Dissertations / Theses: 'Simplex (Mathematics)'

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Alpert, Hannah (Hannah Chang). "Special gradient trajectories counted by simplex straightening." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104608.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 65-67).
We prove three theorems based on lemmas of Gromov involving the simplicial norm on stratified spaces. First, the Gromov singular fiber theorem (with proof originally sketched by Gromov) relates the simplicial norm to the number of maximum multiplicity critical points of a smooth map of manifolds that drops in dimension by 1. Second, the multitangent trajectory theorem (proved with Gabriel Katz) relates the simplicial norm to the number of maximum-multiplicity tangent trajectories of a nowhere-vanishing gradient-like vector field on a manifold with boundary. And third, the Morse broken trajectory theorem relates the simplicial volume to the number of maximally broken trajectories of the gradient flow of a Morse--Smale function. Corollary: a Morse function on a closed hyperbolic manifold must have a critical point of every Morse index.
by Hannah Alpert.
Ph. D.

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Webb, Simon Peter. "Central slices of the regular simplex." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338771.

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Trevisan, Eberson Paulo. "O uso da programação linear na separação de pontos." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306659.

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Orientador: Valéria Abrão de Podestá
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho são apresentados alguns assuntos iniciais da teoria de Programação Linear e o método Simplex. Mostramos também como a Programação Linear pode ser utilizada na separação de dois conjuntos de pontos (padrões), através de um modelo linear cuja solução é um hiperplano separador. Finalizamos o trabalho com a apresentação de alguns exemplos de aplicação da Programação Linear na separação de dois conjuntos linearmente separáveis e linearmente inseparáveis
Abstract: In this work we present some introductory issues from Linear Programming theory and the Simplex method. We also show how we can use Linear Programming in two patterns separation by constructing a linear model which solution is a separating hyperplane. Finaly, we also present some examples of Linear Programming application in the linear separability and inseparability of two patterns sets
Mestrado
Programação Linear
Mestre em Matemática

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Alajmi, Abdulrahman N. "On The Lattice Size With Respect To The Standard Simplex in 3D." Kent State University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=kent1598893373379275.

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Passos, Adão Nascimento dos. "Estudos em programação linear." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306658.

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Orientador: Valeria Abrão de Podesta
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho é feito um estudo sobre Programação Linear e um texto sobre alguns de seus assuntos básicos, construído com uma linguagem didática, visando sua utilização em sala de aula. São apresentados alguns problemas lineares, os fundamentos matemáticos da Programação Linear e o método Simplex, finalizando com um estudo do princípio da decomposição de Dantzig-Wolfe, que é um procedimento para a resolução de problemas lineares de grande porte e com estrutura especial.
Abstract: In this work we have done a study on Linear Programming and a text with some basic issues, using a didactic language, and aiming its utilization in the classroom. Some linear problems are shown here, the mathematical background of Linear Programming and the Simplex method. Finaly, we have also presented a study on the principle of Dantzig-Wolfe's decomposition, which is a procedure for solving large linear problems with special structure.
Mestrado
Programação Linear
Mestre em Matemática

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Tinaztepe, Ramazan. "Modulation spaces, BMO and the Zak transform, and minimizing IPH functions over the unit simplex." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34659.

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This thesis consists of two parts. In the first chapter, we give some results on modulation spaces. First the relationship between the classical spaces and the modulation spaces is established. It is proved that certain modulation spaces defined on R² lie in the BMO space. Another result is that the Zak transform, a discrete time-frequency transform, maps a modulation space into a higher dimensional modulation space. And by using these results, an uncertainty principle for Gabor frames via modulation spaces is obtained. In the second part, we deal with optimization of an increasing positively homogeneous functions on the unit simplex. The class of increasing positively homogeneous functions is one of the function classes obtained via min-type functions in the context of abstract convexity. The cutting angle method is used for the minimization of this type functions. The most important step of this method is the minimization of a function which is the maximum of a number of min-type functions on the unit simplex. We propose a numerical algorithm for the minimization of such functions on the unit simplex and we mathematically prove that this algorithm finds the exact solution of the minimization problem. Some experiments have been carried out and the results of the experiments have been presented.

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Linnell, Joshua Randall. "Multilattice Tilings and Coverings." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/8911.

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Let L be a discrete subgroup of \mathbb{R}^n under addition. Let D be a finite set of points including the origin. These two sets will define a multilattice of \mathbb{R}^n. We explore how to generate a periodic covering of the space \mathbb{R}^n based on L and $D$. Additionally, we explore the problem of covering when we restrict ourselves to covering \mathbb{R}^n using only dilations of the right regular simplex in our covering. We show that using a set D= {0,d} to define our multilattice the minimum covering density is 5-\sqrt{13}. Furthermore, we show that when we allow for an arbitrary number of displacements, we may get arbitrarily close to a covering density of 1.

