Dissertations / Theses: 'Geometric analysis'

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Roysdon, Michael A. "ON SOME GEOMETRIC AND FUNCTIONAL INEQUALITIES INASYMPTOTIC GEOMETRIC ANALYSIS." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1599821442510494.

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Wink, Matthias. "Ricci solitons and geometric analysis." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:3aae2c5e-58aa-42da-9a1b-ec15cacafdad.

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This thesis studies Ricci solitons of cohomogeneity one and uniform Poincaré inequalities for differentials on Riemann surfaces. In the two summands case, which assumes that the isotropy representation of the principal orbit consists of two inequivalent Ad-invariant irreducible summands, complete steady and expanding Ricci solitons have been detected numerically by Buzano-Dancer-Gallaugher-Wang. This work provides a rigorous construction thereof. A Lyapunov function is introduced to prove that the Ricci soliton metrics lie in a bounded region of an associated phase space. This also gives an alternative construction of non-compact Einstein metrics of non-positive scalar curvature due to Böhm. It is explained how the asymptotics of the Ricci flat trajectories induce Böhm's Einstein metrics on spheres and other low dimensional spaces. A numerical study suggests that all other Einstein metrics of positive scalar curvature which are induced by the generalised Hopf fibrations occur in an entirely non-linear regime of the Einstein equations. Extending the theory of cohomogeneity one steady and expanding Ricci solitons, an estimate which allows to prescribe the growth rate of the soliton potential at any given time is shown. As an application, continuous families of Ricci solitons on complex line bundles over products of Fano Kähler Einstein manifolds are constructed. This generalises work of Appleton and Stolarski. The method also applies to the Lü-Page-Pope set-up and allows to cover an optimal parameter range in the two summands case. The Ricci soliton equation on manifolds foliated by torus bundles over products of Fano Kähler Einstein manifolds is discussed. A rigidity theorem is obtained and a preserved curvature condition is discovered. The cohomogeneity one initial value problem is solved for m-quasi-Einstein metrics and complete metrics are described. L^p-Poincaré inequalities for k-differentials on closed Riemann surfaces are shown. The estimates are uniform in the sense that the Poincaré constant only depends on p &GE;1, k ≥ 2 and the genus γ ≥ 2 of the surface but not on its complex structure. Examples show that the analogous estimate for 1-differentials cannot be uniform. This part is based on joint work with Melanie Rupflin.

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Gasparini, Riccardo. "Engineering Analysis in Imprecise Geometric Models." FIU Digital Commons, 2014. http://digitalcommons.fiu.edu/etd/1793.

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Engineering analysis in geometric models has been the main if not the only credible/reasonable tool used by engineers and scientists to resolve physical boundaries problems. New high speed computers have facilitated the accuracy and validation of the expected results. In practice, an engineering analysis is composed of two parts; the design of the model and the analysis of the geometry with the boundary conditions and constraints imposed on it. Numerical methods are used to resolve a large number of physical boundary problems independent of the model geometry. The time expended due to the computational process are related to the imposed boundary conditions and the well conformed geometry. Any geometric model that contains gaps or open lines is considered an imperfect geometry model and major commercial solver packages are incapable of handling such inputs. Others packages apply different kinds of methods to resolve this problems like patching or zippering; but the final resolved geometry may be different from the original geometry, and the changes may be unacceptable. The study proposed in this dissertation is based on a new technique to process models with geometrical imperfection without the necessity to repair or change the original geometry. An algorithm is presented that is able to analyze the imperfect geometric model with the imposed boundary conditions using a meshfree method and a distance field approximation to the boundaries. Experiments are proposed to analyze the convergence of the algorithm in imperfect models geometries and will be compared with the same models but with perfect geometries. Plotting results will be presented for further analysis and conclusions of the algorithm convergence

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Raub, Corey Bevan. "Geometric analysis of axisymmetric disk forging." Ohio : Ohio University, 2000. http://www.ohiolink.edu/etd/view.cgi?ohiou1172778393.

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Benkert, Marc. "Construction and Analysis of Geometric Networks." [S.l. : s.n.], 2007. http://digbib.ubka.uni-karlsruhe.de/volltexte/1000007167.

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Litsgård, Malte. "The Orbit Method and Geometric Quantisation." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-351508.

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Arroyave-Tobón, Santiago. "Polyhedral models reduction in geometric tolerance analysis." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0720/document.

