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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 16 of 16 for “"Geometric Algebra"”.
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Applications of Geometric Algebra in Mathematical Engineering
Geometric Algebra (GA) has found success in various areas of the physical sciences and engineering over the last decade but remains relatively underutilised in industry and several key topics in the field remain unexplored. This thesis focuses on the practical applications of Geometric Algebra in …
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Mathematical Advancements in Geometric Algebra for 3D Registration Problems
… PhD thesis investigates the reformulation of geometric registration algorithms using Geometric Algebra (GA) to solve transformation problems traditionally handled with Linear Algebra (LA). Geometric transformations play a key role in fields like robotics, computer vision and 3D modelling, as …
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Machine Learning with Geometric Algebra: Multivectors for Modelling, Understanding and Computing
Geometric Algebra (GA) has been successfully applied in several fields, including physics, graphics, and robotics, but its potential in Machine Learning (ML) and Deep Learning (DL) remains largely unexplored. This thesis addresses that gap by investigating the application of GA to a variety of ML …
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A space-time approach to quantum mechanics
… a systematic development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how …
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Second order error correction in quantum computing
… This work analyzes the proposed code using geometric algebra methods and examines the state of the system after each step in the process.
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Formalizing Clifford algebras and related constructions in the Lean theorem prover
Geometric Algebra (GA) is a mathematical framework used primarily by engineers and physicists, while theorem proving software has its background originally in computer science departments. This thesis brings the former into the language of the latter, in the more abstract setting of Clifford …
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A Theory for Wheezing in Lungs
… also developed new tools in shell theory using geometric algebra to improve our physical understanding of the self-excited oscillations observed when air flows through flexible tubes. In shell theory, the use of rotors from geometric algebra has enabled us to develop improved physical …
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Infinitesimal Models of Algebraic Theories
… a general theory of infinitesimal models of algebraic theories that provides us with a formalisation of these notions, and which is in accordance with the intuition when applied in the context of Synthetic Differential Geometry. This allows us to study well-known geometric structures and …
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Contributions to automated realtime underwater navigation
… adaptive identifier formulated using rotors in Geometric Algebra. This identifier is applied to precisely estimate the unknown alignment between a gyrocompass and Doppler velocity log, with the goal of improving realtime dead reckoning navigation. Laboratory and field results show the identifier …
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Contributions to automated realtime underwater navigation
… adaptive identifier formulated using rotors in Geometric Algebra. This identifier is applied to precisely estimate the unknown alignment between a gyrocompass and Doppler velocity log, with the goal of improving realtime dead reckoning navigation. Laboratory and field results show the identifier …
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Geometric algebras in physics: Eigenspinors and Dirac theory
… of classical relativistic physics. In Clifford's geometric algebra classical relativistic physics has a spinorial formulation that is closely related to the standard Dirac equation. The algebra of physical space, APS, gives clear insight into the quantum/classical interface. Here, APS is compared …
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Tracking and modelling motion for biomechanical analysis
… discussed within this thesis is Conformal Geometric Algebra (CGA).
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Relativistische Quantendynamik in extrem starken Laserfeldern
… den Formalismus der sogenannten Clifford-Algebra über dem 3+1-dimensionalen Minkowski-Raum, die auch als reelle Dirac- oder Raumzeit-Algebra bezeichnet wird. Die erstellten Programme basieren daher auf einer Implementierung dieser Algebra in Form einer C++-Bibliothek. Der Programmcode …