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Tesi sul tema "Mathematical conjectures"

Autore: Grafiati
Pubblicato: 2 novembre 2024

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1

Chilstrom, Peter. "Singular Value Inequalities: New Approaches to Conjectures". UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/443.

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Singular values have been found to be useful in the theory of unitarily invariant norms, as well as many modern computational algorithms. In examining singular value inequalities, it can be seen how these can be related to eigenvalues and how several algebraic inequalities can be preserved and written in an analogous singular value form. We examine the fundamental building blocks to the modern theory of singular value inequalities, such as positive matrices, matrix norms, block matrices, and singular value decomposition, then use these to examine new techniques being used to prove singular value inequalities, and also look at existing conjectures.
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2

Bergqvist, Tomas. "To explore and verify in mathematics". Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2001. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-9345.

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This dissertation consists of four articles and a summary. The main focus of the studies is students' explorations in upper secondary school mathematics. In the first study the central research question was to find out if the students could learn something difficult by using the graphing calculator. The students were working with questions connected to factorisation of quadratic polynomials, and the factor theorem. The results indicate that the students got a better understanding for the factor theorem, and for the connection between graphical and algebraical representations. The second study focused on a the last part of an investigation, the verification of an idea or a conjecture. Students were given three conjectures and asked to decide if they were true or false, and also to explain why the conjectures were true or false. In this study I found that the students wanted to use rather abstract mathematics in order to verify the conjectures. Since the results from the second study disagreed with other research in similar situations, I wanted to see what Swedish teachers had to say of the students' ways to verify the conjectures. The third study is an interview study where some teachers were asked what expectations they had on students who were supposed to verify the three conjectures from the second study. The teachers were also confronted with examples from my second study, and asked to comment on how the students performed. The results indicate that teachers tend to underestimate students' mathematical reasoning. A central focus to all my three studies is explorations in mathematics. My fourth study, a revised version of a pilot study performed 1998, concerns exactly that: how students in upper secondary school explore a mathematical concept. The results indicate that the students are able to perform explorations in mathematics, and that the graphing calculator has a potential as a pedagogical aid, it can be a support for the students' mathematical reasoning.
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3

Keliher, Liam. "Results and conjectures related to the sharp form of the Littlewood conjecture". Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=23402.

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Let $0
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4

Tran, Anh Tuan. "The volume conjecture, the aj conjectures and skein modules". Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/44811.

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This dissertation studies quantum invariants of knots and links, particularly the colored Jones polynomials, and their relationships with classical invariants like the hyperbolic volume and the A-polynomial. We consider the volume conjecture that relates the Kashaev invariant, a specialization of the colored Jones polynomial at a specific root of unity, and the hyperbolic volume of a link; and the AJ conjecture that relates the colored Jones polynomial and the A-polynomial of a knot. We establish the AJ conjecture for some big classes of two-bridge knots and pretzel knots, and confirm the volume conjecture for some cables of knots.
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5

Cheukam, Ngouonou Jovial. "Apprentissage automatique de cartes d’invariants d’objets combinatoires avec une application pour la synthèse d’algorithmes de filtrage". Electronic Thesis or Diss., Ecole nationale supérieure Mines-Télécom Atlantique Bretagne Pays de la Loire, 2024. http://www.theses.fr/2024IMTA0418.

