Dissertations / Theses on the topic 'Extreme problem'
To see the other types of publications on this topic, follow the link: Extreme problem.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Extreme problem.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Medellin, Gabriela. "The rise of the extreme right in France and Germany and the problem of immigration." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0026/MQ34207.pdf.
Full text
2
Oltean, Marius. "Study of the relativistic dynamics of extreme-mass-ratio inspirals." Doctoral thesis, Universitat Autònoma de Barcelona, 2019. http://hdl.handle.net/10803/669448.
Full textAbstract:
El tema principal d’aquesta tesi és el problema gravitacional de dos cossos en el règim de raons de masses extremes - és a dir, on una massa és significativament més petita que l’altra - en el context complet de la nostra teoria contemporània de la gravetat, la relativitat general. Dividim aquest treball en dues grans parts: la primera proporciona una visió general de la teoria de la relativitat general juntament amb els mètodes bàsics matemàtics en què s’hi basa, centrant-se en la seva formulació canònica i les tècniques de pertorbació; la segona està dedicada a presentar la nostra contribució en aquests àmbits, centrada en els problemes de l’entropia, el moviment i la força pròpia en la relativitat general.
Comencem a la primera part, en conseqüència, oferint una introducció històrica a la relativitat general, així com una discussió sobre la motivació actual a partir de l’astronomia d’ones gravitacionals al capítol 1. A continuació, al capítol 2, passem a una exposició tècnica detallada d’aquesta teoria, centrada sobre la seva formulació canònica (hamiltoniana). Acabem aquesta part de la tesi amb un desenvolupament rigorós de mètodes de pertorbació al capítol 3. Per a la comoditat del lector, resumim alguns conceptes bàsics en geometria diferencial necessaris per a tractar aquests temes a l’apèndix A.
A la part II, comencem amb un estudi dels teoremes d’entropia en sistemes clàssics hamiltonians al capítol 4, i en particular, la qüestió de la segona llei de la termodinàmica en la mecànica clàssica i la relativitat general, amb el focus en el problema gravitatori de dos cossos. Al capítol 5, desenvolupem una anàlisi general basada en lleis de conservació per a calcular la correcció en el moviment d’un objecte prou petit a causa de les pertorbacions gravitacionals de la relativitat general. Quan les pertorbacions s’atribueixen al propi objecte petit, aquest efecte es coneix com a força pròpia gravitacional. És el que impulsa l’evolució orbital de les caigudes en espiral amb raó de masses extrema: sistemes binaris compactes on una massa és molt menor que - i per tant, efectivament orbita i, finalment, fa espirals cap a - l’altre. Es preveu que siguin una de les principals fonts del futur detector d’ones gravitacionals LISA, situada en l’espai. Al capítol 6, es presenta un treball sobre el càlcul numèric de la força pròpia escalar - una prova útil per al cas gravitatori - per òrbites circulars en el domini de freqüència, utilitzant un mètode per abordar fonts de distribució en les equacions de camp anomenat el mètode Partícula-sense-Partícula. Incloem també, en l’apèndix B, alguns treballs sobre la generalització d’aquest mètode a equacions diferencials parcials generals amb fonts distribucionals, incloent també aplicacions a altres àrees de matemàtiques aplicades. Resumim els nostres resultats en aquesta tesi i oferim algunes reflexions finals al capítol 7.The principal subject of this thesis is the gravitational two-body problem in the extreme-mass-ratio regime - that is, where one mass is significantly smaller than the other - in the full context of our contemporary theory of gravity, general relativity. We divide this work into two broad parts: the first provides an overview of the theory of general relativity along with the basic mathematical methods underlying it, focusing on its canonical formulation and perturbation techniques; the second is dedicated to a presentation of our novel work in these areas, focusing on the problems of entropy, motion and the self-force in general relativity. We begin in Part I, accordingly, by offering a historical introduction to general relativity as well as a discussion on current motivation from gravitational wave astronomy in Chapter 1. Then, in Chapter 2, we turn to a detailed technical exposition of this theory, focusing on its canonical (Hamiltonian) formulation. We end this part of the thesis with a rigorous development of perturbation methods in Chapter 3. For the convenience of the reader, we summarize some basic concepts in differential geometry needed for treating these topics in Appendix A. In Part II, we begin with a study of entropy theorems in classical Hamiltonian systems in Chapter 4, and in particular, the issue of the second law of thermodynamics in classical mechanics and general relativity, with a focus on the gravitational two-body problem. Then in Chapter 5, we develop a general approach based on conservation laws for calculating the correction to the motion of a sufficiently small object due to gravitational perturbations in general relativity. When the perturbations are attributed to the small object itself, this effect is known as the gravitational self-force. It is what drives the orbital evolution of extreme-mass-ratio inspirals: compact binary systems where one mass is much smaller than - thus effectively orbiting and eventually spiralling into - the other, expected to be among the main sources for the future space-based gravitational wave detector LISA. In Chapter 6, we present some work on the numerical computation of the scalar self-force - a helpful testbed for the gravitational case - for circular orbits in the frequency domain, using a method for tackling distributional sources in the field equations called the Particle-without-Particle method. We include also, in Appendix B, some work on the generalization of this method to general partial differential equations with distributional sources, including also applications to other areas of applied mathematics. We summarize our findings in this thesis and offer some closing reflections in Chapter 7.
3
Babayigit, Cihan. "Genetic Algorithms and Mathematical Models in Manpower Allocation and Cell Loading Problem." Ohio University / OhioLINK, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1079298235.
Full text
4
AL, Nuwairan Muneerah. "SU(2)-Irreducibly Covariant Quantum Channels and Some Applications." Thesis, Université d'Ottawa / University of Ottawa, 2015. http://hdl.handle.net/10393/32123.
Full textAbstract:
In this thesis, we introduce EPOSIC channels, a class of SU(2) -covariant quantum channels. For each of them, we give a Stinespring representation, a Kraus representation, its Choi matrix, a complementary channel, and its dual map. We show that these channels are the extreme points of all SU(2) -irreducibly covariant channels. As an application of these channels to the theory of quantum information, we study the minimal output entropy of EPOSIC channels, and show that a large class of these channels is a potential example of violating the well-known problem, the additivity problem. We determine the cases where their minimal output entropy is not zero, and obtain some partial results on the fulfillment of their entanglement breaking property. We find a bound of the minimal output entropy of the tensor product of two SU(2) -irreducibly covariant channels. We also get an example of a positive map that is not completely positive.
5
Domenicali, Federico. "Ottimizzazione del carico di un mezzo di trasporto: analisi, progettazione e sviluppo di algoritmi." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2022.
Find full textAbstract:
Ottenere il più alto rapporto di occupazione della capacità di un mezzo di trasporto, o, più in generale, di un container, risulta estremamente importante per le compagnie la cui attività si basa su spedizioni. Una sequenza di carico più vicina ad una condizione ottimale riduce indubbiamente i costi della spedizione, senza contare i benefici che apporta in termini di impatto ambientale.
Ad oggi sono molte le compagnie che convivono con percentuali di saturazione dei mezzi di trasporto non sufficientemente elevate. Queste problematiche possono essere frutto di una valutazione del carico errata oppure di un totale affidamento del processo all’esperienza dei singoli addetti alla logistica.
