Relevant bibliographies by topics / Quadratic Formula

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

Academic literature on the topic 'Quadratic Formula'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 June 2025

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Journal articles on the topic "Quadratic Formula"

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March, Robert H. "The mystical ‘‘quadratic formula’’." Physics Teacher 31, no. 3 (1993): 147. http://dx.doi.org/10.1119/1.2343692.

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Hungerbühler, Norbert. "An alternative quadratic formula." Mathematische Semesterberichte 67, no. 1 (2019): 85–95. http://dx.doi.org/10.1007/s00591-019-00262-3.

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Clarke, Robert J. "82.48 The Quadratic Equation Formula." Mathematical Gazette 82, no. 495 (1998): 460. http://dx.doi.org/10.2307/3619896.

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Mahajan, Sanjoy. "Fleeing from the quadratic formula." American Journal of Physics 87, no. 5 (2019): 332–34. http://dx.doi.org/10.1119/1.5097757.

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ALACA, AYŞE, ŞABAN ALACA, and KENNETH S. WILLIAMS. "SEXTENARY QUADRATIC FORMS AND AN IDENTITY OF KLEIN AND FRICKE." International Journal of Number Theory 06, no. 01 (2010): 169–83. http://dx.doi.org/10.1142/s1793042110002880.

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Formulae, originally conjectured by Liouville, are proved for the number of representations of a positive integer n by each of the eight sextenary quadratic forms [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text].
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Jones, Edna. "Local densities of diagonal integral ternary quadratic forms at odd primes." International Journal of Number Theory 17, no. 03 (2021): 547–75. http://dx.doi.org/10.1142/s1793042120400357.

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We give formulas for local densities of diagonal integral ternary quadratic forms at odd primes. Exponential sums and quadratic Gauss sums are used to obtain these formulas. These formulas (along with 2-adic densities and Siegel’s mass formula) can be used to compute the representation numbers of certain ternary quadratic forms.
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Wen, Hui, and Feng Ling Li. "A Simplified Formula to Calculate the Initial Value of Iteration for Contracted Depth in Quadratic Parabola Shaped Channels." Applied Mechanics and Materials 744-746 (March 2015): 1039–44. http://dx.doi.org/10.4028/www.scientific.net/amm.744-746.1039.

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At present, the complexity of calculation process and expression form of the initial value of iteration for contracted depth in quadratic parabola shaped channels,Seek a new iterative initial value formula for contracted depth in quadratic parabola shaped channels. Through an identical deformation on the basic equation for contracted depth in quadratic parabola shaped channels. Deduce the iterative formula for computing the quadratic parabola section contraction water depth. Introduction the dimensionless contraction water depth concept, plot the dimensionless contraction water depth and the dimensionless parameter relationship curves. Determine the iterative formula of initial value form for quadratic parabolic shaped channels, and based on the theory of optimum fitting, by the minimum residual standard differential and simple form of formula as the goal, the initial iteration value formula for calculation contracted depth in quadratic parabola shaped channels was obtained. It is greatly accelerating the convergence rate iterative calculations. The calculation of a practical case and error analysis of the depth calculations show that in the utility range of , its maximum relative error is less than 0.26% after performing one iteration. This formula has definite physics concept, easy calculation, high precision and wide range compared with the existing formulas. It will bring great convenience for designers.
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Alaca, Ayşe, and M. Nesibe Kesicioğlu. "Representations by octonary quadratic forms with coefficients 1, 2, 3 or 6." International Journal of Number Theory 13, no. 03 (2017): 735–49. http://dx.doi.org/10.1142/s1793042117500385.

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Using modular forms, we determine formulas for the number of representations of a positive integer by diagonal octonary quadratic forms with coefficients [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text].
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Edwards, Thomas G., and Kenneth R. Chelst. "Finding Meaning in the Quadratic Formula." Mathematics Teacher 112, no. 4 (2019): 258–61. http://dx.doi.org/10.5951/mathteacher.112.4.0258.

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Sastry, K. R. S. "The Quadratic Formula: A Historic Approach." Mathematics Teacher 81, no. 8 (1988): 670–72. http://dx.doi.org/10.5951/mt.81.8.0670.

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Dissertations / Theses on the topic "Quadratic Formula"

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Bauer-Price, Pia. "The Selberg Trace Formula for PSL(2, OK) for imaginary quadratic number fields K of arbitrary class number." Bonn : [s.n.], 1991. http://catalog.hathitrust.org/api/volumes/oclc/26531368.html.

