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Journal articles on the topic 'Symmetry group'

Author: Grafiati
Published: 4 June 2021
Last updated: 20 February 2023

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1

Grenier, B., and R. Ballou. "Crystallography: Symmetry groups and group representations." EPJ Web of Conferences 22 (2012): 00006. http://dx.doi.org/10.1051/epjconf/20122200006.

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2

Dryzun, Chaim. "Continuous symmetry measures for complex symmetry group." Journal of Computational Chemistry 35, no. 9 (February 6, 2014): 748–55. http://dx.doi.org/10.1002/jcc.23548.

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3

Richey, M. P., and C. A. Tracy. "Symmetry group for a completely symmetric vertex model." Journal of Physics A: Mathematical and General 20, no. 10 (July 11, 1987): 2667–77. http://dx.doi.org/10.1088/0305-4470/20/10/010.

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4

RAUHUT, HOLGER. "WAVELET TRANSFORMS ASSOCIATED TO GROUP REPRESENTATIONS AND FUNCTIONS INVARIANT UNDER SYMMETRY GROUPS." International Journal of Wavelets, Multiresolution and Information Processing 03, no. 02 (June 2005): 167–87. http://dx.doi.org/10.1142/s0219691305000816.

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We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on ℝd.
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5

Klickstein, Isaac, Louis Pecora, and Francesco Sorrentino. "Symmetry induced group consensus." Chaos: An Interdisciplinary Journal of Nonlinear Science 29, no. 7 (July 2019): 073101. http://dx.doi.org/10.1063/1.5098335.

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6

Fernández, Francisco M., and Javier Garcia. "Parity-time symmetry broken by point-group symmetry." Journal of Mathematical Physics 55, no. 4 (April 2014): 042107. http://dx.doi.org/10.1063/1.4870642.

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7

Zamani, Yousef, and Esmaeil Babaei. "SYMMETRY CLASSES OF POLYNOMIALS ASSOCIATED WITH THE DICYCLIC GROUP." Asian-European Journal of Mathematics 06, no. 03 (September 2013): 1350033. http://dx.doi.org/10.1142/s1793557113500332.

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In this paper, we obtain the dimensions of symmetry classes of polynomials with respect to the irreducible characters of the dicyclic group as a subgroup of the full symmetric group. Then we discuss the existence of o-basis of these classes. In particular, the existence of o-basis of symmetry classes of polynomials with respect to the irreducible characters of the generalized quaternion group are concluded.
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8

PIROGOV, YU F. "CHIRAL GAUGE E6 AS A BINDING GROUP FOR COMPOSITE LEPTONS, QUARKS AND HIGGS BOSONS." International Journal of Modern Physics A 09, no. 09 (April 10, 1994): 1397–410. http://dx.doi.org/10.1142/s0217751x94000613.

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The uniqueness of the chiral gauge E6 symmetry in providing the mechanism of binding for composite models is stressed. A maximally symmetric pattern of chiral symmetry breaking, consistent with dynamical mass generation along with preservation of the strongly coupled E6 gauge symmetry, is considered. Chiral anomaly matching conditions for the residual chiral symmetry are studied and likely massless composite fermions are found. The possibility for these fermions as well as Goldstone bosons to be treated eventually as leptons, quarks and Higgs bosons is discussed. The scheme possesses the generic realistic-like features and could serve as a prototype for a realistic composite model.
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9

Matthews, P. C. "Automating Symmetry-Breaking Calculations." LMS Journal of Computation and Mathematics 7 (2004): 101–19. http://dx.doi.org/10.1112/s1461157000001066.

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AbstractThe process of classifying possible symmetry-breaking bifurcations requires a computation involving the subgroups and irreducible representations of the original symmetry group. It is shown how this calculation can be automated using a group theory package such as GAP. This enables a number of new results to be obtained for larger symmetry groups, where manual computation is impractical. Examples of symmetric and alternating groups are given, and the method is also applied to the spatial symmetry-breaking of periodic patterns observed in experiments.
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10

Dmitriev, Victor, Dimitrios C. Zografopoulos, and Luis P. V. Matos. "Analysis of Symmetric Electromagnetic Components Using Magnetic Group Theory." Symmetry 15, no. 2 (February 3, 2023): 415. http://dx.doi.org/10.3390/sym15020415.