Questo lavoro di tesi si colloca in questo contesto e si propone di fornire un approccio innovativo per la generazione di sequenze di carico, volte a minimizzare il numero di mezzi da utilizzare per il trasporto degli oggetti da spedire. I dati relativi ai pacchi e alle tipologie di mezzi di trasporto possono essere inseriti attraverso un’interfaccia semplice ed intuitiva. L’algoritmo sviluppato ritornerà all’utilizzatore la sequenza di carico più vicina a quella ottimale, in base ai vincoli imposti dalla compagnia e, tramite l’applicazione, sarà possibile visualizzare i dati statistici relativi al risultato ed esplorare il modello in tre dimensioni della suddetta sequenza.
6
Ozpeynirci, Nail Ozgur. "Approaches For Multiobjective Combinatorial Optimization Problems." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12609216/index.pdf.
Full textAbstract:
In this thesis, we consider multiobjective combinatorial optimization problems. We address two main topics. We first address the polynomially solvable cases of the Traveling Salesperson Problem and the Bottleneck Traveling Salesperson Problem. We consider multiobjective versions of these problems with different combinations of objective functions, analyze their computational complexities and develop exact algorithms where possible.
We next consider generating extreme supported nondominated points of multiobjective integer programming problems for any number of objective functions. We develop two algorithms for this purpose. The first one is an exact algorithm and finds all such points. The second algorithm finds only a subset of extreme supported nondominated points providing a worst case approximation for the remaining points.
7
Luz, Ramiro Batista da. "A influência do dojo de programação no ensino de práticas ágeis." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/735.
Full textAbstract:
Dojo de Programação é uma atividade dinâmica e colaborativa inspirada em artes marciais onde é possível praticar programação, especialmente técnicas relacionadas a métodos ágeis. Os métodos de ensino atuais tratam todos os alunos da mesma forma. Cada pessoa tem uma história, experiências, habilidades, conhecimentos. Raramente as particularidades de cada indivíduo são respeitadas. Buscamos verificar qual a influência do Dojo de Programação como atividade de ensino a fim de promover a interação entre os alunos. O Dojo de Programação oferece os recursos necessários para ensino acadêmico de programação de computadores? Para responder a questão foram realizados questionários com leigos e participantes ativos de Dojo de Programação, participantes espontâneos de grupos de Dojo de Programação e participantes compulsórios de alunos que participaram de Dojo de Programação em aula de disciplina regular de especialização na Universidade Tecnológica Federal do Paraná. Foram realizadas entrevistas com especialistas organizadores de encontros de Dojo de Programação. Pontos positivos, como a participação dos alunos e negativos, como o fato de não ser uma atividade adequada para apresentação de assuntos teóricos, foram ponderados. Os resultados obtidos sugerem que a atividade pode ser utilizada de forma complementar em disciplinas de programação de computadores a fim de aumentar a participação dos alunos e permitir ao professor conhecer as dificuldades e facilidades de cada aluno individualmente.Coding Dojo is a dynamic and collaborative activity inspired by martial arts where you can practice programming, especially techniques related to agile methods. The existing teaching methods treat all students the same way. Each person has a story, experiences, skills, knowledge. Rarely the particularities of each individual are respected. The purpose of this research is to verify the influence of the Coding Dojo in teaching agile practices. The Coding Dojo offers the required resources to academic teaching computer programming? To answer the question surveys were conducted with novice and active participants of Coding Dojo, also spontaneous participants in groups of Coding Dojo and students who attended compulsorily in a Coding Dojo during a class of a regular discipline of one specialization course in Federal Technological University of Paraná. Interviews were conducted with experts organizers of meetings of Coding Dojo. Strengths, such as student participation and weaknesses, as not being a suitable practice for presenting theoretical contents were considered. The obtained results suggest that the activity can be used complementary in computer programming disciplines to increase student participation and allow the teacher to know the difficulties and facilities of each student individually.
8
Makhmudov, Olimdjan, and Nikolai Tarkhanov. "An extremal problem related to analytic continuation." Universität Potsdam, 2013. http://opus.kobv.de/ubp/volltexte/2013/6363/.
Full textAbstract:
We show that the usual variational formulation of the problem of analytic
continuation from an arc on the boundary of a plane domain does not lead
to a relaxation of this overdetermined problem.
To attain such a relaxation, we bound the domain of the functional, thus
changing the Euler equations.
9
Jakob, Ruben. "Instabile Extremalen des Shiffman-Funktionals." Bonn : Mathematisches Institut der Universität, 2003. http://catalog.hathitrust.org/api/volumes/oclc/62767545.html.
Full text
10
Aschwanden, Dirk. "Jugendlicher Rechtsextremismus als gesamtdeutsches Problem /." Baden-Baden : Nomos, 1996. http://catalogue.bnf.fr/ark:/12148/cb37314961q.
Full text
11
Mendes, Alex Fernandes. "Problemas de otimização: Uma proposta para o Ensino Médio." Universidade Estadual da Paraíba, 2015. http://tede.bc.uepb.edu.br/tede/jspui/handle/tede/2555.
Full textAbstract:
Submitted by Jean Medeiros (jeanletras@uepb.edu.br) on 2016-09-08T13:54:27Z
No. of bitstreams: 1
PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5)Approved for entry into archive by Secta BC (secta.csu.bc@uepb.edu.br) on 2016-09-09T18:51:21Z (GMT) No. of bitstreams: 1 PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5)
Made available in DSpace on 2016-09-09T18:55:06Z (GMT). No. of bitstreams: 1 PDF - Alex Fernandes Mendes.pdf: 2731212 bytes, checksum: 53473c1efa5b616abee7ccdd6fc9236d (MD5) Previous issue date: 2015-12-14
In this work discuss optimization problems involving polynomial functions of de- gree greater than or equal to 2, where use the rate of variation to obtain the extremes, that can bemaximum orminimum. The proposal is to insert in high school the derived as rate of variation and from there to solve optimization problems, without defining the derivative formally. The problems proposed in this work meets the dynamic in the classroom, concrete problems, with some occurrence in our daily lives, may also include the areas of economics, engineering and physics.
No presente trabalho abordaremos problemas de otimização envolvendo funções polinomiais de grau maior ou igual a 2, onde utilizamos a taxa de variação na obtenção de extremos, que podem ser máximos ou mínimos relativos. A proposta é inserir no ensino médio a derivada como taxa de variação e a partir daí resolver problemas de otimização, sem definir a derivada de maneira formal. Os problemas propostos neste trabalho atende à dinâmica de sala de aula, sendo problemas concretos,com certa ocorrência no nosso cotidiano, podendo ainda abranger as áreas de economia, engenharia e física.
12
Haddow, A. A. "Some statistical problems connected with extreme value regression." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.374297.
Full text
13
Darus, M. "Extreme problems for certain classes of analytic functions." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636350.