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Pour améliorer l’efficacité des méthodes de résolution de nombreux problèmes d’optimisation combinatoires de notre vie quotidienne, nous utilisons la programmation par contraintes pour générer automatiquement des conjectures. Ces conjectures caractérisent des objets combinatoires utilisés pour modéliser ces problèmes d’optimisation. Ce sont notamment les graphes, les arbres, les forêts, les partitions et les séquences. Contrairement à l’état de l’art, le système, dénommé Bound Seeker, que nous avons élaboré ne génère pas seulement de manière indépendante les conjectures, mais il explicite aussi des liens existant entre les conjectures. Ainsi, il regroupe les conjectures sous forme de bornes précises sur une même variable associée à un même objet combinatoire. Ce regroupement est appelé carte de bornes de l’objet combinatoire considéré. Enfin, une étude consistant à établir des liens entre les cartes générées est faite. Le but de cette étude est d’approfondir les connaissances sur les objets combinatoires et de développer des prémices de preuves automatiques des conjectures. Pour montrer la cohérence des cartes générées par le Bound Seeker, nous élaborons quelques preuves manuelles des conjectures découvertes parle Bound Seeker, ce qui permet de démontrer la pertinence de quelques nouveaux théorèmes de bornes. Pour illustrer l’une des utilités pratiques de ces bornes, nous introduisons une méthode de génération semi-automatique d’algorithmes de filtrage qui réduisent l’espace de recherche des solutions d’un problème d’optimisation combinatoire. Cette réduction est faite grâce aux nouveaux théorèmes de bornes que nous avons établis après les avoir sélectionnés automatiquement parmi les conjectures générées par le Bound Seeker. Pour montrer l’efficacité de cette technique, nous l’appliquons avec succès au problème d’élaboration des cursus académiques équilibrés d’étudiants
To improve the efficiency of solution methods for many combinatorial optimisation problems in our daily lives, we use constraints programming to automatically generate conjectures. These conjectures characterise combinatorial objects used to model these optimisation problems. These include graphs, trees, forests, partitions and Boolean sequences. Unlike the state of the art, the system, called Bound Seeker, that we have developed not only generates conjectures independently, but it also points to links between conjectures. Thus, it groups the conjectures in the form of bounds of the same variable characterising the same combinatorial object. This grouping is called a bounds map of the combinatorial object considered. Then, a study consisting of establishing links between generated maps is carried out. The goal of this study is to deepen knowledge on combinatorial objects and to develop the beginnings of automatic proofs of conjectures. Then, to show the consistency of the maps and the Bound Seeker, we develop some manual proofs of the conjectures discovered by the Bound Seeker. This allows us to demonstrate the usefulness of some new bound theorems that we have established. To illustrate one of its concrete applications, we introduce a method for semi-automatic generation of filtering algorithms that reduce the search space for solutions to a combinatorial optimisation problem. This reduction is made thanks to the new bound theorems that we established after having automatically selected them from the conjectures generated by the Bound Seeker. To show the effectiveness of this technique, we successfully apply it to the problem of developing balanced academic courses for students
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6

Mostert, Pieter. "Stark's conjectures". Master's thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/18998.

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Includes bibliographical references.
We give a slightly more general version of the Rubin-Stark conjecture, but show that in most cases it follows from the standard version. After covering the necessary background, we state the principal Stark conjecture and show that although the conjecture depends on a choice of a set of places and a certain isomorphism of Q[GJ-modules, it is independent of these choices. The conjecture is shown to satisfy certain 'functoriality' properties, and we give proofs of the conjecture in some simple cases. The main body of this dissertation concerns a slightly more general version of the Rubin-Stark conjecture. A number of Galois modules. Connected with the conjecture are defined in chapter 4, and some results on exterior powers and Fitting ideals are stated. In chapter 5 the Rubin-Stark conjecture is stated and we show how its truth is unaffected by lowering the top field, changing a set S of places appropriately, and enlarging moduli. We end by giving proofs of the conjecture in several cases. A number of proofs, which would otherwise have interrupted the flow of the exposition, have been relegated to the appendix, resulting in this dissertation suffering from a bad case of appendicitis.
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7

Puente, Philip C. "Crystallographic Complex Reflection Groups and the Braid Conjecture". Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011877/.

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Abstract (sommario):
Crystallographic complex reflection groups are generated by reflections about affine hyperplanes in complex space and stabilize a full rank lattice. These analogs of affine Weyl groups have infinite order and were classified by V.L. Popov in 1982. The classical Braid theorem (first established by E. Artin and E. Brieskorn) asserts that the Artin group of a reflection group (finite or affine Weyl) gives the fundamental group of regular orbits. In other words, the fundamental group of the space with reflecting hyperplanes removed has a presentation mimicking that of the Coxeter presentation; one need only remove relations giving generators finite order. N.V Dung used a semi-cell construction to prove the Braid theorem for affine Weyl groups. Malle conjectured that the Braid theorem holds for all crystallographic complex reflection groups after constructing Coxeter-like reflection presentations. We show how to extend Dung's ideas to crystallographic complex reflection groups and then extend the Braid theorem to some groups in the infinite family [G(r,p,n)]. The proof requires a new classification of crystallographic groups in the infinite family that fail the Steinberg theorem.
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8

Narayanan, Sridhar. "Selberg's conjectures on Dirichlet series". Thesis, McGill University, 1994. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=55517.

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In this thesis we introduce the Rankin-Selberg hypothesis in the Selberg Class to obtain a non-vanishing theorem on line $ Re(s)=1$ for a certain sub-class of functions in this class. We also prove that the Selberg's Conjectures imply the $S sb{K}$-primitivity of $ zeta sb{K}.$
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9

Jost, Thomas. "On Donovan's conjecture". Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318785.

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10

Khoury, Joseph. "La conjecture de Serre". Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/9554.

