Relevant bibliographies by topics / Lie quadratic

Contents

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

Academic literature on the topic 'Lie quadratic'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Lie quadratic"

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Ardizzoni, Alessandro, and Fabio Stumbo. "Quadratic Lie Algebras." Communications in Algebra 39, no. 8 (August 2011): 2723–51. http://dx.doi.org/10.1080/00927872.2010.489917.

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Albuquerque, Helena, Elisabete Barreiro, and Saïd Benayadi. "Odd-quadratic Lie superalgebras." Journal of Geometry and Physics 60, no. 2 (February 2010): 230–50. http://dx.doi.org/10.1016/j.geomphys.2009.09.013.

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Zhu, Linsheng. "Solvable quadratic Lie algebras." Science in China Series A 49, no. 4 (March 26, 2006): 477–93. http://dx.doi.org/10.1007/s11425-006-0477-y.

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Duong, Minh Thanh, and Rosane Ushirobira. "Singular quadratic Lie superalgebras." Journal of Algebra 407 (June 2014): 372–412. http://dx.doi.org/10.1016/j.jalgebra.2014.02.034.

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AYADI, IMEN, HEDI BENAMOR, and SAÏD BENAYADI. "LIE SUPERALGEBRAS WITH SOME HOMOGENEOUS STRUCTURES." Journal of Algebra and Its Applications 11, no. 05 (September 26, 2012): 1250095. http://dx.doi.org/10.1142/s0219498812500958.

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We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [A. Aubert, Structures affines et pseudo-métriques invariantes à gauche sur des groupes de Lie, Thèse, Université Montpellier II (1996)]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie superalgebras. Several examples are included to show the existence of homogeneous quadratic symplectic Lie superalgebras other than even-quadratic even-symplectic considered in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. We study the structures of even (respectively, odd)-quadratic odd (respectively, even)-symplectic Lie superalgebras and odd-quadratic odd-symplectic Lie superalgebras and we give its inductive descriptions in terms of quadratic generalized double extensions and odd quadratic generalized double extensions. This study complete the inductive descriptions of homogeneous quadratic symplectic Lie superalgebras started in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. Finally, we generalize to the case of homogeneous quadratic symplectic Lie superalgebras some relations between even-quadratic even-symplectic Lie superalgebras and Manin superalgebras established in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608].
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Barreiro, Elisabete, and Saïd Benayadi. "Quadratic symplectic Lie superalgebras and Lie bi-superalgebras." Journal of Algebra 321, no. 2 (January 2009): 582–608. http://dx.doi.org/10.1016/j.jalgebra.2008.09.026.

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Wang, Song, and Linsheng Zhu. "Non-degenerate Invariant Bilinear Forms on Lie Color Algebras." Algebra Colloquium 17, no. 03 (September 2010): 365–74. http://dx.doi.org/10.1142/s1005386710000362.

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In this paper, we study Lie color algebras 𝔤 with a non-degenerate color-symmetric, 𝔤-invariant bilinear form B, such a (𝔤,B) is called a quadratic Lie color algebra. Our first result generalizes the notion of double extensions to quadratic Lie color algebras. This notion was introduced by Medina and Revoy to study quadratic Lie algebras. In the second theorem, we give a sufficient condition for a quadratic Lie color algebra to be a quadratic Lie color algebra by double extension. At last, we generalize the notion of T*-extensions to Lie color algebras.
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Baklouti, Amir. "Quadratic Hom-Lie triple systems." Journal of Geometry and Physics 121 (November 2017): 166–75. http://dx.doi.org/10.1016/j.geomphys.2017.06.013.

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Kotov, Alexei, and Thomas Strobl. "Integration of quadratic Lie algebroids to Riemannian Cartan–Lie groupoids." Letters in Mathematical Physics 108, no. 3 (January 12, 2018): 737–56. http://dx.doi.org/10.1007/s11005-018-1048-1.