Full textAbstract:
This thesis is concerned with extreme problems for certain classes of analytic functions. In many cases, the classes of functions considered form proper subclasses of the class S of normalised analytic functions which are univalent in the unit disc D. In Chapter 1, we present some definitions and known results which are required in subsequent chapters. In Chapter 2, we state some known results concerning the so-called Fekete-Szegö Theorem. We give some extensions and new results in the case of close-to-convex functions. Chapter 3 contains some miscellaneous Fekete-Szegö Theorems. In this chapter, we introduce a new class of analytic functions, which we call logarithmically convex. These functions are a natural analogue to the so-called α-convex functions, studied extensively over the last decade or so. Some extreme coefficient problems are solved for logarithmically convex functions. The final chapter deals with subordination. We apply a lemma of Miller and Mocanu to obtain a series of best possible subordination theorems when the super-ordinate function lies in a sector, rather than the usual half-plane. A consequence of one such result is that the logarithmically convex functions defined in Chapter 3 form a subset of the starlike functions and are thus univalent in D.
14
Хомяк, Богдан Вікторович. "Математична модель ефективності процесу самозрівноваження обертового тіла з рідиною." Магістерська робота, Хмельницький національний університет, 2020. http://elar.khnu.km.ua/jspui/handle/123456789/9367.
Full textAbstract:
На основі моделювання поведінки рідини в циліндричній камері твердого обертового тіла розроблено методику визначення оптимальних параметрів рідинного автобалансувального пристрою, і програмне забезпечення для реалізації методики.Based on the modeling of the behavior of the liquid in the cylindrical chamber of a solid rotating body, a method for determining the optimal parameters of the liquid self-balancing device and software for implementing the method have been developed.
15
Yoo, Seonguk. "Extremal sextic truncated moment problems." THE UNIVERSITY OF IOWA, 2012. http://pqdtopen.proquest.com/#viewpdf?dispub=3461430.
Full text
16
Young, Andrew Christopher. "Extremal Problems for Dense Digraphs." Thesis, University of Birmingham, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.522060.
Full text
17
Pinto, Trevor Alvaro Anthony. "Extremal problems on the hypercube." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23651.
Full textAbstract:
The hypercube, Qd, is a natural and much studied combinatorial object, and we discuss various extremal problems related to it. A subgraph of the hypercube is said to be (Qd; F)-saturated if it contains no copies of F, but adding any edge forms a copy of F. We write sat(Qd; F) for the saturation number, that is, the least number of edges a (Qd; F)-saturated graph may have. We prove the upper bound sat(Qd;Q2) < 10 2d, which strongly disproves a conjecture of Santolupo that sat(Qd;Q2) = 1 4 + o(1) d2d 1. We also prove upper bounds on sat(Qd;Qm) for general m. Given a down-set A and an up-set B in the hypercube, Bollobás and Leader conjectured a lower bound on the number of edge-disjoint paths between A and B in the directed hypercube. Using an unusual form of the compression argument, we confirm the conjecture by reducing the problem to a the case of the undirected hypercube. We also prove an analogous conjecture for vertex-disjoint paths using the same techniques, and extend both results to the grid. Additionally, we deal with subcube intersection graphs, answering a question of Johnson and Markström of the least r = r(n) for which all graphs on n vertices may be represented as subcube intersection graph where each subcube has dimension exactly r. We also contribute to the related area of biclique covers and partitions, and study relationships between various parameters linked to such covers and partitions. Finally, we study topological properties of uniformly random simplicial complexes, employing a characterisation due to Korshunov of almost all down-sets in the hypercube as a key tool.
18
Yoo, Seonguk. "Extremal sextic truncated moment problems." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1113.
Full textAbstract:
Inverse problems naturally occur in many branches of science and mathematics. An inverse problem entails finding the values of one or more parameters using the values obtained from observed data. A typical example of an inverse problem is the inversion of the Radon transform. Here a function (for example of two variables) is deduced from its integrals along all possible lines. This problem is intimately connected with image reconstruction for X-ray computerized tomography.
Moment problems are a special class of inverse problems. While the classical theory of moments dates back to the beginning of the 20th century, the systematic study of truncated moment problems began only a few years ago. In this dissertation we will first survey the elementary theory of truncated moment problems, and then focus on those problems with cubic column relations.
For a degree 2n real d-dimensional multisequence β ≡ β (2n) ={β i}i∈Zd+,|i|≤2n to have a representing measure μ, it is necessary for the associated moment matrix Μ(n) to be positive semidefinite, and for the algebraic variety associated to β, Vβ, to satisfy rank Μ(n)≤ card Vβ as well as the following consistency condition: if a polynomial p(x)≡ ∑|i|≤2naixi vanishes on Vβ, then Λ(p):=∑|i|≤2naiβi=0. In 2005, Professor Raúl Curto collaborated with L. Fialkow and M. Möller to prove that for the extremal case (Μ(n)= Vβ), positivity and consistency are sufficient for the existence of a (unique, rank Μ(n)-atomic) representing measure.
In joint work with Professor Raúl Curto we have considered cubic column relations in M(3) of the form (in complex notation) Z3=itZ+ubar Z, where u and t are real numbers. For (u,t) in the interior of a real cone, we prove that the algebraic variety Vβ consists of exactly 7 points, and we then apply the above mentioned solution of the extremal moment problem to obtain a necessary and sufficient condition for the existence of a representing measure. This requires a new representation theorem for sextic polynomials in Z and bar Z which vanish in the 7-point set Vβ. Our proof of this representation theorem relies on two successive applications of the Fundamental Theorem of Linear Algebra. Finally, we use the Division Algorithm from algebraic geometry to extend this result to other situations involving cubic column relations.
19
Costa, Marcos Antônio da. "Máximos e Mínimos: uma abordagem para o ensino médio." Universidade Federal de Goiás, 2013. http://repositorio.bc.ufg.br/tede/handle/tde/2947.
Full textAbstract:
Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-08-28T15:33:45Z
No. of bitstreams: 2
license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5)
Dissertacao Marcos Antonio da Costa.pdf: 1237372 bytes, checksum: e4392b806f26f0293114e12b4ed829c9 (MD5)Made available in DSpace on 2014-08-28T15:33:45Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertacao Marcos Antonio da Costa.pdf: 1237372 bytes, checksum: e4392b806f26f0293114e12b4ed829c9 (MD5) Previous issue date: 2013-04-12
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
We deal with extremum values problems. Our focus is the high school students. We present simple ideas and techniques on solving classical optimization problems. Among other problems we cite the classical isoperimetric ploblem and the Heron0s problem. We are based on the book Stories About Maxima and Minima by Tikhomirov which lead with these classical problems using only elementary mathematical subjects.
Estudamos problemas envolvendo valores extremos, com foco nos estudantes do Ensino Médio. Apresentamos de forma simples e resumida, algumas ideias e teorias para a solução de tais problemas. Dentre os quais citamos o Problema de Dido e o de Heron. O principal referencial teórico para confecção deste trabalho foi o livro de Tikhomirov intitulado Stories About Maxima and Minima. Baseados em tal livro, aplicamos métodos e teorias elementares para solucionarmos problemas clássicos de máximos e mínimos.
20
Edwards, C. S. "Some extremal problems in graph theory." Thesis, University of Reading, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.373467.
