Relevant bibliographies by topics / Jacobi groups

Academic literature on the topic 'Jacobi groups'

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Published: 14 March 2023

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Journal articles on the topic "Jacobi groups"

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Rezaei-Aghdam, Adel, and Mehdi Sephid. "Classical r-matrices of real low-dimensional Jacobi–Lie bialgebras and their Jacobi–Lie groups." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1650087. http://dx.doi.org/10.1142/s0219887816500870.

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In this paper, we obtain the classical [Formula: see text]-matrices of real two- and three-dimensional Jacobi–Lie bialgebras. In this way, we classify all non-isomorphic real two- and three-dimensional coboundary Jacobi–Lie bialgebras and their types (triangular and quasi-triangular). Also, we obtain the generalized Sklyanin bracket formula by use of which, we calculate the Jacobi structures on the related Jacobi–Lie groups. Finally, we present a new method for constructing classical integrable systems using coboundary Jacobi–Lie bialgebras.
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Sun, BinYong. "On representations of real Jacobi groups." Science China Mathematics 55, no. 3 (December 24, 2011): 541–55. http://dx.doi.org/10.1007/s11425-011-4333-3.

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Celeghini, E., M. Gadella, and M. A. del Olmo. "Groups, Jacobi functions, and rigged Hilbert spaces." Journal of Mathematical Physics 61, no. 3 (March 1, 2020): 033508. http://dx.doi.org/10.1063/1.5138238.

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Kohnen, W. "Nonholomorphic Poincaré-Type Series on Jacobi Groups." Journal of Number Theory 46, no. 1 (January 1994): 70–99. http://dx.doi.org/10.1006/jnth.1994.1005.

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Macdonald, I. D., and B. H. Neumann. "On commutator laws in groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 45, no. 1 (August 1988): 95–103. http://dx.doi.org/10.1017/s1446788700032304.

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AbstractThere are some well-known laws that the commutator satisfies in groups, and that go by some or all of the names Jacobi, Witt, Hall; and there are also some lesser-known laws. This is an attempt at an axiomatic study of the interdependence and independence of these laws.
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Stroffolini, Bianca. "Homogenization of Hamilton-Jacobi equations in Carnot Groups." ESAIM: Control, Optimisation and Calculus of Variations 13, no. 1 (January 2007): 107–19. http://dx.doi.org/10.1051/cocv:2007005.

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Kerr, Matt, James D. Lewis, and Stefan Müller-Stach. "The Abel–Jacobi map for higher Chow groups." Compositio Mathematica 142, no. 02 (March 2006): 374–96. http://dx.doi.org/10.1112/s0010437x05001867.

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Younes, Laurent. "Jacobi fields in groups of diffeomorphisms and applications." Quarterly of Applied Mathematics 65, no. 1 (February 15, 2007): 113–34. http://dx.doi.org/10.1090/s0033-569x-07-01027-5.

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Shao, Jinghai. "Hamilton–Jacobi semi-groups in infinite dimensional spaces." Bulletin des Sciences Mathématiques 130, no. 8 (December 2006): 720–38. http://dx.doi.org/10.1016/j.bulsci.2006.03.001.

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Celeghini, Enrico, Mariano A. del Olmo, and Miguel A. Velasco. "Lie groups, algebraic special functions and Jacobi polynomials." Journal of Physics: Conference Series 597 (April 13, 2015): 012023. http://dx.doi.org/10.1088/1742-6596/597/1/012023.

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Dissertations / Theses on the topic "Jacobi groups"

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Docherty, Pamela Jane. "Central extensions of Current Groups and the Jacobi Group." Thesis, University of Edinburgh, 2012. http://hdl.handle.net/1842/7838.