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Jurdjevic, Velimir. "Affine-quadratic problems on Lie groups." Mathematical Control & Related Fields 3, no. 3 (2013): 347–74. http://dx.doi.org/10.3934/mcrf.2013.3.347.

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Dissertations / Theses on the topic "Lie quadratic"

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Duong, Minh-Thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Phd thesis, Université de Bourgogne, 2011. http://tel.archives-ouvertes.fr/tel-00673991.

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In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7.
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Duong, Minh thanh. "A new invariant of quadratic lie algebras and quadratic lie superalgebras." Thesis, Dijon, 2011. http://www.theses.fr/2011DIJOS021/document.

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Dans cette thèse, nous définissons un nouvel invariant des algèbres de Lie quadratiques et des superalgèbres de Lie quadratiques et donnons une étude et classification complète des algèbres de Lie quadratiques singulières et des superalgèbres de Lie quadratiques singulières, i.e. celles pour lesquelles l’invariant n’est pas nul. La classification est en relation avec les orbites adjointes des algèbres de Lie o(m) et sp(2n). Aussi, nous donnons une caractérisation isomorphe des algèbres de Lie quadratiques 2-nilpotentes et des superalgèbres de Lie quadratiques quasi-singulières pour le but d’exhaustivité. Nous étudions les algèbres de Jordan pseudoeuclidiennes qui sont obtenues des extensions doubles d’un espace vectoriel quadratique par une algèbre d’une dimension et les algèbres de Jordan pseudo-euclidienne 2-nilpotentes, de la même manière que cela a été fait pour les algèbres de Lie quadratiques singulières et des algèbres de Lie quadratiques 2-nilpotentes. Enfin, nous nous concentrons sur le cas d’une algèbre de Novikov symétrique et l’étudions à dimension 7
In this thesis, we defind a new invariant of quadratic Lie algebras and quadratic Lie superalgebras and give a complete study and classification of singular quadratic Lie algebras and singular quadratic Lie superalgebras, i.e. those for which the invariant does not vanish. The classification is related to adjoint orbits of Lie algebras o(m) and sp(2n). Also, we give an isomorphic characterization of 2-step nilpotent quadratic Lie algebras and quasi-singular quadratic Lie superalgebras for the purpose of completeness. We study pseudo-Euclidean Jordan algebras obtained as double extensions of a quadratic vector space by a one-dimensional algebra and 2-step nilpotent pseudo-Euclidean Jordan algebras, in the same manner as it was done for singular quadratic Lie algebras and 2-step nilpotent quadratic Lie algebras. Finally, we focus on the case of a symmetric Novikov algebra and study it up to dimension 7
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Baker, Audrey. "An algorithm for the strong freeness of quadratic lie polynomials /." Thesis, McGill University, 2006. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=100761.

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The Lie algebra associated to the lower central and p-central series of a group is an important invariant of the group but is difficult to compute. For a finitely presented group this Lie algebra, can be determined under a certain condition on the initial forms of the relators, namely that of strong freeness. We give an algorithm for the strong freeness of 4 quadratic Lie polynomials in 4 variables over an arbitrary field thus extending a result of Bush and Labute.
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Hidri, Samiha. "Formes bilinéaires invariantes sur les algèbres de Leibniz et les systèmes triples de Lie (resp. Jordan)." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0237/document.

