subject:(spherical geometry)

The Ohio State University

1. Nash, Evan D., Nash. Extended Tropicalization of Spherical Varieties.

Degree: PhD, Mathematics, 2018, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

► The first steps in defining a notion of spherical tropicalization were recently takenby Tassos Vogiannou in his thesis and by Kiumars Kaveh and Christopher Manonin… (more)

▼ The first steps in defining a notion of spherical tropicalization were recently takenby Tassos Vogiannou in his thesis and by Kiumars Kaveh and Christopher Manonin a related paper. Broadly speaking, the classical notion of tropicalization concernsitself with valuations on the function field of a toric variety that are invariant underthe action of the torus. Spherical tropicalization is similar, but considers insteadspherical G-varieties and G-invariant valuations.The core idea of my dissertation is the construction of the extended tropicalizationof a spherical embedding. Vogiannou, Kaveh, and Manon only concern themselveswith subvarieties of a spherical homogeneous space G/H. My thesis describes how totropicalize a spherical embedding by tropicalizing the additional G-orbits of X andadding them to the tropicalization of G/H as limit points. This generalizes work doneby Kajiwara and Payne for toric varieties and affords a means for understanding howto tropicalize the compactification of a subvariety of G/H in X.The extended tropicalization construction can be described from three differentperspectives. The first uses the polyhedral geometry of the colored fan and the secondextends the Grobner theory definition given by Kaveh and Manon. The third methodworks by embedding the spherical variety in a specially-constructed toric variety,tropicalizing there with the standard theory, and then applying a particular piecewise-projection map. This final perspective introduces a novel means for tropicalizing a homogeneous space that allows us to prove several statements about the structure of a spherical tropicalization by transferring results from the toric world where more is known.We also suggest a definition for the tropicalization of subvarieties of a homogeneousspace whose defining equations have coefficients with non-trivial valuation. Allthe previous theory has been done in the constant coefficient case, i.e. when thecoefficients of the defining equations all have trivial valuation. Advisors/Committee Members: Kennedy, Gary (Advisor).

Subjects/Keywords: Mathematics; tropical geometry; algebraic geometry; spherical varieties; spherical homogeneous spaces

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APA (6^th Edition):

Nash, Evan D., N. (2018). Extended Tropicalization of Spherical Varieties. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

Chicago Manual of Style (16^th Edition):

Nash, Evan D., Nash. “Extended Tropicalization of Spherical Varieties.” 2018. Doctoral Dissertation, The Ohio State University. Accessed January 27, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178.

MLA Handbook (7^th Edition):

Nash, Evan D., Nash. “Extended Tropicalization of Spherical Varieties.” 2018. Web. 27 Jan 2021.

Vancouver:

Nash, Evan D. N. Extended Tropicalization of Spherical Varieties. [Internet] [Doctoral dissertation]. The Ohio State University; 2018. [cited 2021 Jan 27]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178.

Council of Science Editors:

Nash, Evan D. N. Extended Tropicalization of Spherical Varieties. [Doctoral Dissertation]. The Ohio State University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178

North Carolina State University

2. Fleming, John Thomas III. Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry.

Degree: MS, Nuclear Engineering, 2009, North Carolina State University

URL: http://www.lib.ncsu.edu/resolver/1840.16/226

► A family of numerical methods for solving the particle transport equation in 1-D spherical geometry are developed using the method of characteristics. The development of… (more)

▼ A family of numerical methods for solving the particle transport equation in 1-D spherical geometry are developed using the method of characteristics. The development of these methods is driven by a desire to: (i) provide solutions to transport problems which cannot otherwise be determined using analytic techniques and (ii) provide comparative solutions to test methods developed for other curvilinear geometries. Problems that are of increasing importance to the transport community are those that contain subdomains which are considered optically thick and diffusive. These problems result in high computational costs due to the grid refinement necessary to generate acceptable solutions. As a result, we look to develop vertex-based characteristic methods that can reproduce these diffusive solutions without resorting to significant spatial grid refinement. This research will allow for continued development of advanced conservative characteristic methods with better properties for R-Z geometries. The transport methods derived here are based on a change of coordinates that removes the angular derivative term in the differential operator resulting in a first order differential equation which can be discretized using methods similar to those found in 1-D slab geometry. In this study, we present a family of characteristic methods; Vladimirov's method of characteristics, a conservative long characteristic method, two locally conservative short characteristic methods, a linear long characteristic method, and an explicit slope long characteristic method. The numerical results presented in this thesis demonstrate the performance of each method. We found that the linear and explicit slope long characteristic methods generated numerical solutions which are well behaved in some diffusive problems. Also, we analyzed several of these methods using asymptotic diffusion limit analysis and found that the linear long characteristic method limits to a discretized version of the diffusion equation. Advisors/Committee Members: Dr. Paul J. Turinsky, Committee Member (advisor), Dr. Yousry Y. Azmy , Committee Member (advisor), Dr. Zhilin Li, Committee Member (advisor), Dr. Dmitriy Y. Anistratov, Committee Chair (advisor).

Subjects/Keywords: Characteristic Methods; Spherical Geometry; Particle Transport; Numerical

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APA (6^th Edition):

Fleming, J. T. I. (2009). Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry. (Thesis). North Carolina State University. Retrieved from http://www.lib.ncsu.edu/resolver/1840.16/226

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Fleming, John Thomas III. “Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry.” 2009. Thesis, North Carolina State University. Accessed January 27, 2021. http://www.lib.ncsu.edu/resolver/1840.16/226.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Fleming, John Thomas III. “Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry.” 2009. Web. 27 Jan 2021.

Vancouver:

Fleming JTI. Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry. [Internet] [Thesis]. North Carolina State University; 2009. [cited 2021 Jan 27]. Available from: http://www.lib.ncsu.edu/resolver/1840.16/226.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Fleming JTI. Characteristic Methods for Solving the Particle Transport Equation in 1-D Spherical Geometry. [Thesis]. North Carolina State University; 2009. Available from: http://www.lib.ncsu.edu/resolver/1840.16/226

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Texas – Austin

3. Cowley, Corrie Schaffer. Spherical and hyperbolic geometry in the high school curriculum.

Degree: MA, Mathematics, 2009, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2009-08-188

► The structure of Euclidean, spherical, and hyperbolic geometries are compared, considering specifically postulates, curvature of the plane, and visual models. Implications for distance, the sum… (more)

Subjects/Keywords: spherical geometry; hyperbolic geometry

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APA (6^th Edition):

Cowley, C. S. (2009). Spherical and hyperbolic geometry in the high school curriculum. (Masters Thesis). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2009-08-188

Chicago Manual of Style (16^th Edition):

Cowley, Corrie Schaffer. “Spherical and hyperbolic geometry in the high school curriculum.” 2009. Masters Thesis, University of Texas – Austin. Accessed January 27, 2021. http://hdl.handle.net/2152/ETD-UT-2009-08-188.

MLA Handbook (7^th Edition):

Cowley, Corrie Schaffer. “Spherical and hyperbolic geometry in the high school curriculum.” 2009. Web. 27 Jan 2021.

Vancouver:

Cowley CS. Spherical and hyperbolic geometry in the high school curriculum. [Internet] [Masters thesis]. University of Texas – Austin; 2009. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/2152/ETD-UT-2009-08-188.

Council of Science Editors:

Cowley CS. Spherical and hyperbolic geometry in the high school curriculum. [Masters Thesis]. University of Texas – Austin; 2009. Available from: http://hdl.handle.net/2152/ETD-UT-2009-08-188

McMaster University

4. Stone, Terry Wayne. A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation.

Degree: MEngr, 1977, McMaster University

URL: http://hdl.handle.net/11375/20236

►

This is Part B.

Another approach is adopted for deriving the moments equations in spherical geometry using a spherical harmonics expansion of the neutron… (more)

Subjects/Keywords: spherical; harmonics; neutron; transport; equation; geometry

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APA (6^th Edition):

Stone, T. W. (1977). A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation. (Masters Thesis). McMaster University. Retrieved from http://hdl.handle.net/11375/20236

Chicago Manual of Style (16^th Edition):

Stone, Terry Wayne. “A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation.” 1977. Masters Thesis, McMaster University. Accessed January 27, 2021. http://hdl.handle.net/11375/20236.

MLA Handbook (7^th Edition):

Stone, Terry Wayne. “A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation.” 1977. Web. 27 Jan 2021.

Vancouver:

Stone TW. A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation. [Internet] [Masters thesis]. McMaster University; 1977. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/11375/20236.

Council of Science Editors:

Stone TW. A Modified Spherical Harmonics Approach to Solving the Neutron Transport Equation. [Masters Thesis]. McMaster University; 1977. Available from: http://hdl.handle.net/11375/20236

Brno University of Technology

5. Ležovič, Petr. Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy.

Degree: 2019, Brno University of Technology

URL: http://hdl.handle.net/11012/25227

► The thesis contents the definition of basic notions of the spheric geometry, proofs of the main theorems and application for the spherical triangle. Furthermore there… (more)

Subjects/Keywords: Sférická geometrie; sférický trojúhelník; souřadnicová soustava; Spheric geometry; spherical triangle; system of coordinates

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APA (6^th Edition):

Ležovič, P. (2019). Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy. (Thesis). Brno University of Technology. Retrieved from http://hdl.handle.net/11012/25227

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ležovič, Petr. “Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy.” 2019. Thesis, Brno University of Technology. Accessed January 27, 2021. http://hdl.handle.net/11012/25227.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ležovič, Petr. “Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy.” 2019. Web. 27 Jan 2021.

Vancouver:

Ležovič P. Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy. [Internet] [Thesis]. Brno University of Technology; 2019. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/11012/25227.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ležovič P. Užití sférické geometrie v zeměpise a astronomii: Application of the spheric geometry in geography and astronomy. [Thesis]. Brno University of Technology; 2019. Available from: http://hdl.handle.net/11012/25227

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Universidade do Rio Grande do Sul

6. Ribeiro, Ricardo Silva. Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica.

Degree: 2013, Universidade do Rio Grande do Sul

URL: http://hdl.handle.net/10183/79482

►

Esta dissertação traz ideias para a inserção de novos conteúdos na matemática escolar. Ela trata da exploração de geometrias não-euclidianas, através de dois ambientes de… (more)

Subjects/Keywords: Non-euclidian geometries; Ensino-aprendizagem; Dynamical geometry; Geometria não euclidiana; Ensino de matematica; Geometry in school spherical geometry; Geometria dinâmica; Poincaré disk; Geometria

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APA (6^th Edition):

Ribeiro, R. S. (2013). Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica. (Thesis). Universidade do Rio Grande do Sul. Retrieved from http://hdl.handle.net/10183/79482

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Ribeiro, Ricardo Silva. “Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica.” 2013. Thesis, Universidade do Rio Grande do Sul. Accessed January 27, 2021. http://hdl.handle.net/10183/79482.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Ribeiro, Ricardo Silva. “Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica.” 2013. Web. 27 Jan 2021.

Vancouver:

Ribeiro RS. Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica. [Internet] [Thesis]. Universidade do Rio Grande do Sul; 2013. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/10183/79482.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Ribeiro RS. Geometrias não-euclidianas na escola : uma proposta de ensino através da geometria dinâmica. [Thesis]. Universidade do Rio Grande do Sul; 2013. Available from: http://hdl.handle.net/10183/79482

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Vienna

7. Schaumüller, Melanie. Wie mache ich die Erde flach?.

Degree: 2010, University of Vienna

URL: http://othes.univie.ac.at/10701/

►

Diese Arbeit beschäftigt sich mit der Problematik der Abbildung der Kugeloberoberfläche auf einer Ebene. Es ist zwar möglich, die Sphäre auf eine Ebene zuprojizieren, aber… (more)

▼

Diese Arbeit beschäftigt sich mit der Problematik der Abbildung der Kugeloberoberfläche auf einer Ebene. Es ist zwar möglich, die Sphäre auf eine Ebene zuprojizieren, aber es treten immer Verzerrungen auf. Als praktisches Beispiel dieser Thematik dient die Erde, die durch eine Kugel beschrieben wird. Die Anwendung wäre dann die Erstellung von Karten. Zu Beginn werden wichtige Begriffe und Sätze der Kugelgeometrie erarbeitet, um diese an konkreten Beispielen anzuwenden. Da es von Bedeutung ist zu wissen, welche Verzerrungen in einer Abbildung auftreten können, werden die verschiedenen Arten von Verzerrungen behandelt und Formeln zur Berechnung angeführt. Ein erster Schritt zur Umsetzung der Theorie auf die Erde erfolgt im Abschnitt „Verbindung zur Geographie“. Hier wird kurz darauf eingegangen, welche Form die Erde wirklich aufweist und warum man dennoch an der Vorstellung der Erde als Kugel festhält. Es folgen praktische Aufgaben zur Kursbestimmung und zur Peilung. Am Ende werden unterschiedliche Möglichkeiten der Abbildung und verschiedene Kartennetzentwürfe vorgestellt, die mit Formeln und Karten versehen sind. So kann man auch optisch gut zwischen abstands-, flächen- und winkeltreuen Abbildungen differenzieren.

