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The Rotation Group

Karol Pąk
<span title="2012-01-01">2012</span> <i title="Walter de Gruyter GmbH"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cn54gai6x5addllfxdh4ow6r54" style="color: black;">Formalized Mathematics</a> </i> &nbsp;
MML identifier: MATRTOP3, version: 7.12.01 4.167.1133 The papers [11]  ...  We also introduce rotation which preserves orientation (proper rotation) and reverses orientation (improper rotation).  ...  The functor Rotation(i, j, n, α) yielding an invertible square matrix over R F of dimension n is defined by the conditions (Def. 3).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/v10037-012-0004-2">doi:10.2478/v10037-012-0004-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pd7m3lp73rgbxeldjabj6f3jgq">fatcat:pd7m3lp73rgbxeldjabj6f3jgq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160323225609/http://mizar.uwb.edu.pl/fm/2012-20/pdf20-1/matrtop3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f2/c6/f2c6a0356ed6708b8e027f18103b31efe08a4715.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2478/v10037-012-0004-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Supersymmetry and the rotation group

D. G. C. McKeon
<span title="2018-04-30">2018</span> <i title="World Scientific Pub Co Pte Lt"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/poyprimnivfenn3g643u3vtsxy" style="color: black;">Modern Physics Letters A</a> </i> &nbsp;
A model invariant under a supersymmetric extension of the rotation group O(3) is mapped, using a stereographic projection, from the spherical surface S2 to two dimensional Euclidean space.  ...  The resulting model does not have a manifest local structure.  ...  An analogue exists between the conformal group in Euclidean space and the rotation group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0217732318500748">doi:10.1142/s0217732318500748</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ijsri234krfyhmg7alf7jubsrm">fatcat:ijsri234krfyhmg7alf7jubsrm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200928134605/https://arxiv.org/pdf/1801.10008v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/57/e15759f96b9c8bedf0c89827e89727ce47702f98.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1142/s0217732318500748"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> worldscientific.com </button> </a>

FFTs on the Rotation Group

Peter J. Kostelec, Daniel N. Rockmore
<span title="2008-02-22">2008</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/idl24vxrwbeb3iyj7n4tb4jvzq" style="color: black;">Journal of Fourier Analysis and Applications</a> </i> &nbsp;
In this paper, we discuss an implementation of an O(B 4 ) algorithm for the numerical computation of Fourier transforms of functions defined on the rotation group, SO(3).  ...  This compares with the direct O(B 6 ) approach. The algorithm we implemented is based on the "Separation of Variables" technique, e.g. as presented by Maslen and Rockmore [19].  ...  methods [12] , which depend in part on the three-term recurrence the Wigner-d functions satisfy.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00041-008-9013-5">doi:10.1007/s00041-008-9013-5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o34zsu6xlvekrg6m4kq6vk72le">fatcat:o34zsu6xlvekrg6m4kq6vk72le</a> </span>
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Unbounded formulation of the rotation group

Yoritaka Iwata
<span title="">2019</span> <i title="IOP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wxgp7pobnrfetfizidmpebi4qy" style="color: black;">Journal of Physics, Conference Series</a> </i> &nbsp;
The rotation group is formulated based on the abstract B(X)-module framework.  ...  Although the infinitesimal generators of rotation group include differential operators, the rotation group is formulated utilizing the framework of bounded operator algebra.  ...  Acknowledgments The author is grateful to Prof. Emeritus Hiroki Tanabe of Osaka University for fruitful comments. This work was supported by JSPS KAKENHI Grant No. 17K05440.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1088/1742-6596/1194/1/012053">doi:10.1088/1742-6596/1194/1/012053</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/znr2imwrufdhnhjc2en4nhobbq">fatcat:znr2imwrufdhnhjc2en4nhobbq</a> </span>
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The rotation group of Rubik's cube