Full text
21
Ferra, Gomes de Almeida Girão António José. "Extremal and structural problems of graphs." Thesis, University of Cambridge, 2019. https://www.repository.cam.ac.uk/handle/1810/285427.
Full textAbstract:
In this dissertation, we are interested in studying several parameters of graphs and understanding their extreme values. We begin in Chapter~$2$ with a question on edge colouring. When can a partial proper edge colouring of a graph of maximum degree $\Delta$ be extended to a proper colouring of the entire graph using an `optimal' set of colours? Albertson and Moore conjectured this is always possible provided no two precoloured edges are within distance $2$. The main result of Chapter~$2$ comes close to proving this conjecture. Moreover, in Chapter~$3$, we completely answer the previous question for the class of planar graphs. Next, in Chapter~$4$, we investigate some Ramsey theoretical problems. We determine exactly what minimum degree a graph $G$ must have to guarantee that, for any two-colouring of $E(G)$, we can partition $V(G)$ into two parts where each part induces a connected monochromatic subgraph. This completely resolves a conjecture of Bal and Debiasio. We also prove a `covering' version of this result. Finally, we study another variant of these problems which deals with coverings of a graph by monochromatic components of distinct colours. The following saturation problem proposed by Barrus, Ferrara, Vandenbussche, and Wenger is considered in Chapter~$5$. Given a graph $H$ and a set of colours $\{1,2,\ldots,t\}$ (for some integer $t\geq |E(H)|$), we define $sat_{t}(n, R(H))$ to be the minimum number of $t$-coloured edges in a graph on $n$ vertices which does not contain a rainbow copy of $H$ but the addition of any non-edge in any colour from $\{1,2,\ldots,t\}$ creates such a copy. We prove several results concerning these extremal numbers. In particular, we determine the correct order of $sat_{t}(n, R(H))$, as a function of $n$, for every connected graph $H$ of minimum degree greater than $1$ and for every integer $t\geq e(H)$. In Chapter~$6$, we consider the following question: under what conditions does a Hamiltonian graph on $n$ vertices possess a second cycle of length at least $n-o(n)$? We prove that the `weak' assumption of a minimum degree greater or equal to $3$ guarantees the existence of such a long cycle. We solve two problems related to majority colouring in Chapter~$7$. This topic was recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They raised the problem of determining, for a natural number $k$, the smallest positive integer $m = m(k)$ such that every digraph can be coloured with $m$ colours, where each vertex has the same colour as at most a proportion of $\frac{1}{k}$ of its out-neighbours. Our main theorem states that $m(k) \in \{2k-1, 2k\}$. We study the following problem, raised by Caro and Yuster, in Chapter~$8$. Does every graph $G$ contain a `large' induced subgraph $H$ which has $k$ vertices of degree exactly $\Delta(H)$? We answer in the affirmative an approximate version of this question. Indeed, we prove that, for every $k$, there exists $g(k)$ such that any $n$ vertex graph $G$ with maximum degree $\Delta$ contains an induced subgraph $H$ with at least $n-g(k)\sqrt{\Delta}$ vertices such that $V(H)$ contains at least $k$ vertices of the same degree $d \ge \Delta(H)-g(k)$. This result is sharp up to the order of $g(k)$. %Subsequently, we investigate a concept called $\textit{path-pairability}$. A graph is said to be path-pairable if for any pairing of its vertices there exist a collection of edge-disjoint paths routing the the vertices of each pair. A question we are concerned here asks whether every planar path pairable graph on $n$ vertices must possess a vertex of degree linear in $n$. Indeed, we answer this question in the affirmative. We also sketch a proof resolving an analogous question for graphs embeddable on surfaces of bounded genus. Finally, in Chapter~$9$, we move on to examine $k$-linked tournaments. A tournament $T$ is said to be $k$-linked if for any two disjoint sets of vertices $\{x_1,\ldots ,x_k\}$ and $\{y_1,\dots,y_k\}$ there are directed vertex disjoint paths $P_1,\dots, P_k$ such that $P_i$ joins $x_i$ to $y_i$ for $i = 1,\ldots, k$. We prove that any $4k$ strongly-connected tournament with sufficiently large minimum out-degree is $k$-linked. This result comes close to proving a conjecture of Pokrovskiy.
22
Morrison, Natasha. "Problems in extremal and probabilistic combinatorics." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:83970d50-71d0-4511-9545-5358c3073343.
Full textAbstract:
In this thesis we consider some problems in extremal and probabilistic combinatorics. In Chapter 2 we determine the maximum number of induced cycles that can be contained in a graph on n ≥ n0 vertices, and show that there is a unique graph that achieves this maximum. This answers a question of Tuza. Let Qd denote the hypercube of dimension d. Given d ≥ m, a spanning subgraph G of Qd is said to be (Qd,Qm)-saturated if it does not contain Qm as a subgraph but adding any edge of E(Qd) \ E(G) creates a copy of Qm in G. In Chapter 3, we show that for every fixed m ≥ 2 the minimum number of edges in a (Qd,Qm)-saturated graph is Θ(2d). This answers a question of Johnson and Pinto. We also answer another question of Johnson and Pinto about weak saturation. Given graphs F and H, a spanning subgraph G of F is said to be weakly (F,H)-saturated if the edges of E(F) \setminus E(G) can be added to G one at a time so that each additional edge creates a new copy of H. We determine the minimum number of edges in a weakly (Qd,Qm)-saturated graph for all d ≥ m ≥ 1. More generally, we determine the minimum number of edges in a subgraph of the d-dimensional grid Pk_d which is weakly saturated with respect to 'axis aligned' copies of a smaller grid Prm. In Chapter 4 we consider the r-neighbour bootstrap process in the hypercube. This process starts with an initial set A0 of infected vertices in a graph G and, at each step of the process, a healthy vertex becomes infected if it has at least r infected neighbours (once a vertex becomes infected, it remains infected forever). If every vertex of G eventually becomes infected, then we say that A0 percolates. We prove a conjecture of Balogh and Bollobás which says that, for fixed r and d tending to infinity, every percolating set in the d-dimensional hypercube has cardinality at least 1+o(1)/r (d choose r-1). We also prove an analogous result for multidimensional rectangular grids. Our proofs exploit a connection between bootstrap percolation and weak-saturation. In addition, we improve on the best known upper bound for the minimum size of a percolating set in the hypercube. In particular, when r=3, we determine the exact cardinality of a minimum percolating set in the d-dimensional hypercube, for all d ≥ 3. Finally, we consider a more general bootstrap process in a hypergraph setting. Given an r-uniform hypergraph H, the H-bootstrap process starts with an initial set of infected vertices of H and, at each step, a healthy vertex becomes infected if there exists a hyperedge of H in which it is the only healthy vertex. The initial set of infected vertices is said to percolate if every vertex of H is eventually infected. In Chapter 5, for fixed r and large d, we obtain a sharp threshold for the probability that a p-random set of vertices in a q-random subhypergraph of H percolates when p,q= Θ(d-1/(r-1)) and H is any nearly d-regular r-uniform hypergraph with at most dO(1) vertices which satisfies certain 'codegree' conditions. As it turns out, for this wide class of hypergraphs, the threshold depends only on r and not on the underlying structure of the hypergraph. We apply this result to obtain a sharp threshold for a variant of the graph bootstrap process for strictly $2$-balanced graphs. This result generalises a theorem of Korándi, Peled and Sudakov and the proof involves an application of the differential equations method.