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We discuss a method of analysis of symmetric electromagnetic components with magnetic media based on magnetic group theory. In this description, some of the irreducible corepresentations assume complex values exp(iθ) with the real parameter θ. A possible physical interpretation of this parameter is given. We demonstrate the application of the symmetry-adapted linear combination method combined with the corepresentation theory to the problem of current modes in an array of magnetized graphene elements where Faraday and Kerr effects can exist. The elements are described by the magnetic symmetry C4 or C4v(C4). The scattering matrix of the array and its eigensolutions are defined and analyzed and some numerical simulations are presented as well. An example of a waveguide described by symmetry C4v(C2v) with a specific type of degeneracy is also discussed.
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11

Seungkyu Lee and Yanxi Liu. "Skewed Rotation Symmetry Group Detection." IEEE Transactions on Pattern Analysis and Machine Intelligence 32, no. 9 (September 2010): 1659–72. http://dx.doi.org/10.1109/tpami.2009.173.

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12

Chang, Z. "Quantum group and quantum symmetry." Physics Reports 262, no. 3-4 (November 1995): 137–225. http://dx.doi.org/10.1016/0370-1573(95)00063-m.

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13

Levy, Jean-Claude S. "Clusters of symmetry group Yh." Surface Science Letters 156 (June 1985): A316. http://dx.doi.org/10.1016/0167-2584(85)90422-0.

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14

Levy, Jean-Claude S. "Clusters of symmetry group Yh." Surface Science 156 (June 1985): 386–91. http://dx.doi.org/10.1016/0039-6028(85)90598-9.

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15

Ghorbani, Modjtaba, Mahin Songhori, Ali Reza Ashrafi, and Ante Graovac. "Symmetry Group of (3,6)-Fullerenes." Fullerenes, Nanotubes and Carbon Nanostructures 23, no. 9 (December 31, 2014): 788–91. http://dx.doi.org/10.1080/1536383x.2014.993064.

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16

Shah, Parikshit, and Venkat Chandrasekaran. "Group symmetry and covariance regularization." Electronic Journal of Statistics 6 (2012): 1600–1640. http://dx.doi.org/10.1214/12-ejs723.

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17

Bolonek-Lasoń, Katarzyna. "Bell Inequalities and Group Symmetry." International Journal of Theoretical Physics 56, no. 12 (March 3, 2017): 3831–37. http://dx.doi.org/10.1007/s10773-017-3323-9.

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18

Dimca, Alexandru, and Stefan Papadima. "Arithmetic group symmetry and finiteness properties of Torelli groups." Annals of Mathematics 177, no. 2 (March 1, 2013): 395–423. http://dx.doi.org/10.4007/annals.2013.177.2.1.

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19

Wockel, Christoph. "Lie group structures on symmetry groups of principal bundles." Journal of Functional Analysis 251, no. 1 (October 2007): 254–88. http://dx.doi.org/10.1016/j.jfa.2007.05.016.

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20

Liu, Lucy, Gary P. T. Choi, and L. Mahadevan. "Wallpaper group kirigami." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2252 (August 2021): 20210161. http://dx.doi.org/10.1098/rspa.2021.0161.

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Kirigami, the art of paper cutting, has become a paradigm for mechanical metamaterials in recent years. The basic building blocks of any kirigami structures are repetitive deployable patterns that derive inspiration from geometric art forms and simple planar tilings. Here, we complement these approaches by directly linking kirigami patterns to the symmetry associated with the set of 17 repeating patterns that fully characterize the space of periodic tilings of the plane. We start by showing how to construct deployable kirigami patterns using any of the wallpaper groups, and then design symmetry-preserving cut patterns to achieve arbitrary size changes via deployment. We further prove that different symmetry changes can be achieved by controlling the shape and connectivity of the tiles and connect these results to the underlying kirigami-based lattice structures. All together, our work provides a systematic approach for creating a broad range of kirigami-based deployable structures with any prescribed size and symmetry properties.
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21

SHIRKOV, DMITRIJ V. "RENORMALIZATION GROUP SYMMETRY AND SOPHUS LIE GROUP ANALYSIS." International Journal of Modern Physics C 06, no. 04 (August 1995): 503–12. http://dx.doi.org/10.1142/s0129183195000356.

