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1
Ruviaro, Ricardo. "Teorema de Bernstein." reponame:Repositório Institucional da UnB, 2007. http://repositorio.unb.br/handle/10482/5527.
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Dissertação (mestrado)—Universidade de Brasília, Instituto de Ciências Exatas, Departamento de Matemática, 2007.Texto parcialmente liberado pelo autor.
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O presente trabalho de investigação tem como tema o Teorema de Bernstein. Buscou-se como objetivo demonstrar de formas diferentes o Teorema de Bernstein, já que este teorema é um resultado muito extraordinário, pois levando em conta a multiplicidade de soluções que possui a equação de Lagrange, é realmente instigante que o mero fato da solução estar definida para todo (x, y) exclua todas as soluções menos a solução trivial. Far-se-á também a demonstração para o Teorema de do Carmo-Peng e Fischer Colbrie-Schoen. _____________________________________________________________________________ ABSTRACT
In this dissertation. We give three different proofs of the Bernstein theorem and a proof of the theorem of do Carmo-Peng and Fischer Colbrie-Schoen.
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Růžičková, Michaela. "Leonard Bernstein: MASS." Master's thesis, Akademie múzických umění v Praze.Hudební a taneční fakulta. Knihovna, 2016. http://www.nusl.cz/ntk/nusl-253942.
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This thesis analyzes in detail the work of Leonard Bernstein: MASS. The analysis covers both the theoretical and formal point of view as well as the interpretation issues, while focusing specifically on the issue of interpreting the multi-genre musical work and its definition.
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Varro, Richard. "Algèbres de Bernstein périodiques." Montpellier 2, 1992. http://www.theses.fr/1992MON20256.
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Dans le but de modéliser des populations dont la composition génétique suit une succession cyclique d'états d'équilibre, nous présentons une généralisation de la notion d'algèbre de Bernstein d'ordre n en introduisant la notion de périodicité. Nous nous sommes intéressés aux conditions d'existence d'idempotents généralisés et à leurs propriétés, à la structure vectorielle qui apparaît lors de la décomposition de Peierce et à des problèmes de transport de structures dans la dupliquée de ces algèbres. Enfin nous étudions les algèbres qui modelisent les populations d'organismes soumises seulement à la mutation des gènes et nous établissons la condition nécessaire et suffisante pour que ces populations atteignent à la première génération une situation d'équilibre périodique
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Landis, Johannes. "Le théâtre d'Henry Bernstein /." Paris : l'Harmattan, 2009. http://catalogue.bnf.fr/ark:/12148/cb41467448b.
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Gomes, Marlon de Oliveira. "O problema de Bernstein." reponame:Repositório Institucional da UFC, 2013. http://www.repositorio.ufc.br/handle/riufc/7213.
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GOMES, Marlon de Oliveira. O problema de Bernstein. 2013. 146 f. Dissertação(Mestrado em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Programa de Pós-Graduação em Matemática, Fortaleza, 2013.Submitted by Erivan Almeida (eneiro@bol.com.br) on 2014-02-06T14:14:48Z No. of bitstreams: 1 2013_dis_mogomes.pdf: 3591854 bytes, checksum: 7436eff84b83e17422b3a917b66a2067 (MD5)
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The classical Bernstein problem, solved by S. Bernstein in 1915-1917 in his article [12], asks if there is a complete minimal graph in R3 besides the plane. Bernstein showed that the answer to this question is no using analytical methods for study of equations of prescribed curvature. We will see here how this problem is related to the Gauss map of the graph, and as consequence of this relationship we generalize this theorem to a larger class of surfaces (not necessarily graphs), following the proof given by R. Osserman in [51]. We will see next generalizations of this theorem in higher dimensions, following essentially the methods introduced by W. Fleming in [31], and later refined by E. De Giorgi in [20], F. Almgren in [6] and J. Simons in [62]. In fact, they solve the problem for graphs in Rn, n < 9, namely they prove that the only complete minimal graph in these espaces is the hyperplane. Following the proof given by E. Bombieri, E. De Giorgi and E. Giusti in [14], we also show that, in dimension n ≥ 9, it is possible to construct complete minimal graphs in Rn. At last, we conclude with an extension of Bernstein’s theorem to the class of submanifolds stable with respect to the second variation of volume, under certain conditions of curvature and volume growth, and yet we investigate the case in which the ambient manifold is not the Euclidean space.
O problema de Bernstein clássico, resolvido por S. Bernstein em 1915-1917 em seu artigo [12], pergunta se existe um gráfico mínimo completo em R3 além do plano. Bernstein mostrou que a resposta para este problema é não, utilizando métodos analíticos para o estudo de equações de curvatura prescrita. Veremos aqui como este problema está relacionado com a aplicação de Gauss deste gráfico, e como conseqüência desta relação iremos generalizar este teorema para uma classe de superfícies maior (não necessariamente gráficos), seguindo a prova dada por R. Osserman em [51]. Veremos a seguir generalizações deste teorema em dimensões maiores, seguindo essencialmente os métodos introduzidos Por W. Fleming em [31], e refinados posteriormente por E. De Giorgi, em [20], F. Almgren, em [6], e J. Simons, em [62], que resolvem o problema para gráficos em Rn, n < 9 mostrando que o único gráfico mínimo completo nesses espaços é o hiperplano. Mostraremos também que em dimensão n ≥ 9, é possível construir gráficos mínimos completos em Rn, seguindo a prova apresentada por E. Bombieri, E. Di Giorgi e E. Giusti em [14]. Por fim, concluímos com uma extensão do teorema de Bernstein para a classe das subvariedades estáveis com respeito à segunda variação de volume, sob certas condições de crescimento de curvatura ou volume, e investigaremos ainda o caso que a variedade ambiente não é o espaço euclidiano.
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Jeberien, Alexandra. "Archäologischer Bernstein Untersuchung verschiedener Festigungsmöglichkeiten /." [Berlin] : [S.n.], 2000. https://sisis.rz.fhtw-berlin.de/inhalt/0122027.pdf.
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Zitan, Fouad. "Sur les algèbres de Bernstein." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376109529.
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Piazzon, Federico. "Bernstein Markov Properties and Applications." Doctoral thesis, Università degli studi di Padova, 2016. http://hdl.handle.net/11577/3424517.
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The Bernstein Markov Property for a compact set E and a positive finite mea-
sure μ supported on E is a strong comparability assumption between L μ 2 and uni-
form norms on E of polynomials (or other nested families of functions) as their
degree tends to infinity.