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Michel, Jean-Luc. "Polysimplices in euclidean spaces and the enumeration of domino tilings of rectangles." Doctoral thesis, Universite Libre de Bruxelles, 2011. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209922.

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Nous étudions, dans la première partie de notre thèse, les polysimplexes d’un espace euclidien de dimension quelconque, c’est-à-dire les objets consistant en une juxtaposition de simplexes réguliers (de tétraèdres si la dimension est 3) accolés le long de leurs faces. Nous étudions principalement le groupe des symétries de ces polysimplexes. Nous présentons une façon de représenter un polysimplexe à l’aide d’un diagramme. Ceci fournit une classification complète des polysimplexes à similitude près. De plus, le groupe des symétries se déduit du groupe des automorphismes du diagramme. Il découle en particulier de notre étude qu’en dimension supérieure à 2, une telle structure ne possède jamais deux faces parallèles et ne contient jamais de circuit fermé de simplexes.

Dans la seconde partie de notre thèse, nous abordons un problème classique de combinatoire :l’énumération des pavages d’un rectangle mxn à l’aide de dominos. Klarner et Pollack ont montré qu’en fixant m la suite obtenue vérifie une relation de récurrence linéaire à coefficients constants. Nous établissons une nouvelle méthode nous permettant d’obtenir la fonction génératrice correspondante et la calculons pour m <= 16, alors qu’elle n’était connue que pour m <= 10.

Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Talačkaitė, Simona. "Daugiamačių simpleksinių Lipšico algoritmų su nežinoma Lipšico konstanta ir įvairiais simplekso centrais kūrimas ir eksperimentinis tyrimas." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2014. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2014~D_20140724_105124-61903.

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Globaliojo optimizavimo metodai, pagrįsti Lipšico rėžių apskaičiavimu, yra plačiai taikomi įvairių optimizavimo uždavinių sprendimui. Tačiau Lipšico metodai dažniausiai remiasi prielaida, kad Lipšico konstanta žinoma iš anksto, o tai retas atvejis sprendžiant praktinius uždavinius. Todėl Simonos Talačkaitės magistro darbe yra toliau nagrinėjama aktuali ir svarbi problematika iškylanti realizuojant Lipšico metodus nesiremiančius jokiomis išankstinėmis prielaidomis apie Lipšico konstantą. Praktinio tiriamojo pobūdžio magistro darbe iškeliamas toks pagrindinis tikslas: ištirti daugiamačių simpleksinių globaliojo optimizavimo algoritmų su nežinoma Lipšico konstanta efektyvumą priklausomai nuo naudojamo simplekso centro. Šiam tikslui pasiekti buvo iškelti šie uždaviniai: apžvelgti naujausią literatūrą skirta Lipšico metodams su nežinoma Lipšico konstanta; matematiškai išnagrinėti įvairių daugiamačių simplekso centrų apskaičiavimus bendru atveju bei juos realizuoti Matlab aplinkoje; papildyti simpleksinį globaliojo optimizavimo DISIMPL algoritmą šių simpleksų centrų apskaičiavimo paprogramėmis; eksperimentiškai ištirti pasiūlytų rezultatų praktiškumą sprendžiant testinius optimizavimo uždavinius.
This work analyzes Global optimization objectives, the most important it will be algorithms with simplicial Lipico constant. Also, this work analyzes multidi- mensional DIRECT algorithm. We will provide dividing in higher dimennsions DIRECT algorithm. Then analyzes two simplex and apply the solutions. The hand simplex to smallerpartitions. Perceive multidimensional DIRECT algorithm division rules. In this work wrote a lot about simplicial center about dividing of hyoer-cube. Finally, the experiment it will be about the best way, how we can nd circle center ir diferent way. Simplex centers using 8 test funkcions , changing the number of iterations and mistakes number. Create tables and to analyzes them. The purpose of this paper work is to introduce the simplex algorithm for global optimization with unknown Lipicas constant depending on the e¢ ciency of the division of the rules used in the simplex.

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Soares, Vanessa de Carvalho Alves. "Aplicações do problema de otimização de carteiras de investimento." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/305876.

