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Journal articles on the topic 'Coset representative'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Van Rentergem, Yvan, Alexis De Vos, and Koen De Keyser. "Six Synthesis Methods for Reversible Logic." Open Systems & Information Dynamics 14, no. 01 (2007): 91–116. http://dx.doi.org/10.1007/s11080-007-9032-8.

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The (2w)! reversible transformations on w wires, i.e. reversible logic circuits with w inputs and w outputs, together with the action of cascading, form a group, isomorphic to the symmetric group S2w. Therefore, we investigate the group Sn as well as one of its subgroups isomorphic to Sn/2 × Sn/2. We then consider the left cosets, the right cosets, and the double cosets generated by the subgroup. Each element of a coset can function as the representative of the coset. The coset can then be considered as the set of all group elements that differ from the representative by merely multiplying (ei

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2

JOUNG, YEWON, JIEON KIM та SANG YOUL LEE. "IDEAL COSET INVARIANTS FOR SURFACE-LINKS IN ℝ4". Journal of Knot Theory and Its Ramifications 22, № 09 (2013): 1350052. http://dx.doi.org/10.1142/s0218216513500521.

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In [Towards invariants of surfaces in 4-space via classical link invariants, Trans. Amer. Math. Soc.361 (2009) 237–265], Lee defined a polynomial [[D]] for marked graph diagrams D of surface-links in 4-space by using a state-sum model involving a given classical link invariant. In this paper, we deal with some obstructions to obtain an invariant for surface-links represented by marked graph diagrams D by using the polynomial [[D]] and introduce an ideal coset invariant for surface-links, which is defined to be the coset of the polynomial [[D]] in a quotient ring of a certain polynomial ring mo

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3

Liu, Maw-Yang. "Optical CDMA system using spatial AMI coding scheme and coset representative." Optical and Quantum Electronics 47, no. 3 (2014): 503–14. http://dx.doi.org/10.1007/s11082-014-9885-3.

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4

Pooksombat, Perathorn, and Wittawat Kositwattanarerk. "Cubic Shaping of Lattice Constellations from Multi-Level Constructions from Codes." Mathematics 13, no. 10 (2025): 1562. https://doi.org/10.3390/math13101562.

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Lattice codes play an important role in wireless communication and are closely related to linear codes. Multi-level constructions of complex lattices from codes are known to produce lattice codes with desirable parameters and efficient encoding and decoding of information bits. However, their constellation usually involves superfluous elements that need to be mapped to a representative within the same coset to reduce average transmission power. One such elegant shaping function is a componentwise modulo, which is known to produce a cubic shaping for Barnes–Wall lattices. In this paper, we gene

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5

Liu, Jiang, Siyu Yang, Wencheng Liu, Feng Ni, and Chenfan Zhu. "Practical Canonical Labeling of Multi-Digraphs via Computer Algebra." Symmetry 16, no. 12 (2024): 1638. https://doi.org/10.3390/sym16121638.

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Practical algorithms for computing canonical forms of multi-digraphs do not exist in the literature. This paper proposes two practical approaches for finding canonical forms, from the perspective of nD symbolic computation. Initially, the approaches turn the problem of finding canonical forms of multi-digraphs into computing canonical forms of indexed monomials in computer algebra. Then, the first approach utilizes the double coset representative method in computational group theory for canonicalization of indexed monomials and shows that finding the canonical forms of a class of multi-digraph

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6

XU, FENG. "3-MANIFOLD INVARIANTS FROM COSETS." Journal of Knot Theory and Its Ramifications 14, no. 01 (2005): 21–90. http://dx.doi.org/10.1142/s0218216505003695.

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We construct unitary modular categories for a general class of coset conformal field theories based on our previous study of these theories in the algebraic quantum field theory framework using subfactor theory. We also consider the calculations of the corresponding 3-manifold invariants. It is shown that under certain index conditions the link invariants colored by the representations of coset factorize into the products of the the link invariants colored by the representations of the two groups in the coset. But the 3-manifold invariants do not behave so simply in general due to the nontrivi

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7

MATHIEU, PIERRE, DAVID SÉNÉCHAL, and MARK WALTON. "FIELD IDENTIFICATION IN NONUNITARY DIAGONAL COSETS." International Journal of Modern Physics A 07, supp01b (1992): 731–64. http://dx.doi.org/10.1142/s0217751x92004002.