Admissible meshes are sequences of sampling sets A k ⊂ E whose cardinality
is growing sub-exponentially with respect to k and for which there exists a positive
finite constant C such that max E |p| ≤ C max A k |p| for any polynomial of degree at
most k.
These two mathematical objects have several applications and motivations from
Approximation Theory and Pluripotential Theory, the study of plurisubharmonic
functions in several complex variables.
The properties of Bernstein Markov measures and admissible meshes for a
given compact set E are very similar, indeed they may be seen as the continuous
and the discrete approach to the same problem.
This work is concerned on providing sufficient conditions for some different
instances of the Bernstein Markov property and explicitly constructing admissible
meshes.
As first problem, we study sufficient conditions for a version of the Bernstein
Markov property for rational functions on the complex plane and its relation with
the polynomial Bernstein Markov property.
In Chapter 5, we consider the case of a compact subset E of an algebraic pure
m-dimensional subset A of C n and we prove a sufficient condition for the Bernstein
Markov property for the traces of polynomials on E.
To this aim, we provide two new results in Pluripotential Theory regarding the
convergence and the comparability of the relative capacities, the relative and global
extremal functions and the Chebyshev constants on a (possibly non-smooth) pure
m-dimensional algebraic variety in C n , which are of independent interest.
In the last part of the dissertation, we provide some construction procedures
for admissible meshes on some classes of real compact sets.
Finally, we present some algorithms, based on admissible meshes, for the
numerical approximation of the most relevant objects in Pluripotential Theory,
namely, the transfinite diameter, the Siciak Zaharjuta extremal function and the
pluripotential equilibrium measure.La proprietà di Bernstein Markov per un compatto E ed una misura positiva finita μ avente supporto in E è un’ assunzione di comparabilità asintotica tra le norme uniformi ed L μ 2 dei polinomi di grado al più k (o altre famiglie innestate di funzioni) al tendere all’ infinito di k. Le Admissible Meshes sono sequenze di sottoinsiemi finiti A k del compatto E la cui cardinalità cresce in modo subesponenziale rispetto a k e per i quali esiste una costante positiva C tale che max E |p| ≤ C max A k |p| per ogni polinomi di grado al più k. Questi due oggetti matematici hanno molte appliicazioni e motivazioni prove- nienti dalla Teoria dell’ Approssimazione e dalla Teoria del Pluripotenziale, lo stu- dio delle funzioni plurisubarmoniche in più variabili complesse. Le proprietà delle misure di Bernstein Markov e delle admissible meshes per un dato compatto E sono molto simili, infatti le due definizioni possono essere viste come gli approcci rispettivamente continuo e discreto dello stesso problema. Questo lavoro si concentra nel fornire condizioni sufficienti per la proprietà di Bernstein Markov in diverse situazioni e nella costruzione esplicita di admissible meshes. Come primo problema vengono studiate condizioni sufficienti per una versione della proprietà di Bernstein Markov per successioni di funzioni razionali nel piano complesso in relazione alla stessa proprietà per i polinomi. Nel Capitolo 5 viene considerato il caso di un compatto E sottoinsieme di una varietà algebrica A ⊂ C n di dimensione pura m < n ed irriducibile e quindi provata una condizione sufficiente per la proprietà di Bernstein Markov per le tracce dei polinomi su E. A questo scopo vengono provati due risultati nuovi in Teoria del Pluripoten- ziale riguardanti la convergenza e la comparabilità della capacità relativa (di Monge Ampère), delle funzioni plurisubarmoniche estremali globali e relative e delle co- stanti di Chebyshev per sottoinsiemi E j di un dato compatto E della varietà alge- brica A, anche nel caso A sia singolare. Tali risultati sono di interesse indipendente. Nell’ultima parte della tesi vengono provate ed illustrate alcune procedure per la costruzione di admissible meshes per alcune classi di compatti reali. In ultimo vengono presentati alcuni nuovi algoritmi, basati sulle admissible meshes, per l’ approssimazione numerica delle più rilevanti grandezze in Teoria del Pluripotenziale: il diametro transfinito, la funzione estremale di Siciak-Zaharjuta e la misura di equilibrio pluripotenziale.
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Sadik, Mohamed. "Inégalités de Markov-Bernstein en L2 : les outils mathématiques d'encadrement de la constante de Markov-Bernstein." Phd thesis, INSA de Rouen, 2010. http://tel.archives-ouvertes.fr/tel-00557914.
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Les travaux de recherche de cette thèse concernent l'encadrement de la constante de Markov Bernstein pour la norme L2 associée aux mesures de Jacobi et Gegenbauer généralisée. Ce travail est composé de deux parties : dans la première partie, nous avons développé une généralisation de l'algorithme qd pour les matrices symétriques définies positives à largeur de bande $\ell$ et nous avons construit l'algorithme qd pour les matrices de Jacobi par blocs. Ensuite, nous l'avons généralisé aux cas des matrices par bloc à largeur de bande $\ell$. Ces algorithmes nous permettent de trouver un majorant de la constante. Enfin, nous avons développé le déterminant caractéristique d'une matrice symétrique définie positive pentadiagonale, ce qui nous permet d'obtenir un minorant de la constante en utilisant la méthode de Newton. La deuxième partie est consacrée à l'application de tous les outils développés à l'encadrement de la constante de Markov Bernstein pour la norme L2 associée à la mesure de Gegenbauer généralisée.
10
Oruç, Halil. "Generalized Bernstein polynomials and total positivity." Thesis, University of St Andrews, 1999. http://hdl.handle.net/10023/11183.
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This thesis deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a one-parameter family of polynomials. It also provides a triangular decomposition and 1-banded factorization of the Vandermonde matrix. We first establish the generalized Bernstein polynomials for monomials, which leads to a definition of Stirling polynomials of the second kind. These are q-analogues of Stirling numbers of the second kind. Some of the properties of the Stirling numbers are generalized to their q-analogues. We show that the generalized Bernstein polynomials are monotonic in degree n when the function ƒ is convex ... Shape preserving properties of the generalized Bernstein polynomials are studied by making use of the concept of total positivity. It is proved that monotonic and convex functions produce monotonic and convex generalized Bernstein polynomials. It is also shown that the generalized Bernstein polynomials are monotonic in the parameter q for the class of convex functions. Finally, we look into the degree elevation and degree reduction processes on the generalized Bernstein polynomials.