This thesis deals with the difficulty of mapping the surface of a sphere on a plane. It is possible to project the sphere onto the plane, but there are always distortions. As a concrete example concerning this topic the earth can be chosen, which is described by a sphere. The application is the generation of maps. At first, important terms and definitions, as well as theorems on the geometry of the sphere's surface are worked out in order to apply them to concrete examples. As it is important to know which distortions appear in a map, there are different types of distortions und formulas listed. The preliminary step of the theory's transfer to the earth is in section “Verbindung zur Geographie” (“A link to geography”). This chapter explains which shape the earth really has and why we nevertheless keep the idea that the earth is a sphere. Afterwards, concrete examples for orientation and bearing are given. At the end, different possibilities of mapping and creating map projections with formulas and maps are introduced. This allows a visual distinction between depictions leaving invariant lengths, angles and areas.

Subjects/Keywords: 31.50 Geometrie: Allgemeines; Kugelgeometrie / Sphärische Trigonometrie / Kartenentwurf / Kartennetzentwurf; geometry of the sphere / spherical trigonometry / map projection

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APA (6^th Edition):

Schaumüller, M. (2010). Wie mache ich die Erde flach?. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/10701/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Schaumüller, Melanie. “Wie mache ich die Erde flach?.” 2010. Thesis, University of Vienna. Accessed January 27, 2021. http://othes.univie.ac.at/10701/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Schaumüller, Melanie. “Wie mache ich die Erde flach?.” 2010. Web. 27 Jan 2021.

Vancouver:

Schaumüller M. Wie mache ich die Erde flach?. [Internet] [Thesis]. University of Vienna; 2010. [cited 2021 Jan 27]. Available from: http://othes.univie.ac.at/10701/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Schaumüller M. Wie mache ich die Erde flach?. [Thesis]. University of Vienna; 2010. Available from: http://othes.univie.ac.at/10701/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Freie Universität Berlin

8. León, Emerson. Räume der konvexen n-Aquipartitionen.

Degree: 2015, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-5031

► Wir betrachten den Raum \C(\R^d,n) aller Aufteilungen von \R^d in n konvexe Gebiete für positive d und n. Dafür entwickeln wir grundlegende Konzepte und Definitionen,… (more)

▼ Wir betrachten den Raum \C(\R^d,n) aller Aufteilungen von \R^d in n konvexe Gebiete für positive d und n. Dafür entwickeln wir grundlegende Konzepte und Definitionen, untersuchen allgemeine Eigenschaften und betrachten verwandte Räume sowie Beispiele. Zunächst entwickeln wir dafür die benötigten Konzepte der Konvexgeometrie. In Kapitel 3 definieren wir konvexe n-Aufteilungen und zeigen, dass die Teile immer Polyeder sind. Dann definieren wir sphärische Aufteilungen und Seitenhalbordnungen und leiten grundlegende Strukturergebnisse ab. Kapitel 4 beschäftigt sich mit dem Raum \C(\R^d,n) aller konvexen n-Aufteilungen des~\R^d. Wir beschreiben eine Metrik und damit eine Topologie auf diesem Raum, sowie eine natürliche Kompaktifizierung \C(\R^d, ≤ \\! n), für die auch leere Teile erlaubt sind. Wir stellen den Raum der n-Aufteilungen dann auf zwei Weisen als eine Vereinigung von semialgebraischen Teilmengen dar: Wir betrachten Hyperebenenarrangements, die Auf\\-teilungen induzieren, und beschreiben \C(\R^d,n) so in Abhängikeit von den Hyperebenen, die die Aufteilung erzeugen. Für die zweite Beschreibung führen wir Knoten und Knotensysteme ein, die Eckenmengen verallgemeinern, und definieren den kombinatorischen Typ einer Aufteilung. Diese kombinatorischen Typen ergeben semialgebraische Teile, aus denen die Räume aufgebaut sind (Theorem \ref{semialgebraic}). Am Ende des Kapitels beschreiben wir wir explizit die Räume der n-Aufteilungen von \R^d und ihre Kompaktifizierungen für n=2 und für d=1. In Kapitel 5 diskutieren wir reguläre Aufteilungen. Wir berechnen die Dimension des Raums der regulären Aufteilungen \C_\reg(\R^d,n). Dann beweisen wir einen Universalitätssatz, wonach die Realiserungsräume regulärer Partitionen zu beliebigen primären basischen semialgebraischen Mengen stabil äquivalent sein können. In Kapitel 6 untersuchen wir die Dimension von Realisierungsräumen. Im Fall d=2 ist die Dimension von \C(\R²,n) für große n viel größer als \dim (\C_\reg(\R²,n)). Dann konzentrieren wir uns auf den Fall d=3, wo wir vermuten, dass die Dimension von \C(\R³,n) mit der Dimension von \C_\reg(\R³,n) übereinstimmt, und versuchen das mit einer Heuristik für die Zahl der Freiheitsgrade und damit der Dimensionen der Realisierungsräume zu untermauern. In Kapitel 7 führen wir die Räume von Äquipartitionen \C^\equi(\R^d,n,μ) für beschränkte positive Maße μ ein. Wir untersuchen die topologische Struktur für einige kleine Fälle und beschreiben, darauf aufbauend, die Räume der n-Äquipartitionen für d=2 und n=3. Wir diskutieren auch das Problem von Nandakumar und Ramana Rao über "faire Aufteilungen von Polygonen'' und verschiedene äquivariante Abbildungen, die zeigen, dass es für dieses Problem ausreicht, reguläre Äquipartitionen zu betrachten. Advisors/Committee Members: [email protected] (contact), m (gender), Prof. Günter M. Ziegler (firstReferee), Prof. Thorsten Theobald (furtherReferee).

Subjects/Keywords: convex; polyhedral; partition; spaces; spherical; geometry; equipartitions; face structure; hyperplanes; regular partitions; 500 Naturwissenschaften und Mathematik::510 Mathematik

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APA (6^th Edition):

León, E. (2015). Räume der konvexen n-Aquipartitionen. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-5031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

León, Emerson. “Räume der konvexen n-Aquipartitionen.” 2015. Thesis, Freie Universität Berlin. Accessed January 27, 2021. http://dx.doi.org/10.17169/refubium-5031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

León, Emerson. “Räume der konvexen n-Aquipartitionen.” 2015. Web. 27 Jan 2021.

Vancouver:

León E. Räume der konvexen n-Aquipartitionen. [Internet] [Thesis]. Freie Universität Berlin; 2015. [cited 2021 Jan 27]. Available from: http://dx.doi.org/10.17169/refubium-5031.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

León E. Räume der konvexen n-Aquipartitionen. [Thesis]. Freie Universität Berlin; 2015. Available from: http://dx.doi.org/10.17169/refubium-5031

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Exeter

9. Zhan, Xiaoya. A study of convection and dynamo in rotating fluid systems.

Degree: PhD, 2010, University of Exeter

URL: https://ore.exeter.ac.uk/repository/handle/10036/100074 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517199

► Convection in a Boussinesq fluid confined by a annular channel fast rotating about a vertical axis and uniformly heated from below, is one of our… (more)

▼ Convection in a Boussinesq fluid confined by a annular channel fast rotating about a vertical axis and uniformly heated from below, is one of our concerns in this thesis. An assumption that the channel has a sufficiently large radius in comparison with its gap-width is employed, so that the curvature effect can be neglected. The aspect ratio of the channel has great influence on the convective flow in it. Guided by the result of the linear stability analysis, we perform three-dimensional numerical simulations to investigate the convective flows under three different types of aspect ratios, which are namely the moderate or large aspect ratios, the very small aspect ratios and the moderately small aspect ratios. Also, we numerically study how convection in the channel is affected by inhomogeneous heat fluxes on sidewalls, which is a simple simulation of the thermal interaction between the Earth's core and mantle. Convection and dynamo action in a rapidly rotating, self-gravitating, Boussinesq fluid sphere is the other concern. We develop a finite element model for the dynamo problem in a whole sphere. This model is constructed by incorporating dynamo equations with globally implemented magnetic boundary conditions to a whole sphere convection model, which is also presented here. The coordinate singularity at the center usually encountered when applying the spectral method is no longer an obstacle and no nonphysical assumptions (i.e. hyper-diffusivities) are used in our model. A large effort has been made to efficiently parallelize the model. Consequently, it can take the full advantage of modern massively parallel computers. Based on this dynamo model, we investigate the dynamo process in a sphere and find that self-sustaining dynamos are more difficult to obtain in a sphere than in a spherical shell. They are activated at relatively high Rayleigh numbers. Moreover, the magnetic fields generated are not dipole-dominant, different from those generated in most dynamo simulations.

Subjects/Keywords: 620.106; convection; dynamo theory; spherical geometry; channel

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APA (6^th Edition):

Zhan, X. (2010). A study of convection and dynamo in rotating fluid systems. (Doctoral Dissertation). University of Exeter. Retrieved from https://ore.exeter.ac.uk/repository/handle/10036/100074 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517199

Chicago Manual of Style (16^th Edition):

Zhan, Xiaoya. “A study of convection and dynamo in rotating fluid systems.” 2010. Doctoral Dissertation, University of Exeter. Accessed January 27, 2021. https://ore.exeter.ac.uk/repository/handle/10036/100074 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517199.

MLA Handbook (7^th Edition):

Zhan, Xiaoya. “A study of convection and dynamo in rotating fluid systems.” 2010. Web. 27 Jan 2021.

Vancouver:

Zhan X. A study of convection and dynamo in rotating fluid systems. [Internet] [Doctoral dissertation]. University of Exeter; 2010. [cited 2021 Jan 27]. Available from: https://ore.exeter.ac.uk/repository/handle/10036/100074 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517199.

Council of Science Editors:

Zhan X. A study of convection and dynamo in rotating fluid systems. [Doctoral Dissertation]. University of Exeter; 2010. Available from: https://ore.exeter.ac.uk/repository/handle/10036/100074 ; https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.517199

Pontifícia Universidade Católica de São Paulo

10. João Pedro Marqueze. As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica.

Degree: 2006, Pontifícia Universidade Católica de São Paulo

URL: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4538

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The aim of this study is to present a sequence of problem solving activities through a qualitative approach whose aim is to study how this… (more)

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The aim of this study is to present a sequence of problem solving activities through a qualitative approach whose aim is to study how this sequence can allow high school students to learn basic concepts of Spherical Geometry while reviewing Plane Geometry. That is why we are trying to respond to the following basic question: What contributions a sequence of activities that has as a proposal the tessellation of the phases of the platonic solids on superficial sphere can allow for the teaching and learning of basic notions of Spherical Geometry? We appeal to the passion of the Brazilian people, soccer, in order to contextualize the topic in an ordinary way for the learners. In this ordinary example, not only a soccer ball is included, but also a tennis ball, volleyball, etc. The use of tangible materials such as polystyrene spheres, flexible rulers, colored pens, compasses, strings, pins and other materials that are easy to find, in addition to the traditional pen and paper, can all be used by students in learning about the phases of platonic solids, basis for understanding this task, to tessellate a soccer ball on a spherical surface. We formulate the hypothesis that the utilization of these materials and the departure from traditional methods that have been used will stimulate the interest of the students and create more understanding not only of Plane Geometry, but also Spherical Geometry as in the example above. We have compiled in this study a theoretical reference that includes socioconstructivism, which we believe created more interaction, and therefore made the teaching and learning environment more effective. We ended, in the end of this research, exciting indications that it is possible the teaching- learning of the Spherical Geometry, as it was proposed

O objetivo desta pesquisa é apresentar uma seqüência de atividades, por meio de resolução de problemas, numa abordagem qualitativa, visando a investigar como esta seqüência pode contribuir para que alunos do ensino médio apreendam conceitos básicos da Geometria Esférica enquanto resgatam conceitos da Geometria Plana. Para tanto procuramos responder a seguinte pergunta norteadora: Que contribuições uma seqüência de atividades que tem como proposta a tesselação das faces dos sólidos platônicos na superfície esférica pode proporcionar para o ensino-aprendizagem de Geometria Esférica? Apelamos para a paixão do povo brasileiro, o futebol, para contextualizar o tema no cotidiano dos aprendizes. Neste cotidiano não só a bola de futebol está presente, mas também, a bola de tênis, de vôlei, etc. O uso de materiais concretos como: esferas de isopor, régua flexível, canetas coloridas, compasso, barbantes, alfinetes e outros materiais de fácil acesso, além dos tradicionais lápis e papel, levou o aluno a representar, inspirado nas faces dos sólidos platônicos, base de compreensão para esta tarefa, a bola de futebol em uma superfície esférica. Acreditamos que a utilização destes materiais e a forma diferente da tradicional como é tratado o tema despertam no aluno o…

Advisors/Committee Members: Celina Aparecida Almeida Pereira Abar.

