Relevant bibliographies by topics / Lie transformation groups

Contents

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

Academic literature on the topic 'Lie transformation groups'

Author: Grafiati
Published: 10 March 2023

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Journal articles on the topic "Lie transformation groups"

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Miao, Xu, and Rajesh P. N. Rao. "Learning the Lie Groups of Visual Invariance." Neural Computation 19, no. 10 (October 2007): 2665–93. http://dx.doi.org/10.1162/neco.2007.19.10.2665.

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A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.
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Al-Shomrani, M. M. "Lie Groups Analysis and Contact Transformations for Ito System." Abstract and Applied Analysis 2012 (2012): 1–12. http://dx.doi.org/10.1155/2012/342680.

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Generalized Ito systems of four coupled nonlinear evaluation equations are proposed. New classes of exact invariant solutions by using Lie group analysis are obtained. Moreover, we investigate the existence of a one-parameter group of contact transformations for a generalized Ito system. Consequently, we study the relationship between one-parameter group of a contact transformation and a one-parameter Lie point transformation for a generalized Ito system.
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FIGUEROA-O’FARRILL, JOSÉ M., and SONIA STANCIU. "POISSON LIE GROUPS AND THE MIURA TRANSFORMATION." Modern Physics Letters A 10, no. 36 (November 30, 1995): 2767–73. http://dx.doi.org/10.1142/s0217732395002908.

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We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Poisson Lie property of the second Gel’fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also proved along the same lines.
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Cariñena, Jose F., Mariano A. Del Olmo, and Mariano Santander. "Locally operating realizations of transformation Lie groups." Journal of Mathematical Physics 26, no. 9 (September 1985): 2096–106. http://dx.doi.org/10.1063/1.526974.

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Lin, Feng, Haohang Xu, Houqiang Li, Hongkai Xiong, and Guo-Jun Qi. "Auto-Encoding Transformations in Reparameterized Lie Groups for Unsupervised Learning." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 10 (May 18, 2021): 8610–17. http://dx.doi.org/10.1609/aaai.v35i10.17044.

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Unsupervised training of deep representations has demonstrated remarkable potentials in mitigating the prohibitive expenses on annotating labeled data recently. Among them is predicting transformations as a pretext task to self-train representations, which has shown great potentials for unsupervised learning. However, existing approaches in this category learn representations by either treating a discrete set of transformations as separate classes, or using the Euclidean distance as the metric to minimize the errors between transformations. None of them has been dedicated to revealing the vital role of the geometry of transformation groups in learning representations. Indeed, an image must continuously transform along the curved manifold of a transformation group rather than through a straight line in the forbidden ambient Euclidean space. This suggests the use of geodesic distance to minimize the errors between the estimated and groundtruth transformations. Particularly, we focus on homographies, a general group of planar transformations containing the Euclidean, similarity and affine transformations as its special cases. To avoid an explicit computing of intractable Riemannian logarithm, we project homographies onto an alternative group of rotation transformations SR(3) with a tractable form of geodesic distance. Experiments demonstrate the proposed approach to Auto-Encoding Transformations exhibits superior performances on a variety of recognition problems.
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García‐Prada, Oscar, Mariano A. del Olmo, and Mariano Santander. "Locally operating realizations of nonconnected transformation Lie groups." Journal of Mathematical Physics 29, no. 5 (May 1988): 1083–90. http://dx.doi.org/10.1063/1.527946.

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Nesterenko, Maryna O. "Transformation groups on real plane and their differential invariants." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–17. http://dx.doi.org/10.1155/ijmms/2006/17410.

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Complete sets of bases of differential invariants, operators of invariant differentiation, and Lie determinants of continuous transformation groups acting on the real plane are constructed. As a necessary preliminary, realizations of finite-dimensional Lie algebras on the real plane are revisited.
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Nikonov, V. I. "The application of Lie algebras and groups to the solution of problems of partial stability of dynamical systems." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 3 (September 6, 2018): 295–303. http://dx.doi.org/10.15507/2079-6900.20.201802.295-303.