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Orientador: Luziane Ferreira de Mendonça
Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: Neste trabalho, propomos a determinação de uma carteira de investimento ótima via um método sem derivada. Para isso, utilizamos o modelo de média-variância proposto por Harry M. Markowitz. no qual o problema é formulado de modo a se minimizar o risco do portfolio para um dado nível de retorno esperado, ou maximizar o nível de retorno fixado do portfolio associado a um dado nível de risco e determinar todas as carteiras ótimas, no sentido risco e retorno, formando a Fronteira Eficiente. Nosso algoritmo é baseado no Método Nelder-Mead, destinado à resolução de problemas de programação não linear irrestritos. Assim, adequamos a formulação do portfolio, que depende de restrições, para a utilização do mesmo.
Abstract: In this work we perform a portfolio optimization by using a derivative-free method. For this, we use the Mean-Variance Analysis proposed by Harry M. Markowitz, in which the problem is formulated as one of minimizing portfolio risk subject to a targeted expected portfolio return. Or, for a particular level of risk, we can find a combination of assets that is going to give the highest expected return and determine all the optimal portfolios, towards risk and return, forming the Efficient Frontier. Our algorithm is based on Nelder-Mead method, for solving problems of unconstrained nonlinear programming. Therefore, the formulation of the portfolio, subject to constraints, was adapted for its use.
Mestrado
Mestre em Matemática

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Champion, Patrick D. "An analysis of Fourier transform infrared spectroscopy data to predict herpes simplex virus 1 infection." Atlanta, Ga. : Georgia State University, 2008. http://digitalarchive.gsu.edu/math_theses/62/.

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Thesis (M.S.)--Georgia State University, 2008.
Title from title page (Digital Archive@GSU, viewed July 29, 2010) Yu-Sheng Hsu, committee chair; Gary Hastings, Jun Han, committee members. Includes bibliographical references (p. 41).

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Rocha, Rafael Freitas [UNESP]. "O problema de porte de estoque numa indústria moveleira." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/138458.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Os Problemas de Corte de Estoque (PCE) são frequentemente encontrados em indústrias moveleiras, onde deseja-se cortar objetos maiores (placas de madeira) em objetos menores (itens), cada qual com uma quantidade pré-estabelecida (demanda), a fim de que seja possível a construção de diversos produtos finais demandados. O foco deste trabalho é a solução dos PCE bidimensionais, em que duas dimensões são relevantes durante o processo de corte, utilizando diferentes métodos para elaborar maneiras distintas de se cortar um único objeto em estoque (elaboração de padrões de corte). Devido às diferentes prioridades que se tem dentro de uma indústria moveleira, pode ser que seja necessário cortar placas de madeira mais rapidamente para que os produtos sejam fabricados com maior agilidade. No entanto, esta rapidez na produção pode gerar maior perda de matéria-prima, ocasionando maiores gastos no processo produtivo. Para possibilitar a solução computacional desse problema foi desenvolvido um código computacional e alguns resultados são apresentados. É realizado um estudo comparativo entre a solução encontrada na prática de uma fábrica real de móveis com a solução encontrada neste trabalho. Os dados utilizados foram extraídos de uma empresa localizada na cidade de Jaci, no interior do estado de São Paulo, considerada de médio porte e que atende o mercado moveleiro a nível nacional
The Cutting Stock Problems (CSP) are generally found in furniture industry, where is need to cut larger objects (wooden boards) into smaller objects (items), each one with a specific amount (demand), in order to produce several final products. The focus of this work is to solve the two-dimensional CSP, where two dimensions are relevant during the cutting process, using different methods to create different ways to cut a single object in stock (development of cutting patterns). Due to the different priorities that have in a furniture industry, sometimes could be necessary to cut wooden boards more quickly to make products as fast as possible. However, this agility in production process may generate greater loss of raw materials, making the manufacturing process more expensive. In order to present a computational solution to the problem, was developed a computational code and some computational results are presented. A comparative study is carried out with a solution found in the practice of real furniture factory and a solution found at this work. The data was obtained from a company located in Jaci, in the state of Sao Paulo, considered medium-sized and deal with furniture market at national level

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Rocha, Rafael Freitas. "O problema de porte de estoque numa indústria moveleira /." São José do Rio Preto, 2015. http://hdl.handle.net/11449/138458.