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Une des grandes reussites de l'algebre commutatif des annees soixante-dix etait la preuve de la "conjecture de Serre". Dans ces papiers, j'expose deux solutions differentes de cette conjecture. Les deux solutions sont exposees avec beaucoup de details de facon qu'un lecteur qui n'a pas une connaissance profonde en algebre commutatif puisse les comprendre sans beaucoup de difficultes.
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11

Larson, Eric Kerner. "The maximal rank conjecture". Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117868.

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Abstract (sommario):
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-58).
Let C be a general curve of genus g, embedded in Pr via a general linear series of degree d. In this thesis, we prove the Maximal Rank Conjecture, which determines the Hilbert function of C Pr.
by Eric Kerner Larson.
Ph. D.
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12

Berard, Whitney, e Whitney Berard. "Explicit Serre Weight Conjectures in Dimension Four". Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/621467.

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A generalization of the weight part of Serre's conjecture asks for which Serre weights a given mod p representation of the absolute Galois group of Q is modular. This set is expected to depend only on the restriction of the representation to the Galois group of Q_p. Let rho be a continuous representation of the absolute Galois group of Q_p into GL_n(F_p) that is moreover semisimple. Gee, Herzig, and Savitt [GHS16] defined a certain set W_expl(rho) of Serre weights (which is defined in a very explicit way) that is conjectured to be the correct set of Serre weights as long as rho is sufficiently generic.However, in the non-generic cases that occur in dimensions greater than three, it is not known whether this set behaves in the way it should under certain functorial operations, like tensor products. This thesis shows that in dimension four, the set of explicit Serre weights W_expl(rho) defined in [GHS16] is closed under taking tensor products of two two-dimensional representations.
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13

Johnson, Jared Drew. "An Algebra Isomorphism for the Landau-Ginzburg Mirror Symmetry Conjecture". BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2793.

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Abstract (sommario):
Landau-Ginzburg mirror symmetry takes place in the context of affine singularities in CN. Given such a singularity defined by a quasihomogeneous polynomial W and an appropriate group of symmetries G, one can construct the FJRW theory (see [3]). This construction fills the role of the A-model in a mirror symmetry proposal of Berglund and H ubsch [1]. The conjecture is that the A-model of W and G should match the B-model of a dual singularity and dual group (which we denote by WT and GT). The B-model construction is based on the Milnor ring, or local algebra, of the singularity. We verify this conjecture for a wide class of singularities on the level of Frobenius algebras, generalizing work of Krawitz [10]. We also review the relevant parts of the constructions.
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14

Marshall, David Clark. "Galois groups and Greenberg's conjecture". Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/289181.

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We consider the structure of a certain infinite Galois group over Q(ζp) the cyclotomic field of p-th roots of unity. Namely, we consider the Galois group of the maximal p-ramified pro- p-extension. Very little is known about this group. It has a free pro-p presentation in terms of g generators and s relations where g and s may be explicitly computed in terms of the p-rank of the class group of Q(ζp). The structure of the relations in the Galois group are shown to be very closely related to the relations in a certain Iwasawa module. The main result of this dissertation shows this Iwasawa module to be torsion free for a large class of cyclotomic fields. The result is equivalent to verifying Greenberg's pseudo-null conjecture for the given class of fields. As one consequence, we provide a large class of examples of cyclotomic fields which do not admit free pro-p-extensions of maximal rank.
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15

Bobga, Benkam Benedict Johnson Peter D. "Some necessary conditions for list colorability of graphs and a conjecture on completing partial Latin squares". Auburn, Ala, 2008. http://repo.lib.auburn.edu/EtdRoot/2008/FALL/Mathematics_and_Statistics/Dissertation/Bobga_Benkam_22.pdf.

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16

Harris, A. J. "Problems and conjectures in extremal graph theory". Thesis, University of Cambridge, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305148.

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17

Pappalardi, Francesco. "On Artin's conjecture for primitive roots". Thesis, McGill University, 1993. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=41128.