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The article is devoted to the analysis of partial stability of nonlinear systems of ordinary differential equations using Lie algebras and groups. It is shown that the existence of a group of transformations invariant under partial stability in the system under study makes it possible to simplify the analysis of the partial stability of the initial system. For this it is necessary that the associated linear differential operator Lie in the enveloping Lie algebra of the original system, and the operator defined by the one-parameter Lie group is commutative with this operator. In this case, if the found group has invariance with respect to partial stability, then the resulting transformation performs to the decomposition of the system under study, and the partial stability problem reduces to the investigation of the selected subsystem. Finding the desired transformation uses the first integrals of the original system. Examples illustrating the proposed approach are given.
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Nikonov, Vladimir I. "The application of Lie algebras and groups to the solution of problems of partial stability of dynamical systems." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 20, no. 3 (September 6, 2018): 295–303. http://dx.doi.org/10.15507/2079-6900.20.201803.295-303.

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The article is devoted to the analysis of partial stability of nonlinear systems of ordinary differential equations using Lie algebras and groups. It is shown that the existence of a group of transformations invariant under partial stability in the system under study makes it possible to simplify the analysis of the partial stability of the initial system. For this it is necessary that the associated linear differential operator Lie in the enveloping Lie algebra of the original system, and the operator defined by the one-parameter Lie group is commutative with this operator. In this case, if the found group has invariance with respect to partial stability, then the resulting transformation performs to the decomposition of the system under study, and the partial stability problem reduces to the investigation of the selected subsystem. Finding the desired transformation uses the first integrals of the original system. Examples illustrating the proposed approach are given.
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Russell, Thomas. "Gorman demand systems and lie transformation groups: A reply." Economics Letters 51, no. 2 (May 1996): 201–4. http://dx.doi.org/10.1016/0165-1765(96)00806-3.

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Dissertations / Theses on the topic "Lie transformation groups"

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Günther, Janne-Kathrin. "The C*-algebras of certain Lie groups." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0118/document.

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Dans la présente thèse de doctorat, les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et du groupe de Lie SL(2,R) sont caractérisées. En outre, comme préparation à une analyse de sa C*-algèbre, la topologie du spectre du produit semi-direct U(n) x H_n est décrite, où H_n dénote le groupe de Lie de Heisenberg et U(n) le groupe unitaire qui agit sur H_n par automorphismes. Pour la détermination des C*-algèbres de groupes, la transformation de Fourier à valeurs opérationnelles est utilisée pour appliquer chaque C*-algèbre dans l'algèbre de tous les champs d'opérateurs bornés sur son spectre. On doit trouver les conditions que satisfait l'image de cette C*-algèbre sous la transformation de Fourier et l'objectif est de la caractériser par ces conditions. Dans cette thèse, il est démontré que les C*-algèbres des groupes de Lie connexes réels nilpotents de pas deux et la C*-algèbre de SL(2,R) satisfont les mêmes conditions, des conditions appelées «limites duales sous contrôle normique». De cette manière, ces C*-algèbres sont décrites dans ce travail et les conditions «limites duales sous contrôle normique» sont explicitement calculées dans les deux cas. Les méthodes utilisées pour les groupes de Lie nilpotents de pas deux et pour le groupe SL(2,R) sont très différentes l'une de l'autre. Pour les groupes de Lie nilpotents de pas deux, on regarde leurs orbites coadjointes et on utilise la théorie de Kirillov, alors que pour le groupe SL(2,R), on peut mener les calculs plus directement
In this doctoral thesis, the C*-algebras of the connected real two-step nilpotent Lie groups and the Lie group SL(2,R) are characterized. Furthermore, as a preparation for an analysis of its C*-algebra, the topology of the spectrum of the semidirect product U(n) x H_n is described, where H_n denotes the Heisenberg Lie group and U(n) the unitary group acting by automorphisms on H_n. For the determination of the group C*-algebras, the operator valued Fourier transform is used in order to map the respective C*-algebra into the algebra of all bounded operator fields over its spectrum. One has to find the conditions that are satisfied by the image of this C*-algebra under the Fourier transform and the aim is to characterize it through these conditions. In the present thesis, it is proved that both the C*-algebras of the connected real two-step nilpotent Lie groups and the C*-algebra of SL(2,R) fulfill the same conditions, namely the “norm controlled dual limit” conditions. Thereby, these C*-algebras are described in this work and the “norm controlled dual limit” conditions are explicitly computed in both cases. The methods used for the two-step nilpotent Lie groups and the group SL(2,R) are completely different from each other. For the two-step nilpotent Lie groups, one regards their coadjoint orbits and uses the Kirillov theory, while for the group SL(2,R) one can accomplish the calculations more directly
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Ramgulam, Usha. "Lie groups and Bäcklund transformations : application to nonlinear physical models." Thesis, Loughborough University, 1991. https://dspace.lboro.ac.uk/2134/26895.