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Orientador: Silvio Alexandre de Araujo
Banca: Maria do Socorro Nogueira Rangel
Banca: Adriana Cristina Cherri
Resumo: Os Problemas de Corte de Estoque (PCE) são frequentemente encontrados em indústrias moveleiras, onde deseja-se cortar objetos maiores (placas de madeira) em objetos menores (itens), cada qual com uma quantidade pré-estabelecida (demanda), a fim de que seja possível a construção de diversos produtos finais demandados. O foco deste trabalho é a solução dos PCE bidimensionais, em que duas dimensões são relevantes durante o processo de corte, utilizando diferentes métodos para elaborar maneiras distintas de se cortar um único objeto em estoque (elaboração de padrões de corte). Devido às diferentes prioridades que se tem dentro de uma indústria moveleira, pode ser que seja necessário cortar placas de madeira mais rapidamente para que os produtos sejam fabricados com maior agilidade. No entanto, esta rapidez na produção pode gerar maior perda de matéria-prima, ocasionando maiores gastos no processo produtivo. Para possibilitar a solução computacional desse problema foi desenvolvido um código computacional e alguns resultados são apresentados. É realizado um estudo comparativo entre a solução encontrada na prática de uma fábrica real de móveis com a solução encontrada neste trabalho. Os dados utilizados foram extraídos de uma empresa localizada na cidade de Jaci, no interior do estado de São Paulo, considerada de médio porte e que atende o mercado moveleiro a nível nacional
Abstract: The Cutting Stock Problems (CSP) are generally found in furniture industry, where is need to cut larger objects (wooden boards) into smaller objects (items), each one with a specific amount (demand), in order to produce several final products. The focus of this work is to solve the two-dimensional CSP, where two dimensions are relevant during the cutting process, using different methods to create different ways to cut a single object in stock (development of cutting patterns). Due to the different priorities that have in a furniture industry, sometimes could be necessary to cut wooden boards more quickly to make products as fast as possible. However, this agility in production process may generate greater loss of raw materials, making the manufacturing process more expensive. In order to present a computational solution to the problem, was developed a computational code and some computational results are presented. A comparative study is carried out with a solution found in the practice of real furniture factory and a solution found at this work. The data was obtained from a company located in Jaci, in the state of Sao Paulo, considered medium-sized and deal with furniture market at national level
Mestre

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Rodriguez, Paul Fabian. "Mathematical foundations of simple recurrent networks /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1999. http://wwwlib.umi.com/cr/ucsd/fullcit?p9935464.

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Cloyd, James Dale. "Data mining with Newton's method." [Johnson City, Tenn. : East Tennessee State University], 2002. http://etd-submit.etsu.edu/etd/theses/available/etd-1101102-081311/unrestricted/CloydJ111302a.pdf.

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Thorne, Jack A. "The Arithmetic of Simple Singularities." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10339.

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We investigate some arithmetic orbit problems in representations of linear algebraic groups arising from Vinberg theory. We aim to give a description of the orbits in these representations using methods with an emphasis on representation theory rather than algebraic geometry, in contrast to previous works of other authors. It turns out that for the representations we consider, the orbits are related to the arithmetic of the Jacobians of certain algebraic curves, which appear as the smooth nearby ﬁbers of deformations of simple singularities. We calculate these families of algebraic curves, and show that the 2-torsion in their Jacobians is canonically identiﬁed with the stabilizers of certain orbits in the corresponding representations.
Mathematics

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De, Piro Tristram D. P. (Tristram Denholm P. ). 1974. "Zariski structures and simple theories." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29286.

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Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2003.
Includes bibliographical references (p. 130-133).
In this thesis, I consider generalisations of geometric stability theory to minimal Lascar Strong Types definable in simple theories. Positively, we show that the conditions of linearity and 1-basedness are equivalent for such types. Negatively, we construct an example which is locally modular but not affine using a generalistion of the generic predicate. We obtain reducibility results leading to a proof that in any w-categorical, 1-based non-trivial simple theory a vector space over a finite field is interpretable and I prove natural generalisations of some of the above results for regular types. I then consider some of these ideas in the context of the conjectured non-finite axiomatisability of any w-categorical simple theory. In the non-linear Zariski structure context, I consider Zilber's axiomatization in stable examples, and then in the case of the simple theory given by an algebraically closed field with a generic predicate. Comparing Zariski structure methods with corresponding techniques in algebraic geometry, I show the notions of etale morphism and unramified Zariski cover essentially coincide for smooth algebraic varieties, show the equivalence of branching number and multiplicity in the case of smooth projective curves and give a proof of defining tangency for curves using multiplicities. Finally, I give a partial results in the model theory of fields which supports extending the Zariski structure method to simple theories.
by Tristram D. P. de Piro.
Ph.D.

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Korchagina, Inna A. "Three theorems on simple groups /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486398195328034.

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Orekhova, Ekaterina. "Simple weight q2(C)-supermodules." Thesis, Uppsala universitet, Matematiska institutionen, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119791.

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Belleville, Patrice. "Computing two-covers of simple polygons." Thesis, McGill University, 1991. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60490.

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A set ${ cal P} = P sb1,P sb2, ...,P sb{k}$ of polygons is called a k-cover of a simple polygon P if $P = cup sbsp{i=1}{k} P sb{i}$. It has been shown that finding k-covers of polygons by subpolygons of a given class is almost always NP-hard, whenever k is allowed to vary. Shermer (She91a) gave a linear time algorithm to determine if P has a two-cover by convex polygons, and to find one if it exists. A polygon P is star-shaped if it has a point which sees all the others, and $L sb{k}$-convex if every pair of points can be joined by a polygonal path of at most k links contained in P. In this thesis, we give algorithms to find two-covers of P by $L sb{k}$-convex polygons in $O(n sp2$) time and space, and by star-shaped polygons on $O(n sp4$) time and $O(n sp2$logn) space respectively, provided that they exist. We also give a characterization of the types of changes which occur in the region visible from a point as it moves along a line segment contained in P.

