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Thèses sur le sujet « Higher-Dimensional Mathematics »

Auteur : Grafiati

Publié le 2 juin 2025

Mis à jour le 31 juillet 2025

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1

Durkee, Mark N. "New approaches to higher-dimensional general relativity." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240580.

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This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducin

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2

Chandrasekhar, Karthik. "BOUNDING THE NUMBER OF COMPATIBLE SIMPLICES IN HIGHER DIMENSIONAL TOURNAMENTS." UKnowledge, 2019. https://uknowledge.uky.edu/math_etds/63.

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A tournament graph G is a vertex set V of size n, together with a directed edge set E ⊂ V × V such that (i, j) ∈ E if and only if (j, i) ∉ E for all distinct i, j ∈ V and (i, i) ∉ E for all i ∈ V. We explore the following generalization: For a fixed k we orient every k-subset of V by assigning it an orientation. That is, every facet of the (k − 1)-skeleton of the (n − 1)-dimensional simplex on V is given an orientation. In this dissertation we bound the number of compatible k-simplices, that is we bound the number of k-simplices such that its (k − 1)-faces with the already-specified orientatio

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3

Ramasu, Pako. "Internal monoid actions in a cartesian closed category and higher-dimensional group automorphisms." Doctoral thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/20248.

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The notion of cat¹-group which was introduced by Loday is equivalent to the notions of crossed module and of internal category in the category of groups. This notion of cat¹-groups and their morphisms admits natural generalization to catⁿ-groups, which give rise to n-fold categories in the category of groups. There is also a characterization of catⁿ-groups in terms of crossed n-cubes which was given by Ellis and Steiner. The category Catⁿ (Groups) of internal n-fold categories in the category of groups is a cartesian closed category, however given an object X in Catⁿ (Groups), calculating corr

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4

Godazgar, Mohammad Mahdi. "Aspects of higher dimensional Einstein theory and M-theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/245148.

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This thesis contains two main themes. The first is Einstein's theory of general relativity in higher dimensions, while the second is M-theory. The first part of the thesis concerns the use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is explained. The first application of the tensor approach that is discussed is the systematic classification of higher dimensi

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5

Metzner, Norman. "Twistor theory of higher-dimensional black holes." Thesis, University of Oxford, 2012. http://ora.ox.ac.uk/objects/uuid:0c275046-2d6f-4860-9bb3-5d5e5048cd5a.

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The correspondence of stationary, axisymmetric, asymptotically flat space-times and bundles over a reduced twistor space has been established in four dimensions. The main impediment for an application of this correspondence to examples in higher dimensions is the lack of a higher-dimensional equivalent of the Ernst poten- tial. This thesis will propose such a generalized Ernst potential, point out where the rod structure of the space-time can be found in the twistor picture and thereby provide a procedure for generating solutions to the Einstein field equations in higher dimensions from the ro

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6

Griffiths, Rhiannon Cerys. "Slices of Globular Operads for Higher Categories." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1623155240596704.

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7

Belayneh, Sirak. "The identity of zeros of higher and lower dimensional filter banks and the construction of multidimensional nonseparable wavelets." Fairfax, VA : George Mason University, 2008. http://hdl.handle.net/1920/3417.

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Thesis (Ph.D.)--George Mason University, 2008.<br>Vita: p. 160. Thesis director: Edward J. Wegman. Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Information Technology. Title from PDF t.p. (viewed Mar. 9, 2009). Includes bibliographical references (p. 151-159). Also issued in print.

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8

Whitley, Michael Aaron. "Grid stabilization for the one-dimensional advection equation using biased finite differnces of odd orders and orders higher than twenty-two." Thesis, Kansas State University, 2013. http://hdl.handle.net/2097/16285.

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Master of Science<br>Department of Mathematics<br>Nathan Albin<br>This work utilizes finite differences to approximate the first derivative of non-periodic smooth functions. Math literature indicates that stabilizing Partial Differential Equation solvers based on high order finite difference approximations of spatial derivatives of a non-periodic function becomes problematic near a boundary. Hagstrom and Hagstrom have discovered a method of introducing additional grid points near a boundary, which has proven to be effective in stabilizing Partial Differential Equation solvers. Hagstrom and

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9

Moreno, Agustin. "Algebraic Torsion in Higher-Dimensional Contact Manifolds." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/19849.

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Wir konstruieren Beispiele von Kontaktmannigfaltigkeiten in jeder ungeraden Dimension, welche endliche nicht-triviale algebraische Torsion (im Sinne von Latschev-Wendl) aufweisen, somit straff sind und keine starke symplektische Füllung haben. Wir beweisen, dass Giroux Torsion algebraische 1-Torsion in jeder ungeraden Dimension impliziert, womit eine Vermutung von Massot-Niederkrüger-Wendl bewiesen wird. Wir konstruieren unendlich viele nicht diffeomorphe Beispiele von 5-dimensionalen Kontaktmannigfaltigkeiten, welche straff sind, keine starke symplektische Füllung zulassen und keine Giroux

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10

Markowsky, Peter [Verfasser], and Christoph [Akademischer Betreuer] Schnörr. "Model-based Stochastical Segmentation of Higher-dimensional Data / Peter Markowsky ; Betreuer: Christoph Schnörr." Heidelberg : Universitätsbibliothek Heidelberg, 2019. http://d-nb.info/1200918843/34.