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Dans cette thèse, on étudie la structure de quelques types d'algèbres (binaires et ternaires) munies d'une forme bilinéaire symétrique, non dégénérée et associative (ou invariante). La première partie de cette thèse est consacrée à l'étude des algèbres de Leibniz quadratiques. On montre que ces algèbres sont symétriques. De plus, on utilise la T*-extension et la double extension pour montrer plusieurs résultats sur ce type d'algèbres. Ensuite, on a remarqué que l'anti-commutativité du crochet de Lie donne naissance à de nouveaux types d'invariance pour les algèbres de Leibniz : L'invariance à gauche et l'invariance à droite. Alors, on s'est intéresse à l'étude des algèbres de Leibniz (gauche et droite) munies d'une forme bilinéaire symétrique, non dégénérée et invariante à gauche (et invariante à droite). On prouve que ces algèbres sont Lie admissibles. En second lieu, on s'intéresse aux systèmes triples de Lie et de Jordan. On débute la deuxième partie de cette thèse par la description inductive des systèmes triples de Lie quadratiques au moyen de la double extension. En plus, on introduit la T*extension des systèmes triples de Jordan pseudo-Euclidien. Finalement, on donne deux nouvelles caractérisations des systèmes triples de Jordan semi-simples parmi les systèmes triples de Jordan pseudo-Euclidiens
In this thesis, we study the stucture of several types of algebras endowed with Symmetric, non degenerate and invariant bilinear forms. In the first part, we study quadratic Leibniz algebras. First, we prove that these algebras are symmetric. Then, we use the T*-extension and the double extension to prove some properties of this type of Leibniz algebras. Besides, since we observe that the skew-symmetry of the Leibniz bracket gives rise to other types of invariance for a bilinear form on a Leibniz algebra: The left invariance and the right invariance. We focus on the study of left (resp. right) Leibniz algebras with symmetric, non degenerate and left (resp. right) invariant bilinear form. In particular, we prove that these algebras are Lie admissibles. The second part of this work is dedicated to the study of quadratic Lie triple systems and pseudo-euclidien Jordan triple systems. We start by giving an inductive description of quadratic Lie triple systems using double extension. Next, we introduce the T*-extension of Jordan triple systems. Finally, we give new caracterizations of semi-simple Jordan triple systems among pseudo-euclidian Jordan triple systems
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Sheriff, Jamin Lebbe. "The Convexity of Quadratic Maps and the Controllability of Coupled Systems." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:11019.

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A quadratic form on \(\mathbb{R}^n\) is a map of the form \(x \mapsto x^T M x\), where M is a symmetric \(n \times n\) matrix. A quadratic map from \(\mathbb{R}^n\) to \(\mathbb{R}^m\) is a map, all m of whose components are quadratic forms. One of the two central questions in this thesis is this: when is the image of a quadratic map \(Q: \mathbb{R}^n \rightarrow \mathbb{R}^m\) a convex subset of \(\mathbb{R}^m\)? This question has intrinsic interest; despite being only a degree removed from linear maps, quadratic maps are not well understood. However, the convexity properties of quadratic maps have practical consequences as well: underlying every semidefinite program is a quadratic map, and the convexity of the image of that map determines the nature of the solutions to the semidefinite program. Quadratic maps that map into \(\mathbb{R}^2\) and \(\mathbb{R}^3\) have been studied before (in (Dines, 1940) and (Calabi, 1964) respectively). The Roundness Theorem, the first of the two principal results in this thesis, is a sufficient and (almost) necessary condition for a quadratic map \(Q: \mathbb{R}^n \rightarrow \mathbb{R}^m\) to have a convex image when \(m \geq 4\), \(n \geq m\) and \(n \not= m + 1\). Concomitant with the Roundness Theorem is an important lemma: when \(n < m\), quadratic maps from \(\mathbb{R}^n\) to \(\mathbb{R}^m\)seldom have convex images. This second result in this thesis is a controllability condition for bilinear systems defined on direct products of the form \(\mathcal{G} \times\mathcal{G}\), where \(\mathcal{G}\) is a simple Lie group. The condition is this: a bilinear system defined on \(\mathcal{G} \times\mathcal{G}\) is not controllable if and only if the Lie algebra generated by the system’s vector fields is the graph of some automorphism of \(\mathcal{g}\), the Lie algebra of \(\mathcal{G}\).
Engineering and Applied Sciences
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Gorodnyk, Oleksandr. "Density and equidistribution of integer points." Connect to this title online, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1054487714.

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Thesis (Ph. D.)--Ohio State University, 2003.
Title from first page of PDF file. Document formatted into pages; contains xi, 231 p.; also includes graphics Includes bibliographical references (p. 224-229). Available online via OhioLINK's ETD Center
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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.
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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Popiel, Tomasz. "Geometrically-defined curves in Riemannian manifolds." University of Western Australia. School of Mathematics and Statistics, 2007. http://theses.library.uwa.edu.au/adt-WU2007.0119.