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A current group GX is an infinite-dimensional Lie group of smooth maps from a smooth manifold X to a finite-dimensional Lie group G, endowed with pointwise multiplication. This thesis concerns current groups G§ for compact Riemann surfaces §. We extend some results in the literature to discuss the topology of G§ where G has non-trivial fundamental group, and use these results to discuss the theory of central extensions of G§. The second object of interest in the thesis is the Jacobi group, which we think of as being associated to a compact Riemann surface of genus one. A connection is made between the Jacobi group and a certain central extension of G§. Finally, we define a generalisation of the Jacobi group that may be thought of as being associated to a compact Riemann surface of genus g ≥ 1.
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Bringmann, Kathrin. "Applications of Poincaré series on Jacobi groups." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972389741.

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Dahal, Rabin. "Centers of Invariant Differential Operator Algebras for Jacobi Groups of Higher Rank." Thesis, University of North Texas, 2013. https://digital.library.unt.edu/ark:/67531/metadc283833/.

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Let G be a Lie group acting on a homogeneous space G/K. The center of the universal enveloping algebra of the Lie algebra of G maps homomorphically into the center of the algebra of differential operators on G/K invariant under the action of G. In the case that G is a Jacobi Lie group of rank 2, we prove that this homomorphism is surjective and hence that the center of the invariant differential operator algebra is the image of the center of the universal enveloping algebra. This is an extension of work of Bringmann, Conley, and Richter in the rank 1case.
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Adams, Ross Montague. "A study of a class of invariant optimal control problems on the Euclidean group SE(2)." Thesis, Rhodes University, 2011. http://hdl.handle.net/10962/d1006060.

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The aim of this thesis is to study a class of left-invariant optimal control problems on the matrix Lie group SE(2). We classify, under detached feedback equivalence, all controllable (left-invariant) control affine systems on SE(2). This result produces six types of control affine systems on SE(2). Hence, we study six associated left-invariant optimal control problems on SE(2). A left-invariant optimal control problem consists of minimizing a cost functional over the trajectory-control pairs of a left-invariant control system subject to appropriate boundary conditions. Each control problem is lifted from SE(2) to T*SE(2) ≅ SE(2) x se (2)*and then reduced to a problem on se (2)*. The maximum principle is used to obtain the optimal control and Hamiltonian corresponding to the normal extremals. Then we derive the (reduced) extremal equations on se (2)*. These equations are explicitly integrated by trigonometric and Jacobi elliptic functions. Finally, we fully classify, under Lyapunov stability, the equilibrium states of the normal extremal equations for each of the six types under consideration.
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Hall, Jack Kingsbury Mathematics &amp Statistics Faculty of Science UNSW. "Some branching rules for GL(N,C)." Awarded by:University of New South Wales. Mathematics and Statistics, 2007. http://handle.unsw.edu.au/1959.4/29473.

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This thesis considers symmetric functions and algebraic combinatorics via the polynomial representation theory of GL(N,C). In particular, we utilise the theory of Jacobi-Trudi determinants to prove some new results pertaining to the Littlewood-Richardson coefficients. Our results imply, under some hypotheses on the strictness of the partition an equality between Littlewood-Richardson coefficients and Kostka numbers. For the case that a suitable partition has two rows, an explicit formula is then obtained for the Littlewood-Richardson coefficient using the Hook Length formula. All these results are then applied to compute branching laws for GL(m+n,C) restricting to GL(m,C) x GL(n,C). The technique also implies the well-known Racah formula.
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Webster, Benjamin. "On Representations of the Jacobi Group and Differential Equations." UNF Digital Commons, 2018. https://digitalcommons.unf.edu/etd/858.

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In PDEs with nontrivial Lie symmetry algebras, the Lie symmetry naturally yield Fourier and Laplace transforms of fundamental solutions. Applying this fact we discuss the semidirect product of the metaplectic group and the Heisenberg group, then induce a representation our group and use it to investigate the invariant solutions of a general differential equation of the form .
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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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Bagheri, Aaron R. "Classifying the Jacobian Groups of Adinkras." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/102.

