Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 17 of 17 for “"quaternionic"”.
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On quaternionic line bundles
Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.
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Self maps of quaternionic projective spaces
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1997.
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Real, complex and quaternionic toric spaces
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1993.
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Spectral Properties of Quaternionic Unit Gain Cycles
… to the unit norm quaternions, we can define quaternionic unit gain graphs, or U(H)-gain graphs, as gain graphs where the domain of the gain function is the unit quaternions. Traditional methods from spectral graph theory are not directly extended to quaternionic unit gain graphs due to …
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Color Face Recognition using Quaternionic Gabor Filters
This dissertation reports the development of a technique for automated face recognition, using color images. One of the more powerful techniques for recognition of faces in monochromatic images has been extended to color by the use of hypercomplex numbers called quaternions. Two software …
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Quaternionic slice regular functions on domains without real points
In this thesis I've explored the theory of quaternionic slice regular functions. More precisely I've studied some rigidity properties, some differential issues and an application in complex differential geometry. This application concerns the constructions and classifications of orthogonal complex …
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On Loop Commutators, Quaternionic Automorphic Loops, and Related Topics
… construct a family of automorphic loops, called quaternionic automorphic loops, which have order 2<sup>n</sup> for n ≥ 3, and prove several theorems about their structure. Although quaternionic automorphic loops are nonassociative, many of their properties are reminiscent of the generalized …
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On the Necessity of Complex Numbers in Quantum Mechanics
… admits a representation in real, complex or quaternionic Hilbert spaces as established by Solèr’s theorem (1995) closing a long standing problem that can be traced back to von Neumann’s mathematical formulation of quantum mechanics. However up to now there are no examples of quantum systems …
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Localization genus of classifying spaces
… Second, we use it to study the genus of infinite quaternionic projective space. In particular, we describe spaces in the genus of infinite quaternionic projective space which occur as targets of essential maps from infinite complex projective space, and we compute explicitly the homotopy classes …
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Some Results on Vertex-Minimal Triangulations of Manifolds
… 8-manifold that has the same cohomology as the quaternionic projective plane HP2, and is conjectured to be homeomorphic to HP2.
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Computer-assisted proofs in geometry and physics
… many hitherto unknown tight regular simplices in quaternionic projective spaces and in the octonionic projective plane. We also consider regular simplices in real Grassmannians. The second application is to gravitational choreographies, i.e., periodic trajectories of point particles under …
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Standard model physics from an algebra?
… model particle representations. From the complex quaternionic portion of the algebra, we find generalized ideals, and show that they describe concisely all of the Lorentz representations of the standard model. From the complex octonionic portion of the algebra, we find minimal left ideals, and …
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Wigner functions for a class of semidirect product groups
… are discussed with emphasis on the case of the quaternionic group as a 4-dimensional wavelet group; this is a natural non-abelian extension of the known notions of wavelet groups in 1 and 2 dimensions which have extensive applications in signal analysis
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Wordline approach to higher spin fields
… sp(2) R symmetry, coupled to Hyper K¨ahler and Quaternionic-K¨ahler (QK) backgrounds.
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Robust Wireless Communications with Applications to Reconfigurable Intelligent Surfaces
… in use. I propose the use of complex-valued and quaternionic neural networks (QNN) to decode JSCC codes, where the complex-valued neural networks show a significant improvement over real-valued networks and the QNNs have an exceptionally high performance. Furthermore, I propose mapping encoded …
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On the parallels between the Maxwell and Dirac equations
… can be reformulated into closely related quaternionic equations, which directly reveal the difference in how these equations transform under Lorentz transformations. Building on this observation, we propose a possible (spin) geometry underlying both the Maxwell and Dirac equations. Within …