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Ravindran, Hari Alangat. "On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690.

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Tempesta, Patricia. "Simmetries in binary differential equations." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-11072017-170308/.

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The purpose of this thesis in to introduce the systematic study of symmetries in binary differential equations (BDEs). We formalize the concept of a symmetric BDE, under the linear action of a compact Lie group. One of the main results establishes a formula that relates the algebraic and geometric effects of the occurrence of the symmetry in the problem. Using tools from invariant theory and representation theory for compact Lie groups we deduce the general forms of equivariant binary differential equations under compact subgroups of O(2). A study about the behavior of the invariant straight lines on the configuration of homogeneous BDEs of degree n is done with emphasis on cases in which n = 0 and n = 1. Also for the linear case (n = 1) the equivariant normal forms are presented. Symmetries of linear 1-forms are also studied and related with symmetries of tangent orthogonal vectors fields associated with it.<br>O objetivo desta tese é introduzir o estudo sistemático de simetrias em equações diferenciais binárias (EDBs). Neste trabalho formalizamos o conceito de EDB simétrica sobre a ação de um grupo de Lie compacto. Um dos principais resultados é uma fórmula que relaciona o efeito geométrico e algébrico das simetrias presentes no problema. Utilizando ferramentas da teoria invariante e de representação para grupos compactos deduzimos as formas gerais para EDBs equivariantes. Um estudo sobre o comportamento das retas invariantes na configuração de EDBs com coeficientes homogêneos de grau n é feito com ênfase nos casos de grau 0 e 1, ainda no caso de grau 1 são apresentadas suas formas normais. Simetrias de 1-formas lineares são também estudadas e relacionadas com as simetrias dos seus campos tangente e ortogonal.
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Prado, Janete do [UNESP]. "Forma traço sobre algumas extensões galoisianas de corpos p-Ádicos." Universidade Estadual Paulista (UNESP), 2005. http://hdl.handle.net/11449/94234.

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Made available in DSpace on 2014-06-11T19:26:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2005-02-28Bitstream added on 2014-06-13T20:08:01Z : No. of bitstreams: 1 prado_j_me_sjrp.pdf: 438115 bytes, checksum: 072493cefd49a6603f89810da896f173 (MD5)<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)<br>Seja K um corpo p-ádico, com p 6= 2 e F K uma extensão galoisiana de K de grau n: Então F pode ser visto como espa»co quadrático sobre K, com a forma quadrática dada por T(x) = trFjK(x2), para x 2 F: Determinaremos os invariantes determinante, dimensão e invariante de Hasse desta forma quadrática para n igual a 2,3 e 4.<br>Let K be a p-adic eld with p 6= 2 and F a Galois extension eld of K of degree n: Then F can be viewed as a quadratic space over K under the quadratic form T(x) = trFjK(x2) for x 2 F. The invariants of this quadratic form dimension, determinant and Hasse invariant are given in the case when n is equal to 2,3 and 4.
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Soares, Jobson Hugo de Sousa. "Fun??o quadr?tica." Universidade Federal do Rio Grande do Norte, 2013. http://repositorio.ufrn.br:8080/jspui/handle/123456789/18654.

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Made available in DSpace on 2015-03-03T15:36:08Z (GMT). No. of bitstreams: 1 JobsonHSS_DISSERT.pdf: 1416900 bytes, checksum: 677228c50dc507b009762057a3ac8330 (MD5) Previous issue date: 2013-03-15<br>In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning<br>Em geral, o estudo de fun??es quadr?ticas ? baseado numa quantidade excessiva de f?rmulas, todo conte?do ? abordado sem justificativas. Apresentamos a fun??o quadr?tica e suas propriedades a partir de problemas envolvendo equa??es do segundo grau e da t?cnica de completar quadrado. Partindo das defini??es mostraremos que o gr?fico da fun??o quadr?tica ? a par?bola e terminamos nosso estudos verificando que v?rias propriedades da fun??o podem ser lidas a partir da simples observa??o do seu gr?fico. Dessa forma, constru?mos todo o assunto justificando cada passo, abandonando o uso de f?rmulas decoradas e prezando pelo racioc?nio
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AraÃjo, Adenildo Texeira de. "NÃmeros complexos: um estudo de aplicaÃÃes a trigonometria e as equaÃÃes algÃbricas." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=14006.