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Ebert, Svend [Verfasser], Swanhild [Akademischer Betreuer] Bernstein, Swanhild [Gutachter] Bernstein, and Franciscus [Gutachter] Sommen. "Wavelets on Lie groups and homogeneous spaces / Svend Ebert ; Gutachter: Swanhild Bernstein, Franciscus Sommen ; Betreuer: Swanhild Bernstein." Freiberg : Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2011. http://d-nb.info/1220698555/34.
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Cripps, Robert J. "Trend identification and the Bézier-Bernstein Operator." Thesis, Loughborough University, 1986. https://dspace.lboro.ac.uk/2134/26973.
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The techniques for identifying or describing the trend of data sequences generally rely on fitting either globally or locally piecewise, a low order polynomial to the observations. For data sequences containing trend with random and/or oscillatory movement the choice of the trend descriptor relies more on experience than technique.
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Silva, Jose Wilker de Lima. "Resultados tipo Bernstein em M2 x R." Universidade Federal do CearÃ, 2007. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=532.
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Apresentaremos uma fÃrmula para o Laplaciano da funÃÃo Θ =
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Okada, Hidetoshi. "Computational Study on Ion-Bernstein Wave Heating." Kyoto University, 1988. http://hdl.handle.net/2433/162244.
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Strada, Alberto Riccardo. "Polinomi di Bernstein e curve di Bezier." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/6302/.
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Questo lavoro si pone come obiettivo l'approfondimento della natura e delle proprietà dei polinomi espressi mediante la base di Bernstein. Introdotti originariamente all'inizio del '900 per risolvere il problema di approssimare una funzione continua su un intervallo chiuso e limitato della retta reale (Teorema di Stone-Weierstrass), essi hanno riscosso grande successo solo a partire dagli anni '60 quando furono applicati alla computer-grafica per costruire le cosiddette curve di Bezier. Queste, ereditando le loro proprietà geometriche da quelle analitiche dei polinomi di Bernstein, risultano intuitive e facilmente modellabili da un software interattivo e sono alla base di tutti i più moderni disegni curvilinei: dal design industriale, ai sistemi CAD, dallo standard SVG alla rappresentazione di font di caratteri.
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Spencer, Melvin R. "Polynomial Real Root Finding in Bernstein Form." BYU ScholarsArchive, 1994. https://scholarsarchive.byu.edu/etd/4246.
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This dissertation addresses the problem of approximating, in floating-point arithmetic, all real roots (simple, clustered, and multiple) over the unit interval of polynomials in Bernstein form with real coefficients.
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Youn, Jeen. "Le temps dans le théâtre d'Henry Bernstein." Paris 3, 1994. http://www.theses.fr/1994PA030129.
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Notre travail a pour but d'eclaircir la coherence interne des drames de bernstein, qui tient avant tout au genie de l'agencement temporel du texte. D'abord, dans ses premieres pieces qu'on appelle "tragedies bourgeoises", les pieces qui peignent la crise breve et violente, on retient le croisement des deux temporalites complementaires : l'une vers la crise imminente, l'autre vers le souvenir profond. Puis, dans les pieces de la "nouvelle maniere", l'epaisseur temporelle associee au regard vers l'interiorite des personnages engendre une autre temporalite, caracterisee par le statisme des moments iteratifs. Nous avons reconstruit les experiences temporelles fictives que pro-pose le texte, autour des deux axes: evenements-germes qui fonctionnent comme souvenirs-ecrans et evenements d'ailleurs, comme mis entre parentheses, qui se donnent comme espace voile de l'interiorite. Comme la configuration narrative sert de support a l'experience fictive du temps, notre interpretation du temps refigure va s'ancrer dans la forme signifiante du recitTHE OBJECT OF OUR research IS TO RECONSTRUCT THE INNER COHERENCE OF HENRY BERNSTEIN'S PLAYS THROUGHAN ANALYSIS OF THEIR TEMPORAL STRUCTURE. AT FIRST, IN HIS EARLY PLAYS, SOCALLED "TRAGEDIES BOURGEOIS", IN WHICH THE AUTHOR DESCRIBES MOSTLY THE BRIEF AND VIOLENT CRISIS OF THE PERSONS, WE COULD HOLD AN INTERSECTION OF TWO TEMPORALITIES COMPLEMENTARY CONFIGURATED BY THE NARRATION: ONE, TOWARDS THE IMMINENT CRISIS, THE OTHER, TOWARDS THE PROFOUND SOUVENIR. AND THEN, IN THE PLAYS OF THE "NOUVELLE MANIERE", WE CAN SEE THAT THE TEMPORAL DEPTH, ASSOCIATED WITH THE EYES CAST IN THE DIRECTION OF PERSON'S INTERIORITY, PRODUCES ANOTHER TEMPORALITY CHARACTERIZED BY THE STATIC OF THE ITERATIVE MOMENTS. WE HAVE RECOSTRUCTED THE FICTIOUS TEMPORAL EXPERIENCES CONFIGURATED IN THE TEXT AROUND TWO AXIS: THE GERM-EVENTS (EVENEMENTS-GERMES) WHICH WORK AS "SOUVENIR-ECRAN" AND THE MOREOVER-EVENTS (EVENEMENT D'AILLEURS) WORKING AS HIDDEN SPACE OF THE INTERIORITY PUT IN THE PARENTHESES. SEEING THAT THE READERS' FICTIOUS TEMPORAL EXPERIENCE IS DUE TO THE NARRATIVE CONFIGURATION OF THE TEXT, WE ARE TO ANCHOR THE ANALYSIS IN THE NARRATION FORM REGARDED AS THE SIGNIFIANT FORME. REFUSING TO BE ENCLOSED IN THE RIGOROUS STRUCTURALISM, WE WILL TRY TO BRING THE IMMANENT TIME OF THE TEXT INTO THE TRANSCENDENT TIME POF THE EXTRA-TEXT. THAT WOULD BE AT LAST THE RIFUGURATED TIME IN HENRY BERNSTEIN'S DRAMA
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Debouzy, Nathalie. "Nombres presque premiers jumeaux sous une conjecture d'Elliott-Halberstam." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0188/document.