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A diversity of physical phenomena is modelled by systems of nonlinear differential equations not, in general, amenable to exact solution. However, in certain cases, exploitation of hidden symmetries in the nonlinear models can lead to solutions and reduction to canonical systems. Invariance under Lie groups and/or Bäcklund transformations are two pivotal methods in this regard.
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Zahir, Hamid. "Produits STAR et représentation des groupes de Lie." Metz, 1991. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1991/Zahir.Hamid.SMZ9116.pdf.

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La description des représentations des groupes de Lie est possible par une quantification par déformation des orbites de la représentation coadjointe. Ceci permet de définir une transformation de Fourier adaptée. Nous avons montré la grande régularité de cette transformation et établi des généralisations de propriétés importantes du cas abélien au cas nilpotent. Nous avons unifié deux théories de déformations de natures différentes sur des espaces hermitiens compacts en construisant sur ceux-ci un produit déformé de moyal grâce à la symétrie géodésique. Enfin nous avons réalisé la fibre cotangente sur un groupe compact comme une orbite de la représentation coadjointe d'un groupe plus gros, ce qui nous a permis de décrire la représentation régulière en quantifiant celle-ci par déformation
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Mizony, Michel. "Semi-groupes de Lie et fonctions de Jacobi de deuxième espèce." Lyon 1, 1987. http://www.theses.fr/1987LYO19015.

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Cette these a pour but essentiel d'interpreter des formules de produit de fonctions speciales de deuxieme espece et les transformations integrales du type laplace qui leur sont associees, sur des sous-semi-groupes ouverts de groupe de lie. Cette interpretation permet de donner une demonstration simple des formules de produit de ces fonctions en les realisant comme moyenne d'un noyau de poisson qui permet, en outre, de construire des representations hilbertiennes de ces semi-groupes de lie. En particulier, les fonctions de legendre de deuxieme espece sont liees a un sous-semi-groupe ouvert du groupe de lorentz so::(o)(l,n), les fonctions de hankel sont associees aux semi-groupes de poincare, les fonctions de jacobi de deuxieme espece sont liees a un sous-semi-groupe ouvert du groupe sl(3,r). Au passage comme certains sous-semi-groupes ouverts etudies s'interpretent comme semi-groupes de causalite d'invariants cinematiques, nous proposons alors une modification au formalisme hilbertien de la mecanique quantique
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Zahir, Hamid Arnal Didier. "Produits star et représentation des groupes de lie." [S.l.] : [s.n.], 1991. ftp://ftp.scd.univ-metz.fr/pub/Theses/1991/Zahir.Hamid.SMZ9116.pdf.

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Cogliati, A. "CONTINUOUS GROUPS OF TRANSFORMATIONS: ELIE CARTAN'S STRUCTURAL APPROACH." Doctoral thesis, Università degli Studi di Milano, 2012. http://hdl.handle.net/2434/214787.

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The thesis deals with E. Cartan's contributions to the theory of continuous groups of transformations from the early 1890's up to the early 1910's. The analysis is focused on both finite and infinite continuous groups. First, Cartan's doctoral dissertation, in which he provided a rigorous classification of what nowadays we would call simple complex Lie algebras, is taken in. A detailed survey of the theory of infinite continuous groups as developed by Sophus Lie, Friedrich Engel, Paolo Medolaghi and Ernst Vessiot follows. The second part of the dissertation concentrates upon Cartan's contributions to the subject. The analysis of the relevant works is preceded by a historical study of the genesis of Cartan's integration theory of general Pfaffian systems (nowadays known as Cartan-Kaehler theory), in which, for the first time, due attention to the work of the German mathematician Eduard Ritter von Weber is paid. Special emphasis is put on the structural aspects of Cartan's highly innovative approach. At the same time, the role played by group theory in the development of 20th century differential geometry is underlined in respect to Cartan's method of moving frames.
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Dhieb, Semi. "Transformée de Fourier adaptée et convoluteurs de Schwartz sur les groupes de Lie nilpotents." Metz, 1995. http://docnum.univ-lorraine.fr/public/UPV-M/Theses/1995/Dhieb.Semi.SMZ9510.pdf.

