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Showing 1 to 20 of 73 for “"Lie group"”.
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Lie Group Invariance Properties of Radiation Hydrodynamics Equations
Made available in DSpace on 2017-07-06T18:38:03Z (GMT). No. of bitstreams: 3 Coggeshall_Stephen_V_PhD.pdf: 98937878 bytes, checksum: 222756a87e39c2005bab2bbf099508f3 (MD5) Coggeshall_Stephen_V_PhD_ABS.pdf: 451972 bytes, checksum: 4c84d2c1e0b39722d200ae1164d25b0a (MD5) license.txt: 4813 bytes, …
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Relative Pose Uncertainty Quantification Using Lie Group Variational Filtering
… of a variational filtering scheme founded in Lie Group theory to an autonomous rendezvous, proximity operations and docking problem. Two methodologies, a Monte Carlo approach and an Unscented Transform, for propagating uncertainty using a Lie Group Variational Filter are introduced and …
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Applications of Lie Group Methods to the Equations of Magnetohydrodynamics
… and magnetic viscosity. The knowledge of the group structure of these equations is then used to introduce similarity variables to these equations. For each choice of similarity variables, the original set of partial differential equations is transformed into a set of ordinary differential …
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Orbital varieties and unipotent representations of classical semisimple Lie group
Let G be a complex semi-simple and classical Lie group. The notion of a Lagrangian covering can be used to extend the method of polarizing a nilpotent coadjoint orbit to obtain a unitary representation of G. W. Graham and D. Vogan propose such a construction, relying on the notions of orbital …
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Lie group invariant finite-difference schemes for the neutron diffusion equation
… invariant difference approximations of the multi-group neutron diffusion equation were determined in one-dimensional slab and two-dimensional Cartesian coordinates, for multiple region problems. These invariant difference equations were defined to lie upon a cell edged mesh as opposed to the …
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Derivation of Similarith solutions for the One-Dimensional, One-Velocity Neutron Diffusion Equation Using Lie Group Transformation Theory
Made available in DSpace on 2017-07-06T18:55:28Z (GMT). No. of bitstreams: 3 Myers_William_L_MS.pdf: 26862151 bytes, checksum: fb1b194ae8d1df514a990af341ae3487 (MD5) Myers_William_L_MS_ABS.pdf: 596542 bytes, checksum: 6959b7aaf4a682d0c3b55423a0f04de3 (MD5) license.txt: 4813 bytes, checksum: …
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An Application of the Lie Group Theory of Continuous Point Transformations to the Vlasov-Maxwell Equations (Plasma Physics)
… of partial differential equations under Lie groups of continuous point transformations is employed to study the Vlasov-Maxwell equations of plasma physics. These equations are first expressed in arbitrary orthogonal, curvilinear coordinates. Their invariance properties are studied in …
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Construction of a Multi-Dimensional Lagrangian Hydrodynamics Model of a Plasma Using the Lie Group Theory of Point Transformations
The translation conservation laws were used in a two-dimensional computer simulation of the confined eddy problem to demonstrate an application of the equations. Comparison of the results produced by the code using the conservation law governing equations with previous work is limited to …
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Dual Pairs and Disconnected Reductive Groups
… invariant theory,” he introduces the notion of a Lie algebra dual pair (a pair (g₁, g₂) of reductive Lie subalgebras of a Lie algebra g such that g₁ and g₂ equal each other’s centralizers in g) and the notion of a Lie group dual pair (a pair (G₁, G₂) of reductive subgroups of a reductive Lie group …
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[rho]-compact groups as framed manifolds
… a natural way to associate to any [rho]-compact group an element of the [rho]-local stable stems, which, applied to the [rho]-completion of a compact Lie group G, coincides with the element represented by the manifold G with its left-invariant framing. To this end, we construct a d-dimensional …
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The generalized Harish-Chandra homomorphism for Hecke algebras of real reductive Lie groups
For complex reductive Lie algebras g, the classical Harish-Chandra homomorphism allows to link irreducible finite dimensional representations of g to those of certain subalgebras l. The Casselman-Osborne theorem establishes an extension of this link to infinite dimensional irreducible …
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Stochastic Geometric Mechanics and Symmetry
… to these systems are given by the action of a Lie group valued semimartingale on the deterministic solution and consequently, along directions transverse to the group orbits, these systems retain the same dynamics as their deterministic counterpart. Furthermore, we show that these systems can …
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Positive scalar curvature and Callias-type index theorems for proper actions
… on cocompact and non-cocompact manifolds with a Lie group action. The first two chapters are a short resumé of Dirac operators and index theory and form a common introduction to the papers in the appendices. Appendix A is joint work with my supervisors, Elder Professor Mathai Varghese and Dr. …
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On properties of linear control systems on Lie groups
… properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system _x0006_Σ Lie group G is defined by x' = X(x) + Σ<sup>k</sup><sub>j=1</sub> u<sub>j</sub>Y<sub>j</sub>(x), where the drift vector field X is an infinitesimal automorphism, …
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Nonstandard Methods in Lie Theory
"In this thesis, we apply model theory to Lie theory and geometric group theory. These applications of model theory come via nonstandard analysis. In Lie theory, we use nonstandard methods to prove two results. First, we give a positive solution to the local form of Hilbert's Fifth Problem, which …
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Optimal control problems on lie groups with symmetry breaking cost functions
… smooth optimal control systems that evolve on Lie groups. Pontryagin's maximum principle allows us to search for local solutions of the optimal control problem by studying an associated Hamiltonian dynamical system. When the associated Hamiltonian function possess symmetries, we can often study …
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Equivariant coherent sheaves on the nilpotent cone for complex reductive Lie groups
Let G be a connected complex reductive Lie group. We propose a certain bijection between the set of dominant integral weights of G, and the set of pairs consisting of a nilpotent coadjoint orbit and a finite-dimensional irreducible representation of the isotropy group of the orbit. A constructive …
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Laguerre functions associated to Euclidean Jordan algebras
… derived from the representations of a specific Lie algebra on L<sup>2</sup>(Ω,dμ<sub>v</sub>). This Lie algebra is the corresponding Lie algebra of the Lie group G that acts on the tube domain T(Ω)=Ω+iV, where V is the associated Euclidean Jordan algebra of Ω. The representations involved are …
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Θεωρία προσέγγισης με νόρμες του Lorentz πάνω σε ομάδες του Lie
… on functions which are defined on nilpotent Lie groups. When the heat Kernel PT(N) is defined on a general nilpotent Lie group the estimate depends on the value of T i.e. is different for small and large T, hence the need to introduce the new Lorentz spaces which are development in this …
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