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Nous affinons le crible asymptotique de Bombieri afin d’obtenir un asymptotique en variables localisées. Comme conséquence, nous démontrons, sous la conjecture d’Elliott-Halberstam, qu’il existe une infinité de nombres presque premiers jumeaux, c’est à dire tels que pour tout ε > 0, p est premier et p−2 est soit premier, soit de la forme p1p2 où p1 < Xε, et nous en donnons un asymptotique. A ce travail s’ajoutent deux chapitres : d’un côté, une preuve montrant comment une méthode sans crible préliminaire donne un résultat plus faible en nécessitant une hypothèse plus forte, ce qui nous permettra de détailler plusieurs estimations et de souligner l’intérêt de notre approche. D’un autre côté une exposition pédagogique d’une méthode donnant un accès facile et explicite à plusieurs estimations de moyennes de fonctions multiplicativesWe improve Bombieri’s asymptotic sieve to localise the variables. As a consequence, we prove, under a Elliott-Halberstam conjecture, that there exists an infinity of twins almost prime. Those are prime numbers p such that for all ε > 0, p −2 is either a prime number or can be written as p1p2 where p1 and p2 are prime and p1 < Xε, and we give the explicit asymptotic. In addition to this main work, there are two other chapters: the first one gives an asymptotic of prime numbers p such p−2is either a prime number or a product of three primes without using a preliminary sieve and so a stronger conjecture was needed. Hence this part shows the strength of the preliminary sieve and presents a few detailed sommations, most of them involving the Möbius fonction, that could be useful. The second one presents an easy and explicit method to calculate an average order of multiplicative functions
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Engelmann, Angelika. "Bernstein-Bézier-Methoden und Interpolation mit bivariaten Splineräumen." [S.l. : s.n.], 2003. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB10761307.
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Keston, David Arthur. "Bernstein modes in weakly relativistic e'-e'+ plasma." Thesis, University of Glasgow, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264260.
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Min, Lien Kuan. "Sobre um teorema de Bernstein e algumas generalizações." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307105.
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Orientador: Francesco MercuriDissertação (mestrado) - Universidade Estadual de Campinas, Intituto de Matematica, Estatistica e Computação Cientifica
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Resumo: O teorema de Bernstein é um marco importante na teoria das superfícies mínimas. Nesta dissertação apresentaremos três demonstrações deste teorema, cada uma levando a generalizações em diferentes direções
Abstract: The Bernstein's theorem is an important landmark in the theory of the minimal surfaces. In this dissertation we will present three demonstrations of this theorem, each one leading to generalizations in different directions
Mestrado
Geometria Diferencial
Mestre em Matemática
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Fossaluza, Victor. "Estimação de distribuições discretas via cópulas de Bernstein." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45133/tde-30042012-160407/.
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As relações de dependência entre variáveis aleatórias é um dos assuntos mais discutidos em probabilidade e estatística e a forma mais abrangente de estudar essas relações é por meio da distribuição conjunta. Nos últimos anos vem crescendo a utilização de cópulas para representar a estrutura de dependência entre variáveis aleatórias em uma distribuição multivariada. Contudo, ainda existe pouca literatura sobre cópulas quando as distribuições marginais são discretas. No presente trabalho será apresentada uma proposta não-paramétrica de estimação da distribuição conjunta bivariada de variáveis aleatórias discretas utilizando cópulas e polinômios de Bernstein.The relations of dependence between random variables is one of the most discussed topics in probability and statistics and the best way to study these relationships is through the joint distribution. In the last years has increased the use of copulas to represent the dependence structure among random variables in a multivariate distribution. However, there is still little literature on copulas when the marginal distributions are discrete. In this work we present a non-parametric approach for the estimation of the bivariate joint distribution of discrete random variables using copulas and Bernstein polynomials.
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LIMA, JÚNIOR Eraldo Almeida. "Resultados do tipo Calabi-Bernstein em −R × Hn." Universidade Federal de Campina Grande, 2011. http://dspace.sti.ufcg.edu.br:8080/jspui/handle/riufcg/1244.
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Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-25T19:25:58Z
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Neste trabalho, apresentamos um estudo das hipersuperfícies tipo-espaço imersas no ambiente −R × Hn, exibindo condições para que tais hipersuperfícies sejam slices {t0}×Hn. Para uma melhor compreensão das demonstrações e dos resultados, inserimos processos de diferenciação, cálculos de gradientes e Laplacianos que, juntamente com o princípio do máximo de Omori-Yau, foram cruciais no desenvolvimento dos resultados que, em sua maioria são do tipo Bernstein. Também incluímos um resultado do tipo Calabi.
In this work we present a study of the spacelike hypersurfaces immersed in the manifold −R × Hn providing sufficient conditions for such hypersurfaces be slices, {t0}×Hn. For a better understanding of the proofs and results, we have added differentiation processes, gradient computations and Laplacians which jointly with the Omori-Yau Maximum Principle were crucial in the developing of the results whose are mostly Bernstein-type. In the elapsing we also included Calabi-type results.
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Sacchi, Giulia. "La base di Bernstein in spazi polinomiali generalizzati." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/7924/.
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Nella tesi si illustra il passaggio dagli spazi polinomiali agli spazi polinomiali generalizzati, gli spazi di Chebyshev estesi (spazi EC), e viene dato un metodo per costruirli a partire da opportuni sistemi di funzioni dette funzioni peso. Successivamente si tratta il problema dell'esistenza di un analogo della base di Bernstein negli spazi EC: si presenta, in analogia ad una particolare costruzione nel caso polinomiale, una dimostrazione costruttiva dell'esistenza di tale base. Infine viene studiato il problema delle lunghezze critiche di uno spazio EC: si tratta di determinare l'ampiezza dell'intervallo oltre la quale lo spazio considerato perde le proprietà di uno spazio EC, o non possiede più una base di Bernstein generalizzata; l'approccio adottato è di tipo sperimentale: nella tesi sono presentati i risultati ottenuti attraverso algoritmi di ricerca che analizzano le proprietà delle funzioni di transizione e ne traggono informazioni sullo spazio di studio.
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Berchtold, J. "The Bernstein basis in set-theoretic geometric modelling." Thesis, University of Bath, 2000. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323604.
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Parente, Ulisses Lima. "Alguns resultados tipo-Bernstein em variedades semi-riemannianas." reponame:Repositório Institucional da UFC, 2011. http://www.repositorio.ufc.br/handle/riufc/846.