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[Truncated abstract] This thesis is concerned with geometrically-defined curves that can be used for interpolation in Riemannian or, more generally, semi-Riemannian manifolds. As in much of the existing literature on such curves, emphasis is placed on manifolds which are important in computer graphics and engineering applications, namely the unit 3-sphere S3 and the closely related rotation group SO(3), as well as other Lie groups and spheres of arbitrary dimension. All geometrically-defined curves investigated in the thesis are either higher order variational curves, namely critical points of cost functionals depending on (covariant) derivatives of order greater than 1, or defined by geometrical algorithms, namely generalisations to manifolds of algorithms from the field of computer aided geometric design. Such curves are needed, especially in the aforementioned applications, since interpolation methods based on applying techniques of classical approximation theory in coordinate charts often produce unnatural interpolants. However, mathematical properties of higher order variational curves and curves defined by geometrical algorithms are in need of substantial further investigation: higher order variational curves are solutions of complicated nonlinear differential equations whose properties are not well-understood; it is usually unclear how to impose endpoint derivative conditions on, or smoothly piece together, curves defined by geometrical algorithms. This thesis addresses these difficulties for several classes of curves. ... The geometrical algorithms investigated in this thesis are generalisations of the de Casteljau and Cox-de Boor algorithms, which define, respectively, polynomial B'ezier and piecewise-polynomial B-spline curves by dividing, in certain ratios and for a finite number of iterations, piecewise-linear control polygons corresponding to finite sequences of control points. We show how the control points of curves produced by the generalised de Casteljau algorithm in an (almost) arbitrary connected finite-dimensional Riemannian manifold M should be chosen in order to impose desired endpoint velocities and (covariant) accelerations and, thereby, piece the curves together in a C2 fashion. A special case of the latter construction simplifies when M is a symmetric space. For the generalised Cox-de Boor algorithm, we analyse in detail the failure of a fundamental property of B-spline curves, namely C2 continuity at (certain) knots, to carry over to M.
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Feneuil, Joseph. "Analyse harmonique sur les graphes et les groupes de Lie : fonctionnelles quadratiques, transformées de Riesz et espaces de Besov." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAM040/document.