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Various generalizations of the Artin's Conjecture for primitive roots are considered. It is proven that for at least half of the primes p, the first log p primes generate a primitive root. A uniform version of the Chebotarev Density Theorem for the field ${ cal Q}( zeta sb{l},2 sp{1/l})$ valid for the range $l < { rm log} x$ is proven. A uniform asymptotic formula for the number of primes up to x for which there exists a primitive root less than s is established. Lower bounds for the exponent of the class group of imaginary quadratic fields valid for density one sets of discriminants are determined.
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18

Malon, Christopher D. "The p-adic local langlands conjecture". Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33667.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.
Includes bibliographical references (leaves 46-47).
Let k be a p-adic field. Split reductive groups over k can be described up to k- isomorphism by a based root datum alone, but other groups, called rational forms of the split group, involve an action of the Galois group of k. The Galois action on the based root datum is shared by members of an inner class of k-groups, in which one k--isomorphism class is quasi-split. Other forms of the inner class can be called pure or impure, depending on the Galois action. Every form of an adjoint group is pure, but only the quasi-split forms of simply connected groups are pure. A p-adic Local Langlands correspondence would assign an L-packet, consisting of finitely many admissible representations of a p-adic group, to each Langlands parameter. To identify particular representations, data extending a Langlands parameter is needed to make "completed Langlands parameters." Data extending a Langlands parameter has been utilized by Lusztig and others to complete portions of a Langlands classification for pure forms of reductive p- adic groups, and in applications such as endoscopy and the trace formula, where an entire L-packet of representations contributes at once.
(cont.) We consider a candidate for completed Langlands parameters to classify representations of arbitrary rational forms, and use it to extend a classification of certain supercuspidal representations by DeBacker and Reeder to include the impure forms.
by Christopher D. Malon.
Ph.D.
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19

Lee, Joonkyung. "Sidorenko's conjecture, graph norms, and pseudorandomness". Thesis, University of Oxford, 2017. http://ora.ox.ac.uk/objects/uuid:5666a58e-77ae-4709-a41e-587cf176840a.

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This thesis is primarily concerned with correlation inequalities between the number of homomorphic copies of different graphs. In particular, many of the results relate to a beautiful conjecture of Sidorenko, which roughly states that the number of copies of a bipartite graph H in a graph G is asymptotically minimised when G is the Erdos Reyni random graph. The first part of the thesis discusses recent approaches to attack Sidorenko's conjecture. We firstly prove that every graph that admits a special kind of tree decomposition satisfies the conjecture. The proof explicitly uses information theory, which also leads to a general tool for counting fixed graphs that are decomposable in analogous ways. A recursive approach to the conjecture, using Cartesian products of graphs, will also be discussed. We show that the class of graphs that satisfy the conjecture is closed under taking Cartesian products with either trees or even cycles. The second part studies a conjecture of Kohayakawa, Nagle, Rodl, and Schacht, which states that we have a random-like lower count for any graph H in G whenever G is locally dense, i.e., a fixed edge density is guaranteed for every large enough vertex subset. This conjecture is closely related to Sidorenko's conjecture in the sense that it is true for every bipartite graph H that satisfies Sidorenko's conjecture. We prove a partial converse, stating that if H satisfies the Kohayakawa-Nagle-Rodl-Schacht conjecture, then replacing edges of H by internally disjoint paths of length two gives an instance of Sidorenko's conjecture. We also prove some new instances of the Kohayakawa-Nagle-Rodl-Schacht conjecture by adding extra ideas to the information theoretic approach previously discussed.
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20

Wang, Kun. "On the Farrell-Jones Isomorphism Conjecture". The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1404684112.

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21

Sannella, Stefano. "Broué's conjecture for finite groups". Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8462/.

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This research project consists of using the theory of perverse equivalences to study Broue's abelian defect group conjecture for the principal block of some finite groups when the defect group is elementary abelian of rank 2. We will look at G=\Omega^{ +} 8(2} and prove the conjecture in characteristic 5, the only open case for this group. We will also look at which result the application of our algorithm leads when G= { }^2F 4(2}'.2, {}^3D_ 4(2}, Sp_8(2}; for those groups, it seems that a slight modification of our method is required to complete the proof of the conjecture. Finally, we will see what happens when we apply our method -which is mainly used for groups G of Lie type- to some sporadic groups, namely G=j_2, He, Suz, Fi_{22}.
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22

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

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Abstract (sommario):
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 68-70).
This thesis, like all of Gaul, is divided into three parts. In Chapter One, I study minimal surfaces in R⁴ with quadratic area growth. I give the first partial result towards a conjecture of Meeks and Wolf on asymptotic behavior of such surfaces at infinity. In particular, I prove that under mild conditions, these surfaces must have unique tangent cones at infinity. In Chapter Two, I give new results towards a conjecture of Schoen on minimal hypersurfaces in R⁴. I prove that if a stable minimal hypersurface E with weight given by its Jacobi field has a stable minimal weighted subsurface, then E must be a hyperplane inside of R⁴. Finally, in Chapter Three, I do an in-depth analysis of the nodal set results of Logonov-Malinnikova. I give explicit bounds for the eigenvalue exponent in terms of dimension, and make a slight improvement on their methodology.
by Paul Gallagher.
Ph. D.
Ph.D. Massachusetts Institute of Technology, Department of Mathematics
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23

Miller, Sam. "Combinatorial Polynomial Hirsch Conjecture". Scholarship @ Claremont, 2017. https://scholarship.claremont.edu/hmc_theses/109.