23
Sarkar, Amites. "Extremal problems for graphs and hypergraphs." Thesis, University of Cambridge, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.625020.
Full text
24
Slivnik, Tomaz. "Extremal problems for cliques and colourings." Thesis, University of Cambridge, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.627548.
Full text
25
Mitchell, James David. "Extremal problems in combinatorial semigroup theory." Thesis, University of St Andrews, 2002. http://hdl.handle.net/10023/11322.
Full textAbstract:
In this thesis we shall consider three types of extremal problems (i.e. problems involving maxima and minima) concerning semigroups. In the first chapter we show how to construct a minimal semigroup presentation that defines a group of non-negative deficiency given a minimal group presentation for that group. This demonstrates that the semigroup deficiency of a group of non-negative deficiency is equal to the group deficiency of that group. Given a finite monoid we find a necessary and sufficient condition for the monoid deficiency to equal the semigroup deficiency. We give a class of infinite monoids for which this equality also holds. The second type of problem we consider concerns infinite semigroups of relations and transformations. We find the relative rank of the full transformation semigroup, over an infinite set, modulo some standard subsets and subsemigroups, including the set of contraction maps and the set of order preserving maps (for some infinite ordered sets). We also find the relative rank of the semigroup of all binary relations (over an infinite set) modulo the partial transformation semigroup, the full transformation semigroup, the symmetric inverse semigroup, the symmetric group and the set of idempotent relations. Analogous results are also proven for the symmetric inverse semigroup. The third, and final, type of problem studied concerns generalising notions of independence from linear algebra to semigroups and groups. We determine the maximum cardinality of an independent set in finite abelian groups, Brandt semigroups, free nilpotent semigroups, and some examples of infinite groups.
26
Szabó, Tibor. "Extremal problems for graphs and hypergraphs /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487935125880928.
Full text
27
López, Amo Mireia. "El dogmatismo y el problema de la extrema liberalidad." Doctoral thesis, Universitat de Girona, 2016. http://hdl.handle.net/10803/398658.
Full textAbstract:
The main goal of this dissertation is to analyse a view about perceptual justification that is known as dogmatism. Dogmatism is a highly attractive view due to its anti-sceptical force and the fact that it seems to follow from common sense intuitions. However, in this work we will try to examine if there are reasons to think that dogmatism is affected by the problem of extreme liberality, according to which this view does not restrict adequately the kinds of experiences that can confer justification to believe things about the external worldEsta tesis trata de analizar críticamente una posición sobre la justificación perceptiva que se ha popularizado bajo el nombre de dogmatismo. El dogmatismo resulta una posición altamente atractiva por su fuerza anti-escéptica y por su proximidad con las intuiciones del sentido común. Sin embargo, el objetivo principal de este trabajo es el de examinar si hay razones para pensar que el dogmatismo debe hacer frente al problema de la extrema liberalidad de acuerdo con el cual esta posición no restringe adecuadamente el tipo de experiencias que son capaces de conferirnos justificación para creer cosas sobre el mundo externo
28
Wang, Hao. "The Hot Optimal Transportation Meshfree (HOTM) Method for Extreme Multi-physics Problems." Case Western Reserve University School of Graduate Studies / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=case1607533458323004.
Full text
29
Roberts, Ian T. "Extremal problems and designs on finite sets." Curtin University of Technology, School of Mathematics and Statistics, 1999. http://espace.library.curtin.edu.au:80/R/?func=dbin-jump-full&object_id=9909.
Full textAbstract:
This thesis considers three related structures on finite sets and outstanding conjectures on two of them. Several new problems and conjectures are stated.A union-closed collection of sets is a collection of sets which contains the union of each pair of sets in the collection. A completely separating system of sets is a collection of sets in which for each pair of elements of the universal set, there exists a set in the collection which contains the first element but not the second, and another set which contains the second element but not the first. An antichain (Sperner Family) is a collection of distinct sets in which no set is a subset of another set in the collection. The size of an antichain is the number of sets in the collection. The volume of an antichain is the sum of the cardinalities of the sets in the collection. A flat antichain is an antichain in which the difference in cardinality between any two sets in the antichain is at most one.The two outstanding conjectures considered are:The union-closed sets conjecture - In any union-closed collection of non-empty sets there is an element of the universal set in at least half of the sets in the collection;The flat antichain conjecture - Given an antichain with size s and volume V, there is a flat antichain with the same size and volume.Union-closed collections are considered in two ways. Improvements are made to the previously known bounds concerning the minimum size of a counterexample to the union-closed sets conjecture. Results are derived on the minimum size of a union-closed collection generated by a given number of k-sets. An ordering on sets is described, called order R and it is conjectured that choosing a collection of m k-sets in order R will always minimise the size of the union-closed collection generated by m k-sets.Several variants on completely separating systems of sets are considered. A ++determination is made of the minimum size of such collections, subject to various constraints on the collections. In particular, for each n and k, exact values or bounds are determined for the minimum size of completely separating systems on a n-set in which each set has cardinality k.Antichains are considered in their relationship to completely separating systems and the flat antichain conjecture is shown to be true in certain cases.
30
Pokrovskiy, Alexey. "Graph powers, partitions, and other extremal problems." Thesis, London School of Economics and Political Science (University of London), 2013. http://etheses.lse.ac.uk/754/.
Full textAbstract:
Graph theory is the study of networks of objects (called vertices) joined by links (called edges). Since many real world problems can be represented by a graph, graph theory has applications in areas such as sociology, chemistry, and computing. In this thesis, a number of open problems in graph theory are studied.
31
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.
Full text
32
Day, Alan Nicholas. "A collection of problems in extremal combinatorics." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/36669.
Full textAbstract:
Extremal combinatorics is concerned with how large or small a combinatorial structure can be if we insist it satis es certain properties. In this thesis we investigate four different problems in extremal combinatorics, each with its own unique flavour. We begin by examining a graph saturation problem. We say a graph G is H-saturated if G contains no copy of H as a subgraph, but the addition of any new edge to G creates a copy of H. We look at how few edges a Kp- saturated graph can have when we place certain conditions on its minimum degree. We look at a problem in Ramsey Theory. The k-colour Ramsey number Rk(H) of a graph H is de ned as the least integer n such that every k- colouring of Kn contains a monochromatic copy of H. For an integer r > 3 let Cr denote the cycle on r vertices. By studying a problem related to colourings without short odd cycles, we prove new lower bounds for Rk(Cr) when r is odd. Bootstrap percolation is a process in graphs that can be used to model how infection spreads through a community. We say a set of vertices in a graph percolates if, when this set of vertices start off as infected, the whole graph ends up infected. We study minimal percolating sets, that is, percolating sets with no proper percolating subsets. In particular, we investigate if there is any relation between the smallest and the largest minimal percolating sets in bounded degree graph sequences. A tournament is a complete graph where every edge has been given an orientation. We look at the maximum number of directed k-cycles a tournament can have and investigate when there exist tournaments with many more k-cycles than expected in a random tournament.
