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Дисертації з теми "Differential graded Lie algebras"

Автор: Grafiati
Опубліковано: 10 березня 2023

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1

Fialowski, Alice, Michael Penkava, and fialowsk@cs elte hu. "Deformation Theory of Infinity Algebras." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi906.ps.

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2

Yaseen, Hogar M. "Generalized root graded Lie algebras." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/42765.

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Анотація:
Let g be a non-zero finite-dimensional split semisimple Lie algebra with root system Δ. Let Γ be a finite set of integral weights of g containing Δ and {0}. We say that a Lie algebra L over F is generalized root graded, or more exactly (Γ,g)-graded, if L contains a semisimple subalgebra isomorphic to g, the g-module L is the direct sum of its weight subspaces Lα (α ∈ Γ) and L is generated by all Lα with α ̸= 0 as a Lie algebra. If g is the split simple Lie algebra and Γ = Δ∪{0} then L is said to be root-graded. Let g∼= sln and Θn = {0,±εi±ε j,±εi,±2εi | 1 ≤ i ̸= j ≤ n} where {ε1, . . . , εn} i
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3

at, Andreas Cap@esi ac. "Graded Lie Algebras and Dynamical Systems." ESI preprints, 2001. ftp://ftp.esi.ac.at/pub/Preprints/esi1086.ps.

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4

Yang, Qunfeng. "Some graded Lie algebra structures associated with Lie algebras and Lie algebroids." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape9/PQDD_0007/NQ41350.pdf.

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5

Bagnoli, Lucia. "Z-graded Lie superalgebras." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14118/.

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Анотація:
This thesis investigates the role of filtrations and gradings in the study of Lie superalgebras. The main connections between the Z-grading of a Lie superalgebra and its structure are explained. As an example, the simplicity of the Lie superalgebras W(m,n) and S(m,n) is proved. Finally, the strongly symmetric gradings of length three and five of the Lie superalgebras W(m,n) and S(m,n) are classified.
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6

Pauksztello, David. "Homological properties of differential graded algebras." Thesis, University of Leeds, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.493288.

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Анотація:
In this thesis we consider various homological properties of differential graded algebras, and more generally, properties of arbitrary triangulated categories which have set indexed coproducts. A major example of such a triangulated category is the derived category of a differential graded algebra. We present the background material to the theory of triangulated categories, derived categories and differential graded algebras as well as a brief resume of classical homological algebra in Chapters 2 and 3.
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7

Shklyarov, Dmytro. "Hirzebruch-Riemann-Roch theorem for differential graded algebras." Diss., Manhattan, Kan. : Kansas State University, 2009. http://hdl.handle.net/2097/1381.

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8

Maycock, Daniel. "Properties of triangular matrix and Gorenstein differential graded algebras." Thesis, University of Newcastle upon Tyne, 2011. http://hdl.handle.net/10443/1359.

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Анотація:
The main goal of this thesis is to investigate properties of two types of Differential Graded Algebras (or DGAs), namely upper triangular matrix DGAs and Gorenstein DGAs. In doing so we extend a number of corresponding ring theory results to the more general setting of DGAs and DG modules. Chapters 2 and 3 contain background material. In chapter 2 we give a brief summary of some important aspects of homological algebra. Starting with the definition of an abelian category we give the construction of the derived category and the definition of derived functors. In chapter 3 we present the basics
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9

Chung, Myungsuk. "Lie derivations on rings of differential operators." Diss., Virginia Tech, 1995. http://hdl.handle.net/10919/37457.

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10

Martini, Alessio. "Algebras of differential operators on Lie groups and spectral multipliers." Doctoral thesis, Scuola Normale Superiore, 2010. http://hdl.handle.net/11384/85663.

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Анотація:
Let (X, μ) be a measure space, and let L1, . . . ,Ln be (possibly unbounded) selfadjoint operators on L2(X, μ), which commute strongly pairwise, i.e., which admit a joint spectral resolution E on Rn. A joint functional calculus is then defined via spectral integration: for every Borel function m : Rn → C, m(L) = m(L1, . . . ,Ln) = ∫ Rn m(λ) dE(λ) is a normal operator on L2(X, μ), which is bounded if and only if m - called the joint spectral multiplier associated to m(L) - is (E-essentially) bounded. However, the abstract theory of spectral integrals does not tackle the following probl
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11

Dolan, Peter. "A Z2-graded generalization of Kostant's version of the Bott-Borel-Weil theorem /." view abstract or download file of text, 2007. http://proquest.umi.com/pqdweb?did=1400959341&sid=2&Fmt=2&clientId=11238&RQT=309&VName=PQD.