Subjects/Keywords: Sócio-construtivismo; MATEMATICA; Educacao matematica; Matematica – Estudo e ensino; Spherical Geometry; Geometria Esférica; Situação problema; Problem Solving; Socioconstructivism; Geometria Plana; Plane Geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Marqueze, J. P. (2006). As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica. (Thesis). Pontifícia Universidade Católica de São Paulo. Retrieved from http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4538

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Marqueze, João Pedro. “As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica.” 2006. Thesis, Pontifícia Universidade Católica de São Paulo. Accessed January 27, 2021. http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4538.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Marqueze, João Pedro. “As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica.” 2006. Web. 27 Jan 2021.

Vancouver:

Marqueze JP. As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica. [Internet] [Thesis]. Pontifícia Universidade Católica de São Paulo; 2006. [cited 2021 Jan 27]. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4538.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Marqueze JP. As faces dos sólidos platônicos na superfície esférica: uma proposta para o ensino-aprendizagem de noções básicas de Geometria Esférica. [Thesis]. Pontifícia Universidade Católica de São Paulo; 2006. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4538

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Freie Universität Berlin

11. Dai, Jia-Yuan. Das Ginzburg-Landau Paradigma.

Degree: 2017, Freie Universität Berlin

URL: http://dx.doi.org/10.17169/refubium-7709

► In dieser Arbeit etablieren wir eine funktionalanalytische Methode, um die Existenz von Ginzburg-Landau Spiralwellen zu beweisen. Auf der Grundlage von systematischen Erwägungen rechtfertigen wir den… (more)

Subjects/Keywords: complex Ginzburg-Landau equation; spiral waves; circular geometry; spherical geometry; 2-tip spirals; global bifurcation; 500 Naturwissenschaften und Mathematik::510 Mathematik::515 Analysis

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Dai, J. (2017). Das Ginzburg-Landau Paradigma. (Thesis). Freie Universität Berlin. Retrieved from http://dx.doi.org/10.17169/refubium-7709

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Dai, Jia-Yuan. “Das Ginzburg-Landau Paradigma.” 2017. Thesis, Freie Universität Berlin. Accessed January 27, 2021. http://dx.doi.org/10.17169/refubium-7709.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Dai, Jia-Yuan. “Das Ginzburg-Landau Paradigma.” 2017. Web. 27 Jan 2021.

Vancouver:

Dai J. Das Ginzburg-Landau Paradigma. [Internet] [Thesis]. Freie Universität Berlin; 2017. [cited 2021 Jan 27]. Available from: http://dx.doi.org/10.17169/refubium-7709.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Dai J. Das Ginzburg-Landau Paradigma. [Thesis]. Freie Universität Berlin; 2017. Available from: http://dx.doi.org/10.17169/refubium-7709

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Uppsala University

12. Jonsson, Kristoffer. Matching of geometrically and topologically changing meshes.

Degree: Division of Scientific Computing, 2015, Uppsala University

URL: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262249

► The aim for this thesis is to develop a foundation for a compression system for animated mesh sequences, specifically under dynamic change of mesh… (more)

Subjects/Keywords: mesh; meshes; matching; matchings; topology; geometry; manifold; compression; animation; animations; fluid; spherical harmonics; tensor; bijective; game; games; DICE; Computational Mathematics; Beräkningsmatematik; Computer Sciences; Datavetenskap (datalogi); Geometry; Geometri

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Jonsson, K. (2015). Matching of geometrically and topologically changing meshes. (Thesis). Uppsala University. Retrieved from http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262249

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Jonsson, Kristoffer. “Matching of geometrically and topologically changing meshes.” 2015. Thesis, Uppsala University. Accessed January 27, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262249.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Jonsson, Kristoffer. “Matching of geometrically and topologically changing meshes.” 2015. Web. 27 Jan 2021.

Vancouver:

Jonsson K. Matching of geometrically and topologically changing meshes. [Internet] [Thesis]. Uppsala University; 2015. [cited 2021 Jan 27]. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262249.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Jonsson K. Matching of geometrically and topologically changing meshes. [Thesis]. Uppsala University; 2015. Available from: http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-262249

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

University of Alberta

13. Wang, Wenping. Results on conics and quadrics in computer aided geometric designs.

Degree: PhD, Department of Computing Science, 1992, University of Alberta

URL: https://era.library.ualberta.ca/files/q524jr21w

Subjects/Keywords: Geometry – Data processing.; Conics, Spherical – Data processing.; Quadrics – Data processing.; Computer-aided design.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Wang, W. (1992). Results on conics and quadrics in computer aided geometric designs. (Doctoral Dissertation). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/q524jr21w

Chicago Manual of Style (16^th Edition):

Wang, Wenping. “Results on conics and quadrics in computer aided geometric designs.” 1992. Doctoral Dissertation, University of Alberta. Accessed January 27, 2021. https://era.library.ualberta.ca/files/q524jr21w.

MLA Handbook (7^th Edition):

Wang, Wenping. “Results on conics and quadrics in computer aided geometric designs.” 1992. Web. 27 Jan 2021.

Vancouver:

Wang W. Results on conics and quadrics in computer aided geometric designs. [Internet] [Doctoral dissertation]. University of Alberta; 1992. [cited 2021 Jan 27]. Available from: https://era.library.ualberta.ca/files/q524jr21w.

Council of Science Editors:

Wang W. Results on conics and quadrics in computer aided geometric designs. [Doctoral Dissertation]. University of Alberta; 1992. Available from: https://era.library.ualberta.ca/files/q524jr21w

Pontifícia Universidade Católica de São Paulo

14. Irene da Conceição Rodrigues Prestes. Geometria esférica: uma conexão com a geografia.

Degree: 2006, Pontifícia Universidade Católica de São Paulo

URL: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4387

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This work intends to help the teaching-learning process of geometry, mainly the sphere geometry, in order to help the implementation of the purposes that has… (more)

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This work intends to help the teaching-learning process of geometry, mainly the sphere geometry, in order to help the implementation of the purposes that has as a goal the interaction of Math and Geography. It tried to answer the question of the research: Will the study of the contents of the Sphere Geometry help the comprehension of the Earth geometry? In order to clear this up it was done an experimental study, starting with a teaching sequence which could investigate possible relations made by the pupils when they needed i to solve situations involving the notions of the Sphere Geometry. It was used as a research methodology the Teaching Engeneering and the theoric reference was based on the ideas od Vergnauds and Vygotskys theories. The results of the experiments made with the students during the sequence development point to the importance of a work which integrates more than one subject matter

Este trabalho pretende contribuir com o processo de ensino e aprendizagem da Geometria da Esfera, procurando subsidiar a implementação de propostas que visam a interação entre Matemática e Geografia. Procurou-se responder à questão de Pesquisa: Uma introdução à Geometria Esférica pode favorecer o estudo da Geografia do Globo Terrestre e em particular o estudo de mapas?. Para auxiliar no delineamento desta proposta realizou-se um estudo experimental, partindo de uma seqüência de ensino que teve como intuito investigar as possíveis relações que os alunos estabelecem quando solicitados a resolver situações envolvendo noções de geometria esférica. Para tanto foi utilizada como metodologia de pesquisa a Engenharia Didática e o referencial teórico foi baseado na formação de conceitos das teorias de Vergnaud e Vygotsky. As produções e interações dos alunos, durante o desenvolvimento da seqüência de ensino, apontam que um trabalho integrando conteúdos de Geometria Esférica contribui para o processo de compreensão de conteúdos específicos de geografia, em particular do estudo dos mapas

Advisors/Committee Members: Vincenzo Bongiovanni.

Subjects/Keywords: Ensino e Aprendizagem; Educacao matematica; Matematica – Estudo e ensino; Spherical Geometry; Teaching and Learning; Interdisciplinarity; Geografia; Geometria Esférica; Geography; Interdisciplinaridade; MATEMATICA; Geometria – Estudo e ensino; Matemática; Esfera; Mathematic

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Prestes, I. d. C. R. (2006). Geometria esférica: uma conexão com a geografia. (Thesis). Pontifícia Universidade Católica de São Paulo. Retrieved from http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4387

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Prestes, Irene da Conceição Rodrigues. “Geometria esférica: uma conexão com a geografia.” 2006. Thesis, Pontifícia Universidade Católica de São Paulo. Accessed January 27, 2021. http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4387.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Prestes, Irene da Conceição Rodrigues. “Geometria esférica: uma conexão com a geografia.” 2006. Web. 27 Jan 2021.

Vancouver:

Prestes IdCR. Geometria esférica: uma conexão com a geografia. [Internet] [Thesis]. Pontifícia Universidade Católica de São Paulo; 2006. [cited 2021 Jan 27]. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4387.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Prestes IdCR. Geometria esférica: uma conexão com a geografia. [Thesis]. Pontifícia Universidade Católica de São Paulo; 2006. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=4387

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

15. Frenkel, Elena. Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry.

Degree: Docteur es, Mathématiques, 2018, Université de Strasbourg

URL: http://www.theses.fr/2018STRAD028

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L'objet de ce travail est de prouver des théorèmes de géométrie hyperbolique en utilisant des méthodes développées par Euler, Schubert et Steiner en géométrie sphérique.… (more)

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L'objet de ce travail est de prouver des théorèmes de géométrie hyperbolique en utilisant des méthodes développées par Euler, Schubert et Steiner en géométrie sphérique. On donne des analogues hyperboliques de certaines formules trigonométriques en utilisant la méthode des variations et une formule pour l'aire d'un triangle. Euler utilisa cette idée en géométrie sphérique.On résout ensuite le problème de Lexell en géométrie hyperbolique. Cette partie est basée sur un travail en collaboration avec Weixu Su. En utilisant l'analogue hyperbolique des identités de Cagnoli, on prouve deux résultats classiques en géométrie hyperbolique. Ensuite, on donne les solutions aux problèmes de Schubert (en collaboration avec Vincent Alberge) et de Steiner. En suivant les idées de Norbert A'Campo, on donne l'ébauche de la preuve de la formule de Schlafli en utilisant la géométrie intégrale. Cette recherche peut être généralisée partiellement au cas de la dimension 3.

Our aim is to prove sorne theorems in hyperbolic geometry based on the methods of Euler, Schubert and Steiner in spherical geometry. We give the hyperbolic analogues of sorne trigonometrie formulae by method of variations and an a rea formula in terms of sides of triangles, both due to Euler in spherical case. We solve Lexell's problem. This is a joint work with Weixu Su. We give a shorter formula than Euler's a rea formula. Using hyperbolic analogues of Cagnoli's identities, we prove two classical results in hyperbolic geometry. Further, we give solutions of Schubert's and Steiner's problems. The study of Schubert's problem is a joint work with Vincent Alberge. Finally, following ideas of Norbert A' Campo, we give the sketch of the proof of Schlafli formula using integral geometry. The mentioned theorems can be generalized to the case of dimension 3 partially by means of the techniques used developed in this the sis.

Advisors/Committee Members: Papadopoulos, Athanase (thesis director), A'Campo, N. (thesis director).

Subjects/Keywords: Aire; Volume; Géométrie hyperbolique; Géométrie sphérique; Problème de Lexell; Formule de l’aire d’Euler; Problème de Schubert; Formule de Schläfli; Area; Volume; Hyperbolic geometry; Spherical geometry; Lexell’s problem; Euler’s area formula; Schubert’s problem; Schläfli formula; 516.9

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Frenkel, E. (2018). Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry. (Doctoral Dissertation). Université de Strasbourg. Retrieved from http://www.theses.fr/2018STRAD028

Chicago Manual of Style (16^th Edition):

Frenkel, Elena. “Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry.” 2018. Doctoral Dissertation, Université de Strasbourg. Accessed January 27, 2021. http://www.theses.fr/2018STRAD028.

MLA Handbook (7^th Edition):

Frenkel, Elena. “Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry.” 2018. Web. 27 Jan 2021.

Vancouver:

Frenkel E. Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry. [Internet] [Doctoral dissertation]. Université de Strasbourg; 2018. [cited 2021 Jan 27]. Available from: http://www.theses.fr/2018STRAD028.