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L’analyse de tolérances par des ensembles de contraintes repose sur la détermination de l’accumulation de variations géométriques par des sommes et intersections d’ensembles opérandes 6d. Les degrés de liberté des liaisons et les degrés d’invariance des surfaces génèrent des opérandes non-bornés (polyèdres), posant des problèmes de simulation. En 2014, L. Homria proposé une méthode pour résoudre ce problème, consistant à ajouter des limites artificielles(contraintes bouchon) sur les déplacements non-bornés. Même si cette méthode permet la manipulation d’objets bornés (polytopes), les contraintes bouchon augmentent la complexité des simulations. En réponse à cette difficulté, une méthode dérivée est proposée dans cette thèse.Cette méthode consiste à tracer et simplifier les contraintes bouchon au travers des opérations.Puis une seconde stratégie basée sur la décomposition d’un polyèdre en une somme d’un polytope et de lignes droites (associées aux déplacements non-bornés). Cette stratégie consiste à simuler d’une part les sommes de droites, et d’autre part, à déterminer la somme de polytopes dans un sous-espace de dimension inférieur à 6. Ces trois stratégies sont comparées au travers d’une application industrielle. Cela montre que la traçabilité des contraintes bouchons est un aspect fondamental pour contrôler leur propagation et pour réduire le temps de calcul des simulations. Toutefois, cette méthode exige encore de déterminer les limites des déplacements non-bornés. La deuxième méthode, adaptant systématiquement la dimension de l’espace de calcul, elle permet de diminuer davantage le temps de calcul. Ce travail permet d’envisager la mise en oeuvre de cette méthode selon des formulations statistiques avec la prise en compte des défauts de forme des surfaces
The cumulative stack-up of geometric variations in mechanical systems can be modelled summing and intersecting sets of constraints. These constraints derive from tolerance zones or from contact restrictions between parts. The degrees of freedom (DOF) of jointsgenerate unbounded sets (i.e. polyhedra) which are difficult to deal with. L. Homri presented in 2014 a solution based on the setting of fictitious limits (called cap constraints) to each DOFto obtain bounded 6D sets (i.e. polytopes). These additional constraints, however, increase the complexity of the models, and therefore, of the computations. In response to this situation,we defined a derived strategy to control the effects of the propagation of the fictitious limits by tracing and simplifying the generated, new cap constraints. We proposed a second strategy based on the decomposition of polyhedra into the sum of a polytope and a set of straight lines.The strategy consists in isolating the straight lines (associated to the DOF) and summing the polytopes in the smallest sub-space. After solving an industrial case, we concluded that tracing caps constraints during the operations allows reducing the models complexity and,consequently, the computational time; however, it still involves working in 6d even in caseswhere this is not necessary. In contrast, the strategy based on the operands decompositionis more efficient due to the dimension reduction. This study allowed us to conclude that the management of mechanisms’ mobility is a crucial aspect in tolerance simulations. The gain on efficiency resulting from the developed strategies opens up the possibility for doing statistical treatment of tolerances and tolerance synthesis

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Lindgren, Natalia. "Geometric and Mechanical Analysis of Aortic Aneurysm." Thesis, KTH, Hållfasthetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-284352.

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The aorta, the main and largest artery in the human body, is susceptible for many types of problems. One of the most common aortic disease is the formation of an aneurysm. Endovascular aortic aneurysm repair (EVAR) is a minimally invasive treatment option for aortic aneurysms, involving the deployment of an expandable stent graft within the aorta without operating the aneurysm directly. With 1.5 to 43 % of EVAR patients having postoperative complications, research to help predict these complications of EVAR is of essence. In this study, the deformations of the aorta induced by a deployed stent graft have been investigated and visualized in order to aid understanding of the geometrical behaviour of the aorta post EVAR. This has been carried out by the development and analysis of patient-specific aortic 3D reconstruction models, 3D printed physical models and FE simulation models. A qualitative assessment of the deformations was achieved by superimposing reconstructed geometries, revealing a light straightening of the aorta and iliac vessels, as well as anterior movement of the iliac branches. Based on the good agreement between the simulated and reconstructed geometries, the findings suggest that such deformations could be derived from the pressure being removed from the aneurysm due to the deployed stent graft, in combination with stent radial forces from the proximal and distal landing zones. Despite that the simulation seemed to underestimate distal movement of the iliac vessel, this study emphasizes the potential of 3D printing and FE analysis as promising tools for planning and research of EVAR.
Den stora kroppspulsådern, aortan, kan drabbas av flera olika sjukdomstillstånd. En av de vanligaste är bildandet av en aortaaneurysm. Endovaskulär Aneruysm Reparation (EVAR) är en operationsteknik för att behandla aortaaneurysmer och involverar positionering av ett rörformat, självexpanderande stentgraft innanför aortaaneurysmen via ljumskartärerna. Eftersom 1,5 till 43 % av EVAR-patienter råkar ut för postoperativa komplikationer är det väsentligt att bedriva vidare studier för att förutse dessa. I denna studie har deformationerna av en aorta på grund av positionerade stentar undersökts och visualiserade för att underlätta förståelsen av aortans geometriska beteende efter EVAR. Detta har gjorts genom att utveckla och analysera patientspecifika 3D-rekonstruktioner, 3D-printade fysiska modeller och simulerade modeller av en aorta. En kvalitativ bedömning av deformationerna uppnåddes genom att superpositionering av rekonstruerade geometrier, vilket avslöjade en lätt uträtning av aortan och tarmbensartärerna, samt en framförflyttning av de senare. Baserat på den goda överensstämmelsen mellan de simulerade och rekonstruerade modellerna, antyder resultaten att sådana deformationer kan härledas av att trycket avlägsnats från aneurysmen på grund av stentgraften, i kombination med radiellt tryck från stentar över och under aneurysmen. Trots att simuleringen underskattade framförflyttningen av tarmbensartärerna, belyser denna studie potentialen hos 3D-printing och FE-analyser som ett värdefullt verktyg för att planera och studera EVAR.