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PARENTE, Ulisses Lima; MUNIZ NETO, Antonio Caminha. Alguns resultados tipo-Bernstein em variedades semi-riemannianas. 2011. 76 f. : Tese (doutorado) - Universidade Federal do Ceará, Programa de Pós-Graduação em Matemática, Fortaleza-CE, 2011.Submitted by Rocilda Sales (rocilda@ufc.br) on 2011-10-06T11:17:12Z No. of bitstreams: 1 2011_tese_ulparente.pdf: 501643 bytes, checksum: 1fb4d3996c364ea2f5740f5f9e4eb31b (MD5)
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In this thesis, we study complete space-like hypersurfaces immersed in semi-Riemannian manifolds, satisfying some conditions on their higher-order mean curvatures in order to get Bernstein-type results. Analytical tools we use are some versions of the maximum principle. When the ambient space is a generalized Robertson-Walker spacetime which is supposed to obey the strong null convergence condition, we establish new characterizations of totally geodesic spacelike hypersurfaces. Furthermore, we obtain a lower estimate the minimum index of relative nullity when the space-like hypersurface is r-maximal, or when there are two consecutive higher-order mean curvatures that do not change sin. We also obtain rigidity results and new characterizations of totally umbilical hypersurfaces, assuming they have some constant higher-order mean curvature, and that the ambient space is a spacetime Robertson-Walker obeying the null convergence condition. These results are applied to the de Sitter and anti-de Sitter spaces. Finally, we prove a Bernstein-type theorem for constant mean curvature complete hypersurfaces immersed in a riemannian product.
Nesta tese, estudamos hipersuperfícies de tipo-espaço completas imersas em variedades semi-Riemannianas, satisfazendo alguma condição sobre suas curvaturas de ordem superior, a fim de obtermos resultados tipo-Bernstein. As ferramentas analíticas que utilizamos são algumas versões do princípio do máximo. No caso em que o ambiente é um espaço-tempo de Robertson-Walker generalizado satisfazendo a condição forte de convergência nula, obtemos novas caracterizações de hipersuperfícies tipo-espaço totalmente geodésicas. Além disso, obtemos uma estimativa inferior do índice mínimo de nulidade relativa quando a hipersuperfície tipo-espaço é r-máxima ou quando existem duas curvaturas médias de ordem superior consecutivas que não mudam de sinal. Também obtemos resultados de rigidez e novas caracterizações de hipersuperfícies totalmente umbílicas, supondo que estas possuem alguma curvatura de ordem superior constante e que o ambiente é um espaço-tempo de Robertson-Walker satisfazendo a condição de convergência nula. Aplicamos tais resultados aos espaço de de Sitter e anti-de Sitter. Finalmente, provamos um teorema tipo-Bernstein para hipersuperfícies completas, com curvatura média constante, imersas em um produto riemanniano.
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Scheibler, Alexandra. ""Ich glaube an den Menschen" : Leonard Bernsteins religiöse Haltung im Spiegel seiner Werke /." Hildesheim ; Zürich ; New York : G. Olms, 2001. http://catalogue.bnf.fr/ark:/12148/cb37651955d.
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Seredszus, Fabian. "Wasserinsekten des Baltischen Bernsteins unter besonderer Berücksichtigung der Chironomiden." [S.l.] : [s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=971726752.
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Tauber, Marianne. "Analytische Methoden zur Identifizierung von Inhaltsstoffen baltischen Bernsteins." [S.l. : s.n.], 2001. http://deposit.ddb.de/cgi-bin/dokserv?idn=96125128X.
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Joachimsthaler, Jürgen. "Max Bernstein Kritiker, Schriftseller, Rechtsanwalt (1854-1925) : ein Beitrag zur Literatur-, Rechts-, Zensur-, Kultur-, Sozial- und allgemeinen Geschichte zwischen 1878 und 1925 mit Ausführungen zum "Naturalismus", zur praktischen Anwendung des Sozialistengesetzes, zu Ibsen, Conrad, Gerhart Hauptmann und anderen Zeitgenossen /." Frankfurt am Main : P. Lang, 1995. http://catalogue.bnf.fr/ark:/12148/cb37173220v.
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Blanco, Fernández Guillem. "Bernstein-Sato polynomial of plane curves and Yano's conjecture." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669107.
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The main aim of this thesis is the study of the Bernstein-Sato polynomial of plane curve singularities. In this context, we prove a conjecture posed by Yano about the generic b-exponents of a plane irreducible curve.
In a part of the thesis, we study the Bernstein-Sato polynomial through the analytic continuation of the complex zeta function of a singularity. We obtain several results on the vanishing and non-vanishing of the residues of the complex zeta function. Using these results we obtain a proof of Yano's conjecture under the hypothesis that the eigenvalues of the monodromy are pair-wise different. In another part of the thesis, we study the periods of integrals in the Milnor fiber and their asymptotic expansion. These periods of integrals can be related to the b-exponents and can be constructed in terms of resolution of singularities. Using these techniques, we can present a proof for the general case of Yano's conjecture.
In addition to the Bernstein-Sato polynomial, we also study the minimal Tjurina number of a plane irreducible curve and we answer in the positive a question raised by Dimca and Greuel on the quotient between the Milnor and Tjurina numbers. More precisely, we prove a formula for the minimal Tjurina number of a plane irreducible curve in terms of the multiplicities of the strict transform along its minimal resolution. From this formula, we obtain the positive answer to Dimca and Greuel question.
This thesis also contains computational results for the theory of singularities on smooth complex surfaces. First, we describe an algorithm to compute log-resolutions of ideals on a smooth complex surface. Secondly, we provide an algorithm to compute generators for complete ideals on a smooth complex surface. These algorithms have several applications, for instance, in the computation of the multiplier ideals associated to an ideal on a smooth complex surface.El principal objectiu d'aquesta tesi és l'estudi del polinomi de Bernstein-Sato de singularitats de corbes planes. En aquest context, es demostra una conjectura proposada per Yano el 1982 sobre els \( b \)-exponents genèrics d'una corba plana irreductible. En una part d'aquesta tesi, s'estudia el polinomi de Bernstein-Sato utilitzant la continuació analítica de la funció zeta complexa d'una singularitat. S'obtenen diversos resultat sobre l'anul·lació i no anul·lació del residu de la funció zeta complexa d'una corba plana. Utilitzant aquests resultats, s'obté una demostració de la conjectura de Yano sota la hipòtesi de que els valors propis de la monodromia siguin diferents dos a dos. En un altre part de la tesi, s'estudien els períodes d'integrals en la fibra de Milnor i la seva expansió asimptòtica. Aquesta expansió asimptòtica dels períodes pot ser relacionada amb els b-exponents i pot ser construïda en termes de la resolució de singularitats. Utilitzant aquestes tècniques, es presenta una prova del cas general de la conjectura de Yano. A més a més del polinomi de Bernstein-Sato, també s'estudia el nombre de Tjurina mínim d'una corba plana irreductible i responem positivament a una pregunta formulada per Dimca i Greuel sobre el quocient entre els nombres de Milnor i Tjurina. Concretament, es demostra una fórmula pel nombre de Tjurina mínim en un classe d'equisingularitat de corbes planes irreductibles en termes de la seqüència de multiplicitats de la transformada estricta al llarg de la resolució minimal. A partir d'aquesta fórmula, s'obté la resposta positiva a la pregunta de Dimca i Greuel. Aquesta tesi també conté resultats computacionals per la teoria de singularitats en superfícies complexes llises. Primer, es descriu un algorisme que calcula la log-resolució d'ideals en un superfície complexa llisa. En segon lloc, es dona un algorisme per calcular generadors per ideals complets en una superfície complexa llisa. Aquests algorismes tenen diverses aplicacions, com per exemple, en el càlcul d'ideals multiplicadors associats a un ideal en una superfície complexa llisa.