Council of Science Editors:

Frenkel E. Sur l'aire et le volume en géométrie sphérique et hyperbolique : On area and volume in spherical and hyperbolic geometry. [Doctoral Dissertation]. Université de Strasbourg; 2018. Available from: http://www.theses.fr/2018STRAD028

16. Βαφέας, Παναγιώτης. Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes.

Degree: 2003, University of Patras; Πανεπιστήμιο Πατρών

URL: http://hdl.handle.net/10442/hedi/14261

►

Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple but reliable… (more)

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Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple but reliable platform for the analytical or semianalytical solution of heat and mass transport problems. Most of the analytical models in this realm consider either spherical or, in latter versions, non-spherical but still axisymmetric shapes. Despite of the fact that many practical applications involve particles with axial symmetry, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in three and two-dimensional spherical, spheroidal or ellipsoidal domains. Four different complete representations of the solutions for flows that follow the Stokes description are considered here. The first one, named Stokes representation, is obtained, expressing equation of motion in 2-D spherical or spheroidal coordinates, according to which the stream function is expanded in terms of separable or semiseparable eigenmodes, respectively. The other three, valid in non-axisymmetric geometries as well, are the Papkovich - Neuber, the Boussinesq - Galerkin and the Palaniappan et al. differential representations, where the velocity and total pressure fields are expressed in terms of harmonic and biharmonic eigenfunctions. These complete differential solutions hold true also for 2-D flow problems. Connection formulae are obtained for the case of axisymmetric and three-dimensional flows, which relate the harmonic and the stream potential functions. The interrelation is a consequence of the equation of the flow fields and specifies the exact relations of the connection between the corresponding constant coefficients of the potentials. The inversion of this procedure depends on the geometry and the complexity of the differential solutions. It seems that the Papkovich - Neuber differential representation offers us certain important advantages and forms a more complete way in order to solve 2-D and mostly 3-D cell models, where either stationary particles are embedded within a uniformly moving fluid (Kuwabara model) or the particles are moving with a constant uniform velocity and / or rotate with a constant angular velocity in an otherwise quiescent fluid (Happel model, self-sufficient in mechanical energy). The flexibility of the representation, inherited by its degrees of freedom, helps us to confront certain indeterminacies in complicated geometries. This is demonstrated by solving the problem of the flow in a fluid cell filling the space between the surface of the solid particle and the fictitious outer boundary with Kuwabara or Happel-type boundary conditions in several geometries. Thus, we obtain analytical expressions for the velocity, the total pressure, the angular velocity and the stress tensor fields for different particle-in-cell system models. The laborious task of reducing the results to simpler geometries is also included.

Τα μοντέλα…

Subjects/Keywords: Διαφορικές αναπαραστάσεις; Μοντέλα κυττάρων; Σφαιρική γεωμετρία; Σφαιροειδής γεωμετρία; Ελλειψοειδής γεωμετρία; Ροή Stokes; Stokes flow; Differential representations; Cell modells; Spherical geometry; Spheroidal geometry; Ellipsoidal geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Βαφέας, . �. (2003). Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes. (Thesis). University of Patras; Πανεπιστήμιο Πατρών. Retrieved from http://hdl.handle.net/10442/hedi/14261

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Βαφέας, Παναγιώτης. “Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes.” 2003. Thesis, University of Patras; Πανεπιστήμιο Πατρών. Accessed January 27, 2021. http://hdl.handle.net/10442/hedi/14261.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Βαφέας, Παναγιώτης. “Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes.” 2003. Web. 27 Jan 2021.

Vancouver:

Βαφέας �. Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes. [Internet] [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2003. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/10442/hedi/14261.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Βαφέας �. Θεωρία διαφορικών αναπαραστάσεων στη ροή Stokes. [Thesis]. University of Patras; Πανεπιστήμιο Πατρών; 2003. Available from: http://hdl.handle.net/10442/hedi/14261

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

17. JosÃ Adriano Fernandes dos Santos. Applied mathematics to geography.

Degree: Master, 2016, Universidade Federal do Ceará

URL: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058 ;

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Partindo do cenÃrio interdisciplinar em que a MatemÃtica se encontra, este trabalho se resume a apresentar aplicaÃÃes oriundos da Geografia dentro da contextualizaÃÃo matemÃtica. Os… (more)

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Partindo do cenÃrio interdisciplinar em que a MatemÃtica se encontra, este trabalho se resume a apresentar aplicaÃÃes oriundos da Geografia dentro da contextualizaÃÃo matemÃtica. Os PCNâs (1998), documentos que regem a educaÃÃo atual brasileira, deixa clara importÃncia do trabalho interdisciplinar no ensino, bem como a relevÃncia de um ensinamento contextualizado baseado na pratica e vivÃncia histÃrica do homem. Por sua vez, na Geografia foi visto que a cartografia traz contribuiÃÃes relevantes Ã matemÃtica, e que a trigonometria Ã uma das ferramentas principais utilizadas nesta conjuntura, tanto por parte da geometria euclidiana quanto da geometria nÃo-euclidiana. Assim neste trabalho foram apresentadas algumas aplicaÃÃes retiradas do estudo da cartografia que, com a ajuda da matemÃtica e principalmente da trigonometria (plana e esfÃrica) foram resolvidas. Dando sequÃncia, ainda com foco na cartografia, especificamente no estudo de mapas e projeÃÃes, foi dada Ãnfase Ã ProjeÃÃo CilÃndrica de Mercator e respectivas explicaÃÃes matemÃticas para a chamada arte de projetar num plano, no caso, Ã projeÃÃo da esfera num plano, com suas devidas explicaÃÃes matemÃticas para tal feito. Com o tempo e o surgimento do cÃlculo infinitesimal, foi mostrado aqui a determinaÃÃo da chamada variÃvel de Mercator, e sua origem. Em seguida com a ajuda da Geometria Diferencial dando Ãnfase aos estudos de Gauss, foi apresentada a nÃo isometria entre o plano e a esfera, e que a curvatura gaussiana Ã a funÃÃo definidora para tal fato. AtravÃs das formas fundamentais e do Teorema egrÃgio aqui tambÃm apresentadas, os estudos de Gauss dentro da geometria diferencial foram definidores para a explicaÃÃo mais atual da variÃvel de Mercator, contribuindo assim para o esclarecimento da famosa projeÃÃo feita por Mercator que ficou na histÃria por sua perfeiÃÃo.

From the interdisciplinary scenario in which mathematics is, this work comes down to present applications coming from Geography within the mathematical context. The NCP's (1998), documents governing the current Brazilian education, makes clear the importance of interdisciplinary work in education, and the importance of a contextualized teaching based on practical and historical experience of man. In turn, the geography was seen that mapping brings outstanding contributions to mathematics, and trigonometry is one of the main tools used in this context, both by the Euclidean geometry as the non-Euclidean geometry. So in this paper were presented some applications withdrawn from the study of cartography, with the help of mathematics and especially Trigonometry (flat and spherical) were resolved. Continuing, still focusing on cartography, specifically in the study of maps and projections, emphasis was given to Cylindrical Mercator projection and their mathematical explanations for the so-called art of designing a plan in case the projection of the sphere in a plane, with its appropriate mathematical explanations for such a feat. With time and the emergence of infinitesimal calculus, it was shown…

Advisors/Committee Members: Marcelo Ferreira de Melo, Marcos Ferreira de Melo, Paulo Roberto Lopes Thiers.

Subjects/Keywords: MATEMATICA APLICADA; variÃvel de Mercator; contextualizaÃÃo matemÃtica; teorema egrÃgio; Mercator variable; mathematical context; theorem egregious; ProjeÃÃo de Mercator (Cartografia); Trigonometria plana; Trigonometria esfÃrica; Geometria diferencial; Oblique Mercator projection (Cartography); Plane trigonometry; Spherical trigonometry; Differential geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Santos, J. A. F. d. (2016). Applied mathematics to geography. (Masters Thesis). Universidade Federal do Ceará. Retrieved from http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058 ;

Chicago Manual of Style (16^th Edition):

Santos, JosÃ Adriano Fernandes dos. “Applied mathematics to geography.” 2016. Masters Thesis, Universidade Federal do Ceará. Accessed January 27, 2021. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058 ;.

MLA Handbook (7^th Edition):

Santos, JosÃ Adriano Fernandes dos. “Applied mathematics to geography.” 2016. Web. 27 Jan 2021.

Vancouver:

Santos JAFd. Applied mathematics to geography. [Internet] [Masters thesis]. Universidade Federal do Ceará 2016. [cited 2021 Jan 27]. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058 ;.

Council of Science Editors:

Santos JAFd. Applied mathematics to geography. [Masters Thesis]. Universidade Federal do Ceará 2016. Available from: http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058 ;

Université de Montréal

18. Gauthier, Mathieu. Images géométriques de genre arbitraire dans le domaine sphérique.

Degree: 2009, Université de Montréal

URL: http://hdl.handle.net/1866/7210

Subjects/Keywords: Images géométriques; Geometry images; Paramétrisation sphérique; Spherical parameterization; Topologie informatique; Computational topology; Remaillage; Remeshing

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gauthier, M. (2009). Images géométriques de genre arbitraire dans le domaine sphérique. (Thesis). Université de Montréal. Retrieved from http://hdl.handle.net/1866/7210

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Gauthier, Mathieu. “Images géométriques de genre arbitraire dans le domaine sphérique.” 2009. Thesis, Université de Montréal. Accessed January 27, 2021. http://hdl.handle.net/1866/7210.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Gauthier, Mathieu. “Images géométriques de genre arbitraire dans le domaine sphérique.” 2009. Web. 27 Jan 2021.

Vancouver:

Gauthier M. Images géométriques de genre arbitraire dans le domaine sphérique. [Internet] [Thesis]. Université de Montréal; 2009. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/1866/7210.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Gauthier M. Images géométriques de genre arbitraire dans le domaine sphérique. [Thesis]. Université de Montréal; 2009. Available from: http://hdl.handle.net/1866/7210

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

19. Batista, Célia Maria Nogueira. A Geometria esférica e os sólidos platônicos.

Degree: 2007, Universidade Federal do Amazonas

URL: http://tede.ufam.edu.br/handle/tede/3670

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Esta dissertação apresenta uma nova demostração do resultado obtido por Platão no século IV a.C, na Grécia antiga, de que existe um número finito de… (more)

Subjects/Keywords: Poliedros regulares congruentes; Sólidos platônicos; Spherical geometry; Platonic solids; CIÊNCIAS EXATAS E DA TERRA: MATEMÁTICA

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Batista, C. M. N. (2007). A Geometria esférica e os sólidos platônicos. (Masters Thesis). Universidade Federal do Amazonas. Retrieved from http://tede.ufam.edu.br/handle/tede/3670

Chicago Manual of Style (16^th Edition):

Batista, Célia Maria Nogueira. “A Geometria esférica e os sólidos platônicos.” 2007. Masters Thesis, Universidade Federal do Amazonas. Accessed January 27, 2021. http://tede.ufam.edu.br/handle/tede/3670.

MLA Handbook (7^th Edition):

Batista, Célia Maria Nogueira. “A Geometria esférica e os sólidos platônicos.” 2007. Web. 27 Jan 2021.

Vancouver:

Batista CMN. A Geometria esférica e os sólidos platônicos. [Internet] [Masters thesis]. Universidade Federal do Amazonas; 2007. [cited 2021 Jan 27]. Available from: http://tede.ufam.edu.br/handle/tede/3670.

Council of Science Editors:

Batista CMN. A Geometria esférica e os sólidos platônicos. [Masters Thesis]. Universidade Federal do Amazonas; 2007. Available from: http://tede.ufam.edu.br/handle/tede/3670

20. Gueirard, Ninuwe. Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance.

Degree: Docteur es, Philosophie, 2017, Aix Marseille Université

URL: http://www.theses.fr/2017AIXM0478

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Cette thèse se propose d’étudier la difficulté de l’estimation de la distance dans le cadre de la géométrie de l’espace visuel. En philosophie de la… (more)

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Cette thèse se propose d’étudier la difficulté de l’estimation de la distance dans le cadre de la géométrie de l’espace visuel. En philosophie de la perception, cette thèse est d'abord discutée au plan épistémologique : comment savoir que cette distance n'est pas connue ou connaissable, quoique perçue et discutée. Les travaux de Berkeley nous servent de point de départ et fixent un cadre spéculatif, puisque Berkeley soutient en effet que le jugement porté sur la distance résulte entièrement de l'expérience, quoique cette distance ne puisse être vue phénoménalement. La thèse se propose d'examiner une question essentielle supportée par cette alternative centrale mais au plan ontologique cette fois : comme déterminer de quel type est la distance : est-elle inconsciemment visible ? tangible ? ou visible et tangible à la fois ? Peut-elle être une entité assignable dans un espace hyperbolique, ou sphérique, un espace strictement euclidien, ou hyperbolique et sphérique en même temps qu'euclidien ? Pour appuyer notre propos et notre recherche nous mettrons à l’épreuve différents textes et expériences en passant de Berkeley à I. Rock ou de T. Reid à M. Wagner. Notre but aura été d'explorer les limites argumentatives et de montrer ce qui est impliqué par ces différentes appréciations et assignations de la distance dans tel ou tel espace déterminé. A chaque fois s'affrontent la géométrie de l’espace visuel et l’optique physiologique, mais au sein d'un même débat de fond qui consiste à savoir comment définir philosophiquement l’estimation de la distance ?