33
Belch, Rudiger. "Extremal interpolation and nonlinear Riemann-Hilbert problems." Thesis, University of Cambridge, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.624100.
Full text
34
Sali, Attila. "Extremal problems for finite partially ordered sets /." The Ohio State University, 1986. http://rave.ohiolink.edu/etdc/view?acc_num=osu148732358362162.
Full text
35
Jiang, Zilin. "Problems in Discrete Geometry and Extremal Combinatorics." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/819.
Full textAbstract:
We study several problems in discrete geometry and extremal combinatorics. Discrete geometry studies the combinatorial properties of finite sets of simple geometric objects. One theme of the field is geometric Ramsey theory. Given m geometric objects, we want to select a not too small subset forming a configuration that is “regular” in some sense.
36
INABA, F. K. "Generalização do Extreme Learning Machine Regularizado para Problemas de Múltiplas Saídas." Universidade Federal do Espírito Santo, 2018. http://repositorio.ufes.br/handle/10/9693.
Full textAbstract:
Made available in DSpace on 2018-08-02T00:01:48Z (GMT). No. of bitstreams: 1
tese_11838_TeseFernandoKentaro20180704-82519.pdf: 1351429 bytes, checksum: 8f61541bb363877ab5ace62f3dc9e8f3 (MD5)
Previous issue date: 2018-02-28Extreme Learning Machine (ELM) recentemente teve sua popularidade aumentada e com isso tem sido aplicada com sucesso em diversas áreas do conhecimento. No estado da arte, variações usando regularização se tornaram comuns na área de ELM. A regularização mais comum é a norma `2, que melhora a generalização, mas resulta em uma rede densa. Regularização baseada em elastic net também foi proposta, mas geralmente restrita a problemas de regressão de uma saída e classificação binária. Este trabalho tem por objetivo propor uma generalização do ELM regularizado para problemas de classificação multiclasse e regressão multitarget. Nesse sentido, observou-se que o uso da norma `2,1 e de Frobenius proporcionaram uma geralização adequada. Como consequência, foi possível demonstrar que as técnicas R-ELM e OR-ELM, consagradas na literatura, são casos particulares dos métodos propostos nesta Tese, denominados de GR-ELM e GOR-ELM, respectivamete. Além disso, outra proposta deste trabalho é trazer um algoritmo alternativo para o GR- ELM, o DGR-ELM, para tratar dados que são naturalmente distribuídos. O alternating direction method of multipliers (ADMM) é usado para resolver os problemas de otimização resultantes. Message passing interface (MPI) no estilo de programação single program, multiple data (SPMD) é escolhido para implementar o DGR-ELM. Vários experimentos são conduzidos para avaliar os métodos propostos. Nossos experimentos mostram que o GR-ELM, DGR-ELM e GOR-ELM possuem desempenho similar quando comparados ao R-ELM e OR-ELM, embora, em geral, uma estrutura mais compacta é obtida na rede resultante. Palavras-chave: norma `2,1. regularização. extreme learning machine. classificação multi- classe. multitarget regression. robustez à outliers. alternating direction method of multipliers.
37
Person, Yury. "Quasi-random hypergraphs and extremal problems for hypergraphs." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2010. http://dx.doi.org/10.18452/16238.
Full textAbstract:
In dieser Arbeit wird zuerst das Theorem von Chung, Graham und Wilson über quasi-zufällige Graphen zur sogenannten schwachen Quasi-Zufälligkeit für k-uniforme Hypergraphen verallgemeinert und somit eine Reihe äquivalenter Eigenschaften bestimmt. Basierend auf diesen Resultaten werden nichtbipartite Graphen gefunden, welche die Quasi-Zufälligkeit für Graphen ``forcieren''''. Zuvor waren nur bipartite Graphen mit dieser Eigenschaft bekannt. Desweiteren ist ein konzeptionell einfacher Algorithmus zum Verifizieren nicht erfüllbarer zufälliger k-SAT Formeln angegeben. Dann richtet sich der Fokus auf Anwendungen verschiedener Regularitätslemmata für Hypergraphen. Zuerst wird die Menge aller bezeichneten 3-uniformen Hypergraphen auf n Knoten, die keine Kopie des Hypergraphen der Fano Ebene enthalten, studiert. Es wird gezeigt, dass fast jedes Element aus dieser Menge ein bipartiter Hypergraph ist. Dies führt zu einem Algorithmus, der in polynomiell erwarteter Zeit einen zufälligen Fano-freien (und somit einen zufälligen bipartiten 3-uniformen) Hypergraphen richtig färbt. Schließlich wird die folgende extremale Funktion studiert. Es sind r Farben gegeben sowie ein k-uniformer Hypergraph F. Auf wie viele verschiedene Arten kann man die Kanten eines k-uniformen Hypergraphen H färben, so dass keine monochromatische Kopie von F entsteht? Welche Hypergraphen H maximieren die Anzahl erlaubter Kantenfärbungen? Hier wird ein strukturelles Resultat für eine natürliche Klasse von Hypergraphen bewiesen. Es wird für viele Hypergraphen F, deren extremaler Hypergraph bekannt ist, gezeigt, dass im Falle von zwei oder drei Farben die extremalen Hypergraphen die oben beschriebene Funktion maximieren, während für vier oder mehr Farben andere Hypergraphen mehr Kantenfärbungen zulassen.This thesis presents first one possible generalization of the result of Chung, Graham and Wilson to k-uniform hypergraphs, and studies the so-called weak quasi-randomness. As applications we obtain a simple strong refutation algorithm for random sparse k-SAT formulas and we identify first non-bipartite forcing pairs for quasi-random graphs. Our focus then shifts from the study of quasi-random objects to applications of different versions of the hypergraph regularity lemmas; all these versions assert decompositions of hypergraphs into constantly many quasi-random parts, where the meaning of ``quasi-random'''' takes different contexts in different situations. We study the family of hypergraphs not containing the hypergraph of the Fano plane as a subhypergraph, and show that almost all members of this family are bipartite. As a consequence an algorithm for coloring bipartite 3-uniform hypergraphs with average polynomial running time is given. Then the following combinatorial extremal problem is considered. Suppose one is given r colors and a fixed hypergraph F. The question is: In at most how many ways can one color the hyperedges of a hypergraph H on n vertices such that no monochromatic copy of F is created? What are the extremal hypergraphs for this function? Here a structural result for a natural family of hypergraphs F is proven. For some special classes of hypergraphs we show that their extremal hypergraphs (for large n) maximize the number of edge colorings for 2 and 3 colors, while for at least 4 colors other hypergraphs are optimal.
38
Gong, Yun. "Empirical likelihood and extremes." Diss., Georgia Institute of Technology, 2012. http://hdl.handle.net/1853/43581.