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We start with a short discussion of the content of a term Renormalisation Group in modern use. By treating the underlying solution property as a reparametrisation symmetry, we relate it with the self-similarity symmetry well-known in mathematical physics and explain the notion of Functional Self-similarity. Then we formulate a program of constructing a regular approach for discovering RG-type symmetries in different problems of mathematical physics. This approach based upon S. Lie group analysis allows one to analyse a wide class of boundary problems for different type of equations. Several examples are mentioned.
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22

Felix, René P., and Allan O. Junio. "Color groups arising from index-nsubgroups of symmetry groups." Acta Crystallographica Section A Foundations and Advances 71, no. 2 (February 4, 2015): 216–24. http://dx.doi.org/10.1107/s2053273314028071.

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One of the main goals in the study of color symmetry is to classify colorings of symmetrical objects through their color groups. The term color group is taken to mean the subgroup of the symmetry group of the uncolored symmetrical object which induces a permutation of colors in the coloring. This work looks for methods of determining the color group of a colored symmetric object. It begins with an indexnsubgroupHof the symmetry groupGof the uncolored object. It then considersH-invariant colorings of the object, so that the color groupH*will be a subgroup ofGcontainingH. In other words,H≤H*≤G. It proceeds to give necessary and sufficient conditions for the equality ofH*andG. IfH*≠Gandnis prime, thenH*=H. On the other hand, ifH*≠Gandnis not prime, methods are discussed to determine whetherH*isG,Hor some intermediate subgroup betweenHandG.
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23

Skalski, Adam, and Piotr M. Sołtan. "Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 02 (May 28, 2014): 1450012. http://dx.doi.org/10.1142/s021902571450012x.

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The quantum symmetry group of the inductive limit of C*-algebras equipped with orthogonal filtrations is shown to be the projective limit of the quantum symmetry groups of the C*-algebras appearing in the sequence. Some explicit examples of such projective limits are studied, including the case of quantum symmetry groups of the duals of finite symmetric groups, which do not fit directly into the framework of the main theorem and require further specific study. The investigations reveal a deep connection between quantum symmetry groups of discrete group duals and the doubling construction for Hopf algebras.
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24

Lockbaum, Gordon J., Florian Leidner, William E. Royer, Nese Kurt Yilmaz, and Celia A. Schiffer. "Optimizing the refinement of merohedrally twinned P61 HIV-1 protease–inhibitor cocrystal structures." Acta Crystallographica Section D Structural Biology 76, no. 3 (March 1, 2020): 302–10. http://dx.doi.org/10.1107/s2059798320001989.

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Twinning is a crystal-growth anomaly in which protein monomers exist in different orientations but are related in a specific way, causing diffraction reflections to overlap. Twinning imposes additional symmetry on the data, often leading to the assignment of a higher symmetry space group. Specifically, in merohedral twinning, reflections from each monomer overlap and require a twin law to model unique structural data from overlapping reflections. Neglecting twinning in the crystallographic analysis of quasi-rotationally symmetric homo-oligomeric protein structures can mask the degree of structural non-identity between monomers. In particular, any deviations from perfect symmetry will be lost if higher than appropriate symmetry is applied during crystallographic analysis. Such cases warrant choosing between the highest symmetry space group possible or determining whether the monomers have distinguishable structural asymmetries and thus require a lower symmetry space group and a twin law. Using hexagonal cocrystals of HIV-1 protease, a C 2-symmetric homodimer whose symmetry is broken by bound ligand, it is shown that both assigning a lower symmetry space group and applying a twin law during refinement are critical to achieving a structural model that more accurately fits the electron density. By re-analyzing three recently published HIV-1 protease structures, improvements in nearly every crystallographic metric are demonstrated. Most importantly, a procedure is demonstrated where the inhibitor can be reliably modeled in a single orientation. This protocol may be applicable to many other homo-oligomers in the PDB.
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25

Owino, Joseph Owuor. "GROUP ANALYSIS OF A NONLINEAR HEAT-LIKE EQUATION." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 13, 2023): 3113–31. http://dx.doi.org/10.47191/ijmcr/v11i1.03.