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O estudo dos nÃmeros complexos no ensino mÃdio à caracterizado, quase exclusivamente, pela abordagem algÃbrica deixando a parte geomÃtrica e suas aplicaÃÃes sem uma devida importÃncia. Este trabalho apresenta um estudo sobre nÃmeros complexos bem como algumas de suas aplicaÃÃes tanto da parte algÃbrica, aplicada a polinÃmios, quanto da parte geomÃtrica aplicada em especial à trigonometria. De inÃcio fizemos uma abordagem dos fatos histÃricos desses nÃmeros citando alguns matemÃticos que deram suas contribuiÃÃes acerca desse conjunto complexo. Em seguida à apresentada a parte teÃrica, algÃbrica e geomÃtrica, bem como algumas aplicaÃÃes a trigonometria. Por fim apresentamos a teoria das equaÃÃes algÃbricas quadrÃticas e cÃbicas e a interaÃÃo dessas com os nÃmeros complexos.<br>The study of the complex numbers in the medium teaching is characterized, almost exclusively, for the algebraic approach leaving the geometric part and their applications without a due importance. This work presents a study on complex numbers as well as some of their applications so much of the algebraic part, applied to polynomials, as of the geometric part especially applied to the trigonometry. Of I begin did an approach of the historical facts of those numbers mentioning some mathematical that gave their contributions near of that complex group. Soon afterwards the part theoretical, algebraic and geometric is presented, as well as some applications the trigonometry. Finally we presented the theory of the quadratic and cubic algebraic equations and the interaction of those with the complex numbers.
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Furter, Jean-Philippe. "Sur les automorphismes quadratiques de l'espace affiné." Université Joseph Fourier (Grenoble), 1995. http://www.theses.fr/1995GRE10139.

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Cette these, divisee en deux parties, aborde le probleme de la triangularisabilite lineaire des automorphismes quadratiques de l'espace affine c#n: etant donne un automorphisme quadratique f de c#n, a quelle condition existe-t-il une base de l'espace vectoriel c#n dans laquelle f s'ecrit sous forme triangulaire ? dans la premiere partie, nous donnons quelques conditions suffisantes pour cela, la plupart etant a rapprocher du theoreme fondamental de van den essen et hubbers, etablissant l'equivalence entre la notion de triangularisabilite lineaire et la notion de nilpotence forte. Nous prouvons entre autres que f est lineairement triangularisable si et seulement si son algebre non-associative correspondante est une algebre nilpotente. Dans la deuxieme partie, nous prouvons essentiellement que la conjecture de dependance lineaire implique la triangularisabilite lineaire des automorphismes quadratiques 3-nilpotents de c#n pour n 6. La demonstration que nous donnons utilise un outil informatique permettant d'effectuer des calculs formels. Nous exhibons au passage un automorphisme quadratique 3-nilpotent de c#6 dont l'inverse est de degre 6, ce qui repond a une question de meisters et olech (m-o)
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Kebbab, Eric Franck Idir. "Aspects géométriques des principes locaux-globaux dans la théorie abstraite des formes quadratiques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2014. http://tel.archives-ouvertes.fr/tel-00990237.

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Les espaces d'ordres abstraits sont introduits par M. Marshall dans les années 70, dans la perspective d'offrir un cadre abstrait à l'étude des formes quadratiques. Vers le début des années 90, les travaux de M. Dickmann, L. de Lima et de F. Miraglia, ont donné naissance à la version duale des groupes spéciaux. Le premier thème que nous traiterons est la caractérisation des points d'un espace d'ordres du corps de fonctions d'une variété réelle, nous reprendrons un résultat de Brumfiel affirmant l'existence d'une correspondance entre ces ordres et des ultrafiltres de semi-algébriques. Nous appliquerons ceci au corps R(x,y). Suivra la caractérisation des ordres de ce corps à travers la notion de demi-branche de Bézout. Le second thème traite des principes locaux-globaux généralisés (ou Conjecture pp). Le premier résultat de la thèse porte sur la séparation des constructibles et sur la principalité des basiques. Nous montrerons que le langage des groupes spéciaux nous offre une vision claire du fait que ces principes découlent trivialement du principe de l'isotropie étendu. Le second résultat traite des contre-exemples à la conjecture dans le cas de la conique rationnelle donnée par l'équation x2+y2=3. Le dernier résultat (le plus important), aborde la conjecture pp dans le cadre du corps R(x,y). Nous nous intéresserons à des familles de polynômes vérifiant certaines conditions géométriques et montrerons que toute formule pp, ayant ses paramètres dans cette famille, vérifie un principe local-global. Nous les baptiserons formules V-universelles. Nous clorons le dernier chapitre par deux méthodes de construction.
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Silva, João Paulo Arruda da. "Funções afim e quadrática com auxílio do multiplano e blocos cúbicos." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7532.