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Supersymmetry is a theoretical model of particle physics that posits a symmetry between bosons and fermions. Supersymmetry proposes the existence of particles that we have not yet observed and through them, offers a more unified view of the universe. In the same way Feynman Diagrams represent Feynman Integrals describing subatomic particle behaviour, supersymmetry algebras can be represented by graphs called adinkras. In addition to being motivated by physics, these graphs are highly structured and mathematically interesting. No one has looked at the Jacobians of these graphs before, so we attempt to characterize them in this thesis. We compute Jacobians through the 11-cube, but do not discover any significant discernible patterns. We then dedicate the rest of our work to generalizing the notion of the Jacobian, specifically to be sensitive to edge directions. We conclude with a conjecture describing the form of the directed Jacobian of the directed $n$-topology. We hope for this work to be useful for theoretical particle physics and for graph theory in general.
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Mizony, Michel. "Semi-groupes de Lie et fonctions de Jacobi de deuxième espèce." Grenoble 2 : ANRT, 1987. http://catalogue.bnf.fr/ark:/12148/cb376080903.

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Cléry, Fabien. "Relèvement arithmétique et multiplicatif de formes de Jacobi." Thesis, Lille 1, 2009. http://www.theses.fr/2009LIL10033/document.

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La théorie des formes modulaires de Siegel fournit de nombreuses applications en arithmétique, en géométrie algébrique et plus récemment en physique théorique. Le sujet de cette thèse est motivé par la construction d'analogues tridimensionnels de la fonction êta de Dedekind, question apparue dans la théorie des algèbres de Kac-Moody et celle des cordes ainsi qu'en géométrie algébrique. De telles formes modulaires ont été construites par V Gritsenko et V Nlkulln entre 1995 et 1998 pour les groupes paramodulalres complets. Dans cette thèse, nous repondons à cette question pour les sous-groupes de congruence des groupes paramodulaires nous obtenons une classifiation complète des formes de Siegel de diviseur le plus simple et les exhibons Nous les avons nommées dd-formes (diviseur diagonal) Notre solution repose sur l'utilisation de formes de Jacobi et deux types de relèvements. En 1979, H. Maass proposa une construction de formes modulaires de Siegel à partir de formes de Jacobl d'indice 1 En 1993, V Gritsenko généralisa cette construction aux formes de Jacobi d'indice t. Nous les généralisons aux sous-groupes de congruencc de SL(2:Z) On obtient ainsi des formes modulaires de Siegel pour des sous-groupes des groupes paramodulaircs. Il s'agit de relévements artthmétiques Ensuite, nous construisons un relèvement multiplicatif ou produit automorphe de Borcherds à partir de formes de Jacobi presque holomorphes de poids 0 et d'indice t pour le sous-groupe de congruence de type de Heckc Gamma0(N). Cette construction généralise celle proposée par V Gntsenko et V Nikulin en 1998. Les dd-formes sont des formes rètlexives. Elles nous ont permis de retrouvcr la structure de certains anneaux gradués de formes modulaires
The theory of Siegel modular forms gives us a lot of applications in arithmetic, algebraic geometry and more recently in physics. The subject of this dissertation is motivated bv the construction of a three-dimensional analogue of the eta function of Dedekind, problem arisen in the theory of Lorentzian KacMoody Lie algebras, algebraic geometrv and also in string theory Such modular forms have been bullt bv V Gntsenko and V Nikulin betw\een 1995- 1998 for the full paramodular groups. ln this dissertation, wc answer to this problem for congruence subgroups of paramodular groups we obtain a complete classification of thc Siegel modular forms with the simplest divisor and we produce ail of them. We called them dd-forms (modular forms with diagonal diyisor) Our solution is based on the use of Jacobi forms and two types of liftings. ln 1979, H. Maass proposed a construction of Siegel modular forms by using Jacobi forms of index one. ln 1993, V Gritsenko generalized this construction to Jacobi forms of index t. We generalize these ones to congruence subgroups of SL(2;Z). ln this way, we obtain Siegel modular forms for subgroups of the full paramodular groups. We call such a construction artthmetlc lifting. Then we construct a multiplicative lifting or Borcherds' automorphic product by using nearly holomorphic Jacobi forms of weight 0 and index t for congruence subgroups of Heeke type Gamma0(N). This construction generalizes the one proposed bv V Gritsenko and V Nlkulln in 1998 The dd-forms are retlectives modular forms.Thev have allowed us new proofs of the structure of some graded rings of modular forms
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Books on the topic "Jacobi groups"

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1968-, Schmidt Ralf, ed. Elements of the representation theory of the Jacobi group. Boston: Birkhäuser Verlag, 1998.