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Анотація:
Thesis (Ph. D.)--University of Oregon, 2007.<br>Typescript. Includes vita and abstract. Includes bibliographical references (leaves 130-131). Also available for download via the World Wide Web; free to University of Oregon users.
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12

Gover, Ashwin Roderick. "A geometrical construction of conformally invariant differential operators." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329953.

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13

Hansen, Nils Bahne [Verfasser]. "Structure Analysis of the Pohlmeyer-Rehren Lie Algebra and Adaptations of the Hall Algorithm to Non-Free Graded Lie Algebras / Nils Bahne Hansen." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2021. http://d-nb.info/1236401646/34.

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14

Lavau, Sylvain. "Lie infini-algébroides et feuilletages singuliers." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSE1215/document.

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Анотація:
On dit qu'une variété est feuilletée lorsqu'il existe une partition de celle-ci en sous-variétés immergées. La théorie des feuilletages a des applications très profondes dans divers champs des Mathématiques et de la Physique, et il semble d'autant plus intéressant de pouvoir analyser le feuilletage à partir de ce qui semble être une donnée plus fondamentale : sa distribution de champs de vecteurs associée. C'est ainsi que nous avons observé que si le feuilletage est résolu par un fibré gradué, on peut relever le crochet de Lie des champs de vecteurs en une structure de Lie infini-algébroide su
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15

Souza, Manuela da Silva 1985. "Propriedade de Specht e crescimento das identidades polinomiais graduadas de sl_2." [s.n.], 2013. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306362.

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Анотація:
Orientador: Plamen Emilov Kochloukov<br>Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica<br>Made available in DSpace on 2018-08-22T00:36:15Z (GMT). No. of bitstreams: 1 Souza_ManueladaSilva_D.pdf: 983599 bytes, checksum: c9cf8976bde9d56083976fba17e385d9 (MD5) Previous issue date: 2013<br>Resumo: O resumo poderá ser visualizado no texto completo da tese digital<br>Abstract: The abstract is available with the full electronic document<br>Doutorado<br>Matematica<br>Doutora em Matemática
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16

Sánchez, Jesús. "About E-infinity-structures in L-algebras." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC204/document.

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Анотація:
Dans cette thèse nous rappelons la notion de L-algèbre, qui a pour objet d'être un modèle algébrique des types d'homotopie. L'objectif principal de cette thèse est la description d'une structure de E-infini-coalgèbre sur l'élément principal d'une L-algèbre. Ceci peut être vu comme une généralisation de la structure de E-infini-coalgèbre sur le complexe des chaînes d'un ensemble simplicial, telle que décrite par Smith dans Iterating the cobar construction, 1994. Nous construisons une E-infini-opérade, notée K, utilisée pour construire la E-infini-coalgèbre sur l'élément principal d'une L-algèbr
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17

Sene, Renato Tolentino de. "Curvaturas de métricas invariantes em Grupos de Lie." Universidade Federal de Uberlândia, 2015. https://repositorio.ufu.br/handle/123456789/16821.

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Анотація:
In this work we study the geometric aspects of Lie groups from the view point of the Riemannian geometry, by means of invariant geometric structures associated. We present some properties on curvatures of metrics left invariants and bi-invariant one on Lie groups. We also present a treatment of the Lie algebras unimodular, including the tridimensional case. Most of the results studied are from the article of John Milnor: Curvatures of Left Invariant Metrics on Lie Groups.<br>Neste trabalho estudamos os aspectos geometricos de grupos de Lie, do ponto de vista da geometria Riemanniana, por meio
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18

Webster, Benjamin. "On Representations of the Jacobi Group and Differential Equations." UNF Digital Commons, 2018. https://digitalcommons.unf.edu/etd/858.

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Анотація:
In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .
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19

Kunz, Daniel. "Lieovy grupy a jejich fyzikální aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417088.

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Анотація:
In this thesis I describe construction of Lie group and Lie algebra and its following usage for physical problems. To be able to construct Lie groups and Lie algebras we need define basic terms such as topological manifold, tensor algebra and differential geometry. First part of my thesis is aimed on this topic. In second part I am dealing with construction of Lie groups and algebras. Furthermore, I am showing different properties of given structures. Next I am trying to show, that there exists some connection among Lie groups and Lie algebras. In last part of this thesis is used just for show
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20

Singh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.