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Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-20T11:59:28Z No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5)<br>Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-20T11:59:51Z (GMT) No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5)<br>Made available in DSpace on 2015-10-20T11:59:51Z (GMT). No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5) Previous issue date: 2014-08-26<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>This paper presents a new way of discussing concepts involving function, a ne function and quadratic function. Through simple activities with the use of blocks of cubes, and the multiplane software such as GeoGebra, students will move from a passive position, as simple listener, the active member of the teaching-learning process, enabling them to acquire a broader notion the concept of function and apply it later in solving problems in school and in their daily lives. Besides these diversi ed activities, topics that are usually not given prominence in most books of high school such that the analysis of the canonical form of the quadratic function and the theorem of characterization of a ne function will play an important role in developing what is expected of students about this important area of mathematics. All activities were conducted with 1st grade students of high school Natalicia Maria Figueiroa da Silva, located in the city of Surubim, in the state of Pernambuco.<br>Este trabalho apresenta uma nova maneira de se discutir conceitos envolvendo função, função a m e função quadrática. Através de atividades simples com uso dos blocos de cubos, do multiplano e de softwares como o Geogebra, o aluno passará de uma posição passiva, como simples ouvinte, a integrante ativo do processo de ensino-aprendizagem, possibilitando ao mesmo adquirir uma noção mais ampla do conceito de função e aplicá- lo posteriormente na resolução de problemas na escola e em sua vida cotidiana. Além dessas atividades diversi cadas, tópicos que geralmente não são colocados em destaque na maioria dos livros de ensino médio tais quais a análise da forma canônica da função quadrática e o Teorema de caracterização da função a m terão um importante papel no desenvolvimento que se espera dos estudantes a respeito dessa importante área da Matemática. Todas as atividades foram desenvolvidas com alunos da 1a série do ensino médio da Escola Estadual Natalícia Maria Figueiroa da Silva, localizada na cidade de Surubim no Estado de Pernambuco.
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Silva, Adam Oliveira da. "Rigidez de métricas críticas para funcionais riemannianos." reponame:Repositório Institucional da UFC, 2017. http://www.repositorio.ufc.br/handle/riufc/25969.