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1968-, Schmidt Ralf, ed. Elements of the representation theory of the Jacobi group. Basel: Springer Basel, 2011.

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Jay, Jorgenson, and Walling Lynne 1958-, eds. The ubiquitous heat kernel: AMS special session, the ubiquitous heat kernel, October 2-4, 2003, Boulder, Colorado. Providence, R.I: American Mathematical Society, 2006.

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Berndt, Rolf, and Ralf Schmidt. Elements of the Representation Theory of the Jacobi Group. Basel: Springer Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-0283-3.

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Berndt, Rolf, and Ralf Schmidt. Elements of the Representation Theory of the Jacobi Group. Basel: Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8772-4.

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Tongeren, Paul van. Jacoba van Tongeren en de onbekende verzetshelden van Groep 2000 (1940-1945). Soesterberg: Uitgeverij Aspekt, 2015.

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Jacques, Lardoux, and Université d'Angers. Centre d'études et de recherche sur imaginaire, écritures et cultures., eds. Max Jacob et l'École de Rochefort. Angers: Presses de l'Université d'Angers, 2005.

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Jacques, Lardoux, and Universite d'Angers. Centre d'etudes et de recherche sur imaginaire, ecritures et cultures., eds. Max Jacob et l'école de Rochefort. Angers: Presses de l'Université d'Angers, 2005.

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Jacques, Lardoux, and Université d'Angers, eds. Max Jacob et l'Ecole de Rochefort. Angers: Presses de l'Université d'Angers, 2005.

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Marineau, René F. Jacob Levy Moreno, 1889-1974: Father of psychodrama, sociometry, and group psychotherapy. London: Tavistock/Routledge, 1989.

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Book chapters on the topic "Jacobi groups"

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Bump, Daniel. "The Jacobi–Trudi Identity." In Lie Groups, 365–77. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8024-2_35.

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Bump, Daniel. "The Jacobi-Trudi Identity." In Lie Groups, 297–307. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4757-4094-3_37.

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Bertola, Marco. "Jacobi groups, Jacobi forms and their applications." In CRM Proceedings and Lecture Notes, 99–111. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/crmp/031/08.

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Connett, W. C., C. Markett, and A. L. Schwartz. "Jacobi Polynomials and Related Hypergroup Structures." In Probability Measures on Groups X, 45–81. Boston, MA: Springer US, 1991. http://dx.doi.org/10.1007/978-1-4899-2364-6_5.

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Yui, Noriko. "Jacobi quartics, legendre polynomials and formal groups." In Lecture Notes in Mathematics, 182–215. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0078046.

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Raum, Martin. "Indecomposable Harish-Chandra Modules for Jacobi Groups." In Contributions in Mathematical and Computational Sciences, 231–49. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-69712-3_13.

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Helal Ahmed, Md, and Jagmohan Tanti. "Cyclotomic Numbers and Jacobi Sums: A Survey." In Class Groups of Number Fields and Related Topics, 119–40. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-1514-9_12.

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Hawkins, Thomas. "Jacobi and the Analytical Origins of Lie’s Theory." In Emergence of the Theory of Lie Groups, 43–74. New York, NY: Springer New York, 2000. http://dx.doi.org/10.1007/978-1-4612-1202-7_2.

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Hawkins, Thomas. "Jacobi and the Birth of Lie’s Theory of Groups." In Amphora, 289–313. Basel: Birkhäuser Basel, 1992. http://dx.doi.org/10.1007/978-3-0348-8599-7_15.

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Calin, Ovidiu, Der-Chen Chang, and Irina Markina. "Generalized Hamilton—Jacobi Equation and Heat Kernel on Step Two Nilpotent Lie Groups." In Analysis and Mathematical Physics, 49–76. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9906-1_3.