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We study the nonunitary diagonal cosets constructed from admissible representations of Kač-Moody algebras at fractional level, with an emphasis on the question of field identification. Generic classes of field identifications are obtained from the analysis of the modular S matrix. These include the usual class related to outer automorphisms, as well as some intrinsically nonunitary field identifications. They allow for a simple choice of coset field representatives where all field components of the coset are associated with integrable weights.

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8

LASHKEVICH, M. YU. "BOSONIZATION OF 2D CONFORMAL MINIMAL-LIKE FIELD THEORIES." International Journal of Modern Physics A 07, no. 26 (1992): 6623–37. http://dx.doi.org/10.1142/s0217751x92003045.

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Some primary fields of Virasoro algebra in bosonic representation of Kastor-Martinec-Qiu minimal-like theories are constructed and these theories are compared with coset constructions SU (2)k× SU (2)l/ SU (2)k+l. Some properties of more complex cosets are investigated.

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9

Cirilo-Lombardo, Diego Julio. "Supercoherent states, simplest supergroups and associated supergeometries." International Journal of Geometric Methods in Modern Physics 18, no. 06 (2021): 2150087. http://dx.doi.org/10.1142/s0219887821500870.

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In this paper, geometries and supergeometries are analyzed from the point of view of the coset coherent states. To this end, before detailing the different factorizations of the simplest cosets, the dynamics and structure of Supercoherent states of the Klauder–Perelomov type (that are defined taking into account the geometry of the coset based on the simplest supergroup [Formula: see text] in the context of extensions of the standard model that were given previously in [A. B. Arbuzov and D. J. Cirilo-Lombardo, Phys. Scr. 94 (2019) 125302] as structural basis of the electroweak sector of the st

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10

AL-SHOMRANI, M. M. AL-MOSA. "Different choices of coset representatives." Material Science Research India 4, no. 2 (2007): 325–30. http://dx.doi.org/10.13005/msri/040213.

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11

Basaffar, W. H., and R. A. Hijazi. "Tensor categories and right coset representatives." International Journal of Algebra 10 (2016): 53–69. http://dx.doi.org/10.12988/ija.2016.6211.

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12

Mushtaq, Qaiser, and Sadef Baig. "A GRAPHICAL TECHNIQUE TO FIND THE PERMUTATION REPRESENTATION OF THE TRIANGLE GROUPS △(2, 3, k)." Asian-European Journal of Mathematics 05, no. 04 (2012): 1250055. http://dx.doi.org/10.1142/s1793557112500556.

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In this paper we have developed a graphical technique by which a suitably created fragment of a coset diagram for the action of PSL(2, ℤ) on projective lines over Galois fields can be used to obtain a complete coset diagram depicting finite homomorphic images of groups Δ(2, 3, k) = 〈x, y : x2 = y3 = (xy)k = 1〉.

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13

Nishiyama, Seiya, and João da Providência. "$\frac{{\rm SO}(2N)}{U(N)}$ Riccati–Hartree–Bogoliubov equation based on the SO(2N) Lie algebra of the fermion operators." International Journal of Geometric Methods in Modern Physics 12, no. 03 (2015): 1550035. http://dx.doi.org/10.1142/s0219887815500358.

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In this paper we present the induced representation of SO (2N) canonical transformation group and introduce [Formula: see text] coset variables. We give a derivation of the time-dependent Hartree–Bogoliubov (TDHB) equation on the Kähler coset space [Formula: see text] from the Euler–Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion

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14

JITTOH, TOSHIFUMI, MASAFUMI KOIKE, TAKAAKI NOMURA, JOE SATO, and TAKASHI SHIMOMURA. "GAUGE-HIGGS UNIFICATION MODELS WITH COSET SPACE DIMENSIONAL REDUCTION SCHEME." International Journal of Modern Physics A 24, no. 18n19 (2009): 3612–19. http://dx.doi.org/10.1142/s0217751x09047260.

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We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with two types of set up; fourteen-dimensional gauge theory with simple gauge groups and ten-dimensional gauge theory with direct product gauge groups. We found some phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in higher dimension, and fermion representation.

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15

Zhou, Jian. "Representation Rings of Classical Groups and Hopf Algebras." International Journal of Mathematics 14, no. 05 (2003): 461–77. http://dx.doi.org/10.1142/s0129167x03001922.

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We prove a double coset formula for induced representations of compact Lie groups. We apply it to the representation rings of unitary and symplectic groups to obtain Hopf algebras. We also construct a Heisenberg algebra representation based on the restiction and induction of representations of unitary groups.