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SILVA, Adam Oliveira da. Rigidez de métricas críticas para funcionais riemannianos. 2017. 78 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017.<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-19T19:08:04Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 481005 bytes, checksum: 2bdfc6ab68b042a5cfd4f67caf1e21e4 (MD5)<br>Rejected by Rocilda Sales (rocilda@ufc.br), reason: Bom dia, Estou devolvendo a Tese de ADAM OLIVEIRA DA SILVA, para que o arquivo seja substituído, pois o aluno já veio na BCM e orientei quais eram as correções a serem feitas. Atenciosamente, on 2017-09-20T14:03:26Z (GMT)<br>Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-09-20T16:47:21Z No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5)<br>Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-09-21T12:26:34Z (GMT) No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5)<br>Made available in DSpace on 2017-09-21T12:26:35Z (GMT). No. of bitstreams: 1 2017_tese_aosilva.pdf: 480774 bytes, checksum: a1267dd82f8a82a19f79902004e1afb5 (MD5) Previous issue date: 2017-09-15<br>The aim of this work is to study metrics that are critical points for some Riemannian functionals. In the first part, we investigate critical metrics for functionals which are quadratic in the curvature on closed Riemannian manifolds. It is known that space form metrics are critical points for these functionals, denoted by F t,s (g). Moreover, when s = 0, always Einstein metrics are critical to F t (g). We proved that under some conditions the converse is true. For instance, among others results, we prove that if n ≥ 5 and g is a Bach-flat critical metric to F −n/4(n−1) , with second elementary symmetric function of the Schouten tensor σ 2 (A) > 0, then g should be Einstein. Furthermore, we show that a locally conformally flat critical metric with some additional conditions are space form metrics. In the second part, we study the critical metrics to volume functional on compact Riemannian manifolds with connected smooth boundary. We call such critical points of Miao-Tam critical metrics due to the variational study making by Miao and Tam (2009). In this work, we show that the geodesics balls in space forms Rn , Sn and Hn have the maximum possible boundary volume among Miao-Tam critical metrics with connected boundary provided that the boundary be an Einstein manifold. In the same spirit, we also extend a rigidity theorem due to Boucher et al. (1984) and Shen (1997) to n-dimensional static metrics with positive constant scalar curvature, which give us another way to get a partial answer to the Cosmic no-hair conjecture already obtained by Chrusciel (2003).<br>Este trabalho tem como principal objetivo estudar métricas que são pontos críticos de alguns funcionais Riemannianos. Na primeira parte, investigaremos métricas críticas de funcionais que são quadráticos na curvatura sobre variedades Riemannianas fechadas. É de conhecimento que métricas tipo formas espaciais são pontos críticos para tais funcionais, denotados aqui por F t,s (g). Além disso, no caso s = 0, métricas de Einstein são sempre críticas para F t (g). Provamos que sob algumas condições, a recíproca destes fatos são verdadeiras. Por exemplo, dentre outros resultados, provamos que se n ≥ 5 e g é uma métrica Bach-flat crìtica para F−n/4(n−1) com segunda função simétrica elementar do tensor de Schouten σ 2 (A) > 0, então g tem que ser métrica de Einstein. Ademais, mostramos que uma métrica crítica localmente conformemente plana, com algumas hipóteses adicionais, tem que ser tipo forma espacial. Na segunda parte, estudamos as métricas críticas do funcional volume sobre variedades Riemannianas compactas com bordo suave conexo. Chamamos tais pontos críticos de métricas críticas de Miao-Tam, devido ao estudo variacional feito por Miao e Tam (2009). Neste trabalho provamos que as bolas geodésicas das formas espaciais Rn , S n e H n possuem o valor máximo para o volume do bordo dentre todas as métricas críticas de Miao-Tam com bordo conexo, desde que o bordo seja uma variedade de Einstein. No mesmo sentido, também estendemos um teorema de rigidez devido à Boucher et al. (1984) e Shen (1997) para métricas estáticas de dimensão n e com curvatura escalar constante positiva, o qual nos fornece outra maneira para obter uma resposta parcial para a Cosmic no-hair conjecture já obtida por Chrusciel (2003).
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Books on the topic "Quadratic Formula"

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Alladi, Krishnaswami, Frank Garvan, and Ae Ja Yee. Ramanujan 125: International conference to commemorate the 125th anniversary of Ramanujan's birth, Ramanujan 125, November 5--7, 2012, University of Florida, Gainesville, Florida. American Mathematical Society, 2014.

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Beyond the Quadratic Formula. Mathematical Association of America, 2015.

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Fyne-Sinclair, Soroya. Solving Quadratic Equations - Method of Factoring and Using the Quadratic Formula - Pocket Workbook. Independently Published, 2020.

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Deruelle, Nathalie, and Jean-Philippe Uzan. Gravitational radiation. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198786399.003.0054.

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This chapter attempts to calculate the radiated energy of a source in the linear approximation of general relativity to infinity in the lowest order. For this, the chapter first expands the Einstein equations to quadratic order in metric perturbations. It reveals that the radiated energy is then given by the (second) quadrupole formula, which is the gravitational analog of the dipole formula in Maxwell theory. This formula is a priori valid only if the motion of the source is due to forces other than gravity. Finally, this chapter shows that, to prove this formula for the case of self-gravitating systems, the Einstein equations to quadratic order must be solved, and the radiative field in the post-linear approximation of general relativity obtained.
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Back, Kerry E. Brownian Motion and Stochastic Calculus. Oxford University Press, 2017. http://dx.doi.org/10.1093/acprof:oso/9780190241148.003.0012.

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Brownian motion and concepts of the Itôs calculus are explained, including total variation, quadratic variation, Levy’s characterization of Brownian motion, the Itô integral, the difference between martingales and local martingales, the martingale (predictable) representation theorem , Itô’s formula (Itô’s lemma), geometric Brownian motion, covariation (joint variation) processes, the relationship between variance and expected quadratic variation, the relationship between covariance and expected covariation, and rotations of Brownian motions.
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United States. National Aeronautics and Space Administration., ed. A linear quadratic Gaussian with loop transfer recovery proximity operations autopilot for spacecraft. The Charles Stark Draper Laboratory, Inc., 1988.