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Tiwari, Abhishek Murray Richard M. Murray Richard M. "Geometric analysis of spatio-temporal planning problems /." Diss., Pasadena, Calif. : Caltech, 2007. http://resolver.caltech.edu/CaltechETD:etd-05202007-135411.

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Gautam, Sushrut Zubin Sulaksh. "Two geometric obstruction results in harmonic analysis." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=1872162601&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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Zaidi, Syed Ali Raza. "Stochastic geometric analysis of cognitive wireless networks." Thesis, University of Leeds, 2013. http://etheses.whiterose.ac.uk/5490/.

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The prime objective of this thesis is to study these interference management mechanisms for quantifying the potential gains of CRs in terms of spectral utility. Interference modeling is the most important aspect of this extensive evaluation. Accurate modeling of the cognitive network interference, accommodating its stochastic nature (triggered by both spatial and propagation dynamics) is therefore a central contribution of this thesis. Since the aggregate interference from CRs is a function of the access strategy, two wellknown access paradigms, namely, spectrum underlay and interweave, are thoroughly analyzed. For the spectrum underlay access mechanism, a guard-zone based interference control mechanism is examined. Specifically, CRs are obliged to maintain silence in a spatial no-talk zone of a certain radius which is centered on a primary receiver. It is shown that the radius of the guard-zone is strongly coupled with the medium access and routing strategies employed by the CRs. While the guard-zone provides a robust mechanism to protect a single primary user, it is a challenging task to achieve the same for a large scale primary network. An alternative degree of freedom, i.e., medium access probability (MAP), can easily address this issue. Furthermore, for a large CR network (CRN), significant gains can be harnessed by furnishing nodes with multiple antennas. Performance evaluation of such a network with MAP adaptation is one of the key contributions of this dissertation. It is shown that the multi-antenna paradigm results in a “win-win” situation for both primary and secondary users. In order to facilitate multi-hop communication between CRs, a quality-of-service (QoS) aware routing is also devised. We show that there exists an optimal MAP which maximizes the spectral utility of the secondary network. However, such an optimal point often lies outside the permissible operational regime dictated by the primary user’s co-existence constraint. Another approach can be adopted where we exploit a different degree of freedom, i.e., the transmit power employed by the CRs. Thus CRs can extend their operational regime by adapting one degree of freedom and selecting an optimal value for another. The optimality of this adapt-and-optimize strategy is shown for a variety of networking paradigms. Finally, the performance of the primary user in the presence of the interference-channel-aware CRs is quantified. For a CRN employing an interweave configuration, the performance of a legacy user is investigated. The impact of different network parameters is explored. It is shown that the cooperation between the CR transmitter and receiver can significantly improve the performance of the interference avoidance mechanism. Furthermore,we highlight that ignoring the self-coexistence criteria for the secondary network leads to an over-estimation of the aggregate interference and consequently results in pessimistic design strategies. The analysis is extended to consider the performance of a large primary network. Finally, a novel modification in the analytical approach is proposed so that performance guarantees can be provided to the existing users. Another contribution of this dissertation is to evaluate (currently very topical and very important) the energy efficiency of an ad hoc wireless network. The key motivation is to investigate the impact of the co-channel interference on the network-wide energy consumption. Both energy and spectral efficiency problems have a common origin, i.e., growing bandwidth demand. Also the design of both problems require understanding of co-channel interference management strategies. Finally,we try to put pull together all the analysis and simulation results to look at both open problems and directions for future research in this highly topical, and strategically important research areas of enabling high speed, future wireless networks.

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Yaskina, Maryna. "Topics in functional analysis and convex geometry." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4346.

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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.

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Mascellani, Giovanni. "Fourth-order geometric flows on manifolds with boundary." Doctoral thesis, Scuola Normale Superiore, 2017. http://hdl.handle.net/11384/85715.

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Dimitrov, Darko [Verfasser]. "Geometric applications of principal component analysis / Darko Dimitrov." Berlin : Freie Universität Berlin, 2009. http://d-nb.info/102346392X/34.

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Isgro, Francesco. "Geometric methods for video sequence analysis and applications." Thesis, Heriot-Watt University, 2001. http://hdl.handle.net/10399/495.

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Kramer, Glenn Andrew. "Geometric reasoning in the kinematic analysis of mechanisms." Thesis, University of Sussex, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.385673.

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McManigle, John E. "Three-dimensional geometric image analysis for interventional electrophysiology." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:2f36fa8e-9c64-4807-97c0-25e63398da7e.