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Rached, Ziad. "Les systèmes triples de Jordan simples exceptionnels." Thesis, University of Ottawa (Canada), 1996. http://hdl.handle.net/10393/10332.

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Wang, Xueying. "Mechanisms of Simple Perceptual Decision Making Processes." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1249662470.

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Valencia, Elissa Marie. "Progenitors Related to Simple Groups." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/174.

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This thesis contains methods of finding new presentations of finite groups, particularly nonabelian simple groups. We have presented several progenitors such as 2^{*8}:Z_4 wr Z_2, 3^{*3}:_m L(2,7), 2^{*4}:[2:2^2], 2^{*11}:D_{11} and many more on which we've found the mathieu group M12 and 2*[M21:2^2] among their homomorphic images. We give the full monomial automorphism groups of Aut(3^{*2}), Aut(3^{*3}), and Aut(5^{*2}). Included is a proof showing that the full monomial automorphism group of Aut(m^{*n}) is isomorphic to U(m) wr S_n. In addition we have constructed the Cayley Diagrams of PGL(2,7), [3 x A_5]:2, 3:[A_6:2], and 2 x [(3 x L(2,11)):2] using the process of double coset enumeration.

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Stringer, Alex P. "Language and mathematics, the relation between English-French bilingualism and simple arithmetic." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ52371.pdf.

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Stringer, Alex P. (Alexander Paul) Carleton University Dissertation Psychology. "Language and mathematics; the relation between English-French bilingualism and simple arithmetic." Ottawa, 2000.

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Tarkhanov, Nikolai. "A simple numerical approach to the Riemann hypothesis." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/5764/.

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The Riemann hypothesis is equivalent to the fact the the reciprocal function 1/zeta (s) extends from the interval (1/2,1) to an analytic function in the quarter-strip 1/2 < Re s < 1 and Im s > 0. Function theory allows one to rewrite the condition of analytic continuability in an elegant form amenable to numerical experiments.

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Röver, Class H. E. W. "Subgroups of finitely presented simple groups." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312483.

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Khudhur, Peshawa Mohammed. "Sporadic simple groups of low genus." Thesis, University of Birmingham, 2016. http://etheses.bham.ac.uk//id/eprint/6592/.

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Let X be a compact connected Riemann surface of genus g and let f∶ X →P1 be a meromorphic function of degree n. Classes of such covers are in one to one correspondence with the primitive systems, which are tuples of elements (x1,x2,⋯,xr) in the symmetric group Sn taken up to conjugation and the action of the braid group, such that x1.x2.⋯.xr=1 and G=〈x1,x2,⋯,xr〉 is a primitive subgroup G of Sn. This thesis is a contribution to the classification of primitive genus g ≤ 2 systems of sporadic almost simple groups.

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Collett, Torstein Calvin. "Simple SSH Management." BYU ScholarsArchive, 2021. https://scholarsarchive.byu.edu/etd/9130.

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SSH certificates are used by administrators so connections to the server can be verified. This ensures that only authorized administrators can access the server and that the server being accessed is the intended machine. Current solutions for managing SSH certificates are focused on commercial use, which makes them cumbersome for small groups and individuals to use. These solutions require running multiple services that companies already use but add significant overhead for smaller groups. We developed a new standalone system that makes it easy to manage SSH certificates for small amounts of servers and users, without requiring additional servers to be deployed. We evaluated our system with a user study to demonstrate its ease of use. We hope that this implementation can help guide future research toward a more simplified certificate authentication system for SSH.

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Wissel, Daniel [Verfasser]. "Intrinsic Dimension Estimation using Simplex Volumes / Daniel Wissel." Bonn : Universitäts- und Landesbibliothek Bonn, 2018. http://d-nb.info/1153467011/34.

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31

Balduzzi, David. "Geometric realisation of representations of complex semi-simple Lie groups." Master's thesis, University of Cape Town, 2002. http://hdl.handle.net/11427/4950.

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32

Yan, Ping. "Theory of simple genetic algorithms." Thesis, University of Macau, 2000. http://umaclib3.umac.mo/record=b1446649.

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33

Cottrell, David 1979. "Symplectic integration of simple collisions : a backward error analysis." Thesis, McGill University, 2004. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=81322.

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Molecular Dynamics simulations often involve the numerical integration of pair-wise particle interactions with a constant, step size method. Of primary concern in these simulations is the introduction of error in velocity statistics. We consider the simple example of the symplectic Euler method applied to two-particle collisions in one dimension governed by linear restoring force and use backward error analysis to predict, these errors. For nearly all choices of system and method parameters, the post-collision energy is not conserved and depends upon the initial conditions of the particles and the step size of the method. The analysis of individual collisions is extended to predict energy growth in systems of particles in one dimension.

