Relevant bibliographies by topics / Birkhoff

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Birkhoff'

Author: Grafiati
Published: 4 June 2021
Last updated: 19 February 2022

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Journal articles on the topic "Birkhoff"

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Chen, Jin-Yue, and Yi Zhang. "Time-Scale Version of Generalized Birkhoffian Mechanics and Its Symmetries and Conserved Quantities of Noether Type." Advances in Mathematical Physics 2021 (April 26, 2021): 1–9. http://dx.doi.org/10.1155/2021/9982975.

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The time-scale version of Noether symmetry and conservation laws for three Birkhoffian mechanics, namely, nonshifted Birkhoffian systems, nonshifted generalized Birkhoffian systems, and nonshitfed constrained Birkhoffian systems, are studied. Firstly, on the basis of the nonshifted Pfaff-Birkhoff principle on time scales, Birkhoff’s equations for nonshifted variables are deduced; then, Noether’s quasi-symmetry for the nonshifted Birkhoffian system is proved and time-scale conserved quantity is presented. Secondly, the nonshifted generalized Pfaff-Birkhoff principle on time scales is proposed, the generalized Birkhoff’s equations for nonshifted variables are derived, and Noether’s symmetry for the nonshifted generalized Birkhoffian system is established. Finally, for the nonshifted constrained Birkhoffian system, Noether’s symmetry and time-scale conserved quantity are proposed and proved. The validity of the result is proved by examples.
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Gehrke, Mai, and Michael Pinsker. "Uniform Birkhoff." Journal of Pure and Applied Algebra 222, no. 5 (May 2018): 1242–50. http://dx.doi.org/10.1016/j.jpaa.2017.06.016.

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Bodirsky, Manuel, and Michael Pinsker. "Topological Birkhoff." Transactions of the American Mathematical Society 367, no. 4 (August 8, 2014): 2527–49. http://dx.doi.org/10.1090/s0002-9947-2014-05975-8.

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Biswas, HR, and MS Islam. "Ergodic theory of one dimensional Map." Bangladesh Journal of Scientific and Industrial Research 47, no. 3 (December 21, 2012): 321–26. http://dx.doi.org/10.3329/bjsir.v47i3.13067.

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In this paper we study one dimensional linear and non-linear maps and its dynamical behavior. We study measure theoretical dynamical behavior of the maps. We study ergodic measure and Birkhoff ergodic theorem. Also, we study some problems using Birkhoff's ergodic theorem. DOI: http://dx.doi.org/10.3329/bjsir.v47i3.13067 Bangladesh J. Sci. Ind. Res. 47(3), 321-326 2012
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Kurnianto, Arik. "Analisis Layout Surat Kabar berdasarkan Prinsip-Prinsip Desain melalui Metode Estetika Birkhoff." Humaniora 4, no. 2 (October 31, 2013): 986. http://dx.doi.org/10.21512/humaniora.v4i2.3540.

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This study has primary focus to analyze the aesthetic layout of a newspaper with a mathematical approach, which refers to some methods of Birkhoff’s aesthetic measurement developed by David Ngo Chek Ling, et.al. Ngo developed a method of measuring the aesthetic layout that can be used for various design purposes, especially for a computer interface design. Measurement method that he developed refers to the principles of design aesthetics, such as: the principle of balance, the principle of sequence, the principle of unity, and the principle of equilibrium. Birkhoff aesthetic measurement method was used as final analysis to determine the value of aesthetic layout. In this study, some national and local media were selected as samples to determine and assess the aesthetic layout. Based on data analysis, Birkhoff aesthetic measurement method can be applied to measure the aesthetic value of the newspaper layout mathematically.
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Buczolich, Zoltán, Balázs Maga, and Ryo Moore. "Generic Birkhoff spectra." Discrete & Continuous Dynamical Systems - A 40, no. 12 (2020): 6649–79. http://dx.doi.org/10.3934/dcds.2020131.