O. Knill, R. E. Mäder
<span title="1987-08-01">1987</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hab6y3yvcbd2hpuybkxo2pp34a" style="color: black;">ACM SIGSAM Bulletin</a> </i> &nbsp;
In this project, the group theory program "Cayley" is used to solve some problems asso ciated with Rubik's Cube, including the original problem of restoring the initial state of the cube.  ...  After a few rotations, the colors are in disorder and it is nearly impossi ble to rearrange them by accidental rotations.  ...  (In this problem, you should consider also squares and inverses of gen erators as rotations.) "The Rubik Tetrahedron" You will find the group tetra as a file in the library of this project.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/29309.29316">doi:10.1145/29309.29316</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7kvbzq2bibgdfddghciqt7cx6a">fatcat:7kvbzq2bibgdfddghciqt7cx6a</a> </span>
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Distributions covariant under the rotation group

F Riahi
<span title="">1970</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
In this note we present some partial results obtained for the real rotation group.  ...  ROTATION INVARIANT DISTRIBUTIONS Let L = 0+(3, R) be the group of real orthogonal transformations of the real 3diiensional euclidean space and dR the normalised Haar measure on 0+(3, R).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-247x(70)90182-4">doi:10.1016/0022-247x(70)90182-4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xqa675xufradlg2alka43sfgiu">fatcat:xqa675xufradlg2alka43sfgiu</a> </span>
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Stability Properties of Rotational Catenoids in the Heisenberg Groups [article]

Pierre Bérard, Marcos P. Cavalcante
<span title="2013-03-22">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we determine the maximally stable, rotationally invariant domains on the catenoids _a (minimal surfaces invariant by rotations) in the Heisenberg group with a left-invariant metric.  ...  Finally, we study the rotationally symmetric stable domains on the higher dimensional catenoids.  ...  Catenoids in the Heisenberg group Nil(3) are complete minimal surfaces which are invariant under a one-parameter subgroup of rotations with axis the center of the group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1010.0774v3">arXiv:1010.0774v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/h6mxeuhtsvbhtka2veah3zm4yq">fatcat:h6mxeuhtsvbhtka2veah3zm4yq</a> </span>
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Bayesian Recursive Estimation on the Rotation Group [article]

Sofia Suvorova, Stephen D. Howard, Bill Moran
<span title="2020-03-25">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Tracking on the rotation group is a key component of many modern systems for estimation of the motion of rigid bodies.  ...  To address this problem, here we describe a Bayesian algorithm that relies on directional measurements for tracking on the special orthogonal (rotation) group.  ...  the rotation group as, for instance, linear approximation methods do.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.09792v2">arXiv:2003.09792v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fag7rynayzccnhabg5i4wol3e4">fatcat:fag7rynayzccnhabg5i4wol3e4</a> </span>
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On representations of the rotation group and magnetic monopoles

Alexander I Nesterov, Fermı́n Aceves de la Cruz
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j5vumr4o65agbmeqovmzt67pqe" style="color: black;">Physics Letters A</a> </i> &nbsp;
A302 (2002) 253, hep-th/0208210; hep-th/0403146) employing bounded infinite-dimensional representations of the rotation group we have argued that one can obtain the consistent monopole theory with generalized  ...  Dirac quantization condition, 2κμ∈ Z, where κ is the weight of the Dirac string.  ...  Acknowledgments One of the authors, F.A., thanks Center for Theoretical Physics of the Massachusetts Institute of Technology where the part of this work has been done, for the warm hospitality.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.physleta.2004.02.051">doi:10.1016/j.physleta.2004.02.051</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/robsy2q3x5arzjwzvpbevw5pqe">fatcat:robsy2q3x5arzjwzvpbevw5pqe</a> </span>
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Gauss-Legendre Sampling on the Rotation Group

Zubair Khalid, Salman Durrani, Rodney A. Kennedy, Yves Wiaux, Jason D. McEwen
<span title="">2016</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/msfmoh6v7bdk7lrsmtbklto74i" style="color: black;">IEEE Signal Processing Letters</a> </i> &nbsp;
We propose a Gauss-Legendre quadrature based sampling on the rotation group for the representation of a band-limited signal such that the Fourier transform (FT) of a signal can be exactly computed from  ...  For the computation of FT and inverse FT, we also develop fast algorithms of complexity similar to the complexity attained by the fast algorithms for the existing sampling schemes.  ...  The design of sampling schemes on the rotation group and the development of computationally efficient FT's on the rotation group have been actively investigated in the literature [7] - [13] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lsp.2015.2503295">doi:10.1109/lsp.2015.2503295</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/d4s7fdmbc5f27ijnnxcgn4dchq">fatcat:d4s7fdmbc5f27ijnnxcgn4dchq</a> </span>
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Approximation on the rotation group SO(3)

