Literatura académica sobre el tema "Lie Algebras Expansion"
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Artículos de revistas sobre el tema "Lie Algebras Expansion"
Rowe, D. J. y J. Carvalho. "Boson expansion of lie algebras: The fermion pair algebra". Physics Letters B 175, n.º 3 (agosto de 1986): 243–48. http://dx.doi.org/10.1016/0370-2693(86)90848-8.
Texto completoCaroca, R., N. Merino y P. Salgado. "S expansion of higher-order Lie algebras". Journal of Mathematical Physics 50, n.º 1 (enero de 2009): 013503. http://dx.doi.org/10.1063/1.3036177.
Texto completoCurry, Charles, Kurusch Ebrahimi-Fard y Brynjulf Owren. "The Magnus expansion and post-Lie algebras". Mathematics of Computation 89, n.º 326 (26 de mayo de 2020): 2785–99. http://dx.doi.org/10.1090/mcom/3541.
Texto completoNieto, L. M., J. Negro y M. Santander. "Two Dimensional Cayley-Klein Algebras Generated by Expansions". International Journal of Modern Physics A 12, n.º 01 (10 de enero de 1997): 259–64. http://dx.doi.org/10.1142/s0217751x97000384.
Texto completoYan, Wang y Yufeng Zhang. "Expansion of the Lie algebras and integrable couplings". Chaos, Solitons & Fractals 38, n.º 2 (octubre de 2008): 541–47. http://dx.doi.org/10.1016/j.chaos.2006.12.002.
Texto completoAndrianopoli, L., N. Merino, F. Nadal y M. Trigiante. "General properties of the expansion methods of Lie algebras". Journal of Physics A: Mathematical and Theoretical 46, n.º 36 (21 de agosto de 2013): 365204. http://dx.doi.org/10.1088/1751-8113/46/36/365204.
Texto completoEbrahimi-Fard, Kurusch y Dominique Manchon. "Twisted dendriform algebras and the pre-Lie Magnus expansion". Journal of Pure and Applied Algebra 215, n.º 11 (noviembre de 2011): 2615–27. http://dx.doi.org/10.1016/j.jpaa.2011.03.004.
Texto completoMencattini, Igor y Alexandre Quesney. "Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion". Communications in Algebra 49, n.º 8 (28 de marzo de 2021): 3507–33. http://dx.doi.org/10.1080/00927872.2021.1900212.
Texto completoPei, Yufeng y Jinwei Yang. "Strongly graded vertex algebras generated by vertex Lie algebras". Communications in Contemporary Mathematics 21, n.º 08 (20 de octubre de 2019): 1850069. http://dx.doi.org/10.1142/s0219199718500694.
Texto completoQuesne, C. "Boson realisations of Lie algebras and expansion of shift operators". Journal of Physics A: Mathematical and General 20, n.º 12 (21 de agosto de 1987): L753—L758. http://dx.doi.org/10.1088/0305-4470/20/12/001.
Texto completoTesis sobre el tema "Lie Algebras Expansion"
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.
Texto completoNesta 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 são representadas pelas chamadas séries de Chen. Estuda-se a representação formal destas séries através da introdução de várias álgebras não associativas e técnicas específicas de álgebras de Lie livres. Sistemas de coordenadas para estes sistemas são estudados, nomeadamente, coordenadas de primeiro tipo e de segundo tipo. Apresenta-se uma demonstração alternativa para as coordenadas de segundo tipo e obtêm-se expressões explícitas para as coordenadas de primeiro tipo. Estas últimas estão intimamente ligadas ao logaritmo da série de Chen que, por sua vez, tem fortes relações com uma fórmula designada na literatura por “continuous Baker-Campbell- Hausdorff formula”. São ainda apresentadas aplicações à teoria de funções simétricas não comutativas. É, por fim, caracterizado o mapa de monodromia de um campo de vectores não linear e periódico no tempo em relação a uma truncatura do logaritmo de Chen. No segundo tópico é estudada a estabilizabilidade de um sistema de quaisquer dois corpos que rolem um sobre o outro sem deslizar ou torcer. Constroem-se controlos fechados e dependentes do tempo que tornam a origem do sistema de dois corpos num sistema localmente assimptoticamente estável. Vários exemplos e algumas implementações em Maple°c são discutidos. No terceiro tópico, em apêndice, constroem-se algoritmos para calcular o valor de várias funções fundamentais na aritmética digital, sendo possível a sua implementação em microprocessadores. São também obtidos os seus domínios de convergência. No último tópico, também em apêndice, demonstra-se a existência e unicidade de solução para uma classe de equações integrais não lineares com atraso. O atraso tem um carácter funcional, mostrando-se ainda a diferenciabilidade no sentido de Fréchet da solução em relação à função de atraso.