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Källstrand, Bengt. "Those spooky troonns. Leonard Bernstein och the Norton lectures." Thesis, Kungl. Musikhögskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kmh:diva-955.
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Lemke, Matthias. "Republikanischer Sozialismus Positionen von Bernstein, Kautsky, Jaurès und Blum." Frankfurt, M. New York, NY Campus-Verl, 2007. http://d-nb.info/986752983/04.
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Lemke, Matthias. "Republikanischer Sozialismus : Positionen von Bernstein, Kautsky, Jaurès und Blum /." Frankfurt am Main [u.a.] : Campus-Verl, 2008. http://www.gbv.de/dms/sub-hamburg/555665364.pdf.
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Liang, Jie Ling. "Approximation by Bernstein polynomials at the point of discontinuity." Honors in the Major Thesis, University of Central Florida, 2011. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/460.
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Chlodovsky showed that if x₀ is a point of discontinuity of the first kind of the function f, then the Bernstein polynomials Bsubscript n](f, x₀) converge to the average of the one-sided limits on the right and on the left of the function f at the point x₀. In 2009, Telyakovskii in (5) extended the asymptotic formulas for the deviations of the Bernstein polynomials from the differentiable functions at the first-kind discontinuity points of the highest derivatives of even order and demonstrated the same result fails for the odd order case. Then in 2010, Tonkov in (6) found the right formulation and proved the result that was missing in the odd-order case. It turned out that the limit in the odd order case is related to the jump of the highest derivative. The proofs in these two cases look similar but have many subtle differences, so it is desirable to find out if there is a unifying principle for treating both cases. In this thesis, we obtain a unified formulation and proof for the asymptotic results of both Telyakovskii and Tonkov and discuss extension of these results in the case where the highest derivative of the function is only assumed to be bounded at the point under study.B.S.
Bachelors
Sciences
Mathematics
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Fortuna, Giorgia. "The Beilinson-Bernstein localization theorem for the affine Grassmannian." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/82437.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2013.Cataloged from PDF version of thesis.
Includes bibliographical references (pages. 171-173).
This thesis mainly deals with the study of the category of admissible modules for the affine Kac-Moody algebra at the critical level, and the study of its center.
by Giorgia Fortuna.
Ph.D.
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Moody, J. D. (John D. ). "Ion Bernstein wave experiments of the Alcator C tokamak." Thesis, Massachusetts Institute of Technology, 1988. http://hdl.handle.net/1721.1/14578.
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Richardson, Matthew. "Rhetorical hybridity : Ashbery, Bernstein and the poetics of citation /." The Ohio State University, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486401895206864.
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Baranov, Anton. "Inégalités de Bernstein dans les espaces modèles, et applications." Bordeaux 1, 2005. http://www.theses.fr/2005BOR12980.
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On étudie les opérateurs de différentiation et de plongement dans les sous-espaces modèles de l'espace de Hardy du demi-plan supérieur. On obtient les inégalités de Bernstein généralisées, c'est-à-dire, des majorations pondérées pour les dérivées dans les sous-espaces modèles où les poids dépendent du spectre de la fonction intérieure associée. Ces inégalités sont utilisées pour obtenir certains nouveaux théorèmes de plongement généralisant les résultats de Cohn, Volberg et Treil, ainsi que des critères de stabilité des bases de noyaux reproduisantsWe study the differentiation and embedding operators in the model subspaces of the Hardy class in the upper half-plane. We obtain Bernstein-type inequalities, that is, the weighted estimates of the derivatives in the model subspaces, where the weight depends on the spectrum of the assocuiated inner function. These inequlaities are then used to obtain certain new embedding theorems generalizing the results of Cohn, Volberg and Treil, as well as criteria of stability for bases of reproducing kernels
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Chen, Li-Jen. "Bernstein-Greene-Kruskal electron solitary waves in collisionless plasmas /." Thesis, Connect to this title online; UW restricted, 2002. http://hdl.handle.net/1773/9644.
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Yang, Ning. "Structured matrix methods for computations on Bernstein basis polynomials." Thesis, University of Sheffield, 2013. http://etheses.whiterose.ac.uk/3311/.
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This thesis considers structure preserving matrix methods for computations on Bernstein polynomials whose coefficients are corrupted by noise. The ill-posed operations of greatest common divisor computations and polynomial division are considered, and it is shown that structure preserving matrix methods yield excellent results. With respect to greatest common divisor computations, the most difficult part is the computation of its degree, and several methods for its determination are presented. These are based on the Sylvester resultant matrix, and it is shown that a new form of the Sylvester resultant matrix in the modified Bernstein basis yields the best results. The B´ezout resultant matrix in the modified Bernstein basis is also considered, and it is shown that the results from it are inferior to those from the Sylvester resultant matrix in the modified Bernstein basis.
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Freitas, Ana Paula. "Superficies Minimas em R4 e um Teorema Tipo Bernstein." Instituto de Matemática, 2012. http://repositorio.ufba.br/ri/handle/ri/19487.
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CAPES
Apresentaremos neste trabalho dois teoremas que caracterizam as curvas anal ticas complexas, isto e, os gr a cos de fun c~oes holomorfas ou anti-holomorfas, que mostraremos serem superf cies m nimas em R4. O primeiro resultado, que e um Teorema tipo Bernstein para superf cies m nimas em R4, caracteriza as curvas anal ticas complexas atrav es do Jacobiano. Este teorema e de grande import^ancia, uma vez que alguns resultados tipo Bernstein para superf cies em R4, obtidos anteriormente, seguem como corol ario deste. O segundo teorema caracteriza as curvas anal ticas complexas a partir de dois invariantes geom etricos, as curvaturas Gaussiana e Normal.
