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Contributions to the study of nonholonomic Riemannian manifolds
- Authors: Barrett, Dennis Ian
- Date: 2017
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/7554 , vital:21272 , DOI https://doi.org/10.21504/10962/7554
- Description: In this thesis we consider nonholonomic Riemannian manifolds, and in particular, left- invariant nonholonomic Riemannian structures on Lie groups. These structures are closely related to mechanical systems with (positive definite) quadratic Lagrangians and nonholo- nomic constraints linear in velocities. In the first chapter, we review basic concepts of non- holonomic Riemannian geometry, including the left-invariant structures. We also examine the class of left-invariant structures with so-called Cartan-Schouten connections. The second chapter investigates the curvature of nonholonomic Riemannian manifolds and the Schouten and Wagner curvature tensors. The Schouten tensor is canonically associated to every non- holonomic Riemannian structure (in particular, we use it to define isometric invariants for structures on three-dimensional manifolds). By contrast, the Wagner tensor is not generally intrinsic, but can be used to characterise flat structures (i.e., those whose associated parallel transport is path-independent). The third chapter considers equivalence of nonholonomic Rie- mannian manifolds, particularly up to nonholonomic isometry. We also introduce the notion of a nonholonomic Riemannian submanifold, and investigate the conditions under which such a submanifold inherits its geometry from the enveloping space. The latter problem involves the concept of a geodesically invariant distribution, and we show it is also related to the curvature. In the last chapter we specialise to three-dimensional nonholonomic Riemannian manifolds. We consider the equivalence of such structures up to nonholonomic isometry and rescaling, and classify the left-invariant structures on the (three-dimensional) simply connected Lie groups. We also characterise the flat structures in three dimensions, and then classify the flat structures on the simply connected Lie groups. Lastly, we consider three typical examples of (left-invariant) nonholonomic Riemannian structures on three-dimensional Lie groups, two of which arise from problems in classical mechanics (viz., the Chaplygin problem and the Suslov problem). , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2017
- Full Text:
- Date Issued: 2017
- Authors: Barrett, Dennis Ian
- Date: 2017
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/7554 , vital:21272 , DOI https://doi.org/10.21504/10962/7554
- Description: In this thesis we consider nonholonomic Riemannian manifolds, and in particular, left- invariant nonholonomic Riemannian structures on Lie groups. These structures are closely related to mechanical systems with (positive definite) quadratic Lagrangians and nonholo- nomic constraints linear in velocities. In the first chapter, we review basic concepts of non- holonomic Riemannian geometry, including the left-invariant structures. We also examine the class of left-invariant structures with so-called Cartan-Schouten connections. The second chapter investigates the curvature of nonholonomic Riemannian manifolds and the Schouten and Wagner curvature tensors. The Schouten tensor is canonically associated to every non- holonomic Riemannian structure (in particular, we use it to define isometric invariants for structures on three-dimensional manifolds). By contrast, the Wagner tensor is not generally intrinsic, but can be used to characterise flat structures (i.e., those whose associated parallel transport is path-independent). The third chapter considers equivalence of nonholonomic Rie- mannian manifolds, particularly up to nonholonomic isometry. We also introduce the notion of a nonholonomic Riemannian submanifold, and investigate the conditions under which such a submanifold inherits its geometry from the enveloping space. The latter problem involves the concept of a geodesically invariant distribution, and we show it is also related to the curvature. In the last chapter we specialise to three-dimensional nonholonomic Riemannian manifolds. We consider the equivalence of such structures up to nonholonomic isometry and rescaling, and classify the left-invariant structures on the (three-dimensional) simply connected Lie groups. We also characterise the flat structures in three dimensions, and then classify the flat structures on the simply connected Lie groups. Lastly, we consider three typical examples of (left-invariant) nonholonomic Riemannian structures on three-dimensional Lie groups, two of which arise from problems in classical mechanics (viz., the Chaplygin problem and the Suslov problem). , Thesis (PhD) -- Faculty of Science, Mathematics (Pure and Applied), 2017
- Full Text:
- Date Issued: 2017