In this PhD thesis several subjects are studied regarding the following topics: formulas for nonlinear control systems on free Lie algebras, stabilizability of nonlinear control systems, digital arithmetic algorithms, and nonlinear Fredholm integral equations with delay. The first and principal topic is mainly related with a problem known as the continuous Baker-Campbell-Hausdorff exponents. We propose a calculus to deal with formal nonautonomous ordinary differential equations evolving on the algebra of formal series defined on an alphabet. We introduce and connect several (non)associative algebras as Lie, shuffle, zinbiel, pre-zinbiel, chronological (pre-Lie), pre-chronological, dendriform, D-I, and I-D. Most of those notions were also introduced into the universal enveloping algebra of a free Lie algebra. We study Chen series and iterated integrals by relating them with nonlinear control systems linear in control. At the heart of all the theory of Chen series resides a zinbiel and shuffle homomorphism that allows us to construct a purely formal representation of Chen series on algebras of words. It is also given a pre-zinbiel representation of the chronological exponential, introduced by A.Agrachev and R.Gamkrelidze on the context of a tool to deal with nonlinear nonautonomous ordinary differential equations over a manifold, the so-called chronological calculus. An extensive description of that calculus is made, collecting some fragmented results on several publications. It is a fundamental tool of study along the thesis. We also present an alternative demonstration of the result of H.Sussmann about coordinates of second kind using the mentioned tools. This simple and comprehensive proof shows that coordinates of second kind are exactly the image of elements of the dual basis of a Hall basis, under the above discussed homomorphism. We obtain explicit expressions for the logarithm of Chen series and the respective coordinates of first kind, by defining several operations on a forest of leaf-labelled trees. It is the same as saying that we have an explicit formula for the functional coefficients of the Lie brackets on a continuous Baker-Campbell-Hausdorff-Dynkin formula when a Hall basis is used. We apply those formulas to relate some noncommutative symmetric functions, and we also connect the monodromy map of a time-periodic nonlinear vector field with a truncation of the Chen logarithm. On the second topic, we study any system of two bodies rolling one over the other without twisting or slipping. By using the Chen logarithm expressions, the monodromy map of a flow and Lyapunov functions, we construct time-variant controls that turn the origin of a control system linear in control into a locally asymptotically stable equilibrium point. Stabilizers for control systems whose vector fields generate a nilpotent Lie algebra with degree of nilpotency · 3 are also given. Some examples are presented and Maple°c were implemented. The third topic, on appendix, concerns the construction of efficient algorithms for Digital Arithmetic, potentially for the implementation in microprocessors. The algorithms are intended for the computation of several functions as the division, square root, sines, cosines, exponential, logarithm, etc. By using redundant number representations and methods of Lyapunov stability for discrete dynamical systems, we obtain several algorithms (that can be glued together into an algorithm for parallel execution) having the same core and selection scheme in each iteration. We also prove their domains of convergence and discuss possible extensions. The last topic, also on appendix, studies the set of solutions of a class of nonlinear Fredholm integral equations with general delay. The delay is of functional character modelled by a continuous lag function. We ensure existence and uniqueness of a continuous (positive) solution of such equation. Moreover, under additional conditions, it is obtained the Fr´echet differentiability of the solution with respect to the lag function.
Al-Kaabi, Mahdi Jasim Hasan. "Bases de monômes dans les algèbres pré-Lie libres et applications". Thesis, Clermont-Ferrand 2, 2015. http://www.theses.fr/2015CLF22599/document.
Texto completoIn this thesis, we study the concept of free pre-Lie algebra generated by a (non-empty) set. We review the construction by A. Agrachev and R. Gamkrelidze of monomial bases in free pre-Lie algebras. We describe the matrix of the monomial basis vectors in terms of the rooted trees basis exhibited by F. Chapoton and M. Livernet. Also, we show that this matrix is unipotent and we find an explicit expression for its coefficients, adapting a procedure implemented for the free magmatic algebra by K. Ebrahimi-Fard and D. Manchon. We construct a pre-Lie structure on the free Lie algebra $\mathcal{L}$(E) generated by a set E, giving an explicit presentation of $\mathcal{L}$(E) as the quotient of the free pre-Lie algebra $\mathcal{T}$^E, generated by the (non-planar) E-decorated rooted trees, by some ideal I. We study the Gröbner bases for free Lie algebras in tree version. We split the basis of E- decorated planar rooted trees into two parts O(J) and $\mathcal{T}$(J), where J is the ideal defining $\mathcal{L}$(E) as a quotient of the free magmatic algebra generated by E. Here $\mathcal{T}$(J) is the set of maximal terms of elements of J, and its complement O(J) then defines a basis of $\mathcal{L}$(E). We get one of the important results in this thesis (Theorem 3.12), on the description of the set O(J) in terms of trees. We describe monomial bases for the pre-Lie (respectively free Lie) algebra $\mathcal{L}$(E), using the procedure of Gröbner bases and the monomial basis for the free pre-Lie algebra obtained in Chapter 2. Finally, we study the so-called classical and pre-Lie Magnus expansions, discussing how we can find a recursion for the pre-Lie case which already incorporates the pre-Lie identity. We give a combinatorial vision of a numerical method proposed by S. Blanes, F. Casas, and J. Ros, on a writing of the classical Magnus expansion in $\mathcal{L}$(E), using the pre-Lie structure
Kaur, Amandeep. "Analytic and numerical aspects of isospectral flows". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/270631.