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Ce mémoire est consacré à des résultats d'analyse harmonique réelle dans des cadres géométriques discrets (graphes) ou continus (groupes de Lie).Soit $\Gamma$ un graphe (ensemble de sommets et d'arêtes) muni d'un laplacien discret $\Delta=I-P$, où $P$ est un opérateur de Markov.Sous des hypothèses géométriques convenables sur $\Gamma$, nous montrons la continuité $L^p$ de fonctionnelles de Littlewood-Paley fractionnaires. Nous introduisons des espaces de Hardy $H^1$ de fonctions et de $1$-formes différentielles sur $\Gamma$, dont nous donnons plusieurs caractérisations, en supposant seulement la propriété de doublement pour le volume des boules de $\Gamma$. Nous en déduisons la continuité de la transformée de Riesz sur $H^1$. En supposant de plus des estimations supérieures ponctuelles (gaussiennes ou sous-gaussiennes) sur les itérées du noyau de l'opérateur $P$, nous obtenons aussi la continuité de la transformée de Riesz sur $L^p$ pour $10$, $1\leq p\leq+\infty$ et $1\leq q\leq +\infty$. Les résultats sont valables en croissance polynomiale ou exponentielle du volume des boules
This thesis is devoted to results in real harmonic analysis in discrete (graphs) or continuous (Lie groups) geometric contexts.Let $\Gamma$ be a graph (a set of vertices and edges) equipped with a discrete laplacian $\Delta=I-P$, where $P$ is a Markov operator.Under suitable geometric assumptions on $\Gamma$, we show the $L^p$ boundedness of fractional Littlewood-Paley functionals. We introduce $H^1$ Hardy spaces of functions and of $1$-differential forms on $\Gamma$, giving several characterizations of these spaces, only assuming the doubling property for the volumes of balls in $\Gamma$. As a consequence, we derive the $H^1$ boundedness of the Riesz transform. Assuming furthermore pointwise upper bounds for the kernel (Gaussian of subgaussian upper bounds) on the iterates of the kernel of $P$, we also establish the $L^p$ boundedness of the Riesz transform for $10$, $1\leq p\leq+\infty$ and $1\leq q\leq +\infty$.These results hold for polynomial as well as for exponential volume growth of balls
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Araújo, Leonardo Rodrigues de. "Congruências quadráticas, reciprocidade e aplicações em sala de aula." Universidade Federal da Paraíba, 2013. http://tede.biblioteca.ufpb.br:8080/handle/tede/7480.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this study, we evaluate if the congruence x2 a (mod m), where m is prime and (a;m) = 1, has or not solutions, highlighting the importance of Quadratic Residues and consequently the cooperation of the Legendre's Symbol, the Euler's Criterion and the Gauss' Lemma. Also, we demonstrate the Law of Quadratic Reciprocity generalizing situations for composite numbers, that is, the Jacobi's Symbol and its properties. We present some proposals of activities for the High School involving the subject matter and its possible applications, through an understandable language for students of this level.
Neste estudo, vamos avaliar se a congruência x2 a (mod m), onde m é primo e (a;m) = 1, apresenta ou não solução, destacando a importância dos Resíduos Quadráticos e, consequentemente da cooperação do Símbolo de Legendre, do Critério de Euler e do Lema de Gauss. Também, demonstraremos a Lei de Reciprocidade Quadrática generalizando situações para números compostos, ou seja, o Símbolo de Jacobi e suas propriedades. Apresentamos algumas propostas de atividades para o Ensino Médio envolvendo o assunto abordado e suas possíveis aplicações, através de uma linguagem compreensível aos alunos deste nível de ensino.
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Books on the topic "Lie quadratic"

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Strade, Helmut, Thomas Weigel, Marina Avitabile, and Jörg Feldvoss. Lie algebras and related topics: Workshop in honor of Helmut Strade's 70th birthday : lie algebras, May 22-24, 2013, Università degli studi di Milano-Bicocca, Milano, Italy. Providence, Rhode Island: American Mathematical Society, 2015.

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1932-, Bass Hyman, and Lam, T. Y. (Tsit-Yuen), 1942-, eds. Algebra. Providence, R.I: American Mathematical Society, 2010.

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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. Providence, Rhode Island: American Mathematical Society, 2014.

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Csárdás im Quadrat: Ungarische Avantgarde (1919-1930) und traditionelle Bauernkultur. Mainz: H. Schmidt, 1995.

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Book chapters on the topic "Lie quadratic"

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Ammar, Faouzi, Imen Ayadi, Sami Mabrouk, and Abdenacer Makhlouf. "Quadratic Color Hom-Lie Algebras." In Associative and Non-Associative Algebras and Applications, 287–312. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-35256-1_16.

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Donin, J. "On The Quantization of Quadratic Poisson Brackets on a Polynomial Algebra of Four Variables." In Lie Groups and Lie Algebras, 17–25. Dordrecht: Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5258-7_2.

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Benayadi, Saïd. "Construction of Symplectic Quadratic Lie Algebras from Poisson Algebras." In Springer Proceedings in Mathematics & Statistics, 111–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-642-55361-5_8.

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Seligman, George B. "Construction of exceptional algebras from quadratic forms." In Constructions of Lie Algebras and their Modules, 52–83. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079300.

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Seligman, George B. "Representations of exceptional algebras constructed from quadratic forms." In Constructions of Lie Algebras and their Modules, 84–114. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0079301.

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Baklouti, Amir, and Samiha Hidri. "Inductive Description of Quadratic Lie and Pseudo-Euclidean Jordan Triple Systems." In Forum for Interdisciplinary Mathematics, 65–93. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8498-5_4.