A green approach for the synthesis of symmetrical and unsymmetrical 1,2,4,5-tetraoxanes as anti-protozoal agents
- Authors: Cossa, Teresa Manuel
- Date: 2021-10-29
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/192786 , vital:45264
- Description: Thesis (PhD) -- Faculty of Science, Chemistry, 2021
- Full Text:
- Date Issued: 2021-10-29
- Authors: Cossa, Teresa Manuel
- Date: 2021-10-29
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral theses , text
- Identifier: http://hdl.handle.net/10962/192786 , vital:45264
- Description: Thesis (PhD) -- Faculty of Science, Chemistry, 2021
- Full Text:
- Date Issued: 2021-10-29
Exploring structures and beliefs underlying textbook praxis in German foreign language courses at a South African university – a social realist perspective
- Authors: Engelbrecht, Natasha
- Date: 2022-04
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral thesis , text
- Identifier: http://hdl.handle.net/10962/232657 , vital:50011 , DOI 10.21504/10962/232657
- Description: Commercial textbooks, aligned with the Common European Framework of Reference for Languages (CEFR), are prescribed in almost all undergraduate GFL courses offered at South African universities. Although providing practical relevance and quality assurance, the CEFR-level descriptors were developed for the European context. The projected relevance and appropriateness of teaching materials presently implemented in German curricula in South African higher education have been determined in Germany, not for local contexts, but for learners vaguely described as “Anfänger” (Evans, et al., 2012, p. 8) and “Erwachsene und Jugendliche ab 16 Jahren” (Hueber, 2019, p. 11), often with a focus on learning for prospective German immigrants or for the use in refugee- or immigrant integration courses. However, the textbook occupies a central position in the GFL course because of the structured grammar progression that it lends to the curriculum. The variety of resources available to lecturers (tests, worksheets, online learning platform) and students (exercises, English-German glossary, English grammar explanations) is also an asset to GFL courses. Calls for the transformation and decolonisation of higher education have prompted academic disciplines to re-evaluate the common-sense assumptions which underpin knowledge practices in their curriculum. Following a social realist perspective and an exploratory case-study approach, this study presents a critical analysis of the textbook prescribed in the German Studies 1 course at Rhodes University and student experiences of the textbook to disentangle the complex relations which cause textbook praxis and lay bare power structures and tensions in the system. , Thesis (PhD) -- Humanities, School of Languages, 2022
- Full Text:
- Date Issued: 2022-04
- Authors: Engelbrecht, Natasha
- Date: 2022-04
- Subjects: Uncatalogued
- Language: English
- Type: Doctoral thesis , text
- Identifier: http://hdl.handle.net/10962/232657 , vital:50011 , DOI 10.21504/10962/232657
- Description: Commercial textbooks, aligned with the Common European Framework of Reference for Languages (CEFR), are prescribed in almost all undergraduate GFL courses offered at South African universities. Although providing practical relevance and quality assurance, the CEFR-level descriptors were developed for the European context. The projected relevance and appropriateness of teaching materials presently implemented in German curricula in South African higher education have been determined in Germany, not for local contexts, but for learners vaguely described as “Anfänger” (Evans, et al., 2012, p. 8) and “Erwachsene und Jugendliche ab 16 Jahren” (Hueber, 2019, p. 11), often with a focus on learning for prospective German immigrants or for the use in refugee- or immigrant integration courses. However, the textbook occupies a central position in the GFL course because of the structured grammar progression that it lends to the curriculum. The variety of resources available to lecturers (tests, worksheets, online learning platform) and students (exercises, English-German glossary, English grammar explanations) is also an asset to GFL courses. Calls for the transformation and decolonisation of higher education have prompted academic disciplines to re-evaluate the common-sense assumptions which underpin knowledge practices in their curriculum. Following a social realist perspective and an exploratory case-study approach, this study presents a critical analysis of the textbook prescribed in the German Studies 1 course at Rhodes University and student experiences of the textbook to disentangle the complex relations which cause textbook praxis and lay bare power structures and tensions in the system. , Thesis (PhD) -- Humanities, School of Languages, 2022
- Full Text:
- Date Issued: 2022-04
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