This thesis examines the difficulties in estimating the geometrical distance of visual space. Submitted in the field of Philosophy of Perception, this thesis is first discussed from an epistemological standpoint: how does one know that this distance is unknown or unknowable despite being perceived and discussed. The various works of Berkeley serve as a point of depart and establish a speculative framework as Berkeley held that judgment of distance results entirely from experience despite the fact that this distance cannot be seen in a phenomenal way. This thesis examines an essential question supported by this central problem, this time from an ontological position: how is the type of distance to be determined: is it unconsciously visible?tangible? or both visible and tangible at the same time? Can it be categorized in a hyperbolic space, or spherical space, or a strictly Euclidean space, or hyperbolic and spherical at the same time as Euclidean? In support of the thesis and research, various texts and experiences have been examined and contrasted, including those of Berkeley and I. Rock as well as T. Reid and M. Wagner. The goal has been to explore the limits of argumentation and to show what is implicated by these different accounts and assignment of distance in one, versus another, determined space; additionally studying subjects including the experience of the alleys or the so-called the moon illusion, which appeared to be demonstrative examples. In each instance,…

Advisors/Committee Members: Monnoyer, Jean-Maurice (thesis director).

Subjects/Keywords: Espace visuel; géométrie; euclidien; sphérique; hyperbolique; illusion de la lune; figure visible; figure tangible; distance; taille; angle; paradoxe taille/distance; Berkeley; Reid; Wagner; Rock; Kaufman; Indow; Luneburg; Descartes.; Key words : Visual space; geometry; euclidean; spherical; hyperbolic; moon illu-Sion; visible figure; tangible figure; distance; size; angle; size/distance paradox; Berkeley; Reid; Wagner; Rock; Kaufman; Indow; Luneburg; Descartes.

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Gueirard, N. (2017). Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance. (Doctoral Dissertation). Aix Marseille Université. Retrieved from http://www.theses.fr/2017AIXM0478

Chicago Manual of Style (16^th Edition):

Gueirard, Ninuwe. “Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance.” 2017. Doctoral Dissertation, Aix Marseille Université. Accessed January 27, 2021. http://www.theses.fr/2017AIXM0478.

MLA Handbook (7^th Edition):

Gueirard, Ninuwe. “Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance.” 2017. Web. 27 Jan 2021.

Vancouver:

Gueirard N. Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance. [Internet] [Doctoral dissertation]. Aix Marseille Université 2017. [cited 2021 Jan 27]. Available from: http://www.theses.fr/2017AIXM0478.

Council of Science Editors:

Gueirard N. Recherches sur la géométrie de l'espace visuel : le cas particulier de l'appréciation de la distance : Research on the geometry of the visual space : the particular case of the appreciation of the distance. [Doctoral Dissertation]. Aix Marseille Université 2017. Available from: http://www.theses.fr/2017AIXM0478

21. Šabeder, Aljaž. Sončne ure pri poučevanju matematičnih in fizikalnih vsebin.

Degree: 2016, Univerza v Mariboru

URL: https://dk.um.si/IzpisGradiva.php?id=62461 ; https://dk.um.si/Dokument.php?id=107471&dn= ; https://plus.si.cobiss.net/opac7/bib/22560776?lang=sl

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V magistrskem delu je obravnavana problematika sončnih ur iz matematičnega in fizikalnega vidika. Podan je pregled različnih tipov sončnih ur s poudarkom na ekvatorialnih sončnih… (more)

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V magistrskem delu je obravnavana problematika sončnih ur iz matematičnega in fizikalnega vidika. Podan je pregled različnih tipov sončnih ur s poudarkom na ekvatorialnih sončnih urah. Podrobno je razloženo delovanje ekvatorialnih ur in analematične sončne ure, ki so lahko vključene v posamezne vsebine pri poučevanju v osnovnih in srednjih šolah. Razlaga delovanja sončnih ur temelji na Keplerjevih zakonih, navideznem potovanju Sonca čez nebesno sfero, geometriji in enačbi stožnic (predvsem elipse). Poglobljeno je razložena osnova nebesne mehanike s poudarkom na sfernih koordinatnih sistemih (horizontskem in ekvatorialnem), ki so ključni za določanje koordinat nebesnih teles na nebesni sferi. Obravnavana je razlika med dnevnim in letnim gibanjem Sonca in posledično med dnevnim in letnim gibanjem sence, ki jo opiše konec (navpične) palice (gnomon). Opisana je razlika med zvezdnim (siderskim), sončnim (sinodskim) in povprečnim dnevom, ki so ključni pri umerjanju sončne ure. S tem namenom so pojasnjene tudi vse korekcije časa, s katerimi lahko ločimo med časom, ki ga kaže sončna in ročna ura. Ena izmed glavnih korekcij je zagotovo enačba časa, ki nam pove za razliko med pravim in srednjim Soncem. Opisan je način za iskanje lokalnega meridiana, ki je poleg določanja geografske širine in dolžine kraja, na kateri je sončna ura, ključen za njeno konstrukcijo. Podrobneje je predstavljena odvisnost urnih črt posameznih sončnih ur, ki so narisane na njihovih številčnicah. Za lažjo predstavo so omenjene številčnice predstavljene tudi na grafični način z matematičnim programom Geogebra. Raziskani so učni načrti predmetov matematike, fizike in astronomije v srednjih in osnovnih šolah ter učne vsebine, pri katerih je tematika sončnih ur lahko vpeljana v redno izobraževalno snov.

The problem of sundials is discussed from the mathematical and physical point of view. A review of several types of equatorial sundials is presented. The origin of equatorial, analematic and polar sundials is explained. In particular, some original ideas how to include the topics of sundials in some related contents in teaching at elementary and secondary schools is considered. The interpretation of functioning of the sundials is based on Kepler's laws, the virtual movement of the Sun over the celestial sphere, the geometry and conics section equations (in particular of ellipses). More in-depth explanation of how the sundials work is given by the basis of celestial mechanics with the emphasis on spherical coordinate systems (horizontal and equatorial). Horizontal and equatorial coordinate systems are known to be crucial for determining the coordinates of celestial bodies on the celestial sphere. The difference between the daily and annual movement of the sun and consequently the difference between the daily and annual movements of the shadow (of the gnomon) is described. The difference between astronomical, solar and the average day is considered. All this different times and the corresponding time corrections are crucial for the calibration of…

Advisors/Committee Members: Mencinger, Matej, Repnik, Robert.

Subjects/Keywords: sončne ure; Keplerjevi zakoni; nebesna mehanika; dnevno in letno navidezno gibanje Sonca; zvezdni dan; sončni dan; enačba časa; lokalni meridian; urne črte; stožnice; sferni koordinatni sistem.; Sundials; Kepler's laws; celestial mechanics; daily and annual movement of the Sun; astronomical day; solar day; equation of time; local meridian; hour lines; conics; spherical coordinate; sferical geometry.; info:eu-repo/classification/udc/37.091.3:51/53(043.2)

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Šabeder, A. (2016). Sončne ure pri poučevanju matematičnih in fizikalnih vsebin. (Masters Thesis). Univerza v Mariboru. Retrieved from https://dk.um.si/IzpisGradiva.php?id=62461 ; https://dk.um.si/Dokument.php?id=107471&dn= ; https://plus.si.cobiss.net/opac7/bib/22560776?lang=sl

Chicago Manual of Style (16^th Edition):

Šabeder, Aljaž. “Sončne ure pri poučevanju matematičnih in fizikalnih vsebin.” 2016. Masters Thesis, Univerza v Mariboru. Accessed January 27, 2021. https://dk.um.si/IzpisGradiva.php?id=62461 ; https://dk.um.si/Dokument.php?id=107471&dn= ; https://plus.si.cobiss.net/opac7/bib/22560776?lang=sl.

MLA Handbook (7^th Edition):

Šabeder, Aljaž. “Sončne ure pri poučevanju matematičnih in fizikalnih vsebin.” 2016. Web. 27 Jan 2021.

Vancouver:

Šabeder A. Sončne ure pri poučevanju matematičnih in fizikalnih vsebin. [Internet] [Masters thesis]. Univerza v Mariboru; 2016. [cited 2021 Jan 27]. Available from: https://dk.um.si/IzpisGradiva.php?id=62461 ; https://dk.um.si/Dokument.php?id=107471&dn= ; https://plus.si.cobiss.net/opac7/bib/22560776?lang=sl.

Council of Science Editors:

Šabeder A. Sončne ure pri poučevanju matematičnih in fizikalnih vsebin. [Masters Thesis]. Univerza v Mariboru; 2016. Available from: https://dk.um.si/IzpisGradiva.php?id=62461 ; https://dk.um.si/Dokument.php?id=107471&dn= ; https://plus.si.cobiss.net/opac7/bib/22560776?lang=sl

22. Giaier, Kevin Stanton. Designing Shape Changing Mechanisms for Planar and Spatial Applications.

Degree: MS(M.S.), Mechanical Engineering, 2014, University of Dayton

URL: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1418043619

► Rigid-body shape changing mechanisms are a growing area of research due to their numerous practical uses. Rigid-body shape-change describes mechanisms comprised of rigid links connected… (more)

▼ Rigid-body shape changing mechanisms are a growing area of research due to their numerous practical uses. Rigid-body shape-change describes mechanisms comprised of rigid links connected with revolute and prismatic joints that are able to approximate a set of prescribed “morphing” curves. Planar rigid-body shape-changing mechanisms are synthesized to achieve different positions within a common plane. Designing for spatial tasks, however, is an area of emerging research. This thesis addresses topics in both planar and spatial shape-changing devices. First, a practical application for planar shape-changing devices is developed through the design and testing of variable geometry dies for polymer extrusion. Second, a synthesis methodology for spatial shape-changing is developed for serial chains of spherical four-bar mechanisms that can achieve specified helices. Variable geometry dies enable the extrusion of plastic parts with a varying cross-section. Extrusion accounts for 40% of all manufactured plastic parts due to its relatively low-cost and high-production-rate. Conventional polymer extrusion technology, however, is limited to fixed dies that produce continuous plastic products of constant cross section defined by the die exit profile. A shape-changing die allows the cross-section of the extruded part to change over its length, thereby introducing the capacity to manufacture plastic faster and with lower tooling costs than injection molding. This thesis discusses design guidelines that were developed for movable die features including revolute and prismatic joint details, land length, and the management of die leakage. To assess these guidelines, multiple dies have been designed and constructed to include an arbitrary four-sided exit profile where changes were made to the internal angles and length of sides as the extruder was operating. Experimental studies were conducted by using different extruder line settings and time between die movements. Test results are presented that include shape repeatability and the relationship between extrudate profile and die exit geometry.A spatial shape-change application is then introduced with serial chains of spherical four-bar mechanisms. The chains are comprised of identical copies of the same four-bar mechanism by connecting the coupler of the prior spherical mechanism to the base link of the subsequent spherical mechanism. Although having a degree of freedom per mechanism, the design methodology is based upon identically actuating each mechanism. With these conditions, the kinematic synthesis task of matching periodically spaced points on up to five arbitrary helices may be achieved. Due to the constraints realized via the spherical equivalent of planar Burmester Theory, spherical mechanisms produce at most five prescribed orientations resulting in this maximum. The methodology introduces a companion helix to each design helix along which the intersection locations of each spherical mechanisms axes must lie. As the mechanisms are connected by rigid links, the distance… Advisors/Committee Members: Murray, Andrew (Advisor), Myszka, David (Advisor).

Subjects/Keywords: Mechanical Engineering; polymer extrusion; shape change; spherical four-bar mechanism; variable geometry die; polymer manufacturing; spatial curve matching; mechanical helix

…12 2.1 . . . . . . . . . 12 15 15 16 18 19 20 22 26 VARIABLE GEOMETRY DIES FOR POLYMER… …Motivation for Variable Geometry Dies . Spatial Shape Changing Curve Segments Organization… …Design of Spherical Four-Bar Mechanisms… …SPHERICAL FOUR-BAR MECHANISMS TO ACHIEVE DESIGN HELICES… …Spherical Four-Bar Mechanism Parameters . . . . . . . . . . . . . Construction of the Chain…

10 more images…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Giaier, K. S. (2014). Designing Shape Changing Mechanisms for Planar and Spatial Applications. (Masters Thesis). University of Dayton. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=dayton1418043619

Chicago Manual of Style (16^th Edition):

Giaier, Kevin Stanton. “Designing Shape Changing Mechanisms for Planar and Spatial Applications.” 2014. Masters Thesis, University of Dayton. Accessed January 27, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1418043619.