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16

Nishiyama, Seiya. "Time Dependent Hartree–Bogoliubov Equation on the Coset Space SO(2N + 2)/U(N + 1) and Quasi Anti-Commutation Relation Approximation." International Journal of Modern Physics E 07, no. 06 (1998): 677–707. http://dx.doi.org/10.1142/s0218301398000397.

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An induced representation of an SO(2N + 1) group has been obtained from a group extension of the SO(2N) Bogoliubov transformation for fermions to a new canonical transformation group. Embedding the SO(2N + 1) group into an SO(2N + 2) group and using the SO(2N + 2)/U(N + 1) coset variables, we develop an extended time dependent Hartree–Bogoliubov (TDHB) theory in which paired and unpaired modes are treated in an equal manner. The extended TDHB theory applicable to both even and odd fermion systems is a time dependent self-consistent field (TDSCF) theory with the same level of the mean field app

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17

ITO, KATSUSHI. "QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA." International Journal of Modern Physics A 07, no. 20 (1992): 4885–98. http://dx.doi.org/10.1142/s0217751x92002210.

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We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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18

Litvin, Daniel B. "Magnetic subperiodic groups." Acta Crystallographica Section A Foundations of Crystallography 55, no. 5 (1999): 963–64. http://dx.doi.org/10.1107/s0108767399003487.

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The magnetic subperiodic groups, the 31 magnetic frieze-group types, the 394 magnetic rod-group types and the 528 magnetic layer-group types, are derived and given symbols based on the symbols for the nonmagnetic subperiodic groups in Volume E of International Tables for Crystallography. The symbols are constructed in analogy to the Opechowski–Guccione symbols for magnetic space groups. Tables are given that list one group from each type. Each group is specified not only by its symbol but also by explicitly listing the coset representatives of the coset decomposition of the group with respect

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19

Al-harbi, Bashayer, Wafa M. Fakieh, and Mohammed Mosa Al-shomrani. "On Non-trivially Associated Tensor Categories." European Journal of Pure and Applied Mathematics 11, no. 4 (2018): 1027–45. http://dx.doi.org/10.29020/nybg.ejpam.v11i4.3322.

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The purpose of this article is to provide mathematical formulas for some operationson the objects of a non-trivially associated tensor category constructed from a factorization of a group into a subgroup and a set of left coset representatives. A detailed example is provided.

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20

Gerasimov, A., A. Marshakov, and A. Morozov. "Free field representation of parafermions and related coset models." Nuclear Physics B 328, no. 3 (1989): 664–76. http://dx.doi.org/10.1016/0550-3213(89)90224-1.

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21

Gerasimov, A. A., A. Marshakov, and A. Yu Morozov. "Free field representation of parafermions and related coset models." Theoretical and Mathematical Physics 83, no. 2 (1990): 466–73. http://dx.doi.org/10.1007/bf01260942.

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22

Beggs, Edwin. "Making non-trivially associated tensor categories from left coset representatives." Journal of Pure and Applied Algebra 177, no. 1 (2003): 5–41. http://dx.doi.org/10.1016/s0022-4049(02)00119-6.

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23

Borges-Quintana, M., M. A. Borges-Trenard, I. Márquez-Corbella, and E. Martínez-Moro. "Computing coset leaders and leader codewords of binary codes." Journal of Algebra and Its Applications 14, no. 08 (2015): 1550128. http://dx.doi.org/10.1142/s0219498815501285.

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In this paper we use the Gröbner representation of a binary linear code [Formula: see text] to give efficient algorithms for computing the whole set of coset leaders, denoted by [Formula: see text] and the set of leader codewords, denoted by [Formula: see text]. The first algorithm could be adapted to provide not only the Newton and the covering radius of [Formula: see text] but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the

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24

HALPERN, M. B., and N. SOCHEN. "FLAT CONNECTIONS FOR CHARACTERS IN IRRATIONAL CONFORMAL FIELD THEORY." International Journal of Modern Physics A 10, no. 08 (1995): 1181–218. http://dx.doi.org/10.1142/s0217751x95000565.