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Анотація:
The computation of Schrödinger equations in the semiclassical regime presents several enduring challenges due to the presence of the small semiclassical parameter. Standard approaches for solving these equations commence with spatial discretisation followed by exponentiation of the discretised Hamiltonian via exponential splittings. In this thesis we follow an alternative strategy${-}$we develop a new technique, called the symmetric Zassenhaus splitting procedure, which involves directly splitting the exponential of the undiscretised Hamiltonian. This technique allows us to design methods tha
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21

Ouzina, Mostafa. "Théorème du support en théorie du filtrage non-linéaire." Rouen, 1998. http://www.theses.fr/1998ROUES029.

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Анотація:
La thèse comporte essentiellement quatre parties. Dans la première partie, la preuve simple de A. Millet et Marta-Sanz-Sole du théorème du support de Stroock-Varadhan dans le cas indépendant du temps est étendue au cas dépendant du temps. Dans la seconde partie, soit (x#t) la solution de l'équation différentielle stochastique x#t = x + #r#i# #=# #1#t#0#i(x#s)dw#i#s + #l#j# #=# #1#t#0$$#j(x#s)odw$$#j#s + #t#0b(x#s)ds nous considérons cette solution comme fonction de w a valeurs dans l'espace l#p des fonctions de w$$ a valeurs dans l'espace des fonctions continues. Le résultat concernant le théo
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22

Rocha, Eugénio Alexandre Miguel. "Uma Abordagem Algébrica à Teoria de Controlo Não Linear." Doctoral thesis, Universidade de Aveiro, 2003. http://hdl.handle.net/10773/21444.

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Doutoramento em Matemática<br>Nesta tese de Doutoramento desenvolve-se principalmente uma abordagem algébrica à teoria de sistemas de controlo não lineares. No entanto, outros tópicos são também estudados. Os tópicos tratados são os seguidamente enunciados: fórmulas para sistemas de controlo sobre álgebras de Lie livres, estabilidade de um sistema de corpos rolantes, algoritmos para aritmética digital, e equações integrais de Fredholm não lineares. No primeiro e principal tópico estudam-se representações para as soluções de sistemas de controlo lineares no controlo. As suas trajetórias
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23

Gartz, Kaj M. "A construction of a differential graded Lie algebra in the category of effective homological motives /." 2003. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3088737.

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24

TORTORELLA, ALFONSO GIUSEPPE. "Deformations of coisotropic submanifolds in Jacobi manifolds." Doctoral thesis, 2017. http://hdl.handle.net/2158/1077777.

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In this thesis, we investigate deformation theory and moduli theory of coisotropic submanifolds in Jacobi manifolds. Originally introduced by Kirillov as local Lie algebras with one dimensional fibers, Jacobi manifolds encompass, unifying and generalizing, locally conformal symplectic manifolds, locally conformal Poisson manifolds, and non-necessarily coorientable contact manifolds. We attach an L-infinity-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), a
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25

Euler, Norbert. "Continuous symmetries, lie algebras and differential equations." Thesis, 2014. http://hdl.handle.net/10210/9131.

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Анотація:
D.Sc. (Mathematics)<br>In this thesis aspects of continuous symmetries of differential equations are studied. In particular the following aspects are studied in detail: Lie algebras, the Lie derivative, the jet bundle formalism for differential equations, Lie point and Lie-Backlund symmetry vector fields, recursion operators, conservation laws, Lax pairs, the Painlcve test, Lie algebra valued differenmtial forms and Dose operators as a representation of differential operators. The purpose of the study is to gain a better understanding of complicated nonlinear dirrerential equations that descri
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26

Donin, Dmitry. "Lie Algebras of Differential Operators and D-modules." Thesis, 2008. http://hdl.handle.net/1807/16779.

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Анотація:
In our thesis we study the algebras of differential operators in algebraic and geometric terms. We consider two problems in which the algebras of differential operators naturally arise. The first one deals with the algebraic structure of differential and pseudodifferential operators. We define the Krichever-Novikov type Lie algebras of differential operators and pseudodifferential symbols on Riemann surfaces, along with their outer derivations and central extensions. We show that the corresponding algebras of meromorphic differential operators and pseudodifferential symbols have many invariant
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27

PASQUALI, MARCO. "On the structure of Borel stable abelian subalgebras in Z2-graded Lie algebras." Doctoral thesis, 2012. http://hdl.handle.net/11573/917818.

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28

Kara, A. H. "On lie and Noether symmetries of differential equations." Thesis, 1994. https://hdl.handle.net/10539/26093.

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Анотація:
A thesis submitted to the faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Doctor of Philosophy,<br>The inverse problem in the Calculus of Variations involves determining the Lagrangians, if any, associated with a given (system of) differential equation(s). One can classify Lagrangians according to the Lie algebra of symmetries of the Action integral (the Noether algebra). We give a complete classification of first-order Lagrangians defined on the line and produce results pertaining to the dimensionality of the algebra of Noether sy
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29

Wills, Luis Alberto. "Finite group graded lie algebraic extensions and trefoil symmetric relativity, standard model, yang mills and gravity theories." Thesis, 2008. http://hdl.handle.net/10125/11725.