Texto completoSingh, Pranav. "High accuracy computational methods for the semiclassical Schrödinger equation". Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/274913.
Texto completoRamos, Alberto Gil Couto Pimentel. "Numerical solution of Sturm–Liouville problems via Fer streamers". Thesis, University of Cambridge, 2016. https://www.repository.cam.ac.uk/handle/1810/256997.
Texto completoLibros sobre el tema "Lie Algebras Expansion"
Tao, Terence. Expansion in finite simple groups of Lie type. Providence, Rhode Island: American Mathematical Society, 2015.
Buscar texto completoChristensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.
Buscar texto completoDzhamay, Anton, Ken'ichi Maruno y Christopher M. Ormerod. Algebraic and analytic aspects of integrable systems and painleve equations: AMS special session on algebraic and analytic aspects of integrable systems and painleve equations : January 18, 2014, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.
Buscar texto completoAlladi, Krishnaswami, Frank Garvan y Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. Providence, Rhode Island: American Mathematical Society, 2014.
Buscar texto completoEynard, Bertrand. Random matrices and loop equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0007.
Texto completoCapítulos de libros sobre el tema "Lie Algebras Expansion"
Watanabe, Yu. "Expansion of Linear Operators by Generators of Lie Algebra $$\mathfrak {su}(d)$$ su ( d )". En Formulation of Uncertainty Relation Between Error and Disturbance in Quantum Measurement by Using Quantum Estimation Theory, 45–70. Tokyo: Springer Japan, 2013. http://dx.doi.org/10.1007/978-4-431-54493-7_5.
Texto completoPierrus, J. "Static electric fields in vacuum". En Solved Problems in Classical Electromagnetism. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198821915.003.0002.
Texto completoActas de conferencias sobre el tema "Lie Algebras Expansion"
CAROCA, RICARDO, NELSON MERINO y PATRICIO SALGADO. "DUAL FORMULATION OF THE S-EXPANSION PROCEDURE FOR HIGHER ORDER LIE ALGEBRAS". En Proceedings of the MG12 Meeting on General Relativity. WORLD SCIENTIFIC, 2012. http://dx.doi.org/10.1142/9789814374552_0367.
Texto completoDi Matteo, A. "Line element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions". En AIMETA 2022. Materials Research Forum LLC, 2023. http://dx.doi.org/10.21741/9781644902431-99.
Texto completoKornhauser, Alan A. "Dynamics and Thermodynamics of a Free-Piston Expander-Compressor". En ASME 2011 International Mechanical Engineering Congress and Exposition. ASMEDC, 2011. http://dx.doi.org/10.1115/imece2011-63517.
Texto completoWang, Chung-Hao. "Cylindrically Anisotropic Tubes Containing a Line Dislocation". En ASME 2006 Pressure Vessels and Piping/ICPVT-11 Conference. ASMEDC, 2006. http://dx.doi.org/10.1115/pvp2006-icpvt-11-93188.
Texto completoSekrani, Ghofrane, Jean-Sebastien Dick, Sébastien Poncet y Sravankumar Nallamothu. "Numerical Investigation of Air-Oil Two-Phase Flow Pattern Transition in the Scavenge Line of an Aeroengine". En ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/gt2021-58988.
Texto completoAkyuzlu, K. M. y K. Hallenbeck. "A Study of Unsteady Mixed Convection in a Lid Driven Flow Inside a Rectangular Cavity". En ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-37888.
Texto completoEl Dine Matbouli, Houssam y Iyad Fayssal. "Performance Assessment of a NACA-2412 Surrogate Model Using Non-Intrusive Polynomial Chaos Method". En ASME 2020 Fluids Engineering Division Summer Meeting collocated with the ASME 2020 Heat Transfer Summer Conference and the ASME 2020 18th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/fedsm2020-20212.
Texto completoHallenbeck, K. y K. M. Akyuzlu. "A Parametric Study of Laminar Mixed Convection in a Square Cavity Using Numerical Simulation Techniques". En ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-86903.
Texto completoSurana, K. S. y H. Vijayendra Nayak. "Computations of the Numerical Solutions of Higher Class of Navier-Stokes Equations: 2D Newtonian Fluid Flow". En ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17143.
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