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Somberg, Petr. "Deformations of Quadratic Algebras, the Joseph Ideal for Classical Lie Algebras, and Special Tensors." In Symmetries and Overdetermined Systems of Partial Differential Equations, 527–36. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-73831-4_28.

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Bajja, Salwa, Khalifa Es-Sebaiy, and Lauri Viitasaari. "Limit Theorems for Quadratic Variations of the Lei–Nualart Process." In Stochastic Processes and Applications, 105–21. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-02825-1_5.

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Pollard, David. "Another Look at Differentiability in Quadratic Mean." In Festschrift for Lucien Le Cam, 305–14. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1880-7_19.

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Goswami, Kundan, Sonjoy Das, and Biswa Nath Datta. "Robust Control of Stochastic Structures Using Minimum Norm Quadratic Partial Eigenvalue Assignment Technique." In Mathematical and Statistical Applications in Life Sciences and Engineering, 43–69. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5370-2_2.

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Conference papers on the topic "Lie quadratic"

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Yanovski, Alexandar B., and Moses C. dos Santos. "Quadratic Casimir Invariants for “Universal” Lie Algebra Extensions." In INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES, INTEGRABILITY AND VECTOR FIELDS. AIP, 2011. http://dx.doi.org/10.1063/1.3567135.

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Pesheck, E., and C. Pierre. "A Global Methodology for the Modal Reduction of Large Nonlinear Systems Containing Quadratic and Cubic Nonlinearities." In ASME 1997 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1997. http://dx.doi.org/10.1115/detc97/vib-3952.

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Abstract A methodology is presented for the systematic modal reduction of structural systems which contain quadratic and cubic nonlinearities in displacement. The procedure is based on the center manifold approach for describing individual nonlinear modes, but it has been extended to account for simultaneous motion within several chosen modal coordinates. Motions of the reduced system are constrained to lie on high-dimensional manifolds within the phase space of the original system. Polynomial approximations of these manifolds are obtained through third order for arbitrary system parameters. Algorithms have been developed for automation of this procedure, and they are applied to an example system. Free and forced responses of the reduced system are discussed and compared to responses reduced through simple modal truncation. A more rigorous treatment of harmonic forcing is proposed, which will allow for the production of high-dimensional, time-dependent manifolds through a simple adaptation of the unforced procedure.
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Wu, Liheng, Andreas Müller, and Jian S. Dai. "Matrix Analysis of Second-Order Kinematic Constraints of Single-Loop Linkages in Screw Coordinates." In ASME 2018 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/detc2018-85433.

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Higher order loop constraints play a key role in the local mobility, singularity and dynamic analysis of closed loop linkages. Recently, closed forms of higher order kinematic constraints have been achieved with nested Lie product in screw coordinates, and are purely algebraic operations. However, the complexity of expressions makes the higher order analysis complicated and highly reliant on computer implementations. In this paper matrix expressions of first and second-order kinematic constraints, i.e. involving the Jacobian and Hessian matrix, are formulated explicitly for single-loop linkages in terms of screw coordinates. For overconstrained linkages, which possess self-stress, the first- and second-order constraints are reduced to a set of quadratic forms. The test for the order of mobility relies on solutions of higher order constraints. Second-order mobility analysis boils down to testing the property of coefficient matrix of the quadratic forms (i.e. the Hessian) rather than to solving them. Thus, the second-order analysis is simplified.
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Wampler, Charles W. "Locating N Points of a Rigid Body on N Given Planes." In ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2004. http://dx.doi.org/10.1115/detc2004-57182.