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Conference papers on the topic "Jacobi groups"

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Guo, Yun, Yuki Ishiwatari, Satoshi Ikejiri, and Yoshiaki Oka. "Parallel Computation for Particle-Grid Hybrid Method." In ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting collocated with 8th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2010. http://dx.doi.org/10.1115/fedsm-icnmm2010-30117.

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In this paper, parallel computational technology is used in the numerical analysis code of particle-grid hybrid method. Particle-grid hybrid method is a rising solution method to analyze two-phase flow problem. It has shown its ability in several two-dimensional simulations. However, when this method was used to predict the droplet entrainment ratio of annulus flow the calculation time was insufferable. When the droplet occurs in the gas core, the density field varying near the droplet is strenuous. The pressure correction equations are very hard to be convergence. Hence, the MPI (Message Passing Interface) library is chosen as the parallel technology to decrease the calculation time. The grid and particle calculation parts are paralleled, separately. Jacobi point iteration method and ADI (alternating direction implicit) combined with divide and flow line programming techniques for grid calculation are discussed. All the particles are divided into several groups depending on the processor number. Then several cases are set for testing the parallel efficiency. Generally, with four processors the efficiency is about 60%. If the processor number is more than four the parallel efficiency will decrease rapidly. This method can accelerate the hybrid method; however, it still needs improving. Finally, some droplet entrainment cases calculated by parallel code are summarized.
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Berceanu, S., Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Generalized squeezed states for the Jacobi group." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043874.

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Berceanu, S., Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmeier, and Theodore Voronov. "Coherent states associated to the real Jacobi group." In XXVI INTERNATIONAL WORKSHOP ON GEOMETRICAL METHODS IN PHYSICS. AIP, 2007. http://dx.doi.org/10.1063/1.2820972.

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Berceanu, S., Piotr Kielanowski, S. Twareque Ali, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "The Jacobi Group and the Squeezed States—Some Comments." In XXVIII WORKSHOP ON GEOMETRICAL METHODS IN PHYSICS. AIP, 2009. http://dx.doi.org/10.1063/1.3275594.

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BERNDT, ROLF. "MARSDEN–WEINSTEIN REDUCTION, ORBITS AND REPRESENTATIONS OF THE JACOBI GROUP." In Proceedings of the Conference in Memory of Tsuneo Arakawa. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774415_0002.

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Vigouroux a, Nadine, Damien Sauzin a, and Frédéric Vella a. "Software Interfaces of the Jaco Robotic Arm: Results of a Focus Group." In Applied Human Factors and Ergonomics Conference (2022). AHFE International, 2022. http://dx.doi.org/10.54941/ahfe1001244.

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Robotics is a good opportunity for developing assistive technologies that could provide greater functionalities to provide for more independent activities of daily living. The Jaco robotic arm is one of these devices. Using standard joystick control requires fine motor skills, which are often lacking in persons with spinal cord injury (SCI). A user-centered approach was conducted to design two alternative graphical user interfaces to control the Jaco arm. Firs, five Graphical User Interfaces (GUI) were designed: three based on a software keyboard and two on pie menu concepts. The three software keyboards differ from the visual representation: text buttons, icon buttons, or color organization and are adapted to the Jaco’s control modes. The two pie menus differ according to the interaction technique used to access the second level of the pie menu, i.e. the two techniques designed: pointing and “goal crossing”. Then two groups (one of occupational therapists and another of persons with quadriplegia caused by SCI) were invited to answer a questionnaire to collect their feedback and evaluate their future needs regarding the five GUIs presented. Following the focus group two GUIs were proposed taking into account these issues. The paper will discuss the user-centered approach and the issues that arose at each stage of the design.
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Arikawa, Keisuke. "Analyzing Internal Motion of Proteins From Viewpoint of Robot Kinematics: Formulation of Group Forced Response Method." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70591.