MLA Handbook (7^th Edition):

Giaier, Kevin Stanton. “Designing Shape Changing Mechanisms for Planar and Spatial Applications.” 2014. Web. 27 Jan 2021.

Vancouver:

Giaier KS. Designing Shape Changing Mechanisms for Planar and Spatial Applications. [Internet] [Masters thesis]. University of Dayton; 2014. [cited 2021 Jan 27]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1418043619.

Council of Science Editors:

Giaier KS. Designing Shape Changing Mechanisms for Planar and Spatial Applications. [Masters Thesis]. University of Dayton; 2014. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=dayton1418043619

23. Weller, Frank. Geometrische Algorithmen in der Flächenrückführung.

Degree: 2000, Universität Dortmund

URL: http://hdl.handle.net/2003/2567

► Gegenstand der Flächenrückführung ist, aus einer gegebenen Menge von Abtastpunkten einer Fläche eine Näherung zu rekonstruieren, die die Fläche möglichst gut repräsentiert. Ein weit verbreiteter… (more)

Subjects/Keywords: Algorithmische Geometrie; Aufzählungsalgorithmen; computational geometry; Delaunaydiagramme; delaunay diagrams; enumeration algorithms; Flächenrückführung; Polygonale Hüllen; polygonal hulls; reverse engineering; Sphärische konvexe Hüllen; spherical convex hulls; surface reconstruction; triangulation; Triangulierung; 004

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Weller, F. (2000). Geometrische Algorithmen in der Flächenrückführung. (Thesis). Universität Dortmund. Retrieved from http://hdl.handle.net/2003/2567

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Weller, Frank. “Geometrische Algorithmen in der Flächenrückführung.” 2000. Thesis, Universität Dortmund. Accessed January 27, 2021. http://hdl.handle.net/2003/2567.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Weller, Frank. “Geometrische Algorithmen in der Flächenrückführung.” 2000. Web. 27 Jan 2021.

Vancouver:

Weller F. Geometrische Algorithmen in der Flächenrückführung. [Internet] [Thesis]. Universität Dortmund; 2000. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/2003/2567.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Weller F. Geometrische Algorithmen in der Flächenrückführung. [Thesis]. Universität Dortmund; 2000. Available from: http://hdl.handle.net/2003/2567

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Pontifícia Universidade Católica de São Paulo

24. Irene Pataki. Geometria esférica para a formação de professores: uma proposta interdisciplinar.

Degree: 2003, Pontifícia Universidade Católica de São Paulo

URL: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=5060

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This work concerns the inservice education of mathematics teachers. One of its aims is to propose, to teachers, a teaching sequence, with activities that show… (more)

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This work concerns the inservice education of mathematics teachers. One of its aims is to propose, to teachers, a teaching sequence, with activities that show the interdisciplinary relationship that exists between spherical geometry and geography, forming interconnections between these domains, at the same time as contextualising the content to be considered and motivating learning in a way that articulates the object of study with reality. Another aim is to provide to the teachers involved reflections about aspects related to the teaching of spherical geometry. Based on the Theory of Didactic Situation developed by G. BROUSSEAU (1986), the research methodology Didactic Engineering of M. ARTIGUE (1988) and the theory of Britt-Mari BARTH (1993) concerning teacher education, we elaborate a teaching sequence, composed of a motivating problem-situation along with eight other activities involving notions of spherical geometry. We investigate the question: How can a teaching sequence permit the appropriation of a new domain spherical geometry and encourage educators to re-elaborate their thinking? Our research hypotheses assume that geometrical knowledge allows different perspectives about our world, that the apprehension of content can lead to changes in our behaviour as teachers and that the use of interdisciplinarity and contextualisation will establish connections between different fields of knowledge. The analysis of the results points to a change in the attitudes and values of the teachers, which confirms our research hypothesis and emphasises the importance of the methodology adopted, leading us to believe that some aspects of the geometry studies were learnt and became institutionalised knowledge

Este trabalho dirige-se à formação continuada de professores de Matemática. Um dos seus objetivos é propor, aos professores, uma seqüência didática, com atividades, que mostre a relação interdisciplinar existente entre a Geometria esférica e a Geografia, formando interconexões entre esses domínios, ao mesmo tempo em que contextualiza os conteúdos a serem considerados e possibilita uma aprendizagem motivadora, que articule o objeto de estudo com a realidade. Outro objetivo é proporcionar aos professores envolvidos reflexões e questionamentos sobre alguns aspectos do ensino da Geometria esférica. Fundamentados na Teoria das Situações Didáticas desenvolvida por G. BROUSSEAU (1986), na Metodologia de Pesquisa denominada Engenharia Didática de M. ARTIGUE (1988) e na Teoria de Britt-Mari BARTH (1993) concernente à Formação de Professores, elaboramos uma seqüência didática, a partir de uma situação-problema motivadora e mais oito atividades, abordando noções de Geometria esférica. Investigamos a questão: Como uma seqüência de ensino pode possibilitar a apropriação de um novo domínio a Geometria esférica e levar o educador a reelaborar seu pensar? Nossas hipóteses de pesquisa pressupõem que o conhecimento geométrico nos permite ter olhares diferentes do nosso mundo, que a apreensão dos conteúdos poderá nos conduzir a mudanças…

Advisors/Committee Members: Saddo Ag Almouloud.

Subjects/Keywords: Situacao-problema; Formação de professores; Matematica – Estudo e ensino; Professores de matematica – Formacao profissional; Didactic situations; Contextualizacao; Contextualisation; Matematica: Educacao Matematica; Interdisciplinaridade; MATEMATICA; Problem situations; Spherical geometry; Teacher education; Educacao matematica; Situacoes didaticas; Interdisciplinarity; Geometria esferica

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Pataki, I. (2003). Geometria esférica para a formação de professores: uma proposta interdisciplinar. (Thesis). Pontifícia Universidade Católica de São Paulo. Retrieved from http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=5060

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Pataki, Irene. “Geometria esférica para a formação de professores: uma proposta interdisciplinar.” 2003. Thesis, Pontifícia Universidade Católica de São Paulo. Accessed January 27, 2021. http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=5060.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Pataki, Irene. “Geometria esférica para a formação de professores: uma proposta interdisciplinar.” 2003. Web. 27 Jan 2021.

Vancouver:

Pataki I. Geometria esférica para a formação de professores: uma proposta interdisciplinar. [Internet] [Thesis]. Pontifícia Universidade Católica de São Paulo; 2003. [cited 2021 Jan 27]. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=5060.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Pataki I. Geometria esférica para a formação de professores: uma proposta interdisciplinar. [Thesis]. Pontifícia Universidade Católica de São Paulo; 2003. Available from: http://www.sapientia.pucsp.br//tde_busca/arquivo.php?codArquivo=5060

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

25. Weller, Frank. Geometrische Algorithmen in der Flächenrückführung.

Degree: 2001, Technische Universität Dortmund

URL: http://dx.doi.org/10.17877/DE290R-3205

► Gegenstand der Flächenrückführung ist, aus einer gegebenen Menge von Abtastpunkten einer Fläche eine Näherung zu rekonstruieren, die die Fläche möglichst gut repräsentiert. Ein weit verbreiteter… (more)

Subjects/Keywords: Algorithmische Geometrie; Aufzählungsalgorithmen; Delaunaydiagramme; Flächenrückführung; Polygonale Hüllen; Sphärische konvexe Hüllen; Triangulierung; computational geometry; delaunay diagrams; enumeration algorithms; polygonal hulls; reverse engineering; spherical convex hulls; surface reconstruction; triangulation; 004

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Weller, F. (2001). Geometrische Algorithmen in der Flächenrückführung. (Doctoral Dissertation). Technische Universität Dortmund. Retrieved from http://dx.doi.org/10.17877/DE290R-3205

Chicago Manual of Style (16^th Edition):

Weller, Frank. “Geometrische Algorithmen in der Flächenrückführung.” 2001. Doctoral Dissertation, Technische Universität Dortmund. Accessed January 27, 2021. http://dx.doi.org/10.17877/DE290R-3205.

MLA Handbook (7^th Edition):

Weller, Frank. “Geometrische Algorithmen in der Flächenrückführung.” 2001. Web. 27 Jan 2021.

Vancouver:

Weller F. Geometrische Algorithmen in der Flächenrückführung. [Internet] [Doctoral dissertation]. Technische Universität Dortmund; 2001. [cited 2021 Jan 27]. Available from: http://dx.doi.org/10.17877/DE290R-3205.

Council of Science Editors:

Weller F. Geometrische Algorithmen in der Flächenrückführung. [Doctoral Dissertation]. Technische Universität Dortmund; 2001. Available from: http://dx.doi.org/10.17877/DE290R-3205

26. Rennert, Julian. Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces.

Degree: 2018, University of Waterloo

URL: http://hdl.handle.net/10012/13851

► In this thesis we study two separate problems concerning improvements to the Loop quantum gravity and spinfoam approach to quantum gravity. In the first part… (more)

▼ In this thesis we study two separate problems concerning improvements to the Loop quantum gravity and spinfoam approach to quantum gravity. In the first part we address the question about the origin of quantum group symmetries in Loop quantum gravity with non-vanishing cosmological constant Λ. Our focus is mainly the 3-dimensional Euclidean case with Λ > 0. We clarify, both at the classical and the quantum level, the quasi-Poisson and quasi-Hopf structures that arise in this case, respectively. This type of symmetry has, until recently, seen not much attention in the Loop quantum gravity literature, despite its importance for the approach. We explain the connection of our work with the Turaev-Viro state sum model, which relies heavily on the notion of twisting. To analyze our q - deformed model, for q being a root of unity, we construct for the first time certain gauge invariant geometric observables for the (restricted) weak quasi-Hopf algebra 𝓤ʳᵉˢq(𝔰𝔩(2,ℂ)) with truncated coproduct, using so-called tensor operators. We show that these tensor operators satisfy the quasi-Hopf version of the Wigner-Eckart theorem and explicitly calculate the action of length- and angle- operators, which confirms the spherical curvature of our quantum geometry. The second topic investigated in this thesis is the problem of timelike contributions for 4-dimensional Lorentzian spinfoam models, using the twistorial parametrization of Loop quantum gravity. We prove how the cotangent bundle T*SU(1,1) can be embedded into T*SL(2,C) via symplectic reduction by the simplicity constraints for a spacelike normal vector and an area matching constraint. This mathematical result is used to study timelike 2-surfaces in 4D Lorentzian gravity, both at the classical and quantum level. We investigate in particular the spectrum of the area operator for timelike faces and find that it is discrete. Furthermore, building on our results, we propose a new Lorentzian spinfoam model, which allows to include timelike contributions.

Subjects/Keywords: Loop quantum gravity; Spinfoam models; Cosmological constant; quasi-Hopf algebra; q root of unity; Tensor operators; quasi-Poisson manifold; Twisting; Timelike twisted geometries; Spherical quantum geometry

…quantum states of spatial quantum geometry. These states are obtained via a generalized Fourier… …HΓ,kin . (1.2) Γ The information about the quantum geometry represented by this… …On the classical side we present a detailed investigation into the quasi-Poisson geometry… …construct so-called tensor operators that allow us to probe the quantum geometry of our q… …represent spherically curved quantum geometry. Our calculations for our geometrical observables…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Rennert, J. (2018). Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces. (Thesis). University of Waterloo. Retrieved from http://hdl.handle.net/10012/13851

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

Rennert, Julian. “Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces.” 2018. Thesis, University of Waterloo. Accessed January 27, 2021. http://hdl.handle.net/10012/13851.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

Rennert, Julian. “Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces.” 2018. Web. 27 Jan 2021.

Vancouver:

Rennert J. Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces. [Internet] [Thesis]. University of Waterloo; 2018. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/10012/13851.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Rennert J. Quasi-Hopf Symmetry in Loop Quantum Gravity with Cosmological constant and Spinfoams with timelike surfaces. [Thesis]. University of Waterloo; 2018. Available from: http://hdl.handle.net/10012/13851

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

27. ΜΑΣΟΥΡΟΣ, ΧΡΗΣΤΟΣ. ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ.