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Reinhardt, Martin [Verfasser], Swanhild [Akademischer Betreuer] Bernstein, Swanhild [Gutachter] Bernstein, and Konrad [Gutachter] Froitzheim. "Applications of Riesz Transforms and Monogenic Wavelet Frames in Imaging and Image Processing / Martin Reinhardt ; Gutachter: Swanhild Bernstein, Konrad Froitzheim ; Betreuer: Swanhild Bernstein." Freiberg : Technische Universität Bergakademie Freiberg, 2019. http://d-nb.info/1226101542/34.
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Geandier, Françoise. "Polynômes de Bernstein et déformations à nombre de Milnor constant." Nice, 1989. http://www.theses.fr/1989NICE4278.
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On étudie une déformation à un paramètre y, appartenant à un voisinage de l'origine dans C, d'une singularité isolée d'hypersurface de Cn d'équation F(x, y)=0. On prouve d'abord l'existence d'un polynôme de Bernstein générique de F à l'origine, c'est-à-dire correspondant à un opérateur différentiel relatif polynomial en S et en L/y. Si on suppose de plus que la déformation est à nombre de Milnor constant, alors il existe un polynôme de Bernstein en famille de F à l'origine, c'est-à-dire correspondant à un opérateur différentiel relatif polynomial en S. On prouve ensuite que l'existence d'un opérateur différentiel relatif polynomial et unitaire en S, annulant Fs, caractérise les déformations à nombre de Milnor constant. D'autre part, on démontre un théorème de structure des D-modules cohérents à support l'axe des paramètres, ou D désigne le faisceau des opérateurs différentiels relatifs. Ce théorème permet de prouver que lors d'une déformation à nombre de Milnor constant, le polynôme de Bernstein by de F(x, y) à l'origine est égal au polynôme de Bernstein générique de F, pour y non nul voisin de l'origine dans C. Enfin, on montre que le polynôme de Bernstein bo(s) de la fibre spéciale divise by(s)by(s+1). . . By(s+n-1)
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Herath, Dushanthi N. "Nonparametric Estimation of Receiver Operating Characteristic Surfaces Via Bernstein Polynomials." Thesis, University of North Texas, 2012. https://digital.library.unt.edu/ark:/67531/metadc177212/.
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Receiver operating characteristic (ROC) analysis is one of the most widely used methods in evaluating the accuracy of a classification method. It is used in many areas of decision making such as radiology, cardiology, machine learning as well as many other areas of medical sciences. The dissertation proposes a novel nonparametric estimation method of the ROC surface for the three-class classification problem via Bernstein polynomials. The proposed ROC surface estimator is shown to be uniformly consistent for estimating the true ROC surface. In addition, it is shown that the map from which the proposed estimator is constructed is Hadamard differentiable. The proposed ROC surface estimator is also demonstrated to lead to the explicit expression for the estimated volume under the ROC surface . Moreover, the exact mean squared error of the volume estimator is derived and some related results for the mean integrated squared error are also obtained. To assess the performance and accuracy of the proposed ROC and volume estimators, Monte-Carlo simulations are conducted. Finally, the method is applied to the analysis of two real data sets.
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Decker, Joan 1977. "Electron Bernstein wave current drive modeling in toroidal plasma confinement." Thesis, Massachusetts Institute of Technology, 2005. http://hdl.handle.net/1721.1/33937.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 333-340).
The steady-state confinement of tokamak plasmas in a fusion reactor requires non-inductively driven toroidal currents. Radio frequency waves in the electron cyclotron (EC) range of frequencies can drive localized currents and are thus particularly attractive for control of the current profile. In the high-[beta] regimes of spherical tokamaks (ST) such as NSTX and MAST, heating and current drive (CD) by conventional electron cyclotron waves is not possible. However, electron Bernstein waves (EBW) have been proposed as an alternative for CD in these overdense devices. Given the important role predicted for CD by EBWs in high-[beta] STs, a detailed study of EBWCD must be undertaken. In this thesis a systematic analysis of EBWCD is provided. In particular, the characteristics of EBWs, the physics of resonant wave-particle interaction, and the CD mechanisms are investigated in detail. The CD efficiency and the current deposition profile are calculated using the numerical code DKE, which solve the drift-kinetic equation. Two scenarios for EBWCD are identified. The first scenario consists of approaching a harmonic of the EC resonance from a lower B-field region and drives current in the plasma core using the Fisch-Boozer mechanism.
(cont.) The other scenario consists of approaching a harmonic of the EC resonance from a higher B-field region and drives current off-axis on the outboard side using the Ohkawa mechanism. Both schemes drive current in the toroidal direction opposite to the parallel wave vector. The EBWCI) efficiency is found to be higher than ECCD efficiency because the EBW power is deposited in the tail of the electron distribution function. The results of this thesis confirm the important role of EBWs for driving currents in high-[beta] plasmas. The analytical and numerical tools developed as part of this thesis can be used to design, predict, and analyze future EBWCD experiments. Among these tools is the kinetic solver DKE, which can be used for electron current drive calculations in toroidal plasmas for different types of radio-frequency waves, such as lower hybrid and electron cyclotron waves.
by Joan Decker.
Ph.D.
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Andriamaro, Miangaly Gae¨lle. "Bernstein-Bézier techniques and optimal algorithms in finite element analysis." Thesis, University of Strathclyde, 2013. http://oleg.lib.strath.ac.uk:80/R/?func=dbin-jump-full&object_id=25566.
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This thesis focuses on the development of algorithms for the effiecient computation of the element system matrices associated with simplicial elements of arbitrary polynomial order. The algorithms make use of properties intrinsic to Bernstein-Bézier polynomials, allowing for sum factorizations techniques to be applicable. In particular, the presented algorithms are the first to achieve optimal complexity for H¹ elements on simplicial partitions in Rd, for d = 1, 2, 3. The optimal complexity result is extended to two-dimensional vector finite elements presents a clear distinction between the gradient and rotational comonents of the vector field. Numerical results illustrate the optimal cost associated with the computation of the elemental matrices, as well as the efficiency of the Bernstein-Bézier elements. The thesis contains the documentation of BBFEM, a C⁺⁺ implementation of the newly developed algorithms which is available under a GNU General Public Licence. In addition, a report on the work done for a shorter Knowledge Transfer Partnership project on edge elements, with Cobham Technical Services, is also included.