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The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the Combinatorial Polynomial Hirsch Conjecture, which turns the problem into a matter of counting sets. This thesis explores the Combinatorial Polynomial Hirsch Conjecture.
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24

Micu, Eliade Mihai. "Graph minors and Hadwiger's conjecture". Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1123259686.

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Abstract (sommario):
Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains viii, 80 p.; also includes graphics. Includes bibliographical references (p. 80). Available online via OhioLINK's ETD Center
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25

Yihong, Du, e Ma Li. "Some remarks related to De Giorgi's conjecture". Universität Potsdam, 2001. http://opus.kobv.de/ubp/volltexte/2008/2602/.

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Abstract (sommario):
For several classes of functions including the special case f(u) = u − u³, we obtain boundedness and symmetry results for solutions of the problem −Δu = f(u) defined on R up(n). Our results complement a number of recent results related to a conjecture of De Giorgi.
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26

Oporowski, Bogdan Stanislaw. "Seymour's self-minor conjecture for infinite graphs /". The Ohio State University, 1989. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487672245901823.

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27

Nuttall, Joseph John. "Modular symmetric functions and Doty's Conjecture". Thesis, Queen Mary, University of London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.267612.

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28

Felisatti, Marcello. "A topological proof of Bloch's conjecture". Thesis, University of Warwick, 1996. http://wrap.warwick.ac.uk/65224/.

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Abstract (sommario):
The following is an outline of the structure of the thesis. • In the first chapter, after reviewing the Chern Weil construction of characteristic classes of bundles I introduce the constructions of secondary invariants given by Chern and Simons [13]and by Cheeger and Simons [14]. • In the second chapter I introduce Bloch's conjecture and give some of its motivations. In particular we define Deligne cohomology and its smooth analogue, and prove that the latter is isomorphic to Cheeger and Simons ring of differential characters. • In the third chapter I review Lefschetz Theorems and related results about the topology of smooth projective algebraic varieties, including an analysis of the local structure near a singular hyperplane section. • The fourth chapter is the heart the thesis. I prove the two main results Theorem 4.0.1 and Theorem 4.0.2, asserting that the rational three dimensional homology of a smooth projective algebraic variety is generated by the images of the fundamental classes of S2 x S1 and of connected sums of S1 x S2 under some appropriate maps. The rationality of the Chern-Cheeger-Simons class follows directly from this result. I also discuss briefly the difficulties which I encountered when trying to generalize the construction to give inductively generators for all the odd homology groups of smooth projective algebraic manifolds.
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29

Alghamdi, Ahmad M. "The Ordinary Weight conjecture and Dade's Projective Conjecture for p-blocks with an extra-special defect group". Thesis, University of Birmingham, 2004. http://etheses.bham.ac.uk//id/eprint/86/.

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Abstract (sommario):
Let \(p\) be a rational odd prime number, \(G\) be a finite group such that \(|G|=p^am\), with \(p \nmid m\). Let \(B\) be a \(p\)-block of \(G\) with a defect group \(E\) which is an extra-special \(p\)-group of order \(p^3\) and exponent \(p\). Consider a fixed maximal \((G, B)\)-subpair \((E, b_E)\). Let \(b\) be the Brauer correspondent of \(B\) for \(N_G(E, b_E)\). For a non-negative integer \(d\), let \(k_d(B)\) denote the number of irreducible characters \(\chi\) in \(B\) which have \(\chi(1)_p=p^{a-d}\) and let \(k_d(b)\) be the corresponding number of \(b\). Various generalizations of Alperin's Weight Conjecture and McKay's Conjecture are due to Reinhard Knorr, Geoffrey R. Robinson and Everett C. Dade. We follow Geoffrey R. Robinson's approach to consider the Ordinary Weight Conjecture, and Dade's Projective Conjecture. The general question is whether it follows from either of the latter two conjectures that \(k_d(B)=k_d(b)\) for all \(d\) for the \(p\)-block \(B\). The objective of this thesis is to show that these conjectures predict that \(k_d(B)=k_d(b)\), for all non-negative integers \(d\). It is well known that \(N_G(E, b_E)/EC_G(E)\) is a \(p^'\)-subgroup of the automorphism group of \(E\). Hence, we have considered some special cases of the above question.The unique largest normal \(p\)-subgroup of \(G\), \(O_p(G)\) is the central focus of our attention. We consider the case that \(O_p(G)\) is a central \(p\)-subgroup of \(G\), as well as the case that \(O_p(G)\) is not central. In both cases, the common factor is that \(O_p(G)\) is strictly contained in the defect group of \(B\).
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30

Hliněnʹy, Petr. "Planar covers of graphs : Negami's conjecture". Diss., Georgia Institute of Technology, 1999. http://hdl.handle.net/1853/29449.