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La transformée de Fourier adaptée sur les groupes de Lie nilpotents introduite par D. Arnal et J. C. Cortet, sous le nom de la transformation de Fourier nilpotente constitue une généralisation de la transformée de Fourier abélienne usuelle. Cette définition été limitée aux orbites du groupe sous l'action coadjointe. Nous définissons dans cette thèse de nouvelles transformées de Fourier adaptées sur l'espace dual de l'algèbre de Lie et sur le produit de cet espace dual par l'ensemble des bases de Malcev de l'algèbre de Lie. Ensuite, nous donnons une approche de la démonstration de la conjecture de Howe caractérisant les convoluteurs centraux pour l'espace de Schwartz d'un groupe de Lie nilpotent. Une telle caractérisation est donnée comme suit: une distribution tempérée sur un groupe de Lie nilpotent est un convoluteur central si et seulement si sa transformée de Fourier au sens de distributions est une fonction sur le dual de l'algèbre de Lie, ad*-invariante, infiniment différentiable et à croissance modérée ainsi que toutes ses dérivées. Nous définissons enfin les convoluteurs centraux pour les groupes de Lie variables et nous en donnons une caractérisation analogue à celle citée plus haut
The adapted Fourier transform, so-called nilpotent Fourier transform, was first introduced by D. Arnal and J. C. Cortet as a generalisation of the usual abelian Fourier transform. This definition was limited at the orbits of the group under the coadjont action. We define in this thesis new adapted Fourier transforms on the dual of the Lie algebra and the product of this dual space with the set of all Malcev bases. Then, we study Schwartz multipliers for nilpotent Lie groups and we give an idea to prove Howe conjecture that characterizes the bi-invariant Schwartz multipliers on nilpotent Lie groups. Such characterization is given as the following : a tempered distribution on a nilpotent group Lie is a bi-invariant Schwartz multiplier if and only if its Fourier transform as a distribution is a smooth, Ad*-invariant function on the dual of the Lie algebra and all of its derivatives have polynomial bounds. Finally, we define Schwartz multipliers for variable nilpotent Lie groups and we characterize them as a bove
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Garimella, Venkatalakshmi Gayatri. "Théorèmes de Paley-Wiener - opérateurs differentiels invariants sur les groupes de Lie nilpotents." Poitiers, 1997. http://www.theses.fr/1997POIT2277.

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Soient une fonction mesurable sur r#n, et sa transformee de fourier. Une caracterisation de la transformee de fourier de est donnee par le theoreme de paley-wiener pour r#n. Une version faible de ce theoreme dit que si la fonction est mesurable, bornee et a support compact, sa transformee de fourier se prolonge en une fonction holomorphe sur c#n, ce qui permet de conclure que = 0 si est nulle sur un ensemble dont la mesure de plancherel est strictement positive. On generalise cette version du theoreme de paley-wiener aux groupes de lie nilpotents simplement connexes. Cette propriete est conjecturee par d. Scott et a. Sitaram. On demontre cette conjecture par recurrence sur la dimension de g. Dans le chapitre ii on generalise la propriete ci-dessus aux groupes de lie completement resolubles. La demonstration, egalement par recurrence sur la dimension de g, utilise la mesure de plancherel explicite donnee par b. N. Currey. Dans le chapitre iii on etudie des operateurs differentiels sur un espace homogene nilpotent. Soit = ind#g#k#f une representation induite d'un groupe de lie nilpotent connexe et simplement connexe g, ou #f designe un caractere unitaire d'un sous-groupe connexe k = (exp t) et tel que les multiplicites des irreductibles de g apparaissant dans la decomposition de soient finies. Soit d# l'algebre des operateurs differentiels associee a. On demontre que cette algebre est isomorphe a l'algebre des fonctions polynomiales k-invariantes definies sur o# = f + t# g#*, lorsque t est un ideal de g, algebre de lie de g.
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Maillard, Jean-Marie. "Intégrabilité, série discrète des groupes de Lorentz et transformation de Weyl des distributions tempérées." Dijon, 1986. http://www.theses.fr/1986DIJOS025.

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Lanzmann, Emmanuel. "Le théorème d'annulation dans le cadre des super-algèbres de lie complètement réductibles et de leurs groupes quantiques." Paris 6, 2000. http://www.theses.fr/2000PA066260.

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Books on the topic "Lie transformation groups"

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L, Onishchik A., and Vinberg Ė B, eds. Foundations of Lie theory and Lie transformation groups. Berlin: Springer, 1997.

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Transformation groups. Berlin: W. de Gruyter, 1987.

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Straume, Eldar. Compact connected Lie transformation groups on spheres with low cohomogeneity, II. Providence, R.I: American Mathematical Society, 1997.

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Onishchik, A. L. Topology of transitive transformation groups. Leipzig: Johann Ambrosius Barth, 1994.