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Анотація:
Mode of access: World Wide Web.<br>Thesis (Ph. D.)--University of Hawaii at Manoa, 2004.<br>Includes bibliographical references (leaves 159-164).<br>Electronic reproduction.<br>Also available by subscription via World Wide Web<br>x, 164 leaves, bound ill. 29 cm
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30

Schmidt, Karsten [Verfasser]. "Auslander-Reiten theory for simply connected differential graded algebras / vorgelegt von Karsten Schmidt." 2007. http://d-nb.info/987425641/34.

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31

Bhargava, Sandeep. "Realizations of BC(r)-graded intersection matrix algebras with grading subalgebras of type B(r), r greater than or equal to 3 /." 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR45986.

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Анотація:
Thesis (Ph.D.)--York University, 2008. Graduate Programme in Mathematics and Statistics.<br>Typescript. Includes bibliographical references (leaves 275-278). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:NR45986
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32

"Applications of symmetry analysis to physically relevant differential equations." Thesis, 2005. http://hdl.handle.net/10413/2546.

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Анотація:
We investigate the role of Lie symmetries in generating solutions to differential equations that arise in particular physical systems. We first provide an overview of the Lie analysis and review the relevant symmetry analysis of differential equations in general. The Lie symmetries of some simple ordinary differential equations are found t. illustrate the general method. Then we study the properties of particular ordinary differential equations that arise in astrophysics and cosmology using the Lie analysis of differential equations. Firstly, a system of differential equations arising in the m
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33

Kohler, Astri. "Conditional and approximate symmetries for nonlinear partial differential equations." Thesis, 2014. http://hdl.handle.net/10210/11449.

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Анотація:
M.Sc.<br>In this work we concentrate on two generalizations of Lie symmetries namely conditional symmetries in the form of Q-symmetries and approximate symmetries. The theorems and definitions presented can be used to obtain exact and approximate solutions for nonlinear partial differential equations. These are then applied to various nonlinear heat and wave equations and many interesting solutions are given. Chapters 1 and 2 gives an introduction to the classical Lie approach. Chapters 3, 4 and 5 deals with conditional -, approximate -, and approximate conditional symmetries respectively. In
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34

Batistelli, Karina Haydeé. "Subálgebras de álgebra de Lie de operadores pseudo-diferenciales matriciales cuánticos y representaciones de módulos de peso máximo cuasifinitos de subálgebras de tipo ortogonal y simpléticos." Doctoral thesis, 2017. http://hdl.handle.net/11086/5845.

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Анотація:
En esta tesis caracterizamos los módulos irreducibles de peso máximo cuasifinitos de las sub\'algebras del álgebra de Lie de operadores pseudo-diferenciales matriciales cuánticos N x N. En la primer parte, se presentan los resultados que obtenidos, dando una descripción completa de las anti-involuciones que preservan la graduación principal. Obtenemos, salvo conjugación, dos familias de anti-involuciones para un cierto parámetro n con resultados diferentes cuando n=N y n En la segunda parte, nos focalizamos en el estudio de las subálgebras de tipo "ortogonal" y "simpléctico" halladas para el
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35

Mahomed, Komal Shahzadi. "Symmetry properties for first integrals." Thesis, 2015. http://hdl.handle.net/10539/16838.

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Анотація:
A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. July 2014.<br>This is the study of Lie algebraic properties of first integrals of scalar second-, third and higher-order ordinary differential equations (ODEs). The Lie algebraic classification of such differential equations is now well-known from the works of Lie [10] as well as recently Mahomed and Leach [19]. However, the algebraic properties of first integrals are not known except in the maximal cases for the basic firs
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36

Leach, Peter Gavin Lawrence. "Algebraic properties of ordinary differential equations." Thesis, 1995. http://hdl.handle.net/10413/4897.

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Анотація:
In Chapter One the theoretical basis for infinitesimal transformations is presented with particular emphasis on the central theme of this thesis which is the invariance of ordinary differential equations, and their first integrals, under infinitesimal transformations. The differential operators associated with these infinitesimal transformations constitute an algebra under the operation of taking the Lie Bracket. Some of the major results of Lie's work are recalled. The way to use the generators of symmetries to reduce the order of a differential equation and/or to find its first integrals is
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37

Moyo, Sibusiso. "Noether's theorem and first integrals of ordinary differential equations." Thesis, 1997. http://hdl.handle.net/10413/5061.