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Guimarães, Andréa Gomes. "Polinômio de Bernstein-Sato de uma hipersuperfície com singularidade isolada." Universidade de São Paulo, 2005. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-26112014-144207/.
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Neste trabalho estudamos algumas raízes do polinômio de Bernstein bf associado a um germe f(X) ∈ ℂ{X1,. . . , Xn} com ponto crítico isolado na origem. Sabe-se que, para cada raiz de bf, existe um número espectral tal que a soma desses dois números é um inteiro. Em geral, não se sabe exibir explicitamente esses números inteiros, embora existam cotas para eles. M. Saito [Sai93] exibe um subconjunto do conjunto das raízes de bf tal que para esses elementos a soma vale -1. Hertling e Stahlkc [IIS99] conseguiram aumentar esse subconjunto de raízes, supondo f(X) em duas variáveis, com ponto crítico isolado e monodromia finita (hipóteses essas bem restritivas). Conseguimos estender esse último resultado, sem restrições sobre o número de variáveis de, f{X) e apenas com a hipótese de ponto crítico isolado. Além disso, no caso de germes f(X1, X2) irredutíveis e com um único par de Puiseux, mostramos como descrever um subconjunto maior de raízes de bf, quando f pertence a uma dada classe de equidiferenciabilidade.In this work we studv some roots of the Bernstein polynomial bf associated to a germ f(X) in the maximal ideal of ℂ{X1,. . . , Xn} with an isolated criticai point at the origin. It is known that for each root of bf there exists a spectral number such that the sum of these two nurnber is an integer. In general, one doesn\'t. know how to compute explicitly these integers, although there are bounds on them. M. Sai to, in [Sai93], exhibits a subset of the set of roots of bf, such that, for these elements the sum is -1. Heríling and Stahlke, in [HS99], succeeded to increase this subset of roots, assuming f(X) in two variables, with isolated criticai point and finito monodrorny (such hypotheses are very restrictive). We succeeded to extend this last result without any restriction on the number of variables of f(X) and only with the assumption of isolated criticai point. Moreover, in the case of irreducible germs f(X1, X2) with only one Puiseux pair, we show how to describe a. larger subset of roots of bf, when f belongs to a given equidiferentiability class.
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Andrade, Joana El-Jaick. "O revisionismo de Eduard Bernstein e a negação da dialética." Universidade de São Paulo, 2006. http://www.teses.usp.br/teses/disponiveis/8/8132/tde-27092011-100247/.
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Nos fins do século XIX, Eduard Bernstein causou grande espanto e turbulência no interior da social-democracia alemã ao refutar publicamente as teses oficiais propugnadas pelos líderes do partido e, ao mesmo tempo, propor a revisão crítica do pensamento de Marx, desferindo sérios ataques ao que considerava seu elemento \"nefasto\": a dialética hegeliana. Ao defender a rejeição da filosofia da história marxiana - considerada obstáculo ao conhecimento científico da realidade social - Bernstein rompe com a perspectiva revolucionária, aderindo a um reformismo evolucionista. Acreditando no potencial emancipador da democracia burguesa, que tornaria possível a tomada do poder por meios legais e pacíficos, Bernstein passa a sustentar a adoção de uma postura política conciliatória e a mitigação da luta de classes. O surgimento desta corrente revisionista deu início a um grande cisma no interior da social-democracia que veio a ser considerado como \"a primeira crise do marxismo\", introduzindo uma nova tendência de rechaço à concepção dialética da história e de abdicação de quaisquer pretensões revolucionárias. Estas idéias viriam a tornar-se hegemônicas no final do século XX, quando as teses que apregoam o \"fim da história\" são amplamente difundidas e festejadas. Diante deste novo refluxo das teorias e práticas revolucionárias, torna-se fundamental a análise minuciosa do fenômeno revisionista - o contexto em que surge, as razões de seu sucesso no âmbito da esquerda e as críticas que podem lhe ser opostasIn the end of the nineteenth century, Eduard Bernstein caused great turbulence in the German social democracy when he publicly opposed to the official theses of the leaders of the Social Democratic Party and, at the same time, recommended a critical revision of Marx\'s thought, making serious attacks on what he considered its most hideous element: the Hegelian dialectics. While supporting the total rejection of the Marxian philosophy of history - regarded as an obstacle to the scientific knowledge of the social reality - Bernstein breaks up with the revolutionary perspective, joining an evolutionary reformism. Relying in the emancipatory potential of the bourgeois democracy, that would make possible the achievement of power through legal and pacific means, Bernstein sustained a conciliatory political posture and the softening of the class struggle. The appearance of such revisionist tendency gave birth to a schism inside social democracy that was further known as \"the first crisis of Marxism\", as it excluded the dialectical conception of history and the revolutionary aim. These ideas became hegemonic at the end of the twentieth century, when theses proclaiming \"the end of history\" were widely spread. In face of the new reflux of the revolutionary praxis, the analysis of the revisionist phenomenon - the context in which it appears, the reason for its success and the critics opposed to it - becomes crucial
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Veschetti, Adele. "La base di Bernstein in spazi polinomiali generalizzati a tratti." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8570/.
Full textAbstract:
Le funzioni polinomiali possono essere utilizzate per approssimare le funzioni continue. Il vantaggio è che i polinomi, le loro derivate e primitive, possono essere rappresentati in maniera semplice attraverso i loro coefficienti ed esistono algoritmi stabili e veloci per valutarli. Inoltre gli spazi polinomiali godono di numerose proprietà importanti.
In questo lavoro ci occuperemo di altri spazi funzionali, noti in letteratura come spazi di Chebyshev o polinomi generalizzati, per ragioni di riproducibilità. Infatti ciò che si ottiene attraverso i polinomi è soltanto una approssimazione che spesso risulta essere insufficiente. E' importante, quindi, considerare degli spazi in cui sia possibile avere una rappresentazione esatta di curve. Lo studio di questi spazi è possibile grazie alla potenza di elaborazione degli attuali calcolatori e al buon condizionamento di opportune basi di rappresentazione di questi spazi. Negli spazi polinomiali è la base di Bernstein a garantire quanto detto. Negli spazi di Chebyshev si definisce una nuova base equivalente. In questo lavoro andremo oltre gli spazi di Chebyshev ed approfondiremo gli spazi di Chebyshev a tratti, ovvero gli spazi formati dall'unione di più spazi del tipo precedente. Si dimostrerà inoltre l'esistenza di una base a tratti con le stesse proprietà della base di Bernstein per gli spazi polinomiali.