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Madden, James J. "Pierce-Birkhoff rings." Archiv der Mathematik 53, no. 6 (December 1989): 565–70. http://dx.doi.org/10.1007/bf01199816.

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Möller, Manfred. "Expansion theorems for Birkhoff-regular differential-boundary operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 107, no. 3-4 (1987): 349–74. http://dx.doi.org/10.1017/s0308210500031218.

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SynopsisIn this paper we consider differential-boundary operators T over a finite interval depending on a complex parameter. A differential-boundary operator admits boundary conditions in the differential part. The boundary part contains multipoint boundary conditions and integral conditions. For Birkhoff-regular boundary conditions we prove that every Lp -function is expansible into a series with respect to the eigenfunctions and the associated functions of the differential-boundary operator. Here the Birkhoff-regularity only depends on the boundary conditions at the endpoints of the interval, i.e. T is Birkhoff-regular if and only if T0 is Birkhoff-regular where T0 arises from T by omitting the boundary part in the differential equations, the interior point boundary conditions and the integral condition.
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WÓJCIK, PAWEŁ. "BIRKHOFF ORTHOGONALITY IN CLASSICAL -IDEALS." Journal of the Australian Mathematical Society 103, no. 2 (November 8, 2016): 279–88. http://dx.doi.org/10.1017/s1446788716000537.

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The Birkhoff orthogonality has been recently intensively studied in connection with the geometry of Banach spaces and operator theory. The main aim of this paper is to characterize the Birkhoff orthogonality in ${\mathcal{L}}(X;Y)$ under the assumption that ${\mathcal{K}}(X;Y)$ is an $M$-ideal in ${\mathcal{L}}(X;Y)$. Moreover, we survey the known results, as well as giving some new and more general ones. Furthermore, we characterize an approximate Birkhoff orthogonality in ${\mathcal{K}}(X;Y)$.
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Snamina, Mateusz, and Emil J. Zak. "Dynamical Semigroups in the Birkhoff Polytope of Order 3 as a Tool for Analysis of Quantum Channels." Open Systems & Information Dynamics 27, no. 01 (March 2020): 2050001. http://dx.doi.org/10.1142/s1230161220500018.

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In the present paper we show a link between bistochastic quantum channels and classical maps. The primary goal of this work is to analyse the multiplicative structure of the Birkhoff polytope of order 3 (the simplest nontrivial case). A suitable complex parametrization of the Birkhoff polytope is proposed, which reveals several its symmetries and characteristics, in particular: (i) the structure of Markov semigroups inside the Birkhoff polytope, (ii) the relation between the set of Markov time evolutions, the set of positive definite matrices and the set of divisible matrices. A condition for Markov time evolution of semigroups in the set of symmetric bistochastic matrices is derived, which leads to an universal conserved quantity for all Markov evolutions. Finally, the complex parametrization is extended to the Birkhoff polytope of order 4.
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Dissertations / Theses on the topic "Birkhoff"

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Cirilo, Patricia Romano. "Órbitas de Birkhoff e não Birkhoff para aplicações do tipo Twist." Universidade Federal de Minas Gerais, 2007. http://hdl.handle.net/1843/EABA-72VJWU.