Zhuyuan Yang, Xin Wang, Xinzhi Liu
<span title="2017-04-11">2017</span> <i title="International Scientific Research Publications MY SDN. BHD."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cbh6szwkzndpbdlkh6gqziyr6i" style="color: black;">Journal of Nonlinear Science and its Applications</a> </i> &nbsp;
In this paper we study the approximation on rotation group SO(3), we consider the partial sum, Féjer and Jackson-type operators and obtain the approximation theorems in L p (1 p +∞) respectively.  ...  Acknowledgment This work was supported by the National Natural Science Foundation of China (No. 11361076). Z. Y. Yang, X. Wang, X. Z. Liu, J. Nonlinear Sci. Appl., 10 (2017), 1561-1568  ...  We first give the definition of the r-th moduli of smoothness of function f on the rotation group.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.22436/jnsa.010.04.22">doi:10.22436/jnsa.010.04.22</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ej3l2ur4wvdq7hjslnpvecwnoy">fatcat:ej3l2ur4wvdq7hjslnpvecwnoy</a> </span>
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Note on Reduction for the Rotation Group

J. M. Keller
<span title="1939-03-01">1939</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/h35pf4panvende3pfmaz2mxbea" style="color: black;">Physical Review</a> </i> &nbsp;
Note on Reduction for the Rotation Group The reduction of a product representation of the rotation group into irreducible representations is important in many physical problems.  ...  In the branch near the end of the lower track the angle of the fork is measurable when the track is repro- jected.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrev.55.508.2">doi:10.1103/physrev.55.508.2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tufbdlxscvhlllqhquaxlcqzka">fatcat:tufbdlxscvhlllqhquaxlcqzka</a> </span>
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The Element of Volume of the Rotation Group

F. D. Murnaghan
<span title="1950-11-01">1950</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
The pseudo-angle characterizes the pseudo-conformal group G." Let S2m be a fixed 2m dimensional manifold contained in 2;2 so that m . n. Let P be an arbitrary point of S2m.  ...  If w = 4 + i4, is monogenic over R, then the curves of k = const. are pseudo-orthogonal to the manifolds P = const.  ...  The net result of this is that the element of volume of the n-dimensional rotation group involves the element of volume of the (n -l)-dimensional rotation group as a factor.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1073/pnas.36.11.670">doi:10.1073/pnas.36.11.670</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/16588981">pmid:16588981</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC1063265/">pmcid:PMC1063265</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nwknthllmvdadpd3vz2x4774k4">fatcat:nwknthllmvdadpd3vz2x4774k4</a> </span>
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The Element of Volume of the Rotation Group

F. D. Murnaghan
<span title="1952-01-01">1952</span> <i title="Proceedings of the National Academy of Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nvtuoas5pbdsllkntnhizy4f4q" style="color: black;">Proceedings of the National Academy of Sciences of the United States of America</a> </i> &nbsp;
The pseudo-angle characterizes the pseudo-conformal group G." Let S2m be a fixed 2m dimensional manifold contained in 2;2 so that m . n. Let P be an arbitrary point of S2m.  ...  If w = 4 + i4, is monogenic over R, then the curves of k = const. are  ...  The net result of this is that the element of volume of the n-dimensional rotation group involves the element of volume of the (n -l)-dimensional rotation group as a factor.  ... 
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Infinite-dimensional representations of the rotation group and Dirac monopole problem

Alexander I. Nesterov, Fermín Aceves de la Cruz
<span title="">2008</span> <i title="AIP Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/nwwheyjjk5hnlmj6q5mtpqmmhi" style="color: black;">Journal of Mathematical Physics</a> </i> &nbsp;
Within the context of infinite-dimensional representations of the rotation group the Dirac monopole problem is studied in details.  ...  , which is related to the weight of the Dirac string.  ...  of the rotation group [11, 12, 13, 14, 15, 16, 17, 18] .  ... 
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