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Ray, James David. "Base Counting and Simple Mathematic Applications for the Special Education Classroom." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2236.

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This thesis was designed as a self study unit for middle school aged students with special needs. The unit is broken in to sub-units that specifically cater to each number base. Also included in this plan is a brief history of counting and practical uses for the mathematics of different number bases. This has been designed to be a "fun" unit to study after taking S.O.L. tests or other state standard testing. Included in each unit are worksheets for assessment of understanding.

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Ryba, A. J. E. "Algebras related to some sporadic simple groups." Thesis, University of Cambridge, 1985. https://www.repository.cam.ac.uk/handle/1810/272929.

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36

Orekhova, Ekaterina. "Simple weight q₂(C)-supermodules." Thesis, Uppsala University, Department of Mathematics, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-119791.

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37

Brache, Chad. "The Classical Lie algebras are more simple than they may appear." Master's thesis, Faculty of Science, 2021. http://hdl.handle.net/11427/33684.

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The purpose of this dissertation is to consider the classical Lie Algebras, namely: so(n, C), sl(n, C) and sp(n, C), n ≥ 2. Our aim will be to prove that if a Lie Algebra L is classical, except for so(2, C) and so(4, C), then it is simple. The classification and analysis will include finding their root systems and the associated Dynkin diagrams. The phrase it's the journey that teaches you a lot about your destination applies quite well here, as the bulk of our discussion will be assembling the tools necessary for proving simplicity. We will begin with some linear algebra proving the Primary decomposition theorem and the Cayley-Hamilton Theorem. Following this, we dive into the world of Lie algebras where we look at Lie algebras of dimensions 1, 2 and 3, representations of Lie algebras, weight spaces, Cartan's criteria and the root space decomposition of a Lie algebra L and define the Dynkin diagram and Cartan matrix. This will all culminate and serve as our arsenal in proving that these classical Lie algebras are all rather simple.

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38

Bradford, Jeremy. "Commutative endomorphism rings of simple abelian varieties over finite fields." Thesis, University of Maryland, College Park, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3557641.

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In this thesis we look at simple abelian varieties defined over a finite field k = [special characters omitted]_pn with End_k( A) commutative. We derive a formula that connects the p -rank r(A) with the splitting behavior of p in E = [special characters omitted](π), where π is a root of the characteristic polynomial of the Frobenius endomorphism. We show how this formula can be used to explicitly list all possible splitting behaviors of p in [special characters omitted]_E, and we do so for abelian varieties of dimension less than or equal to four defined over [special characters omitted]_p. We then look for when p divides [[special characters omitted]_E : [special characters omitted][π, π]]. This allows us to prove that the endomorphism ring of an absolutely simple abelian surface is maximal at p when p ≥ 3. We also derive a condition that guarantees that p divides [[special characters omitted]_E: [special characters omitted][π, π]]. Last, we explicitly describe the structure of some intermediate subrings of p-power index between [special characters omitted][π, π] and [special characters omitted]_E when A is an abelian 3-fold with r(A) = 1.

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Kimmel, Jason. "Simple Games on Networks." Oberlin College Honors Theses / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1307994412.

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Green, David John. "On the cohomology of certain finite simple groups." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239184.

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Farrell, N. "Rationality of blocks of quasi-simple finite groups." Thesis, City, University of London, 2017. http://openaccess.city.ac.uk/17653/.

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The Morita Frobenius number of an algebra is the number of Morita equivalence classes of its Frobenius twists. Introduced by Kessar in 2004, these numbers are important in the context of Donovan's conjecture for blocks of finite group algebras. Let P be a finite ℓ-group. Donovan's conjecture states that there are finitely many Morita equivalence classes of blocks of finite group algebras with defect groups isomorphic to P. Kessar proved that Donovan's conjecture holds if and only if Weak Donovan's conjecture and the Rationality conjecture hold. Our thesis relates to the Rationality conjecture, which states that there exists a bound on the Morita Frobenius numbers of blocks of finite group algebras with defect groups isomorphic to P, which depends only on SPS. In this thesis we calculate the Morita Frobenius numbers, or produce a bound for the Morita Frobenius numbers, of many of the blocks of quasi-simple finite groups. We also discuss the issues faced in the outstanding blocks and outline some possible approaches to solving these cases.

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42

Binh, Thanh Nguyen. "Localisation des fonctions propres du Laplacien dans des domaines simples et irréguliers." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00764806.