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Improving imaging hardware, computational power, and algorithmic design are driving advances in interventional medical imaging. We lay the groundwork here for more effective use of machine learning and image registration in clinical electrophysiology. To achieve identification of atrial fibrosis using image data, we registered the electroanatomic map (EAM) data of atrial fibrillation (AF) patients undergoing pulmonary vein isolation (PVI) with MR (n = 16) or CT (n = 18) images. The relationship between image features and bipolar voltage was evaluated using single-parameter regression and random forest models. Random forest performed significantly better than regression, identifying fibrosis with area under the receiver operating characteristic curve (AUC) 0.746 (MR) and 0.977 (CT). This is the first evaluation of voltage prediction using image data. Next, we compared the character of native atrial fibrosis with ablation scar in MR images. Fourteen AF patients undergoing repeat PVI were recruited. EAM data from their first PVI was registered to the MR images acquired before the first PVI (‘pre-operative’) and before the second PVI ('post-operative' with respect to the first PVI). Non-ablation map points had similar characteristics in the two images, while ablation points exhibited higher intensity and more heterogeneity in post-operative images. Ablation scar is more strongly enhancing and more heterogeneous than native fibrosis. Finally, we addressed myocardial measurement in 3-D echocardiograms. The circular Hough transform was modified with a feature asymmetry filter, epicardial edges, and a search constraint. Manual and Hough measurements were compared in 5641 slices from 3-D images. The enhanced Hough algorithm was more accurate than the unmodified version (Dice coefficient 0.77 vs. 0.58). This method promises utility in segmentation-assisted cross-modality registration. By improving the information that can be extracted from medical images and the ease with which that information can be accessed, this progress will contribute to the advancing integration of imaging in electrophysiology.

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Thakkar, Kairavee K. "A Geometric Analysis of Time Varying Electroencephalogram Vectors." University of Cincinnati / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1613745734396658.

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Sun, Lu. "Geometric transformation and image singularity with wavelet analysis." HKBU Institutional Repository, 2006. http://repository.hkbu.edu.hk/etd_ra/656.

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Lidén, Joel. "Stock Price Predictions using a Geometric Brownian Motion." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-353586.

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Benatti, Luca. "Monotonicity Formulas in Nonlinear Potential Theory and their geometric applications." Doctoral thesis, Università degli studi di Trento, 2022. http://hdl.handle.net/11572/346959.

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In the setting of Riemannian manifolds with nonnegative Ricci curvature, we provide geometric inequalities as consequences of the Monotonicity Formulas holding along the flow of the level sets of the p-capacitary potential. The work is divided into three parts. (1) In the first part, we describe the asymptotic behaviour of the p-capactitary potential in a natural class of Riemannian manifolds. (2) The second part is devoted to the proof of our Monotonicity-Rigidity Theorems. (3) In the last part, we apply the Monotonicity Theorems to obtain geometric inequalities, focusing on the Extended Minkowski Inequality.

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Enqvist, Per. "Spectral Estimation by Geometric, Topological and Optimization Methods." Doctoral thesis, Stockholm, 2001. http://media.lib.kth.se:8080/kthdisseng.html.

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Aydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.

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Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrö
dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.

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Anderson, Joseph T. "Geometric Methods for Robust Data Analysis in High Dimension." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488372786126891.

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Hedén, Isac. "Russell’s hypersurface from a geometric point of view." Licentiate thesis, Uppsala universitet, Algebra, geometri och logik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-144688.

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Mårtensson, Jonas. "Geometric analysis of stochastic model errors in system identification." Doctoral thesis, KTH, Reglerteknik, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4506.

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Models of dynamical systems are important in many disciplines of science, ranging from physics and traditional mechanical and electrical engineering to life sciences, computer science and economics. Engineers, for example, use models for development, analysis and control of complex technical systems. Dynamical models can be derived from physical insights, for example some known laws of nature, (which are models themselves), or, as considered here, by fitting unknown model parameters to measurements from an experiment. The latter approach is what we call system identification. A model is always (at best) an approximation of the true system, and for a model to be useful, we need some characterization of how large the model error is. In this thesis we consider model errors originating from stochastic (random) disturbances that the system was subject to during the experiment. Stochastic model errors, known as variance-errors, are usually analyzed under the assumption of an infinite number of data. In this context the variance-error can be expressed as a (complicated) function of the spectra (and cross-spectra) of the disturbances and the excitation signals, a description of the true system, and the model structure (i.e., the parametrization of the model). The primary contribution of this thesis is an alternative geometric interpretation of this expression. This geometric approach consists in viewing the asymptotic variance as an orthogonal projection on a vector space that to a large extent is defined from the model structure. This approach is useful in several ways. Primarily, it facilitates structural analysis of how, for example, model structure and model order, and possible feedback mechanisms, affect the variance-error. Moreover, simple upper bounds on the variance-error can be obtained, which are independent of the employed model structure. The accuracy of estimated poles and zeros of linear time-invariant systems can also be analyzed using results closely related to the approach described above. One fundamental conclusion is that the accuracy of estimates of unstable poles and zeros is little affected by the model order, while the accuracy deteriorates fast with the model order for stable poles and zeros. The geometric approach has also shown potential in input design, which treats how the excitation signal (input signal) should be chosen to yield informative experiments. For example, we show cases when the input signal can be chosen so that the variance-error does not depend on the model order or the model structure. Perhaps the most important contribution of this thesis, and of the geometric approach, is the analysis method as such. Hopefully the methodology presented in this work will be useful in future research on the accuracy of identified models; in particular non-linear models and models with multiple inputs and outputs, for which there are relatively few results at present.
QC 20100810

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Kwan, Herman Ho Ming. "Multilayer beam analysis including shear and geometric nonlinear effects." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/26711.