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Sigl, Martin [Verfasser], and Alexander [Akademischer Betreuer] Schmidt. "Ramification filtration by moduli in higher-dimensional global class field theory / Martin Sigl ; Betreuer: Alexander Schmidt." Heidelberg : Universitätsbibliothek Heidelberg, 2013. http://d-nb.info/117714865X/34.

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12

Moreno, Agustin [Verfasser], Kai [Gutachter] Cieliebak, Chris [Gutachter] Wendl, and Klaus [Gutachter] Mohnke. "Algebraic Torsion in Higher-Dimensional Contact Manifolds / Agustin Moreno ; Gutachter: Kai Cieliebak, Chris Wendl, Klaus Mohnke." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/118906863X/34.

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13

Schlue, Volker. "Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/243640.

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I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear wave equation on higher dimensional Schwarzschild black holes. I establish uniform energy decay and improved interior first order energy decay in all dimensions with rates in accordance with the 3 + 1-dimensional case. The method of proof departs from earlier work on this problem. I apply and extend the new physical space approach to decay of Dafermos and Rodnianski. An integr

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14

Klaus, Bernd [Verfasser], Anne–Laure [Gutachter] Boulesteix, and Bernd [Gutachter] Kirstein. "False Discovery Rates, Higher Criticism and Related Methods in High-Dimensional Multiple Testing / Bernd Klaus ; Gutachter: Anne–Laure Boulesteix, Bernd Kirstein." Leipzig : Universitätsbibliothek Leipzig, 2013. http://d-nb.info/1238242197/34.

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15

Mesyagutov, Marat [Verfasser], Andreas [Akademischer Betreuer] Fischer, Guntram [Akademischer Betreuer] Scheithauer, and François [Akademischer Betreuer] Clautiaux. "Exact Approaches for Higher-Dimensional Orthogonal Packing and Related Problems / Marat Mesyagutov. Gutachter: Andreas Fischer ; François Clautiaux. Betreuer: Andreas Fischer ; Guntram Scheithauer." Dresden : Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://d-nb.info/1068445904/34.

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Keller, Timo [Verfasser], Uwe [Akademischer Betreuer] Jannsen, and Walter [Akademischer Betreuer] Gubler. "The conjecture of Birch and Swinnerton-Dyer for Jacobians of constant curves over higher dimensional bases over finite fields / Timo Keller. Betreuer: Uwe Jannsen ; Walter Gubler." Regensburg : Universitätsbibliothek Regensburg, 2013. http://d-nb.info/1059569612/34.

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17

Derenthal, Ulrich. "Geometry of universal torsors." Doctoral thesis, [S.l.] : [s.n.], 2006. http://webdoc.sub.gwdg.de/diss/2006/derenthal.

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18

Radha, Santosh Kumar. "Knitting quantum knots-Topological phase transitions in Two-Dimensional systems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=case1595870012750826.

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19

Sasse, Hugh Granville. "Enhancing numerical modelling efficiency for electromagnetic simulation of physical layer components." Thesis, De Montfort University, 2010. http://hdl.handle.net/2086/4406.

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The purpose of this thesis is to present solutions to overcome several key difficulties that limit the application of numerical modelling in communication cable design and analysis. In particular, specific limiting factors are that simulations are time consuming, and the process of comparison requires skill and is poorly defined and understood. When much of the process of design consists of optimisation of performance within a well defined domain, the use of artificial intelligence techniques may reduce or remove the need for human interaction in the design process. The automation of human pro

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20

Moodley, Jothi. "Applications of embedding theory in higher dimensional general relativity." Thesis, 2012. http://hdl.handle.net/10413/10594.

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The study of embeddings is applicable and signicant to higher dimensional theories of our universe, high-energy physics and classical general relativity. In this thesis we investigate local and global isometric embeddings of four-dimensional spherically symmetric spacetimes into five-dimensional Einstein manifolds. Theorems have been established that guarantee the existence of such embeddings. However, most known explicit results concern embedded spaces with relatively simple Ricci curvature. We consider the four-dimensional gravitational field of a global monopole, a simple non-vacuum

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21

Wu, Shengli. "Higher-Dimensional Kloosterman Sums and the Greatest Prime Factor of Integers of the Form a_1a_2\cdots a_{k+1}+1." Thesis, 2007. http://hdl.handle.net/10012/3186.

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22

Feuersänger, Christian [Verfasser]. "Sparse grid methods for higher dimensional approximation / vorgelegt von Christian Feuersänger." 2010. http://d-nb.info/1008921130/34.

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23

Omran, Saleh [Verfasser]. "C*-algebras associated with higher dimensional noncommutative simplicial complexes and their K-theory / vorgelegt von Saleh Omran." 2005. http://d-nb.info/993565824/34.

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24

Schulz, Jochen. "Field reconstructions and range tests for acoustics and electromagnetics in homogeneous and layered media." Doctoral thesis, 2007. http://hdl.handle.net/11858/00-1735-0000-0006-B3A5-B.

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