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The primary goal of the thesis is to study localization of Laplacian eigenfunctions in bounded domains when an eigenfunction is mainly supported by a small region of the domain and vanishing outside this region. The high-frequency and low-frequency localization in simple and irregular domains has been investigated for both Dirichlet and Neumann boundary conditions. Three types of high-frequency localization (whispering gallery, bouncing ball, and focusing eigemodes) have been revisited in circular, spherical and elliptical domains by deriving explicit inequalities on the norm of eigenfunctions. In turn, no localization has been found in most rectangular domains that led to formulating an open problem of characterization of domains that admit high-frequency localization. Using the Maslov-type differential inequalities, the exponential decay of low-frequency Dirichlet eigenfunctions has been extensively studied in various domains with branches of variable cross-sectional profiles. Under an explicit condition, the L2-norm of an eigenfunction has been shown to exponentially decay along the branch with an explicitly computed decay rate. This rigorous upper bound, which is applicable in any dimension and for both finite and infinite branches, presents a new achievement in the theory of classical and quantum waveguides, with potential applications in microelectronics, optics and acoustics. For bounded quantum waveguides with constant cross-sectional profiles, a sufficient condition on the branch lengths has been derived for getting a localized eigenfunction. The existence of trapped modes in typical finite quantum waveguides (e.g L-shape, bent strip and cross of two strips) has been proven provided that their branches are long enough, with an accurate estimate on the required minimal length. The high sensitivity of the localization character of eigenmodes to the length of branches and to the shape of the waveguide may potentially be used for switching devices in microelectronics and optics. The properties of localized eigenmodes in a class of planar spectral graphs have been analyzed. An efficient divide-and-conquer algorithm for solving the eigenproblem of the Laplacian matrix of undirected weighted graphs has been proposed and shown to run faster than traditional algorithms. A spectral approach has been developed to investigate the survival probability of reflected Brownian motion in reactive media. The survival probabilities have been represented in the form of a spectral decomposition over Laplacian eigenfunctions. The role of the geometrical structure of reactive regions and its influence on the overall reaction rate in the long-time regime has been studied. This approach presents a mathematical basis for designing optimal geometrical shapes of efficient catalysts or diffusive exchangers.

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43

Gray, Edward Martin. "Qualitatively different approaches to simple arithmetic." Thesis, University of Warwick, 1993. http://wrap.warwick.ac.uk/2309/.

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This study explores the qualitative difference in performance between those who are more successful and those who are less successful in simple arithmetic. In the event that children are unable to retrieve a basic number combination the study identifies that there is a spectrum of performance between children who mainly use procedures, such as count-all in addition and take-away in subtraction, to those who handle simple arithmetic in a much more flexible way. Two independent studies are described The first contrasts the performances of children in simple arithmetic. It considers teacher selected pupils of different ability from within each year group from 7+ to 12+. It takes a series of snapshots of different groups of children and considers their responses to a series of simple number combinations. This first experiment shows qualitatively different thinking in which the less successful children are seen to focus more on the use of procedures and in the development of competence in utilising them. The more successful appear to have developed a flexible mode of thinking which is not only capable of stimulating their selection of more efficient procedures but, the procedures they select are then used in an efficient and competent way. However, the use of procedures amongst the more successful is seen to be only one of two alternative approaches that they use. The other approach involves the flexible use of mathematical objects, numbers, that are derived from encapsulated processes. The below-average children demonstrate little evidence of the flexible use of encapsulated processes. It is the ability of the more able children to demonstrate flexibility through the use of efficient procedures and/or the use of encapsulated processes that stimulates the development of the theory of procepts. This theory utilises the duality which is ambiguously inherent in arithmetical symbolism to establish a framework from which we may identify the notion of proceptual thinking. The second study considers the development of a group of children over a period of nearly a year. This study relates to aspects of the numerical component of the standardised tests in mathematics which form part of the National Curriculum. It provides the data which gives support to the theory and provides evidence to confirm the snap shots taken of children at the age of 7+ and 8+. It indicates that children who possess procedural competence may achieve the same level of attainment as those who display proceptual flexibility at one level of difficulty but they may not possess the appropriate mental tools to cope with the next. The evidence of the study supports the hypothesis that there is a qualitative difference in children's arithmetical thinking.

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44

Price, Jamie H. "Lego Simple Machine + Math." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etsu-works/2984.

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45

Hoffman, Thomas Rune. "Constructing basic algebras for the principal block of sporadic simple groups." Diss., The University of Arizona, 2004. http://hdl.handle.net/10150/280550.

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This dissertation describes an algorithm for constructing the basic algebra Morita equivalent to the principal block of certain group algebras. This algorithm uses the method of condensation as it is described in [Lux97]. Using an intermediate condensation subalgebra allows for the construction of the projective indecomposable modules required to realize the basic algebra. The group algebras we are concerned with here are for sporadic groups in characteristic dividing the order of the group. In particular, the basic algebra for the principal block of the Higman-Sims group in characteristic 2 is completed and seven of the thirteen projective indecomposable modules for the Mathieu group M24 are constructed. In addition to these algebras, we have also computed the basic algebras for many alternating and symmetric groups.