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This thesis presents an analysis and experimental verification for a multilayer beam in bending. The formulation of the theoretical analysis includes the combined effect of shear and geometric nonlinearity. From this formulation, a finite element program (CUBES) is developed. The experimental tests were done on multilayer, corrugated paper beams. Failure deflections and loads are thus obtained. The experimental results are reasonably predicted by the numerical results. Based upon this comparison, a maximum compressive stress is determined for the tested beam. Finally, design curves for the tested beam are drawn using the determined maximum compressive stress and the finite element program.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

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Wan, Wai-yin. "Analysis of Poisson count data using Geometric Process model." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37836493.

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Mårtensson, Jonas. "Geometric analysis of stochastic model errors in system identification /." Stockholm : Elektro- och systemteknik, Kungliga Tekniska högskolan, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4506.

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Al, Shahrani Ibrahim Sulaiman A. "3D geometric morphometric analysis of tooth shape in hypodontia." Thesis, University of Newcastle Upon Tyne, 2012. http://hdl.handle.net/10443/1464.

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Assessment of tooth morphology is essential in the diagnosis and management of hypodontia patients. Several techniques have been used to quantify tooth shape in hypodontia patients and these have revealed smaller tooth dimensions and anomalous tooth shapes in these patients when compared with controls. However, previous studies have mainly used 2D images and have thus provided limited information. The present study adopted a novel three-dimensional geometric morphometric technique to quantify the crown morphology and sizes of teeth of hypodontia patients and compare them with those of control patients. Allometric variations were also investigated in order to determine whether there was any association between the size and shape of teeth. Landmarks were recorded on each clinical crown of all the permanent teeth, apart from third molars, of 3D scanned study models of hypodontia and control subjects. The study sample comprised 120 hypodontia patients (40 patients with mild, 40 with moderate and 40 with severe hypodontia) and 40 age- and sex-matched controls. Procrustes superimposition was utilized to scale and superimpose the landmark coordinate data and were then subjected to principal component analysis (PCA). Subsequently, shape differences were tested statistically using multivariate statistics. Size variation was for the most part found to be significant, especially when the control subjects were compared to the hypodontia groups. The anterior teeth were more affected than the posterior. Generally speaking, the size differences became greater as the severity of the hypodontia increased. The pattern was virtually the same for both sexes. With regard to shape, most teeth were affected by the hypodontia, although the pattern was less clear. When allometry was taken into account, the pattern of size/shape relationship was found to be significant for most teeth, particularly in the anterior region, and shape differences were still significant after controlling, when possible, for allometry. It was found that the degree of variation in tooth shape was associated with the degree of severity of the hypodontia. The findings of the study therefore indicate that quantitative measurement of the tooth shape in hypodontia patients may enhance the multidisciplinary management of those patients.

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Savriama, Yoland. "Geometric morphometric methods for analysis of complex symmetric structures." Thesis, University of Manchester, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491861.

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Bilateral symmetry is the simplest and most common type of symmetry in organisms and for this reason it has been extensively studied in many biological contexts. Geometric morphometrics is concerned with the quantification of morphological variation in organisms and has been specifically developed for studies of symmetry and asymmetry. Most studies of symmetry have focused on bilaterally symmetric structures (e.g., human faces). However, bilateral symmetry is not the only type of symmetry in biological shapes and other types of symmetry exist as well (e.g., radial symmetry in flowers). So far, there are no general methods for morphological analysis of these types of symmetry. Here, I propose a new and general approach for norphological analysis of structures with any type of symmetry. This framework combines the tools of geometric morphometries with a mathematical definition of symmetry. Depending on the type of symmetry under study, this method can separate a component of symmetric variation among individuals from one or more asymmetry components.

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Wong, Chun-kuen, and 黃春權. "Symmetry reduction for geometric nonlinear analysis of space structures." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31214721.

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Wan, Wai-yin, and 溫慧妍. "Analysis of Poisson count data using Geometric Process model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37836493.

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Dougan, Lewis Thomas. "Fractal geometric analysis of spatially self-affine stochastic fracture." Thesis, Edinburgh Napier University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275458.

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Zhang, Fan. "Geometric and probabilistic methods for non-Euclidean image analysis." Thesis, University of York, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.445471.

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Charmley, James E. (James Edward). "Geometric and dynamic analysis of shoe-type centerless grinding." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/43242.