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31

Dobson, Edward T. (Edward Tauscher). "Ádám's Conjecture and Its Generalizations". Thesis, University of North Texas, 1990. https://digital.library.unt.edu/ark:/67531/metadc504440/.

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This paper examines idam's conjuecture and some of its generalizations. In terms of Adam's conjecture, we prove Alspach and Parson's results f or Zpq and ZP2. More generally, we prove Babai's characterization of the CI-property, Palfy's characterization of CI-groups, and Brand's result for Zpr for polynomial isomorphism's. We also prove for the first time a characterization of the CI-property for 1 SG, and prove that Zn is a CI-Pn-group where Pn is the group of permutation polynomials on Z,, and n is square free.
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32

Ambikkumar, S. (Sithamparappillai). "Stochastic matrices and the Boyle and Handelman conjecture". Thesis, McGill University, 1995. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=22715.

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Let A be an $n times n$ stochastic matrix with rank($A) leq r (1 leq r leq n$). A reformulation of the Boyle and Handelman Conjecture is det($I-tA) leq1-t sp{r}$ for all real numbers t satisfying $0 leq t leq1$.
In this thesis, we prove that this conjecture is true for $n times n$ stochastic matrices whose rank exceeds ${n over2}$.
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33

Popescu, Cristian D. "On a refined stark conjecture for function fields /". The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487940308431494.

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34

Sheppard, Joseph. "The ABC conjecture and its applications". Kansas State University, 2016. http://hdl.handle.net/2097/32924.

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Master of Science
Department of Mathematics
Christopher Pinner
In 1988, Masser and Oesterlé conjectured that if A,B,C are co-prime integers satisfying A + B = C, then for any ε > 0, max{|A|,|B|,|C|}≤ K(ε)Rad(ABC)[superscript]1+ε, where Rad(n) denotes the product of the distinct primes dividing n. This is known as the ABC Conjecture. Versions with the ε dependence made explicit have also been conjectured. For example in 2004 A. Baker suggested that max{|A|,|B|,|C|}≤6/5Rad(ABC) (logRad(ABC))ω [over] ω! where ω = ω(ABC), denotes the number of distinct primes dividing A, B, and C. For example this would lead to max{|A|,|B|,|C|} < Rad(ABC)[superscript]7/4. The ABC Conjecture really is deep. Its truth would have a wide variety of applications to many different aspects in Number Theory, which we will see in this report. These include Fermat’s Last Theorem, Wieferich Primes, gaps between primes, Erdős-Woods Conjecture, Roth’s Theorem, Mordell’s Conjecture/Faltings’ Theorem, and Baker’s Theorem to name a few. For instance, it could be used to prove Fermat’s Last Theorem in only a couple of lines. That is truly fascinating in the world of Number Theory because it took over 300 years before Andrew Wiles came up with a lengthy proof of Fermat’s Last Theorem. We are far from proving this conjecture. The best we can do is Stewart and Yu’s 2001 result max{log|A|,log|B|,log|C|}≤ K(ε)Rad(ABC)[superscript]1/3+ε. (1) However, a polynomial version was proved by Mason in 1982.
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35

Farrugia, James A. "Brun's 1920 Theorem on Goldbach's Conjecture". DigitalCommons@USU, 2018. https://digitalcommons.usu.edu/etd/7153.

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One form of Goldbach’s Conjecture asserts that every even integer greater than 4is the sum of two odd primes. In 1920 Viggo Brun proved that every sufficiently large even number can be written as the sum of two numbers, each having at most nine prime factors. This thesis explains the overarching principles governing the intricate arguments Brun used to prove his result. Though there do exist accounts of Brun’s methods, those accounts seem to miss the forest for the trees. In contrast, this thesis explains the relatively simple structure underlying Brun’s arguments, deliberately avoiding most of his elaborate machinery and idiosyncratic notation. For further details, the curious reader is referred to Brun’s original paper (in French).
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36

Einav, Amit. "Two problems in mathematical physics: Villani's conjecture and trace inequality for the fractional Laplacian". Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42788.

