com esta propriedade veri cam a Conjectura de Jacobson, que e um famoso problema em aberto em teoria de an eis. Neste trabalho investigamos esta propriedade em an eis de operadores diferenciais R[ ; ], onde R e um anel comutativo noetheriano e uma deriva c~ao de R. Mais especi camente, estudamos condi c~oes necess arias e su cientes para que R[ ; ] satisfa ca ( ), quando R e um anel -simples e, tamb em, no caso em que este e um anel -primitivo. Al em disso, caracterizamos os an eis de operadores diferenciais C[x; y][ ; ] que satisfazem ( ). / A Noetherian ring S satis es the property ( ) if any cyclic essential extension of simple S-modules are Artinian. Noetherian rings with this property verify Jacobson's Conjecture, which is a famous open problem in ring theory. In this work we investigate this property in di erential operators rings R[ ; ], where R is a commutative Noetherian ring and is a derivation of R. More precisely, we study necessary and su cient conditions for R[ ; ] to satisfy property ( ) whenever R is a -simple ring and also for the case where it is a -primitive ring. Furthermore, we characterize the di erential operator rings C[x; y][ ; ] satisfying ( ).

Um anel noetheriano S satisfaz a propriedade ( ) se todas as extens~oes essenciais c clicas de S-m odulos simples s~ao artinianas. An eis noetherianos com esta propriedade veri cam a Conjectura de Jacobson, que e um famoso problema em aberto em teoria de an eis. Neste trabalho investigamos esta propriedade em an eis de operadores diferenciais R[ ; ], onde R e um anel comutativo noetheriano e uma deriva c~ao de R. Mais especi camente, estudamos condi c~oes necess arias e su cientes para que R[ ; ] satisfa ca ( ), quando R e um anel -simples e, tamb em, no caso em que este e um anel -primitivo. Al em disso, caracterizamos os an eis de operadores diferenciais C[x; y][ ; ] que satisfazem ( ). / A Noetherian ring S satis es the property ( ) if any cyclic essential extension of simple S-modules are Artinian. Noetherian rings with this property verify Jacobson's Conjecture, which is a famous open problem in ring theory. In this work we investigate this property in di erential operators rings R[ ; ], where R is a commutative Noetherian ring and is a derivation of R. More precisely, we study necessary and su cient conditions for R[ ; ] to satisfy property ( ) whenever R is a -simple ring and also for the case where it is a -primitive ring. Furthermore, we characterize the di erential operator rings C[x; y][ ; ] satisfying ( ).

Um anel noetheriano S satisfaz a propriedade ( ) se todas as extens~oes essenciais c clicas de S-m odulos simples s~ao artinianas. An eis noetherianos com esta propriedade veri cam a Conjectura de Jacobson, que e um famoso problema em aberto em teoria de an eis. Neste trabalho investigamos esta propriedade em an eis de operadores diferenciais R[ ; ], onde R e um anel comutativo noetheriano e uma deriva c~ao de R. Mais especi camente, estudamos condi c~oes necess arias e su cientes para que R[ ; ] satisfa ca ( ), quando R e um anel -simples e, tamb em, no caso em que este e um anel -primitivo. Al em disso, caracterizamos os an eis de operadores diferenciais C[x; y][ ; ] que satisfazem ( ). / A Noetherian ring S satis es the property ( ) if any cyclic essential extension of simple S-modules are Artinian. Noetherian rings with this property verify Jacobson's Conjecture, which is a famous open problem in ring theory. In this work we investigate this property in di erential operators rings R[ ; ], where R is a commutative Noetherian ring and is a derivation of R. More precisely, we study necessary and su cient conditions for R[ ; ] to satisfy property ( ) whenever R is a -simple ring and also for the case where it is a -primitive ring. Furthermore, we characterize the di erential operator rings C[x; y][ ; ] satisfying ( ).

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics

Submitted by JÚLIO HEBER SILVA (julioheber@yahoo.com.br) on 2017-06-13T19:33:36Z No. of bitstreams: 2 Tese - Bruno Rodrigues de Freitas - 2016.pdf: 2506265 bytes, checksum: be3374b7af568ce914be02e5fa39c4ad (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-06-14T15:23:37Z (GMT) No. of bitstreams: 2 Tese - Bruno Rodrigues de Freitas - 2016.pdf: 2506265 bytes, checksum: be3374b7af568ce914be02e5fa39c4ad (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-06-14T15:23:38Z (GMT). No. of bitstreams: 2 Tese - Bruno Rodrigues de Freitas - 2016.pdf: 2506265 bytes, checksum: be3374b7af568ce914be02e5fa39c4ad (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-05-13 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / We consider a class of piecewise linear di erential systems in R3 separated by a plane and we study its global and local dynamics. More precisely, we give conditions to the existence of invariant surfaces and limit cycles, presenting the maximum number of limit cycles and characterizing these invariant surfaces. Also, we obtain results about the T-singularity obtained by a perturbation of piecewise linear di erential systems. In our approach, we use many techniques, as an extension of the theorem’s Rolle for vector fields, Theory of Sturm’s sequence, extendedcomplete Tchebyche systems and extensions of Averaging theory. / Consideramos uma classe de sistemas diferenciais lineares por partes em R3 separados por umplano e estudamos sua dinâmica global e local. Mais precisamente, damos condições para a existência de superfícies invariantes e ciclos limite, apresentando o número máximo de ciclos limite e caracterizando estas superfícies. Obtemos resultados sobre a T-singularidade obtida por uma perturbação de sistemas diferenciais lineares por partes. Em nossa abordagem, usamos várias técnicas como uma extensão do teorema de Rolle para campos, teoria da sequência de Sturm, sistemas estendidos completos de Tchebyche e extensões da teoria da Média.