Degree: 1988, National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ)

URL: http://hdl.handle.net/10442/hedi/0699

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IN THIS DISSERTATION, THE HYPERGROUPS IN GENERAL, AS WELL AS SOME SPECIAL CATEGORIES OF HYPERGROUPS (JOIN, HOMIOGENE, STRONGLY HOMIOGENE) ARE STUDIED. BY THE DEVELOPED THEORY,… (more)

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IN THIS DISSERTATION, THE HYPERGROUPS IN GENERAL, AS WELL AS SOME SPECIAL CATEGORIES OF HYPERGROUPS (JOIN, HOMIOGENE, STRONGLY HOMIOGENE) ARE STUDIED. BY THE DEVELOPED THEORY, CONCLUSIONS ARE DERIVED IN THE LINEAR SPACES, AS WELL AS IN CERTAIN GEOMETRIES. THE SEMI-SUB-HYPERGROUPS AND THE CLOSED SUB-HYPERGROUPS TOGETHER WITH SOME SPECIAL CATEGORIES OF ELEMENTS OF A HYPERGROUP (SUCH AS THE FUNDAMENTAL, DEPENDANT, CORRELATED ETC) PLAY A SIGNIFICANT ROLE IN THE WHOLE STUDY.THEOREMS ON THESE ELEMENTS, DESCRIBING THEIR PROPERTIES (MAINLY GENETIC) IN THE HYPERGROUP, ARE INTRODUCED. MOREOVER THE PROPERTIES WITH WHICH THE ELEMENTS OF SOME SPECIAL HYPERGROUPS ARE LED TO THE INTRODUCTION AND THE STUDY OF THE HOMIOGENE AND STRONGLY HOMIOGENE HYPERGROUPS. BESIDES IT WAS PROVED THAT IN EVERY LINEAR SPACE, CAN BE DEFINED. THIS ALLOWS US TO GET THEOREMS OF THE LINEAR SPACES SUCH AS THE THEOREMS OF KAKUTANI, STONE, HELLY, RANDON, CARATHEODORY, STEINITZ, WHICH DERIVE AS COROLLARIES OF MUCH MORE GENERAL THEOREMS OF THE HYPERGROUPS, THAT HAVE BEEN INTRODUCED AND PROVED, IN THE PROCESS OF THIS DISSERTATION. THE LAST CHAPTER OF THIS DISSERTATION IS A REVIEW OF ALL KNOWN METHODS OF CONSTRUCTING HYPERFIELDS. FURTHERMORE A THEOREM PRESENTING A HYPERFIELD NOT BELONGINGTO THE CLASS OF QUOTIENT HYPERFIELDS, IS PROVED.

ΣΤΗ ΔΙΑΤΡΙΒΗ ΑΥΤΗ ΜΕΛΕΤΩΝΤΑΙ ΟΙ ΥΠΕΡΟΜΑΔΕΣ ΕΝ ΓΕΝΕΙ, ΚΑΘΩΣ ΚΑΙ ΟΡΙΣΜΕΝΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΥΠΕΡΟΟΜΑΔΩΝ (ΣΥΝΔΕΤΙΚΕΣ, ΟΜΟΙΟΓΕΝΕΙΣ, ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΕΙΣ). ΑΠΟ ΤΗΘΕΩΡΙΑ ΠΟΥ ΑΝΑΠΤΥΣΣΕΤΑΙ ΠΡΟΚΥΠΤΟΥΝ ΣΥΜΠΕΡΑΣΜΑΤΑ ΣΤΟΥΣ ΓΡΑΜΜΙΚΟΥΣ ΧΩΡΟΥΣ, ΚΑΘΩΣΚΑΙ ΣΕ ΓΕΩΜΕΤΡΙΕΣ ΟΡΙΣΜΕΝΩΝ ΤΥΠΩΝ. ΣΗΜΑΝΤΙΚΟ ΡΟΛΟ ΣΤΗΝ ΟΛΗ ΜΕΛΕΤΗ ΠΑΙΖΟΥΝ ΟΙ ΗΜΙ-ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΟΙ ΚΛΕΙΣΤΕΣ ΥΠΟ-ΥΠΕΡΟΜΑΔΕΣ, ΚΑΘΩΣ ΚΑΙ ΚΑΠΟΙΕΣ ΕΙΔΙΚΕΣ ΚΑΤΗΓΟΡΙΕΣ ΣΤΟΙΧΕΙΩΝ ΤΗΣ ΥΠΕΡΟΜΑΔΑΣ (ΟΠΩΣ ΤΑ ΘΕΜΕΛΙΩΔΗ, ΕΞΑΡΤΗΜΕΝΑ, ΣΥΣΧΕΤΙΣΜΕΝΑ Κ.Α.). ΓΙΑ ΤΑ ΣΤΟΙΧΕΙΑ ΑΥΤΑ ΔΙΑΤΥΠΩΝΟΝΤΑΙ ΘΕΩΡΗΜΑΤΑ ΠΟΥ ΠΕΡΙΓΡΑΦΟΥΝ ΤΗ ΣΥΜΠΕΡΙΦΟΡΑ ΤΟΥΣ (ΚΥΡΙΩΣ ΓΕΝΕΤΙΚΗ) ΜΕΣΑ ΣΤΗΝ ΥΠΕΡΟΜΑΔΑ. ΟΙ ΓΕΝΕΤΙΚΕΣ ΙΔΙΟΤΗΤΕΣ ΜΑΛΙΣΤΑ, ΜΕ ΤΙΣ ΟΠΟΙΕΣ ΕΙΝΑΙ ΕΦΟΔΙΑΣΜΕΝΑ ΤΑ ΣΤΟΙΧΕΙΑ ΚΑΠΟΙΩΝ ΕΙΔΙΚΩΝ ΥΠΕΡΟΜΑΔΩΝ ΟΔΗΓΗΣΑΝΣΤΗΝ ΕΙΣΑΓΩΓΗ ΚΑΙ ΤΗΝ ΜΕΛΕΤΗ ΤΩΝ ΟΜΟΙΟΓΕΝΩΝ ΚΑΙ ΤΩΝ ΙΣΧΥΡΩΣ ΟΜΟΙΟΓΕΝΩΝ ΥΠΕΡΟΜΑΔΩΝ. ΕΞΑΛΛΟΥ ΑΠΟΔΕΙΧΤΗΚΕ ΟΤΙ ΣΕ ΚΑΘΕ ΓΡΑΜΜΙΚΟ ΧΩΡΟ ΜΠΟΡΟΥΜΕ ΝΑ ΕΠΙΣΥΝΑΨΟΥΜΕ ΜΙΑΣΥΓΚΕΚΡΙΜΕΝΗ ΥΠΕΡΟΜΑΔΑ, ΤΗΝ ΠΡΟΣΔΕΔΕΜΕΝΗ ΥΠΕΡΟΜΑΔΑ ΤΟΥ ΓΡΑΜΜΙΚΟΥ ΧΩΡΟΥ. ΑΥΤΟ ΜΑΣ ΕΠΙΤΡΕΠΕΙ ΝΑ ΕΞΑΓΟΥΜΕ ΘΕΩΡΗΜΑΤΑ ΤΩΝ ΓΡΑΜΜΙΚΩΝ ΧΩΡΩΝ, ΟΠΩΣ ΤΩΝ KAKATANI, STONE, HELLY, RANDON, STEINITZ, ΚΑΡΑΘΕΟΔΩΡΗ ΩΣ ΠΟΡΙΣΜΑΤΑ ΠΟΛΥ ΓΕΝΙΚΟΤΕΡΩΝ ΘΕΩΡΗΜΑΤΩΝ, ΤΑ ΟΠΟΙΑ ΕΧΟΥΝ ΔΙΑΤΥΠΩΘΕΙ ΚΑΙ ΑΠΟΔΕΙΧΘΕΙ ΓΙΑ ΤΙΣ ΥΠΕΡΟΜΑΔΕΣ ΣΤΑ ΠΛΑΙΣΙΑ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΑΥΤΗΣ. ΣΤΟ ΤΕΛΕΥΤΑΙΟ ΚΕΦΑΛΑΙΟ ΤΗΣ ΔΙΑΤΡΙΒΗΣ ΓΙΝΕΤΑΙ ΜΙΑ ΣΥΝΟΨΗ ΟΛΩΝ ΤΩΝ ΓΝΩΣΤΩΝ ΜΕΘΟΔΩΝ ΚΑΤΑΣΚΕΥΗΣ ΥΠΕΡΣΩΜΑΤΩΝ ΚΑΙ ΕΠΙΠΛΕΟΝ ΑΠΟΔΕΙΚΝΥΕΤΑΙ ΕΝΑ ΘΕΩΡΗΜΑ ΤΟ ΟΠΟΙΟ ΠΑΡΟΥΣΙΑΖΕΙ ΕΝΑ ΥΠΕΡΣΩΜΑ ΠΟΥ ΔΕΝ ΑΝΗΚΕΙ ΣΤΗΝ ΚΛΑΣΗ ΤΩΝ ΥΠΕΡΣΩΜΑΤΩΝ ΠΗΛΙΚΩΝ.

Subjects/Keywords: ΓΡΑΜΜΙΚΟΙ ΥΠΟΧΩΡΟΙ; ΓΡΑΜΜΙΚΟΙ ΧΩΡΟΙ; ΗΜΙ-ΥΠΟ-ΥΠΕΡΟΜΑΔΑ; ΚΛΕΙΣΤΗ ΥΠΟ-ΥΠΕΡΟΜΑΔΑ; ΠΡΟΒΟΛΙΚΟΣ ΧΩΡΟΣ; Σφαιρική γεωμετρία; ΥΠΕΡΔΑΚΤΥΛΙΟΣ; ΥΠΕΡΔΙΑΤΙΜΗΣΗ; ΥΠΕΡΜΕΤΡΙΚΟΣ ΧΩΡΟΣ; ΥΠΕΡΟΜΑΔΑ; ΥΠΕΡΣΩΜΑ; Convex sets; HYPERFIELD; HYPERGROUP; HYPERMETRIC SPACE; HYPERMODULES; LINEAR SPACES; LINEAR SUBSPACES; PROJECTIVE SPACE#; Spherical geometry

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

ΜΑΣΟΥΡΟΣ, . �. (1988). ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ. (Thesis). National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ). Retrieved from http://hdl.handle.net/10442/hedi/0699

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16^th Edition):

ΜΑΣΟΥΡΟΣ, ΧΡΗΣΤΟΣ. “ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ.” 1988. Thesis, National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ). Accessed January 27, 2021. http://hdl.handle.net/10442/hedi/0699.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7^th Edition):

ΜΑΣΟΥΡΟΣ, ΧΡΗΣΤΟΣ. “ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ.” 1988. Web. 27 Jan 2021.

Vancouver:

ΜΑΣΟΥΡΟΣ �. ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ. [Internet] [Thesis]. National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ); 1988. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/10442/hedi/0699.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

ΜΑΣΟΥΡΟΣ �. ΥΠΕΡΟΜΑΔΕΣ ΚΑΙ ΕΦΑΡΜΟΓΕΣ ΤΟΥΣ. [Thesis]. National Technical University of Athens (NTUA); Εθνικό Μετσόβιο Πολυτεχνείο (ΕΜΠ); 1988. Available from: http://hdl.handle.net/10442/hedi/0699

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

28. Γιαπαλάκη, Σοφία. Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας.