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The presented work deals with two distinct problems in the field of Mathematical Physics. The first part is dedicated to an 'almost' solution of Villani's conjecture, a known conjecture related to a Statistical Mechanics model invented by Kac in 1956, giving a rigorous explanation of some simple cases of the Boltzmann equation. In 2003 Villani conjectured that the time it will take the system of particles in Kac's model to equilibrate is proportional to the number of particles in the system. Our main result in this part is a proof, up to an epsilon, of that conjecture, showing that for all practical purposes we can consider it to be true. The second part of the presentation is based on a joint work with Prof. Michael Loss and is dedicated to a newly developed trace inequality for the fractional Laplacian, connecting between the fractional Laplacian of a function and its restriction to intersection of hyperplanes. The newly found inequality is sharp and the functions that attain equality in it are completely classified.
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37

Grove, Colin Michael. "A combinatorial approach to the Cabling Conjecture". Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/3091.

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Dehn surgery and the notion of reducible manifolds are both important tools in the study of 3-manifolds. The Cabling Conjecture of Francisco González-Acuña and Hamish Short describes the purported circumstances under which Dehn surgery can produce a reducible manifold. This thesis extends the work of James Allen Hoffman, who proved the Cabling Conjecture for knots of bridge number up to four. Hoffman built upon the combinatorial machinery used by Cameron Gordon and John Luecke in their solution to the knot complement problem. The combinatorial approach starts with the graphs of intersection of a thin level sphere of the knot and the reducing sphere in the surgered manifold. Gordon and Luecke's proof then proceeds by induction on certain cycles. Hoffman provides more insight into the structure of the base case of the induction (i.e. in an innermost cycle or a graph containing no such cycles). Hoffman uses this structure in a case-by-case proof of the Cabling Conjecture for knots of bridge number up to four. We find trees with specific properties in the graph of intersection, and use them to provethe existence of structure which provides lower bounds on the number of the aforementioned innermost cycles. Our results combined with a recent lower bound on the number of vertices inside the innermost cycles succinctly prove the conjecture for bridge number up to five and suggests an approach to the conjecture for knots of higher bridge number.
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38

Childers, Kevin Ronald. "Octahedral Extensions and Proofs of Two Conjectures of Wong". BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5314.

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Consider a non-Galois cubic extension K/Q ramified at a single prime p > 3. We show that if K is a subfield of an S_4-extension L/Q ramified only at p, we can determine the Artin conductor of the projective representation associated to L/Q, which is based on whether or not K/Q is totally real. We also show that the number of S_4-extensions of this type with K as a subfield is of the form 2^n - 1 for some n >= 0. If K/Q is totally real, n > 1. This proves two conjectures of Siman Wong.
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39

Lemelin, Dominic. "Mazur-Tate type conjectures for elliptic curves defined over quadratic imaginary fields". Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=38217.

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Elliptic curves defined over quadratic imaginary fields K have been studied less than those defined over Q . They are nevertheless conjecturally modular and Birch and Swinnerton-Dyer conjectures have been stated for them as well.
For elliptic curves over Q , Mazur and Tate have formulated some refined conjectures of Birch and Swinnerton-Dyer type. They define an element theta belonging to a group ring Z[G] where G is the Galois group of a finite abelian extension of Q , and conjecture that it belongs to a power of the augmentation ideal I ⊆ Z[G] that is at least the rank of E( Q ). The behavior of theta is similar to the order of vanishing at 1 of p-adic L-functions: for example, primes of split multiplicative reduction for the curve appear in the conjectures.
In this thesis, we use modular symbols computed on some hyperbolic upper-half space to construct theta elements associated to elliptic curves defined over quadratic imaginary fields of class number 1. We state conjectures similar to those of Mazur and Tate for such curves and experimentally test many cases of the conjectures. The tests include situations in which we use prime ideals of OK where the elliptic curves have split multiplicative reduction.
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40

Trudeau, Sidney. "On a special case of the Strong Littlewood conjecture". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape11/PQDD_0002/MQ44303.pdf.

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41

Lafferty, Matthew J. "Eichler-Shimura cohomology groups and the Iwasawa main conjecture". Thesis, The University of Arizona, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=3702136.

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Ohta has given a detailed study of the ordinary part of p-adic Eichler-Shimura cohomology groups (resp., generalized p-adic Eichler-Shimura cohomology groups) from the perspective of p-adic Hodge theory. Assuming various hypotheses, he is able to use the structure of these groups to give a simple proof of the Iwasawa main conjecture over Q. The goal of this thesis is to extend Ohta’s arguments with a view towards removing these hypotheses.