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46

Altok, Serdar. "Reversibility of simple random walk on multi-type Galton-Watson trees." [Bloomington, Ind.] : Indiana University, 2008. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3344629.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2008.
Title from PDF t.p. (viewed on Oct. 8, 2009). Source: Dissertation Abstracts International, Volume: 70-02, Section: B, page: 1065. Adviser: Russell Lyons.

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47

Morris, Andrew John. "Representing spatial interactions in simple ecological models." Thesis, University of Warwick, 1997. http://wrap.warwick.ac.uk/1127/.

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The real world is a spatial world, and all living organisms live in a spatial environment. For mathematical biologists striving to understand the dynamical behaviour and evolution of interacting populations, this obvious fact has not been an easy one to accommodate. Space was considered a disposable complication to systems for which basic questions remained unanswered and early studies ignored it. But as understanding of non-spatial systems developed attention turned to methods of incorporating the effects of spatial structure. The essential problem is how to usefully manage the vast amounts of information that are implicit in a fully heterogeneous spatial environment. Various solutions have been proposed but there is no single best approach which covers all circumstances. High dimensional systems range from partial differential equations which model continuous population densities in space to the more recent individual-based systems which are simulated with the aid of computers. This thesis develops a relatively new type of model with which to explore the middle ground between spatially naive models and these fully complex systems. The key observation is to note the existence of correlations in real systems which may naturally arise as a consequence of their dynamical interaction amongst neighbouring individuals in a local spatial environment. Reflecting this fact - but ignoring other large scale spatial structure - the new models are developed as differential equations (pair models) which are based on these correlations. Effort is directed at a first-principles derivation from explicit assumptions with well stated approximations so the origin of the models is properly understood. The first step is consideration of simple direct neighbour correlations. This is then extended to cover larger local correlations and the implications of local spatial geometry. Some success is achieved in establishing the necessary framework and notation for future development. However, complexity quickly multiplies and on occasion conjectures necessarily replace rigorous derivations. Nevertheless, useful models result. Examples are taken from a range of simple and abstract ecological models, based on game theory, predator-prey systems and epidemiology. The motivation is always the illustration of possibilities rather than in depth investigation. Throughout the thesis, a dual interpretation of the models un-folds. Sometimes it can be helpful to view them as approximations to more complex spatial models. On the other hand, they stand as alternative descriptions of space in their own right. This second interpretation is found to be valuable and emphasis is placed upon it in the examples. For the game theory and predator-prey examples, the behaviour of the new models is not radically different from their non-spatial equivalents. Nevertheless, quantitative behavioural consequences of the spatial structure are discerned. Results of interest are obtained in the case of infection systems, where more realistic behaviour an improvement on non-spatial models is observed. Cautiously optimistic conclusions are reached that this, middle road of spatial modelling has an important contribution to make to the field.

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Ramo, Johanna Maria. "On structural aspects of finite simple groups of Lie type." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/677.

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In this PhD thesis, we consider two problems that are related to finite simple groups of Lie type. First of them is a problem mentioned in the Kourovka notebook: describe the finite simple groups in which every element is a product of two involutions. We consider the simple orthogonal groups in even characteristic, and solve the problem for them. Since other groups have been dealt with elsewhere, the problem is then solved completely. The second part of the thesis is related to Lie algebras. Every complex simple Lie algebra has a compact real form that is associated with a compact Lie group. In this thesis, we consider the Lie algebra of type E8, and give a new construction of its compact real form. The Lie product is defined using the irreducible subgroup of shape 25+10 ·GL5(2) of the automorphism group.

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49

Samuel, David. "Computing the external geodesic diameter of a simple polygon." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61805.

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Evans, Denis J., Debra J. Searles, and Stephen R. Williams. "A simple mathematical proof of boltzmann's equal a priori probability hypothesis." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-190362.

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Using the Fluctuation Theorem (FT), we give a first-principles derivation of Boltzmann’s postulate of equal a priori probability in phase space for the microcanonical ensemble. Using a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we show that if the initial distribution differs from the uniform distribution over the energy hypersurface, then under very wide and commonly satisfied conditions, the initial distribution will relax to that uniform distribution. This result is somewhat analogous to the Boltzmann H-theorem but unlike that theorem, applies to dense fluids as well as dilute gases and also permits a nonmonotonic relaxation to equilibrium. We also prove that in ergodic systems the uniform (microcanonical) distribution is the only stationary, dissipationless distribution for the constant energy ensemble.

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Dissertations / Theses on the topic 'Simplex (Mathematics)'

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