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Following the paradigm on the sphere, we begin the study of irrational conformal field theory (ICFT) on the torus. In particular, we find that the affine-Virasoro characters of ICFT satisfy heatlike differential equations with flat connections. As a first example, we solve the system for the general g/h coset construction, obtaining an integral representation for the general coset characters. In a second application, we solve for the high-level characters of the general ICFT on simple g, noting a simplification for the subspace of theories which possess a nontrivial symmetry group. Finally, we

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25

Faisal, H. Nesayef. "Length Functions and HNN Groups." Journal of Scientific Research & Reports 14, no. 4 (2017): 1–8. https://doi.org/10.9734/JSRR/2017/33282.

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The concept of length functions on groups is first introduced by Lyndon. This is used to give direct proofs of many other results in combinatorial group theory. Two important sets called M and N satisfying some certain axioms of length functions are considered. Finally investigations of the nature and the structures of the sets M and N in relation to the elements of HNN group were carried out.

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26

KÖSTER, S. "LOCAL NATURE OF COSET MODELS." Reviews in Mathematical Physics 16, no. 03 (2004): 353–82. http://dx.doi.org/10.1142/s0129055x0400200x.

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The local algebras of the maximal Coset model [Formula: see text] associated with a chiral conformal subtheory [Formula: see text] are shown to coincide with the local relative commutants of [Formula: see text] in ℬ, provided [Formula: see text] possesses a stress-energy tensor.Making the same assumption, the adjoint action of the unique inner-implementing representation [Formula: see text] associated with [Formula: see text] on the local observables in ℬ is found to define net-endomorphisms of ℬ. This property is exploited for constructing from ℬ a conformally covariant holographic image in (

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27

Oh, Phillial. "Coset representation of closed loop space in string field theory." Physics Letters B 196, no. 3 (1987): 336–38. http://dx.doi.org/10.1016/0370-2693(87)90743-x.

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28

T. Rajeswari та R.Viajayakumar. "S-α Anti Fuzzy Normal Subsemigroups in S-α Anti Fuzzy Semigroups". International Journal of Fuzzy Mathematical Archive 14, № 02 (2017): 339–46. http://dx.doi.org/10.22457/ijfma.v14n2a16.

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The notion of S-α anti fuzzy cosets with representative and S-α anti fuzzy normal subsemi groups are introduced and their characterizations are obtained. It is also proved that the set of all S-α anti fuzzy cosets will form a semigroup under a suitable binary operation and its structural properties are determined. A necessary condition for an S-α anti fuzzy semigroup to be S-α anti fuzzy normal is also proved.

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29

LAM, DAISY, and SAM NELSON. "AN ISOMORPHISM THEOREM FOR ALEXANDER BIQUANDLES." International Journal of Mathematics 20, no. 01 (2009): 97–107. http://dx.doi.org/10.1142/s0129167x09005194.

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We show that two Alexander biquandles M and M′ are isomorphic if and only if there is an isomorphism of ℤ[s±1, t±1]-modules h : (1 - st)M → (1 - st)M′ and a bijection g : Os(A) → Os(A′) between the s-orbits of sets of coset representatives of M/(1 - st)M and M′/(1 - st)M′ respectively satisfying certain compatibility conditions.

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YAGUCHI, YOSHIRO. "ISOTROPY SUBGROUP OF HURWITZ ACTION OF THE 3-BRAID GROUP ON THE BRAID SYSTEMS." Journal of Knot Theory and Its Ramifications 18, no. 07 (2009): 1021–30. http://dx.doi.org/10.1142/s0218216509007270.

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The Hurwitz action of the n-braid group Bn on the n-fold direct product Bmn of the m-braid group Bm is studied. We show that the isotropy subgroup of the Hurwitz group action of B3 at the triple of the standard generators of B4 has index 16, by explicitly describing a complete system of coset representatives. An application to the braided surfaces in 4-space is also given.

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31

Al-Subaie, Najla SH, and Mohammed Mosa Al-shomrani. "On Weak Graded Rings II." European Journal of Pure and Applied Mathematics 12, no. 2 (2019): 332–47. http://dx.doi.org/10.29020/nybg.ejpam.v12i2.3380.

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The G-weak graded rings are rings graded by a set G of left coset representatives for the left action of a subgroup H of a finite group X. The main aim of this article is to study the concept of G-weak graded rings and continue the investigation of their properties. Moreover, some results concerning G-weak graded rings of fractions are derived. Finally, some additional examples of G-weak graded rings are provided.

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KAZAMA, YOICHI, and HISAO SUZUKI. "BOSONIC CONSTRUCTION OF CONFORMAL FIELD THEORIES WITH EXTENDED SUPERSYMMETRY." Modern Physics Letters A 04, no. 03 (1989): 235–42. http://dx.doi.org/10.1142/s0217732389000307.