Full textAbstract:
In 1988, Owen introduced empirical likelihood as a nonparametric method for constructing confidence intervals and regions. Since then, empirical likelihood has been studied extensively in the
literature due to its generality and effectiveness. It is well known that empirical likelihood has several attractive advantages
comparing to its competitors such as bootstrap: determining the shape of confidence regions automatically using only the data;
straightforwardly incorporating side information expressed through constraints; being Bartlett correctable. The main part of this
thesis extends the empirical likelihood method to several interesting and important statistical inference situations. This thesis has four components. The first component (Chapter II)
proposes a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve in order to overcome the computational
difficulty when we have nonlinear constrains in the maximization problem. The second component (Chapter III and IV) proposes smoothed
empirical likelihood methods to obtain interval estimation for the conditional Value-at-Risk with the volatility model being an ARCH/GARCH model and a nonparametric regression respectively, which
have applications in financial risk management. The third component(Chapter V) derives the empirical likelihood for the intermediate
quantiles, which plays an important role in the statistics of extremes. Finally, the fourth component (Chapter VI and VII)
presents two additional results: in Chapter VI, we present an interesting result by showing that, when the third moment is infinity, we may prefer the Student's t-statistic to the sample mean
standardized by the true standard deviation; in Chapter VII, we present a method for testing a subset of parameters for a given
parametric model of stationary processes.
39
Tran, Manh Tuan [Verfasser]. "On problems in Extremal Combinatorics / Manh Tuan Tran." Berlin : Freie Universität Berlin, 2016. http://d-nb.info/111980387X/34.
Full text
40
Mazorow, Moya Michelle Wilson R. M. Wilson R. M. "Extremal problems in codes, finite sets and geometries /." Diss., Pasadena, Calif. : California Institute of Technology, 1991. http://resolver.caltech.edu/CaltechETD:etd-07182007-091952.
Full text
41
Townsend, Timothy Duncan. "Extremal problems on graphs, directed graphs and hypergraphs." Thesis, University of Birmingham, 2016. http://etheses.bham.ac.uk//id/eprint/6453/.
Full textAbstract:
This thesis is concerned with extremal problems on graphs and similar structures. We first study degree conditions in uniform hypergraphs that force matchings of various sizes. Our main result in this area improves bounds of Markstrom and Rucinski on the minimum d-degree which forces a perfect matching in a k-uniform hypergraph on n vertices. We then study connectivity conditions in tournaments that ensure the existence of partitions of the vertex set that satisfy various properties. In 1982 Thomassen asked whether every sufficiently strongly connected tournament T admits a partition of its vertex set into t vertex classes such that the subtournament induced on T by each class is strongly k-connected. Our main result in this area implies an affirmative answer to this question. Finally we investigate the typical structure of graphs and directed graphs with some forbidden subgraphs. We answer a question of Cherlin by finding the typical structure of triangle-free oriented graphs. Moreover, our results generalise to forbidden transitive tournaments and forbidden oriented cycles of any order, and also apply to digraphs. We also determine, for all k > 5, the typical structure of graphs that do not contain an induced 2k-cycle. This verifies a conjecture of Balogh and Butterfield.
42
RadoiÄ, iÄ RadoÅ¡ 1978. "Extremal problems in combinatorial geometry and Ramsey theory." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/32246.
Full textAbstract:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.Includes bibliographical references (p. 207-223).
The work presented in this thesis falls under the broad umbrella of combinatorics of Erd's type. We describe diverse facets of interplay between geometry and combinatorics and consider several questions about existence of structures in various combinatorial settings. We make contributions to specific problems in combinatorial geometry, Ramsey theory and graph theory. We first study extremal questions in geometric graph theory, that is, the existence of collections of edges with a specified crossing pattern in drawings of graphs in the plane with sufficiently many edges. Among other results, we prove that any drawing of a graph on n vertices and Cn edges, where C is a sufficiently large constant, contains each of the following crossing patterns: (1) three pairwise crossing edges, (2) two edges that cross and are crossed by k other edges, (3) an edge crossed by four other edges. In the latter, we show that C = 5.5 is the best possible constant, which, through Szekely's method, gives the best known value for a constant in the well known "Crossing Lemma" due to Ajtai, Chvatal, Leighton, Newborn and Szemeredi. After relaxing graph planarity in several ways, we proceed to study ... the maximum number of edges in a drawing of a graph on n vertices without self-crossing copy of C4, the cycle of four vertices. We prove that ... The importance of this and the above mentioned results comes from numerous applications of "Crossing Lemma" and the bounds on ... in discrete and computational geometry (incidence and Gallai-Sylvester type problems, k-set problems,
(cont.) the distinct distances and the unit distance problems of Erd6s, problems on arrangements of circles and pseudo-parabolas, questions on parametric and kinetic minimum spanning trees), number theory, and the VLSI design. Next, we initiate a new trend in Ramsey theory, which can be categorized as the rainbow Ramsey theory. Drawing a parallel with Moztkin's statement that "complete disorder is impossible", we prove the existence of rainbow/hetero-chromatic structures in a colored universe, under certain density conditions on the coloring. Hence, we provide several striking examples supporting the new philosophy that complete disorder is unavoidable as well. In particular, we prove that every 3-coloring of the color classes being equinumerous, contains a rainbow 3-term arithmetic progression. We also consider rainbow counterparts of other classical theorems in Ramsey theory, such as Rado's and Hales-Jewett theorem. Additionally, we refute one geometric strengthening of van der Waerden's theorem, thus, answering an open problem posed by Pach. We continue with two classical problems in Euclidean Ramsey theory: (1) Hadwiger-Nelson problem on the chromatic number of Rd and (2) the empty convex hexagon question of Erd6s. We prove that the chromatic number of R3 is at most 15, improving the previous bound of 18, due to Coulson. Regarding the latter question, which is one of the most notorious open problem in combinatorial geometry, we discover interesting relations on the numbers Xk(P) of empty convex k-gons in an n-element planar point set P ...
by RadoÅ¡ RadoiÄiÄ.
Ph.D.
43
Gao, Shujun. "Estimation distribution algorithms based on extreme elitism and their application in engineering optimization problems." Thesis, University of British Columbia, 2017. http://hdl.handle.net/2429/63302.
Full textAbstract:
This dissertation modifies several estimation distribution algorithms (EDAs) and implements them in engineering optimization problems. The EDAs are population-based evolutionary algorithms, which employ extreme elitism selection. The main work of the present study is outlined below.
First, an approach of extreme elitism selection is developed for EDAs. This selection highlights the effect of a few top solutions and advances EDAs to form a primary evolutionary direction. Simultaneously, this selection can also maintain population diversity to make EDAs avoid premature convergence. EDAs with the new selection approach are tested using a set of benchmark low-dimensional and high-dimensional optimization problems. The experimental results show that the EDA based on univariate marginal Gaussian distribution (UMGD) with extreme elitism selection can outperform some other classical evolution algorithms for most problems.
Second, the EDA based on UMGD with extreme elitism is implemented for solving the inverse displacement problem (IDP) of a robotic manipulator. This EDA is compared with the EDAs with other selection methods in solving the IDP of a 4-degree-of-freedom (DOF) robotic arm. Next the algorithm is integrated with differential mutation to solve the IDP of a 7-DOF robotic arm. After that, the proposed algorithm is used to search for satisfactory solutions as a continuous curve. The simulation results show this algorithm can reach real time speeds, in practical applications.