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Anthony, Bak, Morimoto Masaharu, and Ushitaki Fumihiro, eds. Current trends in transformation groups. Dordrecht: Kluwer, 2002.

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Compact connected lie transformation groups on spheres with low cohomogeneity, I. Providence, R.I: American Mathematical Society, 1996.

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Sophus Lie and Felix Klein: The Erlangen program and its impact in mathematics and physics. Providence: European Mathematical Society, 2015.

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Bilinear control systems: Matrices in action. Dordrecht: Springer, 2009.

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B, Carrell James, and McGovern William M. 1959-, eds. Algebraic quotients: Torus actions and cohomology / J.B. Carrell. The adjoint representation and the adjoint action / W.M. McGovern. Berlin: Springer, 2002.

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Dynamical systems and group actions. Providence, R.I: American Mathematical Society, 2012.

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Book chapters on the topic "Lie transformation groups"

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Barndorff-Nielsen, Ole E., Preben Blæsild, and Poul Svante Eriksen. "Matrix Lie groups." In Decomposition and Invariance of Measures, and Statistical Transformation Models, 15–27. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-3682-5_3.

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Kawakubo, Katsuo. "G-s-cobordism theorems do not hold in general for many compact lie groups G." In Transformation Groups, 183–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085608.

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Hsiang, Wu-Yi. "Lie transformation groups and differential geometry." In Lecture Notes in Mathematics, 34–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0077679.

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Helgason, Sigurdur. "Lie Transformation Groups and Differential Operators." In Integral Geometry and Radon Transforms, 253–63. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6055-9_8.

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Illman, Sören. "The isomorphism class of a representation of a compact lie group is determined by the equivariant simple-homotopy type of the representation." In Transformation Groups, 98–110. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0085602.

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Ibragimov, Nail H. "Equations with Infinite Lie-Bäcklund Groups." In Transformation Groups Applied to Mathematical Physics, 253–313. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5243-0_5.

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Lie, Sophus. "Three Principles of Thought Governing the Theory of Lie." In Theory of Transformation Groups I, 3–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2015. http://dx.doi.org/10.1007/978-3-662-46211-9_1.

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Ibragimov, Nail H. "Introduction to the Theory of Lie-Bäcklund Groups." In Transformation Groups Applied to Mathematical Physics, 190–252. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-009-5243-0_4.

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Hawkins, Thomas. "Lie’s Theory of Transformation Groups: 1874–1893." In Emergence of the Theory of Lie Groups, 75–99. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1202-7_3.

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Alekseevskij, D. V., V. V. Lychagin, and A. M. Vinogradov. "The Group Approach of Lie and Klein. The Geometry of Transformation Groups." In Geometry I, 92–113. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-02712-7_4.

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Conference papers on the topic "Lie transformation groups"

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Tarama, Daisuke, and Jean-Pierre Françoise. "Dynamical Systems over Lie Groups Associated with Statistical Transformation Models." In MaxEnt 2022. Basel Switzerland: MDPI, 2022. http://dx.doi.org/10.3390/psf2022005021.

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Wang, Ching Ming, Jascha Shol-Dickstein, Ivana Tosic, and Bruno A. Olshausen. "Lie Group Transformation Models for Predictive Video Coding." In 2011 Data Compression Conference (DCC). IEEE, 2011. http://dx.doi.org/10.1109/dcc.2011.93.

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Gaur, Manoj, and K. Singh. "Lie group of transformations for time fractional Gardner equation." In DIDACTIC TRANSFER OF PHYSICS KNOWLEDGE THROUGH DISTANCE EDUCATION: DIDFYZ 2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0080583.

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Bru¨ls, Olivier, Martin Arnold, and Alberto Cardona. "Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48132.

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This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R3 (the Euclidean space) and the group of rotations SO(3) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3) offers the advantage of an almost constant iteration matrix.
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Murakami, Hidenori. "A Moving Frame Method for Multi-Body Dynamics Using SE(3)." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51192.