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Die lehre von der aufstellung empirischer formeln mit hilfe der methode der kleinsten quadrate für mathematiker, physiker, techniker. B. G. Teubner, 1991.

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Olshanski, Grigori. Enumeration of maps. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.26.

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This article discusses the relationship between random matrices and maps, i.e. graphs drawn on surfaces, with particular emphasis on the one-matrix model and how it can be used to solve a map enumeration problem. It first provides an overview of maps and related objects, recalling the basic definitions related to graphs and defining maps as graphs embedded into surfaces before considering a coding of maps by pairs of permutations. It then examines the connection between matrix integrals and maps, focusing on the Hermitian one-matrix model with a polynomial potential and how the formal expansion of its free energy around a Gaussian point (quadratic potential) can be represented by diagrams identifiable with maps. The article also illustrates how the solution of the map enumeration problem can be deduced by means of random matrix theory (RMT). Finally, it explains how the matrix model result can be translated into a bijective proof.
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Book chapters on the topic "Quadratic Formula"

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Gelfand, Israel M., and Alexander Shen. "One more formula concerning quadratic equations." In Algebra. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-0335-3_55.

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Shimura, Goro. "Quadratic Diophantine Equations, the Class Number, and the Mass Formula." In Collected Papers V. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32548-4_4.

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Azamov, Abdulla. "A Language of Terms of Taylor’s Formula for Quadratic Dynamical Systems and Its Fractality." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01476-6_3.

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Ibukiyama, Tomoyoshi, and Masanobu Kaneko. "Class Number Formula and an Easy Zeta Function of the Space of Quadratic Forms." In Bernoulli Numbers and Zeta Functions. Springer Japan, 2014. http://dx.doi.org/10.1007/978-4-431-54919-2_10.

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Kéri, Gerzson. "The Sherman-Morrison Formula for the Determinant and its Application for Optimizing Quadratic Functions on Condition Sets Given by Extreme Generators." In Applied Optimization. Springer US, 2001. http://dx.doi.org/10.1007/978-1-4613-0295-7_9.

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Poorten, A. J. "Explicit formulas for units in certain quadratic number fields." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58691-1_57.

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Rosen, Michael. "The Class Number Formulas in Quadratic and Cyclotomic Function Fields." In Graduate Texts in Mathematics. Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4757-6046-0_16.

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Nees, Georg. "Räumliche Bilder des Quadrats und der Kugelfläche." In Formel, Farbe, Form. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/978-3-642-57865-6_6.

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Bird, John. "Revision Test 3 Simultaneous and quadratic equations, transposition of formulae, inequalities and logarithms." In Engineering Mathematics. Routledge, 2017. http://dx.doi.org/10.4324/9781315561851-17.

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"Quadratic Polynomials." In Beyond the Quadratic Formula. American Mathematical Society, 2020. http://dx.doi.org/10.1090/clrm/062/02.

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Conference papers on the topic "Quadratic Formula"

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Kong, Xianwen, Cle´ment Gosselin, and James M. Ritchie. "Forward Displacement Analysis of a Linearly Actuated Quadratic Spherical Parallel Manipulator." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28126.

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A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a linearly actuated quadratic spherical parallel manipulator. An alternative formulation of the kinematic equations of the quadratic spherical parallel manipulator is proposed. The singularity analysis of the quadratic spherical parallel manipulator is then dealt with. A new type of singularity of parallel manipulators — leg actuation singularity — is identified. If a leg is in a leg actuation singular configuration, the actuated joints in this leg cannot be actuated even if the actuated joints in other legs are released. A formula is revealed that produces a unique current solution to the FDA for a given set of inputs. The input space is also revealed for the quadratic spherical parallel manipulator in order to guarantee that the robot works in the same assembly mode. This work may facilitate the control of the quadratic spherical parallel manipulator.
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Kong, Xianwen, and Cle´ment Gosselin. "Forward Displacement Analysis of a Quadratic Spherical Parallel Manipulator: The Agile Eye." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87467.