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37

Secor, Matthew J. (Matthew Joelson). "Geometric modeling and analysis of dynamic resource allocation mechanisms." Thesis, Massachusetts Institute of Technology, 2001. http://hdl.handle.net/1721.1/8769.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.
Includes bibliographical references (p. 159-163).
The major contribution of this thesis is the investigation of a specific resource allocation optimization problem whose solution has both practical application as well as theoretical interest. It is presented as a specific case of a more general modeling framework we put forth. The underlying question asks how to partition a given resource into a fixed number of parts such that the elements of the resulting partition can be scheduled among a set of user requests to minimize the worst case difference between the schedule and the requests. This particular allocation problem has not been studied before. The general problem is difficult in part because the evaluation of the objective problem is a difficult task by itself. We present a novel algorithm for its exact solution in a constrained setting and discussion of the unconstrained setting in, followed by a number of practical applications of these solutions. The solution to the constrained optimization problem is shown to provide sizable benefits in allocation efficiency in a number of contexts at a minimal implementation cost. The specific contexts we look at include communication over a shared channel, allocation of many small channels to a few users and package delivery from a central office to a number of satellite offices. We also present a set of new fairness results for auction-based allocation mechanisms and show how these mechanisms also fall within our modeling framework. Specifically, we look at using auctions as mechanisms to allocate an indivisible shared resource fairly among a number of users. We establish that a straightforward approach as has been tried in the literature does not guarantee an fair allocation over a long time scale and provide a modified approach that does guarantee a fair allocation. We also show that by allowing users to strategize when bidding on the resource we can avoid the problem of unfairness, for some simple cases. This analysis has not been seen in existing literature. Finally, an analysis of the deterministic and stochastic stability of our class of models is presented that applies to a large subset of the models within our framework. The deterministic stability results presented establish the ultimate boundedness of the lag of deterministically stabilizable models in our framework under a wide variety of quantizer-based scheduling rules. This variety of available rules can be used to further control the behavior of the lag of a stable mechanism. We also discuss the application of existing stochastic stability theory to a large subset of the stochastic models in our framework. This is a straightforward usage of existing stability results based on verifying the satisfaction of a stochastic drift condition.
by Matthew Secor.
Ph.D.

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38

Ashbrook, Anthony P. "Pairwise geometric histograms for object recognition : developments and analysis." Thesis, University of Sheffield, 1999. http://etheses.whiterose.ac.uk/14675/.

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One of the fundamental problems in the field of computer vision is the task of classifying objects, which are present in an image or sequence of images, based on their appearance. This task is commonly referred to as the object recognition problem. A system designed to perform this task must be able to learn visual cues such as shape, colour and texture from examples of objects presented to it. These cues are then later used to identify examples of the known objects in previously unseen scenes. The work presented in this thesis is based on a statistical representation of shape known as a pairwise geometric histogram which has been demonstrated by other researchers in 2-dimensional object recognition tasks. An analysis of the performance of recognition based on this representation has been conducted and a number of contributions to the original recognition algorithm have been made. An important property of an object recognition system is its scalability. This is the. ability of the system to continue performing as the number of known objects is increased. The analysis of the recognition algorithm presented here considers this issue by relating the classification error to the number of stored model objects. An estimate is also made of the number of objects which can be represented uniquely using geometric histograms. One of the main criticisms of the original recognition algorithm based on geometric histograms was the inability to recognise objects at different scales. An algorithm is presented here that is able to recognise objects over a range of scale using the geometric histogram representation. Finally, a novel pairwise geometric histogram representation for arbitrary surfaces has been proposed. This inherits many of the advantages of the 2-dimensional shape descriptor but enables recognition of 3-dimensional object from arbitrary viewpoints.

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39

DiRenzo, Michael T. "A geometric analysis of model reduction of linear systems." Thesis, Virginia Tech, 1989. http://hdl.handle.net/10919/45942.

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In this thesis we study the model reduction problem in terms of the geometric concepts of linear system theory. By appropriate selection of reducing subspaces, useful lower-order system models can be achieved. The reducing subspaces can be chosen as parts of a system which are "mostâ and â leastâ controllable or observable; retaining, of course, the most controllable/observable subspace for model reduction. We review results showing how several measures of controllability and observability can provide this information. Balanced, Jordan canonical form, and dual GHR representations are shown to be state space realizations which naturally identify the reducing subspaces based on these measures. Several results unifying these methods are given.

In another approach, we show that the reducing subspaces can be chosen such that after completing model reduction, a number of Markov parameters and time moments of the full system are retained by the reduced order model. We show how the dual GHR can be used as a tool which identifies these subspaces and state space realizations which naturally display them. Along these lines, a connection between model reduction in the state space and second-order systems is established, particulary the reduction of structures via the Lanczos algorithm.

Master of Science

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40

Gause, Austin R. J., Lance D. Jessee, and Blaine W. Schubert. "Geometric Morphometric Analysis of Intervertebral Variation in Colubrid Snakes." Digital Commons @ East Tennessee State University, 2019. https://dc.etsu.edu/asrf/2019/schedule/199.