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To describe the configuration of a multi-body system, Cartesian coordinate systems are attached to all bodies comprising the system. Their connections through joints and force elements are efficiently expressed by using 4×4 matrices of the homogeneous transformation, presented by Denavit and Hartenberg in 1955. However, at this time, there is no systematic method to compute velocities and angular velocities using the matrices of such homogeneous transformations. In this paper, homogeneous transformation matrices are identified as a subset of a Lie group, called the special Euclidean group denoted by SE(3). This observation enables the usage of the Lie group theory in multibody kinematics. The effective use of the theory is built upon a platform of a moving frame method as presented in this paper. In this method, for each body-attached Cartesian coordinate system, the coordinate vector basis is written explicitly following Élie Cartan. This moving frame notation enables us to use the Lie algebra of SE(3), denoted by se(3), to compute velocities and angular velocities by minimizing the complexities of the Lie group theory. For kinetics, a variational method is established in se(3) by deriving a relationship between a virtual angular velocities and the corresponding virtual rotational displacements. This constrained variation of virtual angular velocities allows the derivation of the d’Alembert principle of virtual work from Hamilton’s principle for multibody systems. Utilizing this variational tool, we present a systematic computation of equations of motion from Hamilton’s principle. Finally, we reduce the spatial dynamics to planar dynamics and list the simplifications achieved in the two-dimensional problems using SE(2). Then, for a two-degree-of-freedom manipulator the analytical equations of motion are obtained to demonstrate the power of the moving frame method.
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Chiao, Raymond Y., Paul G. Kwiat, William A. Vareka, and Thomas F. Jordan. "Lorentz-group Berry phases in squeezed light." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oam.1988.mr17.

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The Berry phases most often observed in experiments are produced by rotations. Berry phases produced by Lorentz transformations are almost as simple mathematically. They have been discussed at length, but there has been no suggestion of observing them in an experiment. Indeed, it has been shown that in one context they can be removed by a canonical transformation; thus they appear to be a property of the mathematical description that could not be observed physically. Here we show that the essential element of these Berry phases could be observed as a change of phase of the electromagnetic field in squeezed states of light or microwaves, as could be produced by degenerate parametric amplifiers. It could be seen as a fringe shift in interference experiments. In this way, a physical effect of the squeezing could be measured without measuring anything like photon statistics or noise.
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Djanelidze, M. G. "Territory Attractiveness for Human Capital and Innovative Development." In Problems of transformation and regulation of regional socio- economic systems. Saint Petersburg State University of Aerospace Instrumentation, 2021. http://dx.doi.org/10.52897/978-5-8088-1635-0-2021-49-25-37.

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The article offers an approach to the analysis of the problems and potential of innovative development of territories from the standpoint of the formation of conditions for their attractiveness for human capital. The groups of these conditions are determined by the state of the regional economy, the quality of life in this regions, the employment opportunities of professional groups, as well as the development of human capital provided by the infrastructure potential of the territory.
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Pecherskaya, Nadezhda. "MENTAL COHESION AS A FACTOR OF POLITICAL CULTURE." In Globalistics-2020: Global issues and the future of humankind. Interregional Social Organization for Assistance of Studying and Promotion the Scientific Heritage of N.D. Kondratieff / ISOASPSH of N.D. Kondratieff, 2020. http://dx.doi.org/10.46865/978-5-901640-33-3-2020-189-195.

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Discussions of the humankind future problems touch upon the aspect of political culture. The involvement of the socio-psychological category of cohesion will make it possible to specify regulatory mechanisms in the format of a human relations model. Interdisciplinary complexity occurs with the involvement of the concepts of worldview transformation, planetary identity and people-globalizers. The language of the topic meets global challenges, demonstrating solidarity as a social-psychological indicator of group dynamics scenario of response to situations associated with risks to health and life. Interdisciplinarity substantively refracts the concept of cohesion into the plane of dynamics of worldview transformations. Political psychology sets the vector of its operationality within the basic scheme of subject-setting – action-object. Mental cohesion leads to a global dimension of planetary identity.
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Chen, Genliang, Hao Wang, Yong Zhong, and Haidong Yu. "A Lie Group Formulation of the Newton-Euler Equations and its Application to Robot Dynamics." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47221.

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Based on the screw theory, this paper presents a Lie group formulation for robot dynamics. Regarding the screws and co-screws as elements of se(3) and its dual se*(3), the shifting law and change-of-coordinates of screw quantities can be uniformly interpreted as the adjoint transformations associated with pure translation and rotation of rigid displacements, respectively. The acceleration screw which enables the Newton-Euler equations of a rigid body to behave in a screw-like manner, is defined with intuitive interpretations. As a result, the advantages of Lie group formulation in robot kinematics can be extended to dynamics, so that both kinematics and dynamics can be formulated about an arbitrary point initially and then transformed to any other. Based on the principle of virtual work, the system N-E equations can be solved conveniently for both forward and inverse dynamics of serial robots. By taking advantage of the adjoint representations for the Lie algebra and its operations, only matrix calculations are required, avoiding the ad hoc definitions and notational conventions, to derive the system dynamic equations.
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Takada, Takumi, Wataru Shimaya, Yoshiyuki Ohmura, and Yasuo Kuniyoshi. "Disentangling Patterns and Transformations from One Sequence of Images with Shape-invariant Lie Group Transformer." In 2022 IEEE International Conference on Development and Learning (ICDL). IEEE, 2022. http://dx.doi.org/10.1109/icdl53763.2022.9962232.