Degree: 2006, University of Patras

URL: http://nemertes.lis.upatras.gr/jspui/handle/10889/1473

►

Η Ηλεκτροεγκεφαλογραφία (ΗΕΓ) και η Μαγνητοεγκεφαλογραφία (ΜΕΓ) αποτελούν δύο από τις πλέον ευρέως χρησιμοποιούμενες μη επεμβατικές μεθόδους μελέτης της λειτουργίας του ανθρώπινου εγκεφάλου, κατά τις… (more)

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Η Ηλεκτροεγκεφαλογραφία (ΗΕΓ) και η Μαγνητοεγκεφαλογραφία (ΜΕΓ) αποτελούν δύο από τις πλέον ευρέως χρησιμοποιούμενες μη επεμβατικές μεθόδους μελέτης της λειτουργίας του ανθρώπινου εγκεφάλου, κατά τις οποίες καταγράφονται εξωτερικά του κρανίου, το ηλεκτρικό και το μαγνητικό πεδίο, που οφείλονται στη διέργεση εγκεφαλικών νευρώνων. Oι κύριες βιοηλεκτρικές πηγές των πεδίων που καταγράφονται σ’ αυτά, είναι ομάδες νευρώνων, που προτυποποιούνται με ένα ηλεκτρικό δίπολο. Αρχικά επιλέγεται το πλέον ρεαλιστικό πρότυπο των τριών φλοιών. Δηλαδή ως αγωγός θεωρείται ολόκληρο το κρανίο, συμπεριλαμβανομένου του δέρματος, των κρανιακών οστών, του εγκεφαλονωτιαίου υγρού και του εγκεφαλικού ιστού – περιοχές διαφορετικής ηλεκτρικής αγωγιμότητας – και υπολογίζεται το ηλεκτρικό δυναμικό και το μαγνητικό πεδίο, επιλύεται δηλαδή τόσο το ευθύ πρόβλημα ΗΕΓ, όσο και το αντίστοιχο ΜΕΓ, στη σφαιρική και στην ελλειψοειδή γεωμετρία. Το δεύτερο πρότυπο αφορά στην επίλυση του ευθέος προβλήματος ΗΕΓ για την περίπτωση όπου ο εγκεφαλικός ιστός θεωρηθεί ως ένα σφαιρικός αγωγός, στο εσωτερικό του οποίου βρίσκεται είτε ομόκεντρα μια σφαιρική περιοχή υγρού, οπότε χρησιμοποιείται για την επίλυση το σφαιρικό σύστημα συντεταγμένων, είτε έκκεντρα, οπότε χρησιμοποιείται αντίστοιχα το δισφαιρικό. Τέλος, ως αγωγός θεωρείται μια ομογενής σφαίρα, περίπτωση όπου η ακριβής και πλήρης αναλυτική λύση για το πρόβλημα του Βιομαγνητισμού είναι γνωστή. Η συνεισφορά όμως της διατριβής για το πρότυπο αυτό είναι στη δημιουργία χρήσιμων εργαλείων για την μετατροπή των αναπτυγμάτων των λύσεων σε σειρές, στις αντίστοιχες κλειστές μορφές μέσω της άθροισης των σειρών, καθώς και στην εξαγωγή συμπερασμάτων σχετικά με το αντίστροφο πρόβλημα ΗΕΓ, τα οποία προκύπτουν από τη γραφική επεξεργασία της κλειστής λύσης του ηλεκτρικού δυναμικού, όπως αυτή προέκυψε από τη μέθοδο των ειδώλων.

Electroenchephalography (EEG) and Magnetoenchephalophy (MEG) are common non invansive methods for studying the function of the human brain. Considering that the data of the generated electric potential (Electroencephalogram) and the magnetic field (Magnetoenchephalogram), takes place on or in the surrounding the head, the entire head, including the skin, the bones, the cerebrospinal fluid and the cerebral, regions which are characterizing by different electric conductivity are including. For this model, the direct Bioelectromagnetism problem is solved in both spherical and ellipsoidal geometry. Specifically, the leading terms of the electric potential in the exterior of the conductor and everywhere in the interior, as well as the leading quadrupolic term of the multipole expansion of the exterior magnetic induction field in the ellipsoidal geometry, are obtained. The reduction of the the ellipsoidal results to the corresponding spherical case, which has brought up useful conclusions concerning these two geometrical models, is also presented. The direct EEG problem is described, for the case where the entire cerebral is considered as a spherical conductor, which surrounds a fluid…

Advisors/Committee Members: Δάσιος, Γεώργιος, Δάσιος, Γεώργιος, Παγιατάκης, Αλκιβιάδης, Παύλου, Σταύρος, Κυριάκη, Κ., Παπαθεοδώρου, Θεόδωρος, Πολύζος, Δημοσθένης, Κωστόπουλος, Βασίλειος.

Subjects/Keywords: Νευροφυσιολογία του εγκεφάλου; Ηλεκτροεγκεφαλογραφία (ΗΕΓ); Μαγνητοεγκεφαλογραφία (ΜΕΓ); Προφίλ αγωγιμότητας; Στρωματοποιημένος αγωγός; Αγωγός τριών φλοιών; Εγκεφαλικός ιστός; Εγκεφαλονωτιαίο υγρό; Κρανιακά οστά; Δέρμα; Προβλήματα συνοριακών τιμών; Μέθοδος των ειδώλων; Σφαιρική γεωμετρία; Ελλειψοειδής γεωμετρία; Δισφαιρική γεωμετρία; Κατανομή ηλεκτρικού δυναμικού; Διαγράμματα μαγνητικού πεδίου; 616.804 754; Neurophysiology of the brain; Electroenchephalography (EEG); Magnetoenchephalography (MEG); Conductivity profile; Layred conductor; Three shells conductor; Cerebrum; Cerebrospinal fluid; Bone; Skin; Boundary value problems; Image theory; Spherical geometry; Ellipsoidal geometry; Bispherical geometry; Electric potential distribution; Diagrams of the magnetic field

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Γιαπαλάκη, �. (2006). Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας. (Doctoral Dissertation). University of Patras. Retrieved from http://nemertes.lis.upatras.gr/jspui/handle/10889/1473

Chicago Manual of Style (16^th Edition):

Γιαπαλάκη, Σοφία. “Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας.” 2006. Doctoral Dissertation, University of Patras. Accessed January 27, 2021. http://nemertes.lis.upatras.gr/jspui/handle/10889/1473.

MLA Handbook (7^th Edition):

Γιαπαλάκη, Σοφία. “Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας.” 2006. Web. 27 Jan 2021.

Vancouver:

Γιαπαλάκη �. Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας. [Internet] [Doctoral dissertation]. University of Patras; 2006. [cited 2021 Jan 27]. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/1473.

Council of Science Editors:

Γιαπαλάκη �. Μελέτη προτύπων ιατρικής φυσικής μέσω της επίλυσης προβλημάτων μαθηματικής νευροφυσιολογίας. [Doctoral Dissertation]. University of Patras; 2006. Available from: http://nemertes.lis.upatras.gr/jspui/handle/10889/1473

29. Bosler, Peter A. Particle Methods for Geophysical Flow on the Sphere.

Degree: PhD, Applied and Interdisciplinary Mathematics, 2013, University of Michigan

URL: http://hdl.handle.net/2027.42/99936

► We present a Lagrangian Particle-Panel Method (LPPM) for geophysical fluid flow on a rotating sphere motivated by problems in atmosphere and ocean dynamics. We focus… (more)

▼ We present a Lagrangian Particle-Panel Method (LPPM) for geophysical fluid flow on a rotating sphere motivated by problems in atmosphere and ocean dynamics. We focus here on the barotropic vorticity equation and 2D passive scalar advection, as a step towards the development of a new dynamical core for global circulation models. The LPPM method employs the Lagrangian form of the equations of motion. The flow map is discretized as a set of Lagrangian particles and panels. Particle velocity is computed by applying a midpoint rule/point vortex approximation to the Biot-Savart integral with quadrature weights determined by the panel areas. We consider several discretizations of the sphere including the cubed sphere mesh, icosahedral triangles, and spherical Voronoi tesselations. The ordinary differential equations for particle motion are integrated by the fourth order Runge-Kutta method. Mesh distortion is addressed using a combination of adaptive mesh refinement (AMR) and a new Lagrangian remeshing procedure. In contrast with Eulerian schemes, the LPPM method avoids explicit discretization of the advective derivative. In the case of passive scalar advection, LPPM preserves tracer ranges and both linear and nonlinear tracer correlations exactly. We present results for the barotropic vorticity equation applied to several test cases including solid body rotation, Rossby-Haurwitz waves, Gaussian vortices, jet streams, and a model for the breakdown of the polar vortex during sudden stratospheric warming events. The combination of AMR and remeshing enables the LPPM scheme to efficiently resolve thin fronts and filaments that develop in the vorticity distribution. We validate the accuracy of LPPM by comparing with results obtained using the Eulerian based Lin-Rood advection scheme. We examine how energy and enstrophy conservation in the LPPM scheme are affected by the time step and spatial discretization. We conclude with a discussion of how the method may be extended to the shallow water equations. Advisors/Committee Members: Krasny, Robert (committee member), Jablonowski, Christiane (committee member), Boyd, John P. (committee member), Viswanath, Divakar (committee member), Arbic, Brian K. (committee member).

Subjects/Keywords: Vortex Methods; Atmosphere and Ocean Dynamics; Adaptive Mesh Refinement (AMR); Global Circulation Modeling (GCM); Particle Method; Spherical Geometry; Atmospheric, Oceanic and Space Sciences; Geology and Earth Sciences; Mathematics; Natural Resources and Environment; Science

…this chapter reviews spherical geometry and the coordinate systems we use throughout this… …16 1.6 Spherical arc length calculation… …29 1.7 Spherical area calculation… …cubed sphere mesh, icosahedral triangles, and spherical Voronoi tesselations. The ordinary… …equations of motion on the spherical surface as a model of the global circulation. From a weather…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Bosler, P. A. (2013). Particle Methods for Geophysical Flow on the Sphere. (Doctoral Dissertation). University of Michigan. Retrieved from http://hdl.handle.net/2027.42/99936

Chicago Manual of Style (16^th Edition):

Bosler, Peter A. “Particle Methods for Geophysical Flow on the Sphere.” 2013. Doctoral Dissertation, University of Michigan. Accessed January 27, 2021. http://hdl.handle.net/2027.42/99936.

MLA Handbook (7^th Edition):

Bosler, Peter A. “Particle Methods for Geophysical Flow on the Sphere.” 2013. Web. 27 Jan 2021.

Vancouver:

Bosler PA. Particle Methods for Geophysical Flow on the Sphere. [Internet] [Doctoral dissertation]. University of Michigan; 2013. [cited 2021 Jan 27]. Available from: http://hdl.handle.net/2027.42/99936.

Council of Science Editors:

Bosler PA. Particle Methods for Geophysical Flow on the Sphere. [Doctoral Dissertation]. University of Michigan; 2013. Available from: http://hdl.handle.net/2027.42/99936

30. Miller, Jason A. Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications.

Degree: PhD, Mathematics, 2014, The Ohio State University

URL: http://rave.ohiolink.edu/etdc/view?acc_num=osu1397599845

► This thesis draws a connection between two areas of algebraic geometry, spherical varieties and Okounkov bodies, in order to study the structure of Borel orbit… (more)

▼ This thesis draws a connection between two areas of algebraic geometry, spherical varieties and Okounkov bodies, in order to study the structure of Borel orbit closures in wonderful group compactifications. Spherical varieties are a natural generalization of many classes of varieties equipped with group actions such as flag varieties, symmetric varieties, and toric varieties. The theory of Okounkov bodies is a fascinating recent development generalizing the polytopes that appear in toric geometry to any projective algebraic variety.Let X be a projective spherical G-variety equipped with a very ample G-line bundle L. Choosing a reduced decomposition of the longest element of the Weyl group determines a valuation v_N on the ring of sections, R(X,L). One can then use Okounkov theory to encode information about the G-orbits of a spherical variety in terms of the associated Newton polytope. Each G-orbit closure of X determines a face of the Newton polytope. This correspondence allows one to use the combinatorial methods of convex geometry to answer questions about the G-orbit closures of the spherical variety X. However for nontoric spherical varieties, the G-orbit structure is too coarse-grained. A great deal of information about the spherical variety, such as the intersection theory, is determined by the structure of the Borel orbits. In this thesis we consider wonderful group compactifications. We prove that one can extend the correspondence between G-orbits and faces to the Borel orbits for this class of varieties. Given any Borel orbit closure of a wonderful group compactification, we show that the Okounkov construction will yield a finite union of faces of the Newton polytope. This correspondence can be shown to enjoy many of the same nice properties as in the case of G-orbits: the dimension of the space of global sections of L is given by the number of lattice points in the union of faces, and the degree of any Borel orbit closure is the sum of the normalized volumes of the associated faces. Advisors/Committee Members: Kennedy, Gary (Advisor).

Subjects/Keywords: Mathematics; spherical varieties; Okounkov; wonderful group compactifications; Borel orbits; toric varieties; flag varieties; Newton-Okounkov; polytopes; string polytope; moment polytope; algebraic geometry; Schubert varieties; standard monomial theory; crystal basis

…geometry. In particular, a connection is drawn between two areas of algebraic geometry: spherical… …varieties and Okounkov bodies. We investigate the geometry of spherical varieties using tools from… …geometry of the Borel orbits of a nontoric spherical variety is still an open question. One… …2.2 Line bundles and G-linearizations . . . . . . . . . . . . . . . . . . 7 11 Spherical… …Theory on Spherical Varieties vii…

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^th Edition):

Miller, J. A. (2014). Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1397599845

Chicago Manual of Style (16^th Edition):

Miller, Jason A. “Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications.” 2014. Doctoral Dissertation, The Ohio State University. Accessed January 27, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1397599845.

MLA Handbook (7^th Edition):

Miller, Jason A. “Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications.” 2014. Web. 27 Jan 2021.

Vancouver:

Miller JA. Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications. [Internet] [Doctoral dissertation]. The Ohio State University; 2014. [cited 2021 Jan 27]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1397599845.

Council of Science Editors:

Miller JA. Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications. [Doctoral Dissertation]. The Ohio State University; 2014. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1397599845

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