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A large class of unitary N = 2 superconformal field theories are constructed in the bosonic representation. In particular, they include an infinite number of models with the Virasoro central charge (c) equaling 9, which are generalizations of the ones recently obtained by a coset space method. Similar results are also obtained for c = 6, for which the algebra extends to that with N = 4 supersymmetry.

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33

Zhu, Yuqing, Jincheng Zhuang, Chang Lv, and Dongdai Lin. "Classifying and generating exact coset representatives of PGL2(Fq) in PGL2(Fq2)." Finite Fields and Their Applications 42 (November 2016): 118–27. http://dx.doi.org/10.1016/j.ffa.2016.07.010.

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34

OLIVIER, D., and G. VALENT. "MULTIPLICATIVE RENORMALIZABILITY AND THE LAPLACE-BELTRAMI OPERATOR." International Journal of Modern Physics A 06, no. 06 (1991): 955–76. http://dx.doi.org/10.1142/s0217751x91000526.

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For some rank 1 non-linear σ models we prove that a necessary and sufficient condition of multiplicative renormalizability for composite fields is that they should be eigenfunctions of the coset Laplace-Beltrami operator. These eigenfunctions span the irreducible representation space of the isometry group and may be finite- or infinite-dimensional. The zero mode of the Laplace-Beltrami operator plays a particular role since it is not renormalized at all.

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35

Hwang, Jena D., Chandra Bhagavatula, Ronan Le Bras, et al. "(Comet-) Atomic 2020: On Symbolic and Neural Commonsense Knowledge Graphs." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6384–92. http://dx.doi.org/10.1609/aaai.v35i7.16792.

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Recent years have brought about a renewed interest in commonsense representation and reasoning in the field of natural language understanding. The development of new commonsense knowledge graphs (CSKG) has been central to these advances as their diverse facts can be used and referenced by machine learning models for tackling new and challenging tasks. At the same time, there remain questions about the quality and coverage of these resources due to the massive scale required to comprehensively encompass general commonsense knowledge. In this work, we posit that manually constructed CSKGs will n

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36

Guang-Zeng Feng and Dian-Wu Yue. "Minimum cyclotomic coset representatives and their applications to BCH codes and Goppa codes." IEEE Transactions on Information Theory 46, no. 7 (2000): 2625–28. http://dx.doi.org/10.1109/18.887870.

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37

Tan, Lin. "On the distinguished coset representatives of the parabolic subgroups in finite coxeter groups." Communications in Algebra 22, no. 3 (1994): 1049–61. http://dx.doi.org/10.1080/00927879408824892.

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Papi, Paolo. "Inversion tables and minimal left coset representatives for Weyl groups of classical type." Journal of Pure and Applied Algebra 161, no. 1-2 (2001): 219–34. http://dx.doi.org/10.1016/s0022-4049(00)00101-8.

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OHTA, NOBUYOSHI, and HISAO SUZUKI. "BOSONIZATION OF A TOPOLOGICAL COSET MODEL AND NON-CRITICAL STRING THEORY." Modern Physics Letters A 09, no. 06 (1994): 541–47. http://dx.doi.org/10.1142/s0217732394003774.

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We analyze the relation between a topological coset model based on super SL(2, R)/U(1) coset and non-critical string theory by using free field realization. We show that the twisted N=2 algebra of the coset model can be naturally transformed into that of non-critical string. The screening operators of the coset models can be identified either with those of the minimal matters or with the cosmological constant operator. We also find that another screening operator, which is intrinsic in our approach, becomes the BRST non-trivial state of ghost number 0 (generator of the ground ring for c=1 grav

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40

Al-Shomrani, Mohammed, and Najlaa Al-Subaie. "A Generalization of Group-Graded Modules." Symmetry 14, no. 4 (2022): 835. http://dx.doi.org/10.3390/sym14040835.

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In this article, we generalize the concept of group-graded modules by introducing the concept of G-weak graded R-modules, which are R-modules graded by a set G of left coset representatives, where R is a G-weak graded ring. Moreover, we prove some properties of these modules. Finally, results related to G-weak graded fields and their vector spaces are deduced. Many considerable examples are provided with more emphasis on the symmetric group S3 and the dihedral group D6, which gives the group of symmetries of a regular hexagon.