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We study a nonlinear heat like equation from a lie symmetry stand point. Heat equation have been employed to study ow of current, information and propagation of heat. The Lie group approach is used on the system to obtain symmetry reductions and the reduced systems studied for exact solutions. Solitary waves have been constructed by use of a linear span of time and space translation symmetries. We also compute conservation laws using multiplier approach and by a conservation theorem due to Ibragimov.
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26

DZHUNUSHALIEV, V., H. J. SCHMIDT, and O. RURENKO. "SPHERICALLY SYMMETRIC SOLUTIONS IN MULTIDIMENSIONAL GRAVITY WITH THE SU(2) GAUGE GROUP AS THE EXTRA DIMENSIONS." International Journal of Modern Physics D 11, no. 05 (May 2002): 685–701. http://dx.doi.org/10.1142/s0218271802001925.

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The multidimensional gravity on the principal bundle with the SU(2) gauge group is considered. The numerical investigation of the spherically symmetric metrics with the center of symmetry is made. The solution of the gravitational equations depends on the boundary conditions of the "SU(2) gauge potential" (off-diagonal metric components) at the symmetry center and on the type of symmetry (symmetrical or antisymmetrical) of these potentials. In the chosen range of the boundary conditions it is shown that there are two types of solutions: wormhole-like and flux tube. The physical application of such kind of solutions as quantum handles in a spacetime foam is discussed.
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27

Dehghani, M. H. "Symmetry group of the Liouville equation in a maximally symmetric spacetime." Classical and Quantum Gravity 14, no. 5 (May 1, 1997): 1207–13. http://dx.doi.org/10.1088/0264-9381/14/5/022.

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28

Clemente, Dore Augusto, and Armando Marzotto. "22 Space-group changes." Acta Crystallographica Section B Structural Science 59, no. 1 (January 28, 2003): 43–50. http://dx.doi.org/10.1107/s0108768102022668.

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This paper reports 22 examples of space-group changes from low to higher symmetry. The revisions involve 15 crystal structures that were originally described in space group P21, six in P\bar 1 and one in P1. The relevance of higher-symmetry elements is discussed in connection with the crystallography, the molecular dimensions and, when possible, the spectroscopic properties.
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29

Liu, Yang. "Structure of symmetry group of some composite links and some applications." Applied General Topology 21, no. 2 (October 1, 2020): 171. http://dx.doi.org/10.4995/agt.2020.10129.

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<p>In this paper, we study the symmetry group of a type of composite topological links, such as 2<sup>2</sup>m#2<sup>2</sup> . We have done a complete analysis on the elements of the symmetric group of this link and show the structure of the group. The results can be generalized to the study of the symmetry group of any composite topological link, and therefore it can be used for the classification of composite topological links, which can also be potentially used to identify synthetics molecules.</p><p> </p>
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30

Lee, Hun Hee, and Sang-Gyun Youn. "Quantum Channels with Quantum Group Symmetry." Communications in Mathematical Physics 389, no. 3 (January 6, 2022): 1303–29. http://dx.doi.org/10.1007/s00220-021-04283-9.

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31

Villain, J. "Symmetry and group theory throughout physics." EPJ Web of Conferences 22 (2012): 00002. http://dx.doi.org/10.1051/epjconf/20122200002.

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32

Hiai, Fumio, Milán Mosonyi, and Masahito Hayashi. "Quantum hypothesis testing with group symmetry." Journal of Mathematical Physics 50, no. 10 (October 2009): 103304. http://dx.doi.org/10.1063/1.3234186.

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33

ĐAPIĆ, N., M. KUNZINGER, and S. PILIPOVIĆ. "SYMMETRY GROUP ANALYSIS OF WEAK SOLUTIONS." Proceedings of the London Mathematical Society 84, no. 3 (April 29, 2002): 686–710. http://dx.doi.org/10.1112/s0024611502013436.

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Methods of Lie group analysis of differential equations are extended to weak solutions of (linear and non-linear) partial differential equations, where the term `weak solution' comprises the following settings: distributional solutions; solutions in generalized function algebras; solutions in the sense of association (corresponding to a number of weak or integral solution concepts in classical analysis). Factorization properties and infinitesimal criteria that allow the treatment of all three settings simultaneously are developed, thereby unifying and extending previous work in this area.2000 Mathematical Subject Classification: 46F30, 22E70, 35Dxx, 35A30.
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34

Hahn, Th. "Status of Volume A:Space-group Symmetry." Acta Crystallographica Section A Foundations of Crystallography 52, a1 (August 8, 1996): C572. http://dx.doi.org/10.1107/s0108767396076714.

