Dissertations / Theses: 'Symmetry'

1

Werning, Margaret Elizabeth. "Fearful symmetry." [Ames, Iowa : Iowa State University], 2008.

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Aparício, James Monteiro. "DNA symmetry." Master's thesis, Universidade de Aveiro, 2011. http://hdl.handle.net/10773/8627.

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Mestrado em Engenharia de Computadores e Telemática
A investigação do DNA tem sido uma das áreas de investigação mais exploradas no último século. Desde a sua primeira descrição até à primeira sequência completa do genoma humano muito foi descoberto, mas ainda estamos longe de o compreender completamente. Neste trabalho tentámos explorar a ordem até à qual se verifica a existência de simetria relevante em genomas, e para esse fim, usámos um conjunto de genomas de vários organismos. Tentámos encontar relação entre os vários genomas através das características de simetria. Foram analisados três tipos de simetria: simetria inversa, simetria reversa e simetria complementar. Usámos, ainda, uma nova medida para classificar a simetria: a proporção de pares equivalentes. A natureza das operações envolvidas, o tamanho da memória e a eficiência temporal são factores a ter em conta aquando do desenvolvimento de ferramentas computacionais. Várias soluções foram exploradas tendo como objectivo minimizar a memória utilizada e minimizar o tempo de execução. Confirma-se uma tendência para a existência de simetria inversa no conjunto dos genomas usados e observou-se que existe associação entre os resultados das medidas de simetria e o tamanho dos genomas.
DNA research has been one of the most explored areas in the last century. From its first description to the first complete human genome sequence a lot has been discovered, but we are still far from fully understanding it. With this work we tried to find until which order is relevant symmetry found in genomes and for that purpose, we used several genomes of different organisms. We tried to find a relation between the various genomes by analysing their symmetry characteristics. Three types of symmetry were analysed: complementary symmetry, reverse symmetry, and inverted symmetry. Also, a new symmetry measure was used: the proportion of equivalent pairs. The nature of the operations involved, memory space and time efficiency are important factors to be considered when developing computational tools. A few different solutions are explored in order to minimize memory allocation and minimize runtimes. This work confirms a tendency for the inverted symmetry in the set of genomes used and it was also observed an association between the symmetry measure results and the size of the genomes.

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Power, Christopher. "Probabilistic symmetry reduction." Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3493/.

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Model checking is a technique used for the formal verification of concurrent systems. A major hindrance to model checking is the so-called state space explosion problem where the number of states in a model grows exponentially as variables are added. This means even trivial systems can require millions of states to define and are often too large to feasibly verify. Fortunately, models often exhibit underlying replication which can be exploited to aid in verification. Exploiting this replication is known as symmetry reduction and has yielded considerable success in non probabilistic verification. The main contribution of this thesis is to show how symmetry reduction techniques can be applied to explicit state probabilistic model checking. In probabilistic model checking the need for such techniques is particularly acute since it requires not only an exhaustive state-space exploration, but also a numerical solution phase to compute probabilities or other quantitative values. The approach we take enables the automated detection of arbitrary data and component symmetries from a probabilistic specification. We define new techniques to exploit the identified symmetry and provide efficient generation of the quotient model. We prove the correctness of our approach, and demonstrate its viability by implementing a tool to apply symmetry reduction to an explicit state model checker.

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Breda, d'Azevedo Antonio Joao. "Hypermaps and symmetry." Thesis, University of Southampton, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303114.

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Matheson, A. "Chiral symmetry breaking." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234997.

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Ismael, Jenann. "Essays on symmetry /." New York ; London : Garland, 2001. http://catalogue.bnf.fr/ark:/12148/cb388115162.

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Nivens, Ryan Andrew. "Fonts and Symmetry." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etsu-works/227.

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Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.

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Nivens, Ryan Andrew. "Fonts and Symmetry." Digital Commons @ East Tennessee State University, 2014. https://dc.etsu.edu/etsu-works/224.

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Using fonts as a context, we will analyze symmetry of fi gures. Diff erent letters and numbers will be measured, and participants will describe items that possess vertical, horizontal, and rotational symmetry. Our discussion and activity will focus on the mathematics of fonts and the presence and absence of symmetry in their design.

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Cassart, Delphine. "Optimal tests for symmetry." Doctoral thesis, Universite Libre de Bruxelles, 2007. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210693.

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Dans ce travail, nous proposons des procédures de test paramétriques et nonparamétrique localement et asymptotiquement optimales au sens de Hajek et Le Cam, pour trois modèles d'asymétrie.

La construction de modèles d'asymétrie est un sujet de recherche qui a connu un grand développement ces dernières années, et l'obtention des tests optimaux (pour trois modèles différents) est une étape essentielle en vue de leur mise en application.

Notre approche est fondée sur la théorie de Le Cam d'une part, pour obtenir les propriétés de normalité asymptotique, bases de la construction des tests paramétriques optimaux, et la théorie de Hajek d'autre part, qui, via un principe d'invariance permet d'obtenir les procédures non-paramétriques.