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Al-Shomrani, M. M., and E. J. Beggs. "Making nontrivially associated modular categories from finite groups." International Journal of Mathematics and Mathematical Sciences 2004, no. 42 (2004): 2231–64. http://dx.doi.org/10.1155/s0161171204308203.

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We show that the double𝒟of the nontrivially associated tensor category constructed from left coset representatives of a subgroup of a finite groupXis a modular category. Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. This definition is shown to be adjoint invariant and multiplicative on tensor products. A detailed example is given. Finally, we show an equivalence of categories between the nontrivially associated double𝒟and the trivially associated category of representations of the Drinfeld double of the groupD(

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42

Muratović, Amela. "Representation of Polynomials Over Finite Fields With Circulants." Sarajevo Journal of Mathematics 1, no. 1 (2024): 21–26. http://dx.doi.org/10.5644/sjm.01.1.04.

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Representation of polynomials over complex fields is well known. In this paper a similar representation is given for polynomials of degree less than $q-1$, over finite fields. The results are theorems that characterize the centralizer of the circulant of a permutation polynomial, and a formula for the calculation of the determinant of the circulant as the product of the determinants of the polynomials defined on the cosets of some multilpicative subgroup. 2000 Mathematics Subject Classification. 12E05, 16S50

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Aamir, Muhammad, Muhammad Awais Yousaf, and Abdul Razaq. "Number of Distinct Homomorphic Images in Coset Diagrams." Journal of Mathematics 2021 (July 31, 2021): 1–39. http://dx.doi.org/10.1155/2021/6669459.

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The representation of the action of PGL 2 , Z on F t ∪ ∞ in a graphical format is labeled as coset diagram. These finite graphs are acquired by the contraction of the circuits in infinite coset diagrams. A circuit in a coset diagram is a closed path of edges and triangles. If one vertex of the circuit is fixed by p q Δ 1 p q − 1 Δ 2 p q Δ 3 … p q − 1 Δ m ∈ PSL 2 , Z , then this circuit is titled to be a length- m circuit, denoted by Δ 1 , Δ 2 , Δ 3 , … , Δ m . In this manuscript, we consider a circuit Δ of length 6 as Δ 1 , Δ 2 , Δ 3 , Δ 4 , Δ 5 , Δ 6 with vertical axis of symmetry, that is, Δ

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John Rafael M. Antalan. "Some Reverse Topological Indices of Comet and Double Comet Graphs." Communications on Applied Nonlinear Analysis 32, no. 3 (2024): 71–83. http://dx.doi.org/10.52783/cana.v32.1920.

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Introduction: Chemical Graph Theory or CGT for short, is a transdisciplinary field of Mathematics wherein graphs are used to represent chemical compounds. Under this representation, the atoms of a chemical compound are expressed as vertices, while the bonds connecting these atoms are expressed as edges. Once the graph representation of a chemical compound has been determined, graph-theoretic techniques can now be used to determine various topological indices associated with the chemical compound. Topological indices are invariants of a graph that have predictive power for the chemical properti

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Grekhova, A. K., L. B. Gorbacheva, N. A. Ivanova, I. A. Efimenko, and A. N. Osipov. "Comparative studies on the genotoxic activity of a new palladium (II) acidocomplex vs cisplatin in human blood lymphocytes." Biomeditsinskaya Khimiya 59, no. 1 (2013): 107–14. http://dx.doi.org/10.18097/pbmc20135901107.

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A comparative study on the genotoxic activity of cisplatin versus morfozol, the first representative of a new class of cation-anion complexes of palladium [AH] [PdCl ] (where A-methylmorpholine) has been performed using human lymphocytes in vitro. The results of the DNA-DNA cross-linking activity investigations showed that both compounds studied exhibited biphasic dose-effect relationship: a linear decrease in the DNA percent in the comet tail and the region of the "plateau". However, in the "plateau" region, morfozol reduced the DNA percent in the comet tail up to 6 times while cisplatin caus

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FLEURY, N., and M. RAUSCH DE TRAUBENBERG. "LOCAL FRACTIONAL SUPERSYMMETRY FOR ALTERNATIVE STATISTICS." Modern Physics Letters A 11, no. 11 (1996): 899–913. http://dx.doi.org/10.1142/s0217732396000916.

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A group theory justification of one-dimensional fractional supersymmetry is proposed using an analog of a coset space, just like the one introduced in 1-D supersymmetry. This theory is then gauged to obtain a local fractional supersymmetry, i.e. a fractional supergravity which is then quantized à la