Submitted by Pedro Guimarães (pedroengel@hotmail.com) on 2012-10-03T00:30:05Z No. of bitstreams: 1 Dissertação.pdf: 709819 bytes, checksum: 11a410ca7be737e1b89ed81a75cd3a0d (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2012-12-20T16:42:02Z (GMT) No. of bitstreams: 1 Dissertação.pdf: 709819 bytes, checksum: 11a410ca7be737e1b89ed81a75cd3a0d (MD5) / Made available in DSpace on 2012-12-20T16:42:10Z (GMT). No. of bitstreams: 1 Dissertação.pdf: 709819 bytes, checksum: 11a410ca7be737e1b89ed81a75cd3a0d (MD5) Previous issue date: 2012-06-29 / I present here an approach that unify a variety of derivative pricing models that consists of attaining a Partial Differential Equation(PDE) by intuitive arguments and give its solution by Feynman-Kac method as a conditinal expectation of a markovian process. The expectation is taken in a risk neutral world(or risk neutral measure) where all the assets grow at the risk free rate. I also present how to make this specific change of measure, connecting the real world to the risk neutral world, and show that the relevant element for the measure change is the market price of factor risk. When the market is complete the market price of risk is unique and when the market is incomplete there is a variety of possible prices to the market price of factor risks that satisfy no arbitrage arguments. In the latter case the parameters are usually chosen to calibrate the model to market data. / Apresento aqui uma abordagem que unifica a literatura sobre os vários modelos de apreçamento de derivativos que consiste em obter por argumentos intuitivos de não arbitragem uma Equação Diferencial Parcial(EDP) e através do método de Feynman-Kac uma solução que é representada por uma esperança condicional de um processo markoviano do preço do derivativo descontado pela taxa livre de risco. Por este resultado, temos que a esperança deve ser tomada com relação a processos que crescem à taxa livre de risco e por este motivo dizemos que a esperança é tomada em um mundo neutro ao risco(ou medida neutra ao risco). Apresento ainda como realizar uma mudança de medida pertinente que conecta o mundo real ao mundo neutro ao risco e que o elemento chave para essa mudança de medida é o preço de mercado dos fatores de risco. No caso de mercado completo o preço de mercado do fator de risco é único e no caso de mercados incompletos existe uma variedade de preços aceitáveis para os fatores de risco pelo argumento de não arbitragem. Neste último caso, os preços de mercado são geralmente escolhidos de forma a calibrar o modelo com os dados de mercado.

Philosophiae Doctor - PhD / In this thesis, we consider some nonlinear di erential models that govern unsteady magneto-hydrodynamic convective ow and mass transfer of viscous, incompressible, electrically conducting uid past a porous plate with/without heat sources. The study focusses on the e ect of a combination of a number of physical parameters (e.g., chem- ical reaction, suction, radiation, soret e ect, thermophoresis and radiation absorption) which play vital role in these models. Non-dimensionalization of these models gives us sets of di erential equations. Reliable solutions of such di erential equations can- not be obtained by standard numerical techniques. We therefore resorted to the use of the singular perturbation approaches. To proceed, each of these model problems is discretized in time by using a suitable time-stepping method and then by using a tted operator nite di erence method in spatial direction. The combined methods are then analyzed for stability and convergence. Aiming to study the robustness of the proposed numerical schemes with respect to change in the values of the key parame-ters, we present extensive numerical simulations for each of these models. Finally, we con rm theoretical results through a set of speci c numerical experiments.

A two-dimensional integrodi erential equation resulting from the use of potential harmonics expansion in the many-body Schr odinger equation is used to study ground-state properties of selected few-body nuclear systems. The equation takes into account twobody correlations in the system and is applicable to few- and many-body systems. The formulation of the equation involves the use of the Jacobi coordinates to de ne relevant global coordinates as well as the elimination of center-of-mass dependence. The form of the equation does not depend on the size of the system. Therefore, only the interaction potential is required as input. Di erent nucleon-nucleon potentials and hyperon-nucleon potentials are employed to construct the Hamiltonian of the systems. The results obtained are in good agreement with those obtained using other methods. / Physics / M.Sc. (Physics)