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Para estudar a dinâmica de transformações que preservam área é interessante se perguntar sobre a existência de órbitas "ordenadas". A importância desta condição geométrica foi observada por G. D. Birkhoff no início do século XX e desde então as órbitas de Birkhoff vêm sendo estudadas com afinco. Nesta dissertação será estudado um critério para que uma aplicação possua entropia topológica positiva e utilizando este critério serão apresentadas condições para a existência de órbitas de Birkhoff. A aplicação em questão é um homeomorfismo do cilindro nele mesmo e são requeridas as hipóteses de que ela seja twist monótona e que preserve orientação. Tal aplicação é obtida através de uma relação de recorrência. Será apresentado um teorema que permite obter soluções da relação de recorrência com certas propriedades de periodicidade e ordem. Com isto é possível, a partir de órbitas da aplicação inicial com estas propriedades, concluir a existência de órbitas de Birkhoff, donde segue, em particular, um teorema de G. R. Hall. Com algumas hipóteses, mostra-se também a existência de órbitas de Birkhoff com um número de rotação pré-determinado. Para terminar, mostra-se que se a aplicação em questão tem entropia topológica nula então toda órbita tem número de rotação para frente e para trás e ainda, um resultado atribuído originalmente a P. Boyland, que se a entropia topológica é nula e a órbita é do tipo (p,q), com mdc(p,q) =1, então esta é necessariamente uma órbita de Birkhoff. Já que não se supõe nenhuma diferenciabilidade sobre a transformação em questão, não podem ser utilizados argumentos como os de hiperbolicidade, transversalidade e nem procedimentos variacionais para a construção de conjuntos caóticos, portanto os métodos aqui utilizados são puramente topológicos, o que ressalta a beleza do assunto. A referência básica do estudo apresentado é o artigo de S. B. Angenent, Monotone recurrence relations, their Birkhoff orbits and topological entropy publicado na Ergodic Theory & Dynamical Systems.
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Costa, Liliana Manuela Gaspar Cerveira da. "Politopo de Birkhoff acíclico." Doctoral thesis, Universidade de Aveiro, 2011. http://hdl.handle.net/10773/8510.

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Doutoramento em Matemática
Neste trabalho estabelece-se uma interpreta c~ao geom etrica, em termos da teoria dos grafos, para v ertices, arestas e faces de uma qualquer dimens~ao do politopo de Birkho ac clico, Tn = n(T), onde T e uma arvore com n v ertices. Generaliza-se o resultado obtido por G. Dahl, [18], para o c alculo do di^ametro do grafo G( t n), onde t n e o politopo das matrizes tridiagonais duplamente estoc asticas. Adicionalmente, para q = 0; 1; 2; 3 s~ao obtidas f ormulas expl citas para a contagem do n umero de q􀀀faces do politopo de Birkho tridiagonal, t n, e e feito o estudo da natureza geom etrica dessas mesmas faces. S~ao, tamb em, apresentados algoritmos para efectuar contagens do n umero de faces de dimens~ao inferior a de uma dada face do politopo de Birkho ac clico.
In this work using graph theory, we give a geometrical interpretation of vertices, edges, and faces of any dimension of the acyclic Birkho polytope, Tn = n(T), were T is a tree with n vertices. We generalize a proposition from G. Dahl, [18], that allows the calculation of the diameter of the graph G( t n), where t n denotes the polytope of tridiagonal doubly stochastic matrices. Furthermore, for q = 0; 1; 2; 3 we obtain some explicit formulae for counting the number of q􀀀faces of the tridiagonal Birkho polytope, t n, and the study of its geometrical nature is done. For a given p-face of t n we determine the number of faces of lower dimension that are contained in it and we discuss its nature. Some algorithms allowing an exhaustive account on the number of edges and faces of the acyclic Birkho polytope are presented.
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Le, Calvez Patrice. "Propriétés des attracteurs de Birkhoff." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376071668.

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MARSON, Guilherme Porfírio. "Órbitas Birkhoff na Ferradura Rotacional." reponame:Repositório Institucional da UNIFEI, 2017. http://repositorio.unifei.edu.br/xmlui/handle/123456789/887.