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35

Carow-Watamura, Ursula, and Satoshi Watamura. "The Quantum Group as a Symmetry." Progress of Theoretical Physics Supplement 118 (1995): 375–89. http://dx.doi.org/10.1143/ptps.118.375.

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36

Belegradek, Igor. "Nonnegative Curvature, Symmetry and Fundamental Group." Geometriae Dedicata 106, no. 1 (June 2004): 169–84. http://dx.doi.org/10.1023/b:geom.0000033839.94207.d1.

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37

Fowler, P. W. "Isomer counting using point group symmetry." Journal of the Chemical Society, Faraday Transactions 91, no. 15 (1995): 2241. http://dx.doi.org/10.1039/ft9959102241.

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38

Zelikin, M. I. "Group symmetry in degenerate extremal problems." Russian Mathematical Surveys 43, no. 2 (April 30, 1988): 189–90. http://dx.doi.org/10.1070/rm1988v043n02abeh001725.

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39

Hardgrove, George L. "Teaching Space Group Symmetry through Problems." Journal of Chemical Education 74, no. 7 (July 1997): 797. http://dx.doi.org/10.1021/ed074p797.

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40

Aguirre, M., and J. Krause. "Point symmetry group of the Lagrangian." International Journal of Theoretical Physics 30, no. 11 (November 1991): 1461–72. http://dx.doi.org/10.1007/bf00675611.

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41

Fichtner, Konrad. "Non-space-group symmetry in crystallography." Computers & Mathematics with Applications 12, no. 3-4 (May 1986): 751–62. http://dx.doi.org/10.1016/0898-1221(86)90421-9.

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42

Shah, Parikshit, and Venkat Chandrasekaran. "Erratum: Group symmetry and covariance regularization." Electronic Journal of Statistics 7 (2013): 3057–58. http://dx.doi.org/10.1214/13-ejs871.

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43

Damljanović, V., R. Kostić, and R. Gajić. "Characters of graphene’s symmetry group Dg80." Physica Scripta T162 (September 1, 2014): 014022. http://dx.doi.org/10.1088/0031-8949/2014/t162/014022.

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44

Craddock, Mark, and Eckhard Platen. "Symmetry group methods for fundamental solutions." Journal of Differential Equations 207, no. 2 (December 2004): 285–302. http://dx.doi.org/10.1016/j.jde.2004.07.026.

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45

Ghaboussi, F. "Group theory of spontaneous symmetry breaking." International Journal of Theoretical Physics 26, no. 10 (October 1987): 957–66. http://dx.doi.org/10.1007/bf00670820.

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46

Craddock, M. J., and A. H. Dooley. "Symmetry group methods for heat kernels." Journal of Mathematical Physics 42, no. 1 (January 2001): 390–418. http://dx.doi.org/10.1063/1.1316763.

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47

Crisman, Karl-Dieter. "The Symmetry Group of the Permutahedron." College Mathematics Journal 42, no. 2 (March 2011): 135–39. http://dx.doi.org/10.4169/college.math.j.42.2.135.

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48

Nardelli, M. "Help for checking space-group symmetry." Journal of Applied Crystallography 29, no. 3 (June 1, 1996): 296–300. http://dx.doi.org/10.1107/s0021889896000672.

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Ten examples of crystal structures, taken from a paper by Marsh & Bernal [Acta Cryst. (1995), B51, 300–307], are considered to show how the PARST program works when it compares atomic sets in the search for lost symmetries.
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49

Min-Si, Li, and Liu Yan-Na. "Quantum Group Symmetry in Hofstadter Problem." Communications in Theoretical Physics 50, no. 2 (August 2008): 517–20. http://dx.doi.org/10.1088/0253-6102/50/2/48.

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50

Loginov, B. V., and O. V. Makeev. "Branching equations with crystallographic group symmetry." Doklady Mathematics 75, no. 1 (February 2007): 62–66. http://dx.doi.org/10.1134/s1064562407010188.

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