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42

Lafferty, Matthew John. "Eichler-Shimura Cohomology Groups and the Iwasawa Main Conjecture". Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/556816.

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Ohta has given a detailed study of the ordinary part of p-adic Eichler-Shimura cohomology groups (resp., generalized p-adic Eichler-Shimura cohomology groups) from the perspective of p-adic Hodge theory [O₁, O₂, O₃]. Assuming various hypotheses, he is able to use the structure of these groups to give a simple proof of the Iwasawa main conjecture over Q [O₂, O₃, O₄, O₅]. The goal of this thesis is to extend Ohta’s arguments with a view towards removing these hypotheses.
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43

Loveland, Susan M. "The Reconstruction Conjecture in Graph Theory". DigitalCommons@USU, 1985. https://digitalcommons.usu.edu/etd/7022.

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In this paper we show that specific classes of graphs are reconstructible; we explore the relationship between the. reconstruction and edge-reconstruction conjectures; we prove that several classes of graphs are actually Harary to the reconstructible; and we give counterexamples reconstruction and edge-reconstruction conjectures for infinite graphs.
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44

Aval, Jean-Christophe. "Conjecture n! et généralisations". Phd thesis, Université Sciences et Technologies - Bordeaux I, 2001. http://tel.archives-ouvertes.fr/tel-00185056.

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Cette thèse est consacrée au problème de combinatoire algébrique appelée conjecture n!.

Plus explicitement, on étudie la structure de certains espaces notés M_mu et indexés par les partitions mu de l'entier n. Chaque espace M_mu est le cône de dérivation d'un polynôme Delta_mu, généralisant en deux alphabets le déterminant de Vandermonde. Le coeur de ce travail, motivé par l'interprétation de certains polynômes de Macdonald en termes de multiplicité des représentations irréductibles du S_n-module M_mu, est la conjecture n!, énoncée en 1991 par A. Garsia et M. Haiman et récemment prouvée par ce dernier.

On s'intéresse ici tout d'abord à l'explicitation de bases monomiales des espaces M_mu. Cette approche est très liée à l'étude de l'idéal annulateur de Delta_mu et nous conduit à introduire certains opérateurs de dérivation, dits opérateurs de sauts. On obtient une base monomiale explicite et une description de l'idéal annulateur pour les partitions en équerres, et pour le sous-espace en un alphabet M_mu(X) avec une partition mu quelconque.

Les opérateurs de sauts se révèlent cruciaux pour l'introduction et l'étude de généralisations de la conjecture n!. Dans le cas des partitions trouées (approche récursive de la conjecture n!), l'obtention d'une base explicite du sous-espace en un alphabet permet de traiter une spécialisation de la fondamentale récurrence à quatre termes. Dans le cas des diagrammes à plusieurs trous, l'introduction de sommes de cônes de dérivation permet d'énoncer une conjecture généralisant la conjecture n!, supportée par l'obtention d'une borne supérieure et la structure du sous-espace en un alphabet.
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45

Cheung, Pak-leong, e 張伯亮. "Smale's inequalities for polynomials and mean value conjecture". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B47054311.

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46

Serrato, Alexa. "Reed's Conjecture and Cycle-Power Graphs". Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/59.

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Reed's conjecture is a proposed upper bound for the chromatic number of a graph. Reed's conjecture has already been proven for several families of graphs. In this paper, I show how one of those families of graphs can be extended to include additional graphs and also show that Reed's conjecture holds for a family of graphs known as cycle-power graphs, and also for their complements.
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47

Brewis, Louis Hugo. "Automorphisms of curves and the lifting conjecture". Thesis, Link to the online version, 2005. http://hdl.handle.net/10019/1050.

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48

Miklós, Dezsö. "Some results related to a conjecture of Chvatal /". The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487267024998336.

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49

Yu, Hoseog. "Idempotent relations and the conjecture of Birch and Swinnerton-Dyer /". The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488190595940334.

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50

Zhao, Yu. "The Birch and Swinnerton-Dyer conjecture for Q-curves". Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103574.

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The main result of this thesis is the proof of a Kolyvagin-like result for Q-curves defined over Q=(square root N) of perfect square conductor (including trivial conductor) over that field. Such a setting lies beyond the scope of the general results of Zhang [Zh1] because of the absence of a Shimura curve parameterization for E. This thesis also describes an explicit construction of Heegner points on E in a setting which so far has not yet studied in the literature and provides numerical examples. In turn, these computations yield numerical evidence for a conjectural connection, which we propose in this thesis, between the Heegner points we construct and the ATR points obtained by Darmon-Logan in [DL].
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