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This paper describes a method for finding the location of a rigid body such that N specified points of the body lie on N given planes in space. Of special interest is the case N = 6, which is the minimum number to fully constrain the body. This geometric problem arises in two seemingly disparate contexts: metrology, as a generalization of so-called “3-2-1” locating schemes; and robotics, as the forward kinematics problem for 6ES or 6SE parallel-link platform robots. For N = 6, the geometric problem can be formulated algebraically as 3 quadratic equations having, in general, eight possible solutions. We give a method for finding all eight solutions via an 8 × 8 eigenvalue problem. We also show that for N ≥ 7, the solution can be found uniquely as a linear least squares problem.
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Müller, Andreas, Zdravko Terze, and Viktor Pandza. "A Non-Redundant Formulation for the Dynamics Simulation of Multibody Systems in Terms of Unit Dual Quaternions." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-60191.

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Quaternions are favorable parameters to describe spatial rotations of rigid bodies since they give rise to simple equations governing the kinematics and attitude dynamics in terms of simple algebraic equations. Dual quaternions are the natural extension to rigid body motions. They provide a singularity-free purely algebraic parameterization of rigid body motions, and thus serve as global parameters within the so-called absolute coordinate formulation of MBS. This attractive feature is owed to the inherent redundancy of these parameters since they must satisfy two quadratic conditions (unit condition and Plcker condition). Formulating the MBS kinematics in terms of dual quaternions leads to a system of differential-algebraic equations (DAE) with index 3. This is commonly transformed to an index 1 DAE system by replacing the algebraic constraints with their time derivative. This leads to the well-known problem of constraint violation. A brute force method, enforcing the unit constraint of quaternions, is to normalize them after each integration step. Clearly this correction affects the overall solution and the dynamic consistency. Moreover, for unit dual quaternions the two conditions cannot simply be enforced in such a way. In this paper a non-redundant formulation of the motion equations in terms of dual quaternions is presented. The dual quaternion constraints are avoided by introducing a local canonical parameterization. The key to this formulation is to treat dual unit quaternions as Lie group. The formulation can be solved with any standard integration scheme. Examples are reported displaying the excellent performance of this formulation regarding the constraint satisfaction as well as the solution accuracy.
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Yuan, Chengzhi, Fen Wu, and Chang Duan. "Robust Gain-Scheduling Output Feedback Control of State-Delayed LFT Systems Using Dynamic IQCs." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9686.

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This paper is concerned with the robust gain-scheduling output feedback control problem for a class of linear parameter-varying systems with time-varying state delay. The controlled plant under consideration is described as a linear fractional transformation (LFT) model of scheduling parameters. Dynamic integral quadratics (IQCs) are employed to characterize the input-output behavior of the state-delay nonlinearity. The robust stability and the L2-gain performance are first analyzed using quadratic Lyapunov function. Then, the design of dynamic output-feedback controllers robust against the plant state-delay nonlinearity and gain-scheduled by parameters is examined. The synthesis conditions of such robust gain-scheduling controllers are formulated in terms of linear matrix inequalities (LMIs) plus a line search, which can be solved effectively using existing algorithms. A numerical example has been used to demonstrate the effectiveness and advantages of the proposed approach.
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Zinflou, Arnaud, Caroline Gagné, and Marc Gravel. "A hybrid genetic/immune strategy to tackle the multiobjective quadratic assignment problem." In European Conference on Artificial Life 2013. MIT Press, 2013. http://dx.doi.org/10.7551/978-0-262-31709-2-ch139.

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FUHRMAN, MARCO, YING HU, and GIANMARIO TESSITORE. "STOCHASTIC CONTROL AND BSDES WITH QUADRATIC GROWTH." In Control Theory and Related Topics - In Memory of Professor Xunjing Li. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812790552_0007.

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Yayun Wan, Rachana Visaria, John C. Bischof, and Emad S. Ebbini. "Quadratic B-mode and pulse inversion imaging of perfusion defects in vivo." In 2007 IEEE/NIH Life Science Systems and Applications Workshop. IEEE, 2007. http://dx.doi.org/10.1109/lssa.2007.4400928.

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XU, YASHAN. "A LINEAR QUADRATIC CONSTRAINED OPTIMAL FEEDBACK CONTROL PROBLEM." In Control Theory and Related Topics - In Memory of Professor Xunjing Li. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812790552_0016.

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