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A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed for producing a unique current solution to the FDA for a given set of inputs. A regular cube in the input space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.
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Cha, J. Z., and R. W. Mayne. "The Symmetric Rank One Formula and its Application in Discrete Nonlinear Optimization." In ASME 1988 Design Technology Conferences. American Society of Mechanical Engineers, 1988. http://dx.doi.org/10.1115/detc1988-0017.

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Abstract The hereditary properties of the Symmetric Rank One (SRI) update formula for numerically accumulating second order derivative information are studied. The unique advantage of the SR1 formula is that it does not require specific search directions for development of the Hessian matrix. This is an attractive feature for optimization applications where arbitrary search directions may be necessary. This paper explores the use of the SR1 formula within a procedure based on recursive quadratic programming (RQP) for solving a class of mixed discrete constrained nonlinear programming (MDCNP) problems. Theoretical considerations are presented along with numerical examples which illustrate the procedure and the utility of SR1.
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Zhao, Yi, Hongning Liu, Bingtao Li, Qiyun Zhang, and Guoliang Xu. "Uniform Design and Quadratic Polynomial Regression Analysis Applied on the Optimization of Compatibility Study in Traditional Chinese Formula." In Proceedings of the 2014 Congress on IEMDA 2014 & Proceedings of the 2nd Congress on CCSA 2014. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814689007_0048.

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Cha, J. C., and R. W. Wayne. "Optimization With Discrete Variables via Recursive Quadratic Programming: Part II — Algorithm and Results." In ASME 1987 Design Technology Conferences. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/detc1987-0003.

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Abstract A discrete recursive quadratic programming algorithm is developed for mixed discrete constrained nonlinear progrmming (MDCNP) problems. The symmetric rank one (SR1) Hessian update formula is used to generate second order information. Also, strategies, such as the watchdog technique (WT), the monotonicity analysis technique (MA), the contour analysis technique (CA) and the restoration strategy of feasibility have been considered. Heuristic aspects of handling discrete variables are treated via the concepts and convergence discussions of Part I. This paper summarizes the details of the algorithm and its implementation. Test results for 25 different problems are presented to allow evaluation of this approach and provide a basis for performance comparison. The results show that the suggested method is a promising one, efficient and robust for the MDCNP problem.
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Hofwing, Magnus, and Niclas Stro¨mberg. "Robustness of Residual Stresses in Castings and an Improved Process Window." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86454.

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In this work the robustness of residual stresses in finite element simulations with respect to deviations in mechanical parameters in castings is evaluated. Young’s modulus, the thermal expansion coefficient and the hardening are the studied parameters. A 2D finite element model of a stress lattice is used. The robustness is evaluated by comparing purely finite element based Monte Carlo simulations and Monte Carlo simulations based on linear and quadratic response surfaces. Young’s modulus, the thermal expansion coefficient and the hardening are assumed to be normal distributed with a standard deviation that is 10% of their nominal value at different temperatures. In this work an improved process window is also suggested to show the robustness graphically. By using this window it is concluded that least robustness is obtained for high hardening values in combination to deviations in Young’s modulus and the thermal expansion coefficient. It is also concluded that quadratic response surface based Monte Carlo simulations substitute finite element based Monte Carlo simulations satisfactory. Furthermore, the standard deviation of the responses are evaluated analytically by using the Gauss formula, and are compared to results from Monte Carlo simulations. The analytical solutions are accurate as long as the Gauss formula is not utilized close to a stationary point.
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Arai, Koichiro, Hiroshi Okada, and Yasunori Yusa. "Formulation of Three-Dimensional J-Integral for Finite Strain Elastic-Plastic Fracture Problems Under Any Load Histories (Monotonic and Cyclic Loads)." In ASME 2018 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/pvp2018-84241.

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In this paper, a redefined three-dimensional J-integral for the quadratic tetrahedral element along with some numerical examples are presented. It is known that the J-integral represents the energy release rate and can be computed on an arbitrary path or a domain of integration. This feature is called the “path-independent property”. It requires the assumption of proportional loading in the case of elastic-plastic material. Because of this assumption, when the J-integral is applied to a problem under a non-proportional loading condition, the computed J-integral value depends on the integral path or the integral domain. To overcome this problem, the authors have proposed a formula to evaluate the energy dissipation inside a finite domain in the vicinity of the crack front, which is an extension of the conventional three-dimensional J-integral. The energy dissipating into a small but finite domain in the vicinity of crack front includes the energy released due to the opening of new crack faces and the deformation energy in the process zone. The numerical evaluation is carried out by the domain integral. In this formula, it is not necessary to evaluate any non-integrable terms at the crack front. Furthermore, the proposed formula has the feature of integral domain independence for any material models without any assumptions in their deformation histories. Therefore, it is possible to evaluate the J-integral for problems with non-proportional loads by using the proposed method. In this paper, computational method using the quadratic tetrahedral element for the redefined J-integral under non-proportional loading is presented first. Some results of three-dimensional semi-circular surface crack problem are presented as numerical examples.
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Xie, Zhitian, and Jeffery Falzarano. "Study on 2nd-Order Wave Loads With Forward Speed Through Aranha’s Formula and Neumann-Kelvin Linearization." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18137.