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Reports on the topic "Lie transformation groups"

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Arvanitoyeorgos, Andreas. Lie Transformation Groups and Geometry. GIQ, 2012. http://dx.doi.org/10.7546/giq-9-2008-11-35.

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James P. Lewis. ?Structural Transformations in Ceramics: Perovskite-like Oxides and Group III, IV, and V Nitrides? Office of Scientific and Technical Information (OSTI), December 2006. http://dx.doi.org/10.2172/909138.

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Taherizadeh, Amir, and Cathrine Beaudry. Vers une meilleure compréhension de la transformation numérique optimisée par l’IA et de ses implications pour les PME manufacturières au Canada - Une recherche qualitative exploratoire. CIRANO, June 2021. http://dx.doi.org/10.54932/jdxb2231.

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Ce rapport présente les principaux résultats d’une étude qualitative exploratoire visant à examiner l’impact de l’intelligence artificielle (IA), en tant que technologie à usage général (TUG) sur la productivité et l’emploi à l’échelle de l’entreprise. À la suite de l’analyse de sources de données primaires et secondaires (comprenant 27 entretiens, rapports et discussions de groupe), nous établissons d’abord une échelle de maturité de l’adoption de l’IA et un classement des petites et moyennes entreprises (PME) qui intègrent l’IA dans leurs processus de travail en quatre archétypes : l’Aspirant, le Fonceur, le Leader et le Visionnaire. Nous définissons chaque archétype de façon à mettre en évidence les changements particuliers à opérer pour qu’une entreprise puisse passer à l’étape suivante de l’adoption de l’IA. Deuxièmement, nous définissons et examinons sept obstacles à l’adoption généralisée de l’IA par les PME manufacturières. Troisièmement, à l’aide de trois études de cas, nous explorons trois projets d’IA menés par des entreprises québécoises axées sur l’IA afin de montrer, d’une part, l’apport de l’intégration de l’apprentissage automatique (AA) aux produits et aux processus de travail sur le plan de la productivité des entreprises, et d’autre part son effet sur leurs effectifs. Dans l’ensemble, les résultats de notre étude suggèrent que la réussite de l’intégration de l’IA nécessite une transformation numérique au niveau de l’entreprise, que nous présentons comme un continuum. Dans les premières étapes, où l’adoption de l’IA se fait autour de projets (en particulier pour les entreprises des catégories Aspirant et Fonceur), les effectifs des entreprises ont tendance à augmenter parallèlement aux gains de productivité en même temps que le perfectionnement indispensable des compétences de la main-d’œuvre existante. En outre, lorsque l’IA est déployée à l’échelle de l’entreprise (chez les Leaders et les Visionnaires) et que cette dernière rehausse le niveau de ses activités d’innovation, on enregistre plutôt des pertes d’emploi parallèlement aux gains de productivité. Par la suite, nous introduisons des indicateurs indirects de l’omniprésence de l’IA, car nous estimons qu’il s’agit de mesures plus réalistes pour évaluer le taux d’adoption de l’IA par les PME en phase fluide. Enfin, nous proposons quatre recommandations qui ont des implications pour les chercheurs, les praticiens et les responsables politiques.
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Haider, Huma. Scalability of Transitional Justice and Reconciliation Interventions: Moving Toward Wider Socio-political Change. Institute of Development Studies (IDS), March 2021. http://dx.doi.org/10.19088/k4d.2021.080.