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Анотація:
The Lie theory of extended groups is a practical tool in the analysis of differential equations, particularly in the construction of solutions. A formalism of the Lie theory is given and contrasted with Noether's theorem which plays a prominent role in the analysis of differential equations derivable from a Lagrangian. The relationship between the Lie and Noether approach to differential equations is investigated. The standard separation of Lie point symmetries into Noetherian and nonNoetherian symmetries is shown to be irrelevant within the context of nonlocality. This also emphasises the rol
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38

Bashe, Mantombi Beryl. "Equivalence and symmetry groups of a nonlinear equation in plasma physics." Thesis, 2016. http://hdl.handle.net/10539/20598.

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Анотація:
Degree awarded with distinction on 6 December 1995. A research report submitted to the Faculty of Science, University of the Witwatersrand, in fulfilment of the requirements for the degree of Masters. Johannesburg, 1995.<br>In this work we give a brief overview of the existing group classification methods of partial differential equations by means of examples. On top of these methods we introduce another new method which classify according to low-dimensional Lie elgebras, One can ask: What is the aim of introducing a new method whilst there are existing methods? This question is answere
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39

Govinder, Kesh S. "Ermakov systems : a group theoretic approach." Thesis, 1993. http://hdl.handle.net/10413/5951.

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Анотація:
The physical world is, for the most part, modelled using second order ordinary differential equations. The time-dependent simple harmonic oscillator and the Ermakov-Pinney equation (which together form an Ermakov system) are two examples that jointly and separately describe many physical situations. We study Ermakov systems from the point of view of the algebraic properties of differential equations. The idea of generalised Ermakov systems is introduced and their relationship to the Lie algebra sl(2, R) is explained. We show that the 'compact' form of generalized Ermakov systems has an infinit
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40

Adams, Conny Molatlhegi. "A Lie symmetry analysis of the heat equation through modified one-parameter local point transformation." Diss., 2014. http://hdl.handle.net/10500/18414.

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Using a Lie symmetry group generator and a generalized form of Manale's formula for solving second order ordinary di erential equations, we determine new symmetries for the one and two dimensional heat equations, leading to new solutions. As an application, we test a formula resulting from this approach on thin plate heat conduction.<br>Applied Mathematics<br>M.Sc. (Applied Mathematics)
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41

Pantazi, Hara. "First integrals for the Bianchi universes : supplementation of the Noetherian integrals with first integrals obtained by using Lie symmetries." 1997. http://hdl.handle.net/10413/5103.

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42

Lemmer, Ryan Lee. "The paradigms of mechanics : a symmetry based approach." Thesis, 1996. http://hdl.handle.net/10413/4899.

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Анотація:
An overview of the historical developments of the paradigms of classical mechanics, the free particle, oscillator and the Kepler problem, is given ito (in terms of) their conserved quantities. Next, the orbits of the three paradigms are found from quadratic forms. The quadratic forms are constructed using first integrals found by the application of Poisson's theorem. The orbits are presented ito expanding surfaces defined by the quadratic forms. The Lie and Noether symmetries of the paradigms are investigated. The free particle is discussed in detail and an overview of the work done on the osc
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43

Edelstein, R. M. "A classification of second order equations via nonlocal transformations." Thesis, 2000. http://hdl.handle.net/10413/3694.

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Анотація:
The study of second order ordinary differential equations is vital given their proliferation in mechanics. The group theoretic approach devised by Lie is one of the most successful techniques available for solving these equations. However, many second order equations cannot be reduced to quadratures due to the lack of a sufficient number of point symmetries. We observe that increasing the order will result in a third order differential equation which, when reduced via an alternate symmetry, may result in a solvable second order equation. Thus the original second order equatio
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44

Ewert, Eske Ellen. "Index theory and groupoids for filtered manifolds." Doctoral thesis, 2020. http://hdl.handle.net/21.11130/00-1735-0000-0005-152D-2.

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45

Moas, Ruth Paola. "La energía de las secciones unitarias normales de la grassmanniana asociadas a productos cruz." Doctoral thesis, 2020. http://hdl.handle.net/11086/19767.

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Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.<br>Sea G(k,n) la grassmanniana de subespacios orientados de Rn de dimensión k con su métrica riemanniana canónica. Estudiamos la energía de funciones que asignan a cada P en G(k,n) un vector unitario normal a P. Son secciones de un fibrado esférico E(k,n) sobre G(k,n). Los productos cruz doble y triple octoniónicos inducen de manera natural secciones de este tipo para k=2, n=7 y k=3, n=8, respectivamente. Probamos que son aplicaciones armónicas en E(k,n) munido de la m
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