Third, EDAs based on five different Gaussian distributions are proposed to solve optimization problems with various types of constraints like equality, inequality, linear, nonlinear, continuous or discontinuous. It is found the EDA based on a single multivariate Gaussian distribution with extreme elitism selection can outperform other EDAs. Besides, this EDA has good performance for four engineering design problems.
Fourth, EDA is combined with differential mutation to solve multi-objective optimization problems (MOPs). The hybrid algorithm seeks to find the Pareto optimal front for MOPs. EDAs guide the search direction in the evolution while differential mutation keeps a diversified population. A new sampling method that uses more Gaussian models to generate offspring is specially designed for the EDAs for MOPs. In light of no-free-lunch theorem, different probabilistic models and programing codes are adopted for different MOPs.Applied Science, Faculty of
Mechanical Engineering, Department of
Graduate
44
Backman, Emil, and David Petersson. "Evaluation of methods for quantifying returns within the premium pension." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-288499.
Full textAbstract:
Pensionsmyndigheten's (the Swedish Pensions Agency) current calculation of the internal rate of return for 7.7 million premium pension savers is both time and resource consuming. This rate of return mirrors the overall performance of the funded part of the pension system and is analyzed internally, but also reported to the public monthly and yearly based on differently sized data samples. This thesis aims to investigate the possibility of utilizing other approaches in order to improve the performance of these calculations. Further, the study aims to verify the results stemming from said calculations and investigate their robustness. In order to investigate competitive matrix methods, a sample of approaches are compared to the more classical numerical methods. The approaches are compared in different scenarios aimed to mirror real practice. The robustness of the results are then analyzed by a stochastic modeling approach, where a small error term is introduced aimed to mimic possible errors which could arise in data management. It is concluded that a combination of Halley's method and the Jacobi-Davidson algorithm is the most robust and high performing method. The proposed method combines the speed and robustness from numerical and matrix methods, respectively. The result show a performance improvement of 550% in time, while maintaining the accuracy of the current server computations. The analysis of error propagation suggests the output error to be less than 0.12 percentage points in 99 percent of the cases, considering an introduced error term of large proportions. In this extreme case, the modeled expected number of individuals with an error exceeding 1 percentage point is estimated to be 212 out of the whole population.Pensionsmyndighetens nuvarande beräkning av internräntan för 7,7 miljoner pensionssparare är både tid- och resurskrävande. Denna avkastning ger en översikt av hur väl den fonderade delen av pensionssystemet fungerar. Detta analyseras internt men rapporteras även till allmänheten varje månad samt årligen baserat på olika urval av data. Denna uppsats avser att undersöka möjligheten att använda andra tillvägagångssätt för att förbättra prestanda för denna typ av beräkningar. Vidare syftar studien till att verifiera resultaten som härrör från dessa beräkningar och undersöka deras stabilitet. För att undersöka om det finns konkurrerande matrismetoder jämförs ett urval av tillvägagångssätt med de mer klassiska numeriska metoderna. Metoderna jämförs i flera olika scenarier som syftar till att spegla verklig praxis. Stabiliteten i resultaten analyseras med en stokastisk modellering där en felterm införs för att efterlikna möjliga fel som kan uppstå i datahantering. Man drar slutsatsen att en kombination av Halleys metod och Jacobi-Davidson-algoritmen är den mest robusta och högpresterande metoden. Den föreslagna metoden kombinerar hastigheten från numeriska metoder och tillförlitlighet från matrismetoder. Resultatet visar en prestandaförbättring på 550 % i tid, samtidigt som samma noggrannhet som ses i de befintliga serverberäkningarna bibehålls. Analysen av felutbredning föreslår att felet i 99 procent av fallen är mindre än 0,12 procentenheter i det fall där införd felterm har stora proportioner. I detta extrema fall uppskattas det förväntade antalet individer med ett fel som överstiger 1 procentenhet vara 212 av hela befolkningen.
45
Feitosa, Osmilcy Lima. "Algumas técnicas de resolução de problemas de mínimos e máximos na geometria euclidiana." Universidade Federal de Roraima, 2015. http://www.bdtd.ufrr.br/tde_busca/arquivo.php?codArquivo=284.
Full textAbstract:
Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorAo analisar a Educação Básica nos dias atuais, observa-se que no Ensino Médio o estudo dos problemas sobre máximos e mínimos é realizado de forma limitada e superficial, resumindo-se basicamente a algumas aplicações de funções quadráticas. A resolução de problemas de otimização de índole geométrica constitui um campo fértil para trabalhar a formação matemática dos alunos nesse nível e contribuir com o aperfeiçoamento da qualidade do ensino da Matemática. Esta categoria de problemas pode ser de utilidade na preparação de alunos para as Olimpíadas de Matemática. Este trabalho aborda o estudo e descrição de métodos de solução de problemas de otimização em geometria euclidana, apresentando uma catalogação devida a Andreescu, junto a vários exemplos resolvidos.
Looking over the Basic Education nowadays, it becomes aware that in high school the study of maxima and minimas problems is carry out in a limited and superficial way. In general, the resolution of these problems lessened to some application of quadratic functions. However, Geometric optimizations problems may be a fecund area to contribute for improving the quality of math education at this level and to develop the mathematical mind of students. That category of problems is also useful for training students for the Math Olympics. This masters dissertation deals with the study of resolutions methods of optimization problems in Euclidean Plane Geometry, presenting a cataloging, according to Andreescu, and some several solved illustrative examples.
46
Kusch, Christopher [Verfasser]. "Problems in Positional Games and Extremal Combinatorics / Christopher Kusch." Berlin : Freie Universität Berlin, 2017. http://d-nb.info/1148426256/34.
Full text
47
Lerma, Miguel Angel. "An extremal majorant for the logarithm and its applications /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.
Full text
48
Gerencsér, Máté. "Stochastic PDEs with extremal properties." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/20445.
Full textAbstract:
We consider linear and semilinear stochastic partial differential equations that in some sense can be viewed as being at the "endpoints" of the classical variational theory by Krylov and Rozovskii [25]. In terms of regularity of the coeffcients, the minimal assumption is boundedness and measurability, and a unique L2- valued solution is then readily available. We investigate its further properties, such as higher order integrability, boundedness, and continuity. The other class of equations considered here are the ones whose leading operators do not satisfy the strong coercivity condition, but only a degenerate version of it, and therefore are not covered by the classical theory. We derive solvability in Wmp spaces and also discuss their numerical approximation through finite different schemes.
49
Moser, Irene. "Applying external optimisation to dynamic optimisation problems." Swinburne Research Bank, 2008. http://hdl.handle.net/1959.3/22526.
Full textAbstract:
Thesis (Ph.D) - Swinburne University of Technology, Faculty of Information & Communication Technologies, 2008.[A thesis submitted in total fulfillment of the requirements of for the degree of Doctor of Philosophy, Faculty of Information and Communication Technologies, Swinburne University of Technology, 2008]. Typescript. Includes bibliographical references p. 193-201.
50
Letzter, Shoham. "Extremal graph theory with emphasis on Ramsey theory." Thesis, University of Cambridge, 2015. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709415.
Full text