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An analogous relationship exists between the kinematic structures of proteins and robotic mechanisms. Hence, using this analogy, we attempt to understand the internal motions of proteins from the perspective of robot kinematics. In this study, we propose a method called group forced response (GFR) method for predicting the internal motion of proteins on the basis of their three-dimensional structural data (PDB data). In this method, we apply forces in static equilibrium to groups of atoms (e.g., secondary structures, domains, and subunits) and not to specific atoms. Furthermore, we predict the internal motion of proteins by analyzing the relative motion caused among groups by the applied forces. First, we show a method for approximately modeling protein structures as a robotic mechanism and the basic kinematic equations of the model. Next, the GFR method is formulated (e.g., Jacobian matrix for group motions, magnitude of forces applied to groups, and decomposition of motions into modes according to structural compliances). Finally, we present example applications of the proposed method in real protein structures. Despite the approximations in the model, low computational cost, and use of simple calculation parameters, the results almost agree with measured internal motions.
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Shin, Hyunpyo, SungCheul Lee, Woosung In, Jay I. Jeong, and Jongwon Kim. "Kinematic Optimization of a Redundantly Actuated Parallel Mechanism for Maximizing Active Stiffness and Workspace Using Taguchi Method." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87192.

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We present an optimization procedure that uses the Taguchi method to optimize the mean stiffness and workspace of a redundantly actuated parallel mechanism. The kinematic parameters of a planar 2-DOF parallel manipulator are optimized to maximize the manipulator’s workspace and mean stiffness at the same time. Kinematic analysis is performed to obtain a constraint Jacobian and forward Jacobian. And stiffness analysis of the redundantly actuated parallel manipulator is performed based on the virtual work theorem. The Taguchi method is applied to separate the more influential and controllable variables from the less influential ones in the optimization procedure. In the first stage of optimization, the number of experimental variables is reduced by response analysis. And after the response analysis, quasi-optimal kinematic parameter group is obtained in the second stage of optimization. The optimization procedure was used to investigate the optimal kinematic parameter groups and the relationship between the length and the stiffness of the link.
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Ploen, Scott R., and Frank C. Park. "A Coordinate Invariant Formulation of the Dynamics of Cooperating Robot Systems." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1160.

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Abstract In this article we formulate the dynamics of cooperating robot systems using standard ideas and notation from the theory of Lie groups. Beginning with the coordinate-invariant formulation of robot dynamics introduced in Ploen and Park (1995), we extend these results to develop the equations of motion of a system of N cooperating robots manipulating a common workpiece. In the resulting dynamic equations the mass matrix, Jacobian, Coriolis, and gravity terms of the closed chain system admit concise block-triangular factorizations in terms of simple linear operators on se(3), the Lie algebra of the Euclidean group SE(3). A straightforward manipulation of the equations of motion and the kinematic constraints leads to a closed-form expression for the forces of constraint in which the robot parameters appear in a transparent manner.
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Mohammadi Daniali, H. R., P. J. Zsombor-Murray, and Jorge Angeles. "On Singularities of Planar Parallel Manipulators." In ASME 1993 Design Technical Conferences. American Society of Mechanical Engineers, 1993. http://dx.doi.org/10.1115/detc1993-0350.

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Abstract:
Abstract The singularities of the Jacobian matrices of two manipulator with three degrees of freedom are analyzed. One is a planar 3-legged manipulator; the other, a planar double-triangular manipulator. A general classification of parallel-manipulator singularities into three groups is described. The classification scheme relies on the properties of the Jacobian matrices of the manipulator. Finally, the three types of singularity are identified for the two manipulators.
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Reports on the topic "Jacobi groups"

1

Berceanu, Stefan. Coherent States Associated to the Jacobi Group - a Variation on a Theme by Erich Kähler. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-9-2007-1-8.

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2

Deryagina, Madina, and Ilia Mednykh Mednykh. On the Jacobian Group for Möbius Ladder and Prism Graphs. GIQ, 2014. http://dx.doi.org/10.7546/giq-15-2014-117-126.

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3

Hydrogeology and ground-water flow, fractured Mesozoic structural-basin rocks, Stony Brook, Beden Brook, and Jacobs Creek drainage basins, west-central New Jersey. US Geological Survey, 1995. http://dx.doi.org/10.3133/wri944147.

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