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Literature focusing on the aftermath of conflict in the Western Balkans, notes that many people remain focused on stereotypes and prejudices between different ethnic groups stoking fear of a return to conflict. This rapid review examines evidence focussing on various interventions that seek to promote inter-group relations that are greatly elusive in the political realm in the Western Balkan. Socio-political change requires a growing critical mass that sees the merit in progressive and conciliatory ethnic politics and is capable of side-lining divisive ethno-nationalist forces. This review provides an evidence synthesis of pathways through which micro-level, civil-society-based interventions can produce ‘ripple effects’ in society and scale up to affect larger geographic areas and macro-level socio-political outcomes. These interventions help in the provision of alternative platforms for dealing with divisive nationalism in post-conflict societies. There is need to ensure that the different players participating in reconciliation activities are able to scale up and attain broader reach to ensure efficacy and hence enabling them to become ‘multiplier of peace.’ One such way is by providing tools for activism. The involvement of key people and institutions, who are respected and play an important role in the everyday life of communities and participants is an important factor in the design and success of reconciliation initiatives. These include the youth, objective media, and journalists. The transformation of conflict identities through reconciliation-related activities is theorised as leading to the creation of peace constituencies that support non-violent approaches to conflict resolution and sustainable peace The success of reconciliation interventions largely depends on whether it contributes to redefining otherwise antagonistic identities and hostile relationships within a community or society.
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De Wit, Paul. Securing Land Tenure for Prosperity of the Planet and its Peoples. Rights and Resources Initiative, February 2023. http://dx.doi.org/10.53892/ogcw7082.

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Indigenous Peoples, Afro-descendant Peoples, and local communities produce up to 70 percent of the world’s food with lower climate change and environmental impact than agribusinesses, but many remain under the poverty threshold. They are the de facto owners and managers of massive carbon stocks in forested and non–forested ecosystems, but markets fail to fairly reward this. This is all achieved with these communities having legal rights over only 20 percent of their land and receiving only 1.7 percent of global climate finance for self–determined investment and nature conservation. Clarifying their rights and establishing solid tenure security and capital to invest in exercising those rights are a must. The need for Indigenous Peoples, Afro-descendant Peoples, and local communities to acquire secure tenure over land and resources to achieve conservation and production goals is twofold. First, these groups need to establish a tenure safety network over their claimed lands and resources to prevent unintended consequences, like spillovers and leakages from other global responses to climate change, environmental rehabilitation, and food systems transformation. Second, they want secure tenure as part of a more enabling environment to fully unlock the potential of delivering their own solutions to current systems, threats, and opportunities.
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Lundgren, Anna, Alex Cuadrado, Mari Wøien Meijer, Hjördís Rut Sigurjónsdottir, Eeva Turunen, Viktor Salenius, Jukka Teräs, Jens Bjørn Gefke Grelck, and Stian Lundvall Berg. Skills Policies - Building Capacities for Innovative and Resilient Nordic Regions. Nordregio, November 2020. http://dx.doi.org/10.6027/r2020:17.1403-2503.

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Long-term trends in Nordic societies (such as ageing populations), along with rapid social transformations (like those brought about by automation and digitalisation), have resulted in increased attention being paid to skills and skills enhancement – not least from policymakers looking to cope with those challenges. However, skills are complex and many actors are involved in their promotion and provision. In this study, we focus on the regional level, which is the point of scale at which the demand for, and supply of, various skills is often articulated. In order to respond to the research question concerning How regions work with skills, six case studies were conducted in 2019 and 2020. That meant one case study in each of the Nordic countries. Those selected were Pohjois-Karjala (North Karelia, Finland), Värmland (Sweden), Hovedstaden (Denmark), Hedmark and Oppland (Norway), Norðurland eystra (Northeastern Region, Iceland), and one in Greenland. This report on skills for resilient and innovative regions is part of a series of reports conducted on behalf of the Nordic Thematic Group for Innovative and Resilient Regions 2017–2020, within the Nordics Cooperation Program for Regional Development and Planning, and under the aegis of the Nordics Council of Ministers.
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Special Bulletin: NDC Invest: Supporting Transformational Climate Policy and Finance in Latin American and the Caribbean. Inter-American Development Bank, July 2021. http://dx.doi.org/10.18235/0003416.

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NDC Invest was created as the one-stop-shop of the IDB Group providing technical and financial support for countries in Latin American and the Caribbean (LAC) in their efforts to achieve the climate objectives under the Paris Agreement, seeking to transition to a net-zero, resilient, and sustainable development pathway that improves the quality of life and prosperity in LAC. We have recently published a paper that describes three NDC Invest products to support Governments to tackle challenges and scale up action towards a climate-aligned and sustainable development path. In this Special Bulletin, we provide a snapshot of our thee products: i) the design of Long-Term Strategies (LTS) for net-zero emissions and resilience; ii) design of ambitious Nationally Determined Contributions (NDCs), aligned to LTS; and iii) design of investment plans and finance strategies.
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