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Abstract The 2nd-order wave loads consist of difference frequency, sum frequency components and a steady drift component that is also called the mean drift load. The first two components are usually not of interest, because of their small amplitudes compared with the 1st-order wave loads. The remaining mean drift load should be taken into consideration due to its steady effect on floating bodies. In the previous research, the full derivation and expression of the 2nd-order wave loads applied to a floating structure was presented. Moreover, numerically estimated quadratic transfer function was also illustrated with both off-diagonal elements and diagonal elements called the mean drift coefficients. Most research topics in this scenario consider the wave only case. In this paper, the mean drift wave loads applied to a floating structure with forward speed or current velocity has been numerically estimated through Aranha’s formula, a far field method and Neumann-Kelvin linearization, a near field method. Therefore, the effect of the floating structure’s forward speed or current velocity on the 2nd-order mean drift loads that is also called the wave drift damping has been discussed through these two methods. This work will provide a meaningful reference and numerical basis for the ongoing projects of the floating structure’s seakeeping and maneuvering problems.
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Ma, Leixin, Shixiao Fu, Ke Hu, Qian Shi, and Runpei Li. "Investigation Into Stability and Accuracy in Predicting Slender Bodies’ Hydroelasticity Using Loose Coupling Methods." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41136.

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Problems concerning fluid-structure-interaction are often encountered in aquaculture engineering. For a moving slender structure like fishing net or floater in currents and waves, modified Morison Equation is a widely employed formula to estimate its hydrodynamic loads. The hydrodynamic forces are closely dependent on the structures’ velocity and acceleration, and quadratic relative velocity in the equation even adds nonlinearity in the forces. To study the hydroelastic response, two time-saving loosely coupling methods, calculating the hydrodynamic forces based on the structure’s response in the previous time step without iteration, are proposed in this paper. The loose coupling methods were proved to affect the traditional stability criteria for time integration. Based on the two loose coupling methods, the stability and accuracy of a slender beam’s hydroelasticity undergoing large deformation were studied. The calculated responses were compared against strong coupling results. It was found that if loose coupling is assumed in added mass force, unconditional instability is likely to occur. On the other hand, the accuracy of numerical results can be improved with smaller time increments set if loose coupling is only assumed in the quadratic relative drag force.
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Zanganeh, Hossein, and Narakorn Srinil. "Two-Dimensional Coupled Vortex-Induced Vibration of Circular Cylinder: Prediction and Extraction of Hydrodynamics Properties." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10240.

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An advanced model for predicting a two-dimensional coupled cross-flow and in-line vortex-induced vibration (VIV) of a flexibly-mounted circular cylinder in a uniform flow is proposed and investigated. Attention is placed on a systematic extraction of variable hydrodynamics properties associated with a bi-directional fluid-structure interaction system. The governing equations of motion are based on double Duffing-van der Pol (structural-wake) oscillators with the two structural equations containing cubic and quadratic nonlinear terms. The cubic nonlinearities capture the geometrical coupling of cross-flow/in-line displacements excited by hydrodynamic lift/drag forces whereas the quadratic nonlinearities allow fluid-structure interactions. The combined analytical and numerical solutions of the proposed model are established. By varying flow velocities in numerical simulations, the derived low-order model qualitatively captures several key VIV characteristics of coupled in-line/cross-flow oscillations. By making use of a newly-derived empirical formula, the predicted maximum cross-flow/in-line VIV amplitudes and associated lock-in ranges compare well with several experimental results for cylinders with low/high mass or damping ratios. Moreover, such important hydrodynamic properties as VIV-induced mean drag, added mass, excitation and damping terms can be systematically determined via the proposed model and compared well with some experimental results in the literature.
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