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1	Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis / Investigation of the Equations Modelling Chemical Waves Using Lie Group Analysis Nikolaishvili, George January 2012 (has links) A system of nonlinear di fferential equations, namely, the Belousov-Zhabotinskii reaction model has been investigated for nonlinear self-adjointness using the recent work of Professor N.H.Ibragimov. It is shown that the model is not nonlinearly self-adjoint. The symmetries of the system and nonlinear conservation laws are calculated. The modi fied system, which is nonlinearly self-adjoint, is also analysed. Its symmetries and conservation laws are presented. Nonlinear Self-adjointness Belousov-Zhabotinskii Reaction Model Symmetry Conservation Law
2	O teorema espectral e a propriedade de \"self-adjointness\" para alguns operadores de Schrödinger / The spectral theorem and the self-adjointness property for some Schrödinger operators Rodrigo Augusto Higo Mafra Cabral 18 December 2014 (has links) Neste texto são demonstrados, a partir do ponto de vista da teoria dos espaços de Hilbert e da teoria das C-álgebras, teoremas relacionados a operadores auto-adjuntos em espaços de Hilbert, entre os quais estão o Teorema Espectral, o teorema de Kato-Rellich e a desigualdade de Kato. Também são dadas aplicações destes teoremas a alguns operadores de Schrödinger provenientes da Física-Matemática. / In this text we prove, within the Hilbert spaces theory and C-algebras points of view, some theorems which are related to self-adjoint operators acting on Hilbert spaces, among which are the Spectral Theorem, the Kato-Rellich theorem and Kato\'s inequality. Also, some applications to Schrödinger operators coming from the Mathematical-Physics context are given. "Self-adjointness" C-álgebras Desigualdade de Kato Kato-Rellich Schrödinger Teorema Espectral C-algebras Kato's inequality Kato-Rellich Schrödinger Self-adjointness Spectral theorem
3	O teorema espectral e a propriedade de \"self-adjointness\" para alguns operadores de Schrödinger / The spectral theorem and the self-adjointness property for some Schrödinger operators Cabral, Rodrigo Augusto Higo Mafra 18 December 2014 (has links) Neste texto são demonstrados, a partir do ponto de vista da teoria dos espaços de Hilbert e da teoria das C-álgebras, teoremas relacionados a operadores auto-adjuntos em espaços de Hilbert, entre os quais estão o Teorema Espectral, o teorema de Kato-Rellich e a desigualdade de Kato. Também são dadas aplicações destes teoremas a alguns operadores de Schrödinger provenientes da Física-Matemática. / In this text we prove, within the Hilbert spaces theory and C-algebras points of view, some theorems which are related to self-adjoint operators acting on Hilbert spaces, among which are the Spectral Theorem, the Kato-Rellich theorem and Kato\'s inequality. Also, some applications to Schrödinger operators coming from the Mathematical-Physics context are given. "Self-adjointness" C-algebras C-álgebras Desigualdade de Kato Kato's inequality Kato-Rellich Kato-Rellich Schrödinger Schrödinger Self-adjointness Spectral theorem Teorema Espectral

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