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Snake vertebrae are common throughout the Cenozoic fossil record, but identification of isolated vertebrae often proves difficult due to inter- and intra-columnar variability. Most fossil identifications are based on comparisons with disarticulated modern specimens, with a focus on mid-trunk vertebrae. One focus of this study was to determine the necessity of identifying a true mid-trunk vertebra prior to identification and to develop a method of locating the columnar position of an isolated vertebra for both modern and fossil identifications. Colubrid genera Farancia and Heterodon were chosen for the analysis because they share distinct morphological similarities, articulated modern specimens were available, and fossil species in these genera need to be reassessed. Every third pre-cloacal vertebra was selected from each specimen to undergo geometric morphometric analysis on its anterior face. Relative warp analyses detailed the inter-columnar variation of each specimen and found that the only significant difference in the column was between the anterior most vertebrae, which are already identifiable, and the remainder of the pre-cloacal vertebrae. Despite concern, the convention of using mid-trunk vertebrae for identification may prove accurate for these genera. Due to Farancia and Heterodon’s vertebral similarities, a discriminant function analysis was utilized to distinguish the two genera from one another. To evaluate this method’s utility in paleontology, vertebrae of two extinct species, Heterodon brevis and Paleofarancia brevispinosus, will undergo identical morphometric and discriminant analyses. This study also emphasizes the need for more modern snake skeletons in collections and the necessity of stringing the vertebral column prior to disarticulation.

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Yan, Zhongcheng. "Geometric tolerance evaluation and uncertainty analysis for coordinate metrology." Connect to resource, 1994. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1243616513.

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42

Chesley, Steven Ross. "The isosceles three-body problem : a global geometric analysis /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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Wong, Chun-kuen. "Symmetry reduction for geometric nonlinear analysis of space structures /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B18379734.

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44

Wong, Yau. "Geometric analysis of reflector systems for solar cell modules." Thesis, The University of Sydney, 1988. https://hdl.handle.net/2123/26247.

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This thesis is a study of the design, analysis and experimentation, of developing a feasible solar cell collector module, which in turn, can improve the output performance of a solar cell. The ﬁrst Chapter is devoted to deﬁning the background, structure and abilities of a solar cell, and to illustrating the long—term attraction to utilising solar energy. The extent of solar energy falling on earth in relation to its orientation with the earth is treated in Chapter two. Chapter three deals with various stages of module development and analysis; Chapter four illustrates the module experiment with simulated sunlight and confirms the result which was analysed previously. The remaining Chapter describes the cost-effectiveness of the module and the limitations, products, and achievements of the solar cell overseas and in this country.

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Gallagher, Paul Ph D. Massachusetts Institute of Technology. "New progress towards three open conjectures in geometric analysis." Thesis, Massachusetts Institute of Technology, 2019. https://hdl.handle.net/1721.1/122163.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 68-70).
This thesis, like all of Gaul, is divided into three parts. In Chapter One, I study minimal surfaces in R⁴ with quadratic area growth. I give the first partial result towards a conjecture of Meeks and Wolf on asymptotic behavior of such surfaces at infinity. In particular, I prove that under mild conditions, these surfaces must have unique tangent cones at infinity. In Chapter Two, I give new results towards a conjecture of Schoen on minimal hypersurfaces in R⁴. I prove that if a stable minimal hypersurface E with weight given by its Jacobi field has a stable minimal weighted subsurface, then E must be a hyperplane inside of R⁴. Finally, in Chapter Three, I do an in-depth analysis of the nodal set results of Logonov-Malinnikova. I give explicit bounds for the eigenvalue exponent in terms of dimension, and make a slight improvement on their methodology.
by Paul Gallagher.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics

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46

Bader, Philipp Karl-Heinz. "Geometric Integrators for Schrödinger Equations." Doctoral thesis, Universitat Politècnica de València, 2014. http://hdl.handle.net/10251/38716.

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The celebrated Schrödinger equation is the key to understanding the dynamics of quantum mechanical particles and comes in a variety of forms. Its numerical solution poses numerous challenges, some of which are addressed in this work. Arguably the most important problem in quantum mechanics is the so-called harmonic oscillator due to its good approximation properties for trapping potentials. In Chapter 2, an algebraic correspondence-technique is introduced and applied to construct efficient splitting algorithms, based solely on fast Fourier transforms, which solve quadratic potentials in any number of dimensions exactly - including the important case of rotating particles and non-autonomous trappings after averaging by Magnus expansions. The results are shown to transfer smoothly to the Gross-Pitaevskii equation in Chapter 3. Additionally, the notion of modified nonlinear potentials is introduced and it is shown how to efficiently compute them using Fourier transforms. It is shown how to apply complex coefficient splittings to this nonlinear equation and numerical results corroborate the findings. In the semiclassical limit, the evolution operator becomes highly oscillatory and standard splitting methods suffer from exponentially increasing complexity when raising the order of the method. Algorithms with only quadratic order-dependence of the computational cost are found using the Zassenhaus algorithm. In contrast to classical splittings, special commutators are allowed to appear in the exponents. By construction, they are rapidly decreasing in size with the semiclassical parameter and can be exponentiated using only a few Lanczos iterations. For completeness, an alternative technique based on Hagedorn wavepackets is revisited and interpreted in the light of Magnus expansions and minor improvements are suggested. In the presence of explicit time-dependencies in the semiclassical Hamiltonian, the Zassenhaus algorithm requires a special initiation step. Distinguishing the case of smooth and fast frequencies, it is shown how to adapt the mechanism to obtain an efficiently computable decomposition of an effective Hamiltonian that has been obtained after Magnus expansion, without having to resolve the oscillations by taking a prohibitively small time-step. Chapter 5 considers the Schrödinger eigenvalue problem which can be formulated as an initial value problem after a Wick-rotating the Schrödinger equation to imaginary time. The elliptic nature of the evolution operator restricts standard splittings to low order, ¿ < 3, because of the unavoidable appearance of negative fractional timesteps that correspond to the ill-posed integration backwards in time. The inclusion of modified potentials lifts the order barrier up to ¿ < 5. Both restrictions can be circumvented using complex fractional time-steps with positive real part and sixthorder methods optimized for near-integrable Hamiltonians are presented. Conclusions and pointers to further research are detailed in Chapter 6, with a special focus on optimal quantum control.
Bader, PK. (2014). Geometric Integrators for Schrödinger Equations [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38716
TESIS
Premiado