Nous considérons dans ce travail deux classes de distributions univariées asymétriques, l'une fondée sur un développement d'Edgeworth (décrit dans le Chapitre 1), et l'autre construite en utilisant un paramètre d'échelle différent pour les valeurs positives et négatives (le modèle de Fechner, décrit dans le Chapitre 2).

Le modèle d'asymétrie elliptique étudié dans le dernier chapitre est une généralisation multivariée du modèle du Chapitre 2.

Pour chacun de ces modèles, nous proposons de tester l'hypothèse de symétrie par rapport à un centre fixé, puis par rapport à un centre non spécifié.

Après avoir décrit le modèle pour lequel nous construisons les procédures optimales, nous obtenons la propriété de normalité locale asymptotique. A partir de ce résultat, nous sommes capable de construire les tests paramétriques localement et asymptotiquement optimaux. Ces tests ne sont toutefois valides que si la densité sous-jacente f est correctement spécifiée. Ils ont donc le mérite de déterminer les bornes d'efficacité paramétrique, mais sont difficilement applicables.

Nous adaptons donc ces tests afin de pouvoir tester les hypothèses de symétrie par rapport à un centre fixé ou non, lorsque la densité sous-jacente est considérée comme un paramètre de nuisance.

Les tests que nous obtenons restent localement et asymptotiquement optimaux sous f, mais restent valides sous une large classe de densités.

A partir des propriétés d'invariance du sous-modèle identifié par l'hypothèse nulle, nous obtenons les tests de rangs signés localement et asymptotiquement optimaux sous f, et valide sous une vaste classe de densité. Nous présentons en particulier, les tests fondés sur les scores normaux (ou tests de van der Waerden), qui sont optimaux sous des hypothèses Gaussiennes, tout en étant valides si cette hypothèse n'est pas vérifiée.

Afin de comparer les performances des tests paramétriques et non paramétriques présentés, nous calculons les efficacités asymptotiques relatives des tests non paramétriques par rapport aux tests pseudo-Gaussiens, sous une vaste classe de densités non-Gaussiennes, et nous proposons quelques simulations.
Doctorat en sciences, Orientation statistique
info:eu-repo/semantics/nonPublished

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Kiziltan, Zeynep. "Symmetry Breaking Ordering Constraints." Doctoral thesis, Uppsala : Univ., Department of Information Science, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-3991.

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Sigrist, Rachel. "Bifurcations with spherical symmetry." Thesis, University of Nottingham, 2010. http://eprints.nottingham.ac.uk/11170/.

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Bifurcations from spherically symmetric states can occur in many physical and biological systems. These include the development of a spherical ball of cells into an asymmetrical state and the buckling of a sphere under pressure. They also occur in the evolution of reaction–diffusion systems on a spherical surface and in Rayleigh–Benard convection in a spherical shell. Many of the behaviours of these systems can be explained by their underlying spherical symmetry alone. Using results from the area of mathematics known as equivariant bifurcation theory we can use group theoretical methods both to predict the symmetries of the solutions which are expected to result from bifurcations with symmetry and compute their stability. In this thesis both stationary and Hopf bifurcation with spherical symmetry are discussed. Firstly, using group theoretical techniques, the symmetries of the periodic solutions which can be found at a Hopf bifurcation with spherical symmetry are computed. This computation has been carried out previously but contains some errors which are corrected here. For one particular representation of the group of symmetries of the sphere the stability properties of the bifurcating branches of periodic solutions resulting from the Hopf bifurcation are analysed and a survey is carried out of other periodic and quasiperiodic solutions which can exist. Secondly, symmetry considerations are used to investigate the existence and stability properties of symmetric spiral patterns on the surface of a sphere which result from stationary bifurcations. It is found that in the case of the Swift–Hohenberg equation spiral patterns with one or more arms can exist and be stable on spheres of certain radii. Although one-armed spirals in the Swift–Hohenberg equation are stationary solutions, it is shown that generically one-armed spirals on spheres must drift.

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Castro, Sofia Balbina Santos Dias de. "Mode interactions with symmetry." Thesis, University of Warwick, 1993. http://wrap.warwick.ac.uk/4041/.

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This thesis deals with steady-state mode interaction problems with symmetry. We prove several results concerning problems invariant under the action of an arbitrary compact Lie group Γ. These include the existence of mixed-mode solutions and secondary Hopf bifurcations. We also consider the unfolding of the equations characterizing such problems. Where appropriate, we distinguish the case when Γ acts trivially on one of the modes. We then apply the results to the problems of the (1,3)-, (1,5)- and (1,3,5)-mode interactions with spherical symmetry. We also consider the (3,5)- and the (1,3,5)-mode interaction problems with SO(3) symmetry.

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Holtom, Paul Andrew. "Affine-invariant symmetry sets." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.367704.

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Carteret, Hilary Ann. "Symmetry and multiparticle entanglement." Thesis, University of York, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341118.

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Twigg, David Eric. "Aspects of superconformal symmetry." Thesis, University of Cambridge, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.708121.

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Linton, Carol. "Trajectory planning using symmetry." Thesis, University of Reading, 2014. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.632860.

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Trajectories of a rigid body are considered where the centre of the body is fixed or moves over any space form (that is, a sphere of any radius, the equivalent with negative curvature, and fiat 3D space). Open loop controls maintain the required trajectory. Three applications illustrate the concepts developed in the thesis. Firstly, a symmetric body moves over a sphere to any position and attitude where one torque maintains a constant rotation. The integration is achieved by specializing the double cover formulation of a rotation over any space form and by using a Lax pair consisting of the Hamiltonian and momentum vectors expressed in the same frame of reference. Secondly, an asymmetric satellite follows a planned trajectory to its target attitude. The natural rotation of an asymmetric satellite cannot be expressed analytically so two simple rotation modes are used; an eigenaxis and a spin stabilized rotation (with optimized spin rate). The profile of the angular velocity is adjusted by reparameterizing time to accelerate and stop the satellite. The controls required for this are compared with those required to maintain the planned rotation. In the final application, a search pattern of linear runs and turns is planned for an Autonomous Underwater Vehicle (AUV) which moves at an oblique angle. Thrusts and torques exerted by the AUV provide the controls to overcome drift, dissipative forces, conservative forces and to accelerate the surrounding fiuid out of the way. The latter consideration changes the effective inertia in different directions and the centre of mass of the AUV. Drift arises from the conservation of momentum and its evaluation is dependent on maintaining a constant inertia matrix along the trajectory. Dissipative forces are expressed in a generalized format applicable to other situations, such as aircraft and vehicles which do not have a preferred direction. In addition, the velocity profile is adjusted to smoothly join the linear run to the turn without coming to rest. The controls required to achieve this search pattern are determined.

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McDonald, Iain. "Symmetry in constraint programming." Thesis, University of St Andrews, 2004. http://hdl.handle.net/10023/14983.

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Constraint programming is an invaluable tool for solving many of the complex NP-complete problems that we need solutions to. These problems can be easily described as Constraint Satisfaction Problems (CSPs) and then passed to constraint solvers: complex pieces of software written to solve general CSPs efficiently. Many of the problems we need solutions to are real world problems: planning (e.g. vehicle routing), scheduling (e.g. job shop schedules) and timetabling problems (e.g. staff rotas) to name but a few. In the real world, we place structure on objects to make them easier to deal with. This manifests itself as symmetry. The symmetry in these real world problems make them easier to deal with for humans. However, they lead to a great deal of redundancy when using computational methods of problem solving. Thus, this thesis examines some of the many aspects of utilising the symmetry of CSPs to reduce the amount of computation needed by constraint solvers. In this thesis we look at the ease of use of previous symmetry breaking methods. We introduce a new and novel method of describing the symmetries of CSPs. We look at previous methods of symmetry breaking and show how we can drastically reduce their computation while still breaking all symmetry. We give the first detailed investigation into the behaviour of breaking only subsets of all symmetry. We look at how this affects the performance of constraint solvers before discovering the properties of a good symmetry. We then present an original method for choosing the best symmetries to use. Finally, we look at areas of redundant computation in constraint solvers that no other research has examined. New ways of dealing with this redundancy are proposed with results of an example implementation which improves efficiency by several orders of magnitude.

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Hewson, Paul Joseph. "Chiral symmetry in nucleons." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/chiral-symmetry-in-nucleons(bc2c5e94-1830-465e-b10c-5b7c162e7381).html.

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Chiral perturbation theory allows us to probe the low energy properties of hadrons. In this thesis we have looked at the axial coupling constant (see chapter 4) and baryon number violation (see chapter 5).We calculated the axial coupling constant up to O(p^4) using the extended on mass shell renormalisation scheme in chiral perturbation theory. We also included the decuplet as an explicit degree of freedom. To fit the free parameters in our expression we used a combination of lattice and experimental data. We found that the fourth order corrections were quite large, and we struggled to produce an acceptable fit to the data. We also saw that the running of g_{A}^{pn} with M_\pi predicted by lattice QCD and ChPT at O(p^4) do not agree well. This is likely due to a combination of finite size effects impacting the low pion mass lattice data and the chiral perturbative series converging slowly. For our work on baryon number violation we looked at determining the values of two low-energy constants that appear in the baryon violating chiral Lagrangian. To do this, we matched our expression to lattice data. Previous determinations of the parameters had been done without calculating the effect of loops, ours was the first investigation to see what impact the loop diagrams would have. We found that our determinations of the parameters were in agreement with previous results, suggesting the effect of the loops is small. We also performed a chiral extrapolation, and found that our results were in agreement with previous results that did not account for loop corrections. This suggests that the impact of higher-order corrections is not significant for this baryon-number-violating process.

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Saïbi, Tanguy. "Symmetry breaking of biofilaments." Electronic Thesis or Diss., Université de Lorraine, 2021. http://www.theses.fr/2021LORR0213.

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L'interprétation des expériences de micromanipulation de macromolécules biologiques n'a été possible que grâce au développement de la science des polymères. En effet, les théories développées en physique des polymères sont l'outil des théoriciens pour interpréter les expériences de plus en plus précises et complexes. Les macromolécules biologiques sont en général plus complexes que les polymères classiques à chaînes flexibles, car leurs motifs de base, leurs "monomères" sont très souvent eux-mêmes des macromolécules. Le modèle le plus approprié pour les biopolymères est celui de la worm-like chaine qui confère une rigidité de courbure aux filaments biologiques. En raison de sa simplicité et de son utilité dans l'interprétation des expériences de micromanipulation de macromolécules biologiques uniques, ce modèle est devenu le modèle de base de toute approche théorique de la biophysique des biofilaments. Le modèle confotronique des microtubules conduit au phénomène fondamental de rupture spontanée de symétrie qui explique comment un microtubule, un cylindre creux, peut, dans certaines circonstances, former une superhélice de la taille d'un micron. Cela nécessite un principe physique général pour le mécanisme de rupture spontanée de ces biofilaments. Dans cette thèse, nous supposons que les biofilaments, étant toujours immergés dans un milieu fluide, peuvent subir des contraintes de surface qui créent un décalage entre les propriétés élastiques de la couche de surface et du noyau. Un tel décalage conduit un filament dans un état élastique frustré. Le filament peut réduire cette frustration et minimiser son énergie élastique en adoptant une conformation courbée dans un processus de rupture de symétrie spontanée induit par un nouveau type d'instabilité élastique auto-fléchissante. Mon travail, présenté dans cette thèse, a tenté d'explorer cette nouvelle instabilité élastique dans différents modèles de biofilaments dans les deux régimes d'élasticité, linéaire et non linéaire. Les éléments de base de l'élasticité linéaire et la physique des chaînes individuelles ou en faisceaux sont présentés dans le chapitre 2. Le chapitre 3 est consacré à la théorie générale du flambage, l'idée de base de cette thèse étant liée à l'auto-flambage. Le chapitre 4 présente les propriétés physiques et biologiques des biofilaments du cytosquelette et quelques expériences clés qui soutiennent notre travail théorique. Dans le chapitre 5, j'ai essayé de revoir les notions générales d'état fondamental et de rupture de symétrie afin de les placer dans le contexte de la biophysique. Ce chapitre présente également les idées de base qui sous-tendent la théorie de la confotronique. Ce chapitre peut donner une perspective nouvelle et plus large sur la physique des biofilaments. Les trois derniers chapitres, 6 à 8, présentent mes travaux sur l'instabilité élastique et la rupture spontanée de symétrie induite par des contraintes de surface. Ce domaine de recherche m'était totalement inconnu lorsque j'ai commencé ce projet, j'ai donc décidé d'écrire une histoire qui raconte tous les sujets que j'ai appris sur la route menant aux résultats présentés ici. En tant qu'enseignant, j'ai essayé d'écrire une thèse très pédagogique avec tous les concepts nécessaires introduits au début de chaque chapitre. J'espère que, de cette manière, la thèse pourra être lue par les débutants dans ce domaine, comme je l'étais lorsque j'ai commencé
The interpretation of micromanipulation experiments of biological macromolecules has only been possible thanks to the development of polymer science. Indeed, the theories developed in polymer physics are the tool of theorists to interpret the increasingly precise and complex experiments. Biological macromolecules are in general more complex than classical polymers with flexible chains, because their basic units, their "monomers" are very often macromolecules themselves. The most appropriate model for biopolymers is the worm-like chain model that imparts bending rigidity to biological filaments. Because of its simplicity and usefulness in interpreting micromanipulation experiments of single biological macromolecules, this model has become the basic model for any theoretical approach to the biophysics of biofilaments. The confotronic model of microtubules leads to the fundamental phenomenon of spontaneous symmetry breaking that explains how a microtubule, a hollow cylinder, can, under certain circumstances, form a micron-sized superhelix. This requires a general physical principle for the mechanism of spontaneous breaking of these biofilaments. In this thesis, we assume that biofilaments, being always immersed in a fluid medium, can experience surface stresses that create a mismatch between the elastic properties of the surface layer and the core. Such a mismatch leads a filament into a frustrated elastic state. The filament can reduce this frustration and minimize its elastic energy by adopting a bent conformation in a spontaneous symmetry breaking process induced by a new type of self-bending elastic instability.My work, presented in this thesis, has attempted to explore this new elastic instability in different biofilament models in both linear and nonlinear elasticity regimes. The basic elements of linear elasticity and the physics of individual chains or bundles are presented in Chapter 2. Chapter 3 is devoted to the general theory of buckling, the basic idea of this thesis being related to self-buckling. Chapter 4 presents the physical and biological properties of cytoskeleton biofilaments and some key experiments that support our theoretical work. In Chapter 5, I have tried to review the general notions of ground state and symmetry breaking in order to place them in the context of biophysics. This chapter also introduces the basic ideas behind confotronics theory. This chapter can provide a new and broader perspective on biofilament physics. The last three chapters, 6 to 8, present my work on elastic instability and spontaneous symmetry breaking induced by surface stresses. This area of research was completely unknown to me when I started this project, so I decided to write a story that tells all the topics I learned on the way to the results presented here. As a teacher, I tried to write a very educational thesis with all the necessary concepts introduced at the beginning of each chapter. I hope that in this way the thesis can be read by beginners in this field, as I was when I started

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Jäger, Sebastian [Verfasser], and Alfred J. [Akademischer Betreuer] Meixner. "Symmetry matching excitation of rotational symmetric plasmonic nanostructures / Sebastian Jäger ; Betreuer: Alfred J. Meixner." Tübingen : Universitätsbibliothek Tübingen, 2014. http://d-nb.info/1162898399/34.

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Sydnes, Lars. "Simple mechanical Systems with Symmetry." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9616.

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We go through the basic theory of simple mehcanical systems on Riemannain manifolds with symmetry, in an attempt to understand some of the main features of configuration space reduction. As a part of this, we will look at some special cases for whom this works out well, and also indicate a direction of further development.

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Aydogdu, Oktay. "Pseudospin Symmetry And Its Applications." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12611298/index.pdf.

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The pseudospin symmetry concept is investigated by solving the Dirac equation for the exactly solvable potentials such as pseudoharmonic potential, Mie-type potential, Woods-Saxon potential and Hulthé
n plus ring-shaped potential with any spin-orbit coupling term $kappa$. Nikiforov-Uvarov Method, Asymptotic Iteration Method and functional analysis method are used in the calculations. The energy eigenvalue equations of the Dirac particles are found and the corresponding radial wave functions are presented in terms of special functions. We look for the contribution of the ring-shaped potential to the energy spectra of the Dirac particles. Particular cases of the potentials are also discussed. By considering some particular cases, our results are reduced to the well-known ones presented in the literature. In addition, by taking equal mixture of scalar and vector potentials together with tensor potential, solutions of the Dirac equation are found and then the energy splitting between the two states in the pseudospin doublets is investigated. We indicate that degeneracy between members of pseudospin doublet is removed by tensor interactions. Effects of the potential parameters on the pseudospin doublet splitting are also studied. Radial nodes structure of the Dirac spinor are presented.

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Huyal, Ulas. "Conformal Symmetry In Field Theory." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613136/index.pdf.

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In this thesis, conformal transformations in d and two dimensions and the results of conformal symmetry in classical and quantum field theories are reviewed. After investigating the conformal group and its algebra, various aspects of conformal invariance in field theories, like conserved charges, correlation functions and the Ward identities are discussed. The central charge and the Virasoro algebra are briefly touched upon.

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Jukes, Alice Claire. "On homoclinic bifurcations with symmetry." Thesis, Imperial College London, 2007. http://hdl.handle.net/10044/1/1265.

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This thesis deals with the description of solutions of symmetric dynamical systems that lie in the neighbourhood of a homoclinic or heteroclinic cycle. Homoclinic and heteroclinic cycles are the main mechanism by which complicated behaviour is known to arise in dynamical systems. A starting point for studying the consequences of the existence of homoclinic and heteroclinic cycles is to focus on non-wandering dynamics, that is, solutions that remain in the neighbourhood of such cycles, both in the phase space and in parameter space. For general vector fields, such studies have been carried out extensively. In the context of applications differential equations often possess some additional structure. In order to describe generic phenomena in such systems, it is important to take into account this structure. Symmetry is an example of such a structure, which naturally arises in many applications. The methodology used in this thesis, based on a technique introduced by X.B. Lin in 1990, yields an effective description of the dynamics near homoclinic and heteroclinic cycles in terms of solutions of a low dimensional bifurcation equation. In the presence of symmetry, the bifurcation equation naturally inherits a structure that is directly related to the symmetry properties of the original vector field. Within this framework, robust networks with time-preserving and time-reversing symmetries are described and it is shown what the non-wandering dynamics are. For generic codimension-one equivariant systems with real leading eigenvalues the non-wandering dynamics is shown to be conjugate to a topological Markov chain. The situation is more complicated in codimension-two and a novel example is given to illustrate the difficulties and interesting phenomena that occur.

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Fujihira, Takeo. "Hamiltonian Hopf bifurcation with symmetry." Thesis, Imperial College London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.444087.

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Gripaios, B. M. "Field theories with local symmetry." Thesis, University of Oxford, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.403719.

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Shrimpton, John. "Graphs, symmetry and categorical methods." Thesis, Bangor University, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.235884.

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Wissner-Gross, Zachary Daniel. "Symmetry Breaking in Neuronal Development." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10639.

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Many physical systems break symmetry in their evolution. Biophysical systems, such as cells, developing organisms, and even entire populations, are no exception. Developing neurons represent a striking example of a biophysical system that breaks symmetry: neurons cultured in vitro begin as cell bodies with several tendrils (“neurites”) growing outward. A few days later, these same neurons invariably have the same new morphology: exactly one of the neurites (the “axon”) has grown hundreds of microns in length, while the others (the “dendrites”) are much shorter and are more branched. Previous work has shown that any of the neurites can become the axon, and so neurons must break symmetry during their development. The mechanisms underlying neuronal symmetry breaking and axon specification have recently attracted attention, with multiple groups proposing biophysical models to explain the phenomena. In this thesis, we perform the first analytical comparisons of these models by conducting multiple phenotypic and morphological studies of neurite growth in developing neurons. Studying neurite dynamics is technically challenging because neurites have unpredictable morphologies. In Chapter 4, we study neurite competition and neuronal symmetry breaking in hundreds of neurons by optically patterning micron-wide stripes to which the neurons adhere, and on which they grow exactly two neurites. We then use our measurements to test the accuracy of the models in the simple case when a neuron has exactly two neurites. In Chapter 5, we no longer constrain neuronal morphology. One characteristic of symmetry breaking systems is how the system’s complexity affects the symmetry breaking. We find that a majority of the models predict that neurons with more neurites break symmetry much slower than neurons with fewer neurites. Experimentally, we find that neurons with different neurite counts break symmetry at the same rate, consistent with previous observations. We then determine why the models disagree in their predictions, and rectify the models using our own experimental data. In particular, we find that neurons with higher neurite counts have higher concentrations of key proteins involved in symmetry breaking, so that neurons, regardless of neurite count, can break symmetry at the same rate.
Physics

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Winarski, Rebecca R. "Symmetry, isotopy, and irregular covers." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51868.

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We say that a covering space of the surface S over X has the Birman--Hilden property if the subgroup of the mapping class group of X consisting of mapping classes that have representatives that lift to S embeds in the mapping class group of S modulo the group of deck transformations. We identify one necessary condition and one sufficient condition for when a covering space has this property. We give new explicit examples of irregular branched covering spaces that do not satisfy the necessary condition as well as explicit covering spaces that satisfy the sufficient condition. Our criteria are conditions on simple closed curves, and our proofs use the combinatorial topology of curves on surfaces.

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30

Mulvey, Joseph Anthony. "Symmetry methods for integrable systems." Thesis, Durham University, 1996. http://etheses.dur.ac.uk/5379/.

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This thesis discusses various properties of a number of differential equations which we will term "integrable". There are many definitions of this word, but we will confine ourselves to two possible characterisations — either an equation can be transformed by a suitable change of variables to a linear equation, or there exists an infinite number of conserved quantities associated with the equation that commute with each other via some Hamiltonian structure. Both of these definitions rely heavily on the concept of the symmetry of a differential equation, and so Chapters 1 and 2 introduce and explain this idea, based on a geometrical theory of p.d.e.s, and describe the interaction of such methods with variational calculus and Hamiltonian systems. Chapter 3 discusses a somewhat ad hoc method for solving evolution equations involving a series ansatz that reproduces well-known solutions. The method seems to be related to symmetry methods, although the precise connection is unclear. The rest of the thesis is dedicated to the so-called Universal Field Equations and related models. In Chapter 4 we look at the simplest two-dimensional cases, the Bateman and Born-lnfeld equations. By looking at their generalised symmetries and Hamiltonian structures, we can prove that these equations satisfy both the definitions of integrability mentioned above. Chapter Five contains the general argument which demonstrates the linearisability of the Bateman Universal equation by calculation of its generalised symmetries. These symmetries are helpful in analysing and generalising the Lagrangian structure of Universal equations. An example of a linearisable analogue of the Born-lnfeld equation is also included. The chapter concludes with some speculation on Hamiltoian properties.

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31

Walmsley, N. P. "Using symmetry for feature recognition." Thesis, University of Nottingham, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.282835.

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Petrie, Karen E. "Constraint programming, search and symmetry." Thesis, University of Huddersfield, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.430277.

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Melbourne, I. "Bifurcation problems with octahedral symmetry." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383295.

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Silva, Dias Ana Paula da. "Bifurcations with wreath product symmetry." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302657.

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Baines, Clare Elizabeth. "Topics in functions with symmetry." Thesis, University of Liverpool, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.343778.

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Low, David J. "Affine symmetry in general relativity." Thesis, University of Aberdeen, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386299.

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Affine vector fields in 4-dimensional Lorentz manifolds have recently been investigated in some detail by Hall and da Costa. The picture is completed in this thesis by studying the zeros of affine vector fields. Hall and da Costa show that the problem of finding affine vector fields in non-degenerately reducible 4-dimensional Lorentz manifolds can be reduced, with one exceptional case, to the problem of finding homothetic vector fields in lower dimensional manifolds. This means that the study of affine vector fields with zeros in 4-dimensional Lorentz manifolds is aided by investigating proper homothetic and Killing vector fields with zeros in 2- or 3-dimensional manifolds. To this end proper homothetic vector fields with zeros are investigated in 2- and 3-dimensional Manifolds using techniques similar to those used by Hall. It is shown that in the 2-dimensional case the zero is necessarily isolated, whereas in the 3-dimensional case the zero set may either be isolated or 1-dimensional. In the latter case the manifold is shown to be a 3-dimensional plane wave space-time, and all of the affine and conformal vector fields that it admits are found. These results are then used to determine the nature of the zero sets of affine vector fields in 4-dimensional Lorentz manifolds. The algebraic structure of the Riemann, Ricci and Weyl tensors at such zeros is also described. This work is extended by studying affine vector fields, and their zero sets, in 3-dimensional Lorentz manifolds. An investigation of the zero sets of affine vector fields in 3- and 4-dimensional positive-definite manifolds is included for comparison.

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Rostami, M. "Symmetry types of convex polyhedra." Thesis, University of Southampton, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375365.

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Patt, Brian Lawrence. "Higgs family symmetry and supersymmetry." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/36397.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2006.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 77-79).
In this thesis we investigate building models of family symmetry that give the Higgs fields family structure. We construct several models, starting with 2 generation models then moving onto 3 generation models. These models are described sequentially in chapters 2 through 6. All of these models are supersymmetric and they did not previously exists in the literature. In these models, quark (and lepton) masses and mixings are determined the vacuum expectation values of the family sector. These vacuum expectation values (VEV) can have a hierarchal structure because they correspond to flat directions of a superpotential. At low energies these models contain just one light pair of Higgs fields. Experimentally, the most interesting feature of these models are couplings between the low energy Higgs and moduli of the family sector. These couplings should be observable at the Large Hadron Collider.
by Brian Lawrence Patt.
Ph.D.

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Lin, Francesco Ph D. Massachusetts Institute of Technology. "Monopoles and Pin(2)-symmetry." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104585.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 321-326).
In this thesis we generalize the construction of monopole Floer homology due to Kronheimer and Mrowka to the case of a gradient flow with Morse-Bott singularities. Focusing then on the special case of a three-manifold equipped equipped with a spinc structure which is isomorphic to its conjugate, we define the counterpart in this context of Manolescu's recent Pin(2)-equivariant Seiberg-Witten-Floer homology. In particular, we provide an alternative approach to his disproof of the celebrated Triangulation conjecture. Furthermore, we discuss the analogue in this setting of the surgery exact triangle, and perform some sample computations.
by Francesco Lin.
Ph. D.

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40

Nirschl, Michael. "Superconformal symmetry and correlation functions." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615123.

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Klaui, Mathias Michael. "Nanomagnetism of high-symmetry structures." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619940.

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Sorensen, Robyn Elizabeth. "The perception of visual symmetry." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624479.

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Carlin, Patricia. "On symmetry in visual perception." Thesis, University of Stirling, 1996. http://hdl.handle.net/1893/1777.

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This thesis is concerned with the role of symmetry in low-level image segmentation. Early detection of local image properties that could indicate the presence of an object would be useful in segmentation, and it is proposed here that approximate bilateral symmetry, which is common to many natural and man made objects, is a candidate local property. To be useful in low-level image segmentation the representation of symmetry must be relatively robust to noise interference, and the symmetry must be detectable without prior knowledge of the location and orientation of the pattern axis. The experiments reported here investigated whether bilateral symmetry can be detected with and without knowledge of the axis of symmetry, in several different types of pattern. The pattern properties found to aid symmetry detection in random dot patterns were the presence of compound features, formed from locally dense clusters of dots, and contrast uniformity across the axis. In the second group of experiments, stimuli were designed to enhance the features found to be important for global symmetry detection. The pattern elements were enlarged, and grey level was varied between matched pairs, thereby making each pair distinctive. Symmetry detection was found to be robust to variation in the size of matched elements, but was disrupted by contrast variation within pairs. It was concluded that the global pattern structure is contained in the parallelism between extended, cross axis regions of uniform contrast. In the third group of experiments, detection performance was found to improve when the parallel structure was strengthened by the presence of matched strings, rather than pairs of elements. It is argued that elongation, parallelism, and approximate alignment between pattern constituents are visual properties that are both presegmentally detectable, and sufficient for the representation of global symmetric structure. A simple computational property of these patterns is described.

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Potanka, Karen Sue. "Groups, Graphs, and Symmetry-Breaking." Thesis, Virginia Tech, 1998. http://hdl.handle.net/10919/36630.

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A labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(D_n) is found where D_n is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined and the automorphism groups and distinguishing numbers of such graphs are given.
Master of Science

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45

Jing, Li Ph D. Massachusetts Institute of Technology. "Physical symmetry enhanced neural networks." Thesis, Massachusetts Institute of Technology, 2020. https://hdl.handle.net/1721.1/128294.

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This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Physics, February, 2020
Cataloged from student-submitted PDF version of thesis
Includes bibliographical references (pages 91-99).
Artificial Intelligence (AI), widely considered "the fourth industrial revolution", has shown its potential to fundamentally change our world. Today's AI technique relies on neural networks. In this thesis, we propose several physical symmetry enhanced neural network models. We first developed unitary recurrent neural networks (RNNs) that solve gradient vanishing and gradient explosion problems. We propose an efficient parametrization method that requires [sigma] (1) complexity per parameter. Our unitary RNN model has shown optimal long-term memory ability. Next, we combine the above model with a gated mechanism. This model outperform popular recurrent neural networks like long short-term memory (LSTMs) and gated recurrent units (GRUs) in many sequential tasks. In the third part, we develop a convolutional neural network architecture that achieves logarithmic scale complexity using symmetry breaking concepts. We demonstrate that our model has superior performance on small image classification tasks. In the last part, we propose a general method to extend convolutional neural networks' inductive bias and embed other types of symmetries. We show that this method improves prediction performance on lens-distorted image
by Li Jing.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Physics

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Seyedi, Shila Seyedi. "QFT and Spontaneous Symmetry Breaking." Thesis, Uppsala universitet, Teoretisk fysik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-425891.

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The aim of this project is to understand the structure of the Standard Model of the particle physics. Therefore quantum field theories (QFT) are studied in the both cases of abelian and non-abelian gauge theories i.e. quantum electrodynamics (QED), quantum chromodynamics (QCD) and electroweak interaction are reviewed. The solution to the mass problem arising in these theories i.e. spontaneous symmetry breaking is also studied.
Syftet med detta projekt är att förstå strukturen för partikelfysikens standardmodell. Därför studeras kvantfältsteorier (QFT) i båda fallen av abelska och icke-abelska gaugeteorier, dvs kvantelektrodynamik (QED), kvantkromodynamik (QCD) och elektrosvag växelverkan granskas. Lösningen på massproblemet som uppstår i dessa teorier, dvs. spontant symmetribrott studeras också.

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Davies, I. O. G. "Atomic tests of symmetry principles." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379924.

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Williamson, Dominic. "Symmetry-protected adiabatic quantum transistors." Thesis, The University of Sydney, 2014. http://hdl.handle.net/2123/13083.

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The standard circuit model of quantum computation differs in principle from a modern day computer chip in that computation is brought to stationary qubits in the former whereas information is routed spatially across a chip by transistors in the latter. Recently a model was proposed that addresses this key difference in implementation, it was dubbed the adiabatic quantum transistor model to emphasise its similarity to a classical transistor. Here we generalise this model to the setting of spin chains in inherently quantum phases of matter with a property called symmetry-protected order. Our generalisation is significant as it shows the computational properties of the model persist robustly throughout each symmetry-protected quantum phase of matter.

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Hicks, Jesse W. "Classification of Spacetimes with Symmetry." DigitalCommons@USU, 2016. https://digitalcommons.usu.edu/etd/5054.

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Spacetimes with symmetry play a critical role in Einstein's Theory of General Relativity. Missing from the literature is a correct, usable, and computer accessible classification of such spacetimes. This dissertation fills this gap; specifically, we i) give a new and different approach to the classification of spacetimes with symmetry using modern methods and tools such as the Schmidt method and computer algebra systems, resulting in ninety-two spacetimes; ii) create digital databases of the classification for easy access and use for researchers; iii) create software to classify any spacetime metric with symmetry against the new database; iv) compare results of our classification with those of Petrov and find that Petrov missed six cases and incorrectly normalized a significant number of metrics; v) classify spacetimes with symmetry in the book Exact Solutions to Einstein’s Field Equations Second Edition by Stephani, Kramer, Macallum, Hoenselaers, and Herlt and in Komrakov’s paper Einstein-Maxwell equation on four-dimensional homogeneous spaces using the new software.

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Henninger, Helen Clare. "The symmetry group of a model of hyperbolic plane geometry and some associated invariant optimal control problems." Thesis, Rhodes University, 2012. http://hdl.handle.net/10962/d1018232.

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In this thesis we study left-invariant control offine systems on the symmetry group of a. model of hyperbolic plane geometry, the matrix Lie group SO(1, 2)₀. We determine that there are 10 distinct classes of such control systems and for typical elements of two of these classes we provide solutions of the left-invariant optimal wntrol problem with quauratic costs. Under the identification of the Lie allgebra .so(l, 2) with Minkowski spacetime R¹̕'², we construct a controllabilility criterion for all left-invariant control affine systems on 50(1. 2)₀ which in the inhomogeneous case depends only on the presence or absence of an element in the image of the system's trace in R¹̕ ²which is identifiable using the inner product. For the solutions of both the optimal control problems, we provide explicit expressions in terms of Jacobi elliptic functions for the solutions of the reduced extremal equations and determine the nonlinear stability of the equilibrium points.

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Dissertations / Theses on the topic 'Symmetry'

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