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Submitted by repositorio repositorio (repositorio@unifei.edu.br) on 2017-08-08T17:54:49Z No. of bitstreams: 1 dissertacao_marson_2017.pdf: 776627 bytes, checksum: df33dd3df7b05a7198177473faf66292 (MD5)
Made available in DSpace on 2017-08-08T17:54:49Z (GMT). No. of bitstreams: 1 dissertacao_marson_2017.pdf: 776627 bytes, checksum: df33dd3df7b05a7198177473faf66292 (MD5) Previous issue date: 2017-07
Neste trabalho, estudamos difeomorfismos de classe C¹ do anel com uma órbita homoclínica transversal K-rotacional a um ponto fixo hiperbólico. Primeiramente, recuperamos um resultado clássico de Poincaré, Birkhoff e Smale: Um ponto homoclínico implica a existência de uma ferradura topológica para alguma iterada. Além disso, obtemos informações interessantes sobre o comportamento rotacional das órbitas em um conjunto de Cantor invariante e maximal (chamado ferradura rotacional). Usando conjugação e dinâmica simbólica associada ao conjunto de Cantor não-errante da ferradura, provamos a existência de um intervalo de rotação não trivial I, e de incontáveis conjuntos de Cantor invariantes para cada número de rotação irracional em I. Finalizamos o trabalho caracterizando a codificação das órbitas Birkhoff da aplicação de duplicação em S¹, as quais implicam a existência de órbitas Birkhoff da ferradura rotacional.
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Le, Calvez Patrice. "Proprietes des attracteurs de birkhoff." Paris 7, 1987. http://www.theses.fr/1987PA077014.

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Ce travail a pour base un article de g. D. Birkhoff consacre aux diffeomorphismes de l'anneau deviant la verticale, et se divise en trois parties. Dans le premier chapitre, on donne des demonstrations completes et rigoureuses des resultats de cet article, on definit l'attracteur de birkhoff d'un diffeomorphisme de l'anneau dissipatif et deviant la verticale, ainsi que les nombres de rotation inferieur et superieur d'un tel ensemble. Dans le second chapitre, on montre qu'il existe pour tout reel compris entre les deux nombres de rotation d'un attracteur de birkhoff, un ensemble d'aubry-mather, contenu dans cet ensemble, dont c'est le nombre de rotation. Dans le troisieme chapitre, on repond a diverses questions sur les attracteurs de birkhoff, on montre en particulier que ceux-ci ne dependent pas continument des diffeomorphismes
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Paolantoni, Thibault. "Application de Riemann-Hilbert-Birkhoff." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS410/document.

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L'application exponentielle duale est une façon d'encoder les matrices de Stokes d'une connexion sur un fibré trivial sur la sphère de Riemann avec deux pôles : un pôle double en 0 et un pôle simple en l'infini.On donne ici une formule pour l'application exponentielle duale comme une série formelle non commutative. D'autres généralisations de cette formule sont données
The exponential dual map is a way to encode Stokes data of a connection on a trivial vector bundle on the Riemann sphere with two poles: one double pole at 0 and one simple pole at infinity.We give here a formula for the exponential dual map expressed as a non commutative serie. Others generalizations of this formula are given
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Palacios, Quiñonero Francesc. "Contribución al problema de interpolación de Birkhoff." Doctoral thesis, Universitat Politècnica de Catalunya, 2004. http://hdl.handle.net/10803/6711.

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El objetivo de esta tesis es desarrollar la interpolación de Birkhoff mediante polinomios lacunarios.

En la interpolación algebraica de Birkhoff se determina un polinomio de grado menor que n, para ello se emplean n condiciones que fijan el valor del polinomio o sus derivadas. Los problemas clásicos de interpolación de Lagrange, Taylor, Hermite, Hermite-Sylvester y Abel-Gontcharov son casos particulares de interpolación algebraica de Birkhoff.

Un espacio de polinomios lacunarios de dimensión n es el conjunto de los polinomios que pueden generarse por combinación lineal de n potencias distintas de grados, en general, no consecutivos. En particular, cuando tomamos potencias de grados 0,1,.,n-1, se obtiene el espacio de polinomios de grado menor que n, empleado en la interpolación algebraica clásica.

En la interpolación algebraica clásica, el número de condiciones determina el espacio de interpolación. En contraste, en la interpolación mediante polinomios lacunarios las condiciones de interpolación determinan únicamente la dimensión del espacio de interpolación y pueden existir una infinidad de espacios sobre los que realizar la interpolación. Esto nos permite construir mejores estrategias de interpolación en ciertos casos, como la interpolación de funciones de gran crecimiento (interpolación de exponenciales y de ramas asintóticas).