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47

Beil, Joel S. "Geometric Properties of Orbits of Integral Operators." Kent State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=kent1270503593.

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48

Fleming, Alan Duncan. "Analysis of uncertainties and geometric tolerances in assemblies of parts." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/6626.

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Computer models of the geometry of the real world have a tendency to assume that the shapes and positions of objects can be described exactly. However, real surfaces are subject to irregularities such as bumps and undulations and so do not have perfect, mathematically definable forms. Engineers recognise this fact and so assign tolerance specifications to their designs. This thesis develops a representation of geometric tolerance and uncertainty in assemblies of rigid parts. Geometric tolerances are defined by tolerance zones which are regions in which the real surface must lie. Parts in an assembly can slop about and so their positions are uncertain. Toleranced parts and assemblies of toleranced parts are represented by networks of tolerance zones and datums. Each arc in the network represents a relationship implied by the tolerance specification or by a contact between the parts. It is shown how all geometric constraints can be converted to an algebraic form. Useful results can be obtained from the network of tolerance zones and datums. For example it is possible to determine whether the parts of an assembly can be guaranteed to fit together. It is also possible to determine the maximum slop that could occur in the assembly assuming that the parts satisfy the tolerance specification. Two applications of this work are (1) tolerance checking during design and (2) analysis of uncertainty build-up in a robot assembly plan. I n the former, a designer could check a proposed tolerance specification to make sure that certain design requirements are satisfied. In the latter, knowledge of manufacturing tolerances of parts being manipulated can be used to determine the constraints on the positions of the parts when they are in contact with other parts.

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Lu, Tung-Wu. "Geometric and mechanical modelling of the human locomotor system." Thesis, University of Oxford, 1997. https://ora.ox.ac.uk/objects/uuid:789d619c-f32e-4efa-9935-6ec8ce82ece4.

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A critical review of studies related to the modelling of the human locomotor system is given. Kinematic and dynamic modelling and analysis of the pelvis-leg apparatus as an ensemble of four rigid body segments are described. Experiments were performed on two patients with custom-made instrumented massive proximal femoral prostheses implanted after tumour resection. Telemetered axial forces transmitted along the prostheses, together with kinematic, force plate and electromyographic data, were recorded synchronously during level walking, single and double leg stance, and isometric tests of the hip muscles. A sagittal plane model of the locomotor system, with an anatomical model of the knee joint, was developed from an existing model and used for a comparative study of methods for the calculation of the internal forces. A three-dimensional computer graphics-based animated model of the locomotor system was developed, with the hip as a ball-and-socket joint, the knee as a parallel spatial mechanism and the ankle as a two-hinge complex. Thirty-four muscles or muscle groups were included. A method for the determination of the orientation of multi-joint systems from surface markers was developed to take account of measurement errors including skin movement artefacts. Both the 2D and 3D models of the locomotor system were evaluated and validated quantitatively with the telemetered femoral axial forces. It is concluded that (a) a significant part of the bending moments along limbs are transmitted by a combination of tensile forces in muscles and compressive forces in bones so that moments transmitted by the bones are much less than the limb moments, (b) bi-articular muscles play a major role in modulating forces in bones, (c) appropriate simulation of muscle forces is important in experimental or theoretical studies of load transmission along bones, (d) computer graphics-based modelling and animation are important tools in bridging the gap between clinical users and biomechanists.

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Klisinska, Anna. "Clarkson type inequalities and geometric properties of banach spaces." Licentiate thesis, Luleå tekniska universitet, Pedagogik, språk och Ämnesdidaktik, 1999. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-25946.

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In this thesis Clarkson's inequalities and their generalizations are the main tools. The technique that can be used to prove Clarkson type inequalities in more dimensions is shown. We also establish Clarkson type inequalities in general Banach spaces and point out the connections between Clarkson's inequalities and the concept of type and cotype. The classical results on the von Neumann-Jordan constant, closely related to Clarkson's inequalities, are shortly presented. The concepts of moduli of convexity and smoothness, which are connected with the geometry of Banach spaces, are discussed. Some equivalent ways of describing modulus of convexity and some properties of this function are formulated. The estimation of the modulus of convexity for L(p)-spaces is presented as well. Finally, several examples of moduli of convexity and smoothness for different spaces are described.

Godkänd; 1999; 20070320 (ysko)

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Dissertations / Theses on the topic 'Geometric analysis'

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