La aportación de la tesis consiste en la definición de un marco teórico adecuado para la interpolación de Birkhoff mediante polinomios lacunarios y en la extensión al nuevo marco de los principales elementos de la interpolación algebraica de Birkhoff. En concreto, se generaliza la condición de Pólya, se caracteriza la regularidad condicionada, se establecen condiciones suficientes de regularidad ordenada que extienden el teorema de Atkhison-Sharma, se extiende la descomposición normal y se establecen condiciones suficientes de singularidad en los casos indescomponibles.
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Cortiñas, Guillermo. "Cuantización y teorema de Poincaré-Birkhoff-Witt." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95761.

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Nguyen, Thu Huong. "Strong Stability Preserving Hermite-Birkhoff Time Discretization Methods." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23491.

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The main goal of the thesis is to construct explicit, s-stage, strong-stability-preserving (SSP) Hermite–Birkhoff (HB) time discretization methods of order p with nonnegative coefficients for the integration of hyperbolic conservation laws. The Shu–Osher form and the canonical Shu–Osher form by means of the vector formulation for SSP Runge–Kutta (RK) methods are extended to SSP HB methods. The SSP coefficients of k-step, s-stage methods of order p, HB(k,s,p), as combinations of k-step methods of order (p − 3) with s-stage explicit RK methods of order 4, and k-step methods of order (p-4) with s-stage explicit RK methods of order 5, respectively, for s = 4, 5,..., 10 and p = 4, 5,..., 12, are constructed and compared with other methods. The good efficiency gains of the new, optimal, SSP HB methods over other SSP methods, such as Huang’s hybrid methods and RK methods, are numerically shown by means of their effective SSP coefficients and largest effective CFL numbers. The formulae of these new, optimal methods are presented in their Shu–Osher form.
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Reff, Nathan. "A generalization of the Birkhoff-von Neumann theorem /." Online version of thesis, 2007. http://hdl.handle.net/1850/5967.

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Books on the topic "Birkhoff"

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Lorentz, Rudoph A. Multivariate Birkhoff interpolation. Berlin: New York, 1992.

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Lorentz, Rudolph A. Multivariate Birkhoff Interpolation. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0088788.

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Theory of Birkhoff interpolation. Hauppauge, N.Y: Nova Science Publishers, 2003.

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Lorentz, G. G. Three Papers on Bivariate Birkhoff Interpolation. Darmstadt: GMD, 1986.

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Guang yi Birkhoff xi tong dong li xue. Beijing: Ke xue chu ban she, 2013.

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Rota, Gian-Carlo, and Joseph S. Oliveira, eds. Selected Papers on Algebra and Topology by Garrett Birkhoff. Boston, MA: Birkhäuser Boston, 1987. http://dx.doi.org/10.1007/978-1-4612-5373-0.

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Abgeleitete Birkhoff-Reihen bei Randeigenwertproblemen zu N(y) = [lambda] P(y) mit [lambda]-abhängigen Randbedingungen. Giessen: Selbstverlag des Mathematischen Instituts, 1989.

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Natanzon, Tsevi. Birkhot ha-tefilah. Bene Beraḳ: Ts. Natanzon, 1989.

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Barukh ben Ḥayim Zeʼev Ṿais. Sefer Birkhot shamayim. Yerushalayim: B. Ṿais, 1989.

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Sefer Birkhot shamayim. 2nd ed. Yerushalayim: B. ben Ḥ.Z. Ṿais, 1997.

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Book chapters on the topic "Birkhoff"

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Kappeler, Thomas, and Jürgen Pöschel. "Birkhoff Coordinates." In KdV & KAM, 51–109. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-08054-2_3.

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Amir, Dan. "Birkhoff Orthogolaity." In Operator Theory: Advances and Applications, 33–39. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5487-0_5.

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van Oostrom, Vincent. "Sub-Birkhoff." In Functional and Logic Programming, 180–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24754-8_14.

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Durham, Ian T. "Birkhoff, George David." In Biographical Encyclopedia of Astronomers, 228–29. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4419-9917-7_160.

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Broer, Henk, Igor Hoveijn, Gerton Lunter, and Gert Vegter. "4. Birkhoff normalization." In Lecture Notes in Mathematics, 71–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-540-36398-9_4.

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Lorentz, G. G., and S. D. Riemenschneider. "Birkhoff Quadrature Matrices." In Mathematics from Leningrad to Austin, 352–67. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-5329-7_37.

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Amiraslani, Amir, Heike Faßbender, and Nikta Shayanfar. "Birkhoff Polynomial Basis." In Springer Proceedings in Mathematics & Statistics, 1–25. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49984-0_1.

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Kappeler, Thomas, and Jürgen Pöschel. "Birkhoff Normal Forms." In KdV & KAM, 233–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-08054-2_9.

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Florence, Ronald, Steven N. Shore, Steven N. Shore, Christian Nitschelm, Thomas R. Williams, Raghini S. Suresh, Stephen Gaukroger, et al. "Birkhoff, George David." In The Biographical Encyclopedia of Astronomers, 128–29. New York, NY: Springer New York, 2007. http://dx.doi.org/10.1007/978-0-387-30400-7_160.

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Polishchuk, Alexander, and Leonid Positselski. "Poincaré-Birkhoff-Witt bases." In University Lecture Series, 81–99. Providence, Rhode Island: American Mathematical Society, 2005. http://dx.doi.org/10.1090/ulect/037/04.

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Conference papers on the topic "Birkhoff"

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Goswami, Rituparno, and George F. R. Ellis. "Almost Birkhoff theorem." In TOWARDS NEW PARADIGMS: PROCEEDING OF THE SPANISH RELATIVITY MEETING 2011. AIP, 2012. http://dx.doi.org/10.1063/1.4734450.

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Karasev, M. "Birkhoff resonances and quantum ray method." In Proceedings of the International Seminar Days on Diffraction, 2004. IEEE, 2004. http://dx.doi.org/10.1109/dd.2004.186021.

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Zhang, Jinghui, Tong Ye, Tony T. Lee, Fangfang Yan, and Weisheng Hu. "Deflection-compensated Birkhoff-von-Neumann switches." In 2013 22nd Wireless and Optical Communication Conference (WOCC 2013). IEEE, 2013. http://dx.doi.org/10.1109/wocc.2013.6676423.

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Escolano, Francisco, Edwin R. Hancock, and Miguel A. Lozano. "Birkhoff polytopes, heat kernels and graph complexity." In 2008 19th International Conference on Pattern Recognition (ICPR). IEEE, 2008. http://dx.doi.org/10.1109/icpr.2008.4761921.

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PUCACCO, GIUSEPPE. "ON BIRKHOFF METHOD FOR INTEGRABLE LAGRANGIAN SYSTEMS." In Proceedings of the International Conference on SPT 2004. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702142_0033.

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Croitoru, Anca, Alina Iosify, Nikos Mastorakisz, and Alina Gavrilut. "Fuzzy Multimeasures in Birkhoff Weak Set-Valued Integrability." In 2016 Third International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2016. http://dx.doi.org/10.1109/mcsi.2016.034.

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BAMBUSI, DARIO. "Birkhoff normal form for some quasilinear Hamiltonian PDEs." In XIVth International Congress on Mathematical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812704016_0024.

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BOCHI, JAIRO. "ERGODIC OPTIMIZATION OF BIRKHOFF AVERAGES AND LYAPUNOV EXPONENTS." In International Congress of Mathematicians 2018. WORLD SCIENTIFIC, 2019. http://dx.doi.org/10.1142/9789813272880_0119.

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LEE, M. HOWARD. "BIRKHOFF THEOREM AND ERGOMETER: MEETING OF TWO CULTURES." In Proceedings of the 31st International Workshop. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812836625_0029.

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Lawson, Jimmie, and Yongdo Lim. "A Birkhoff contraction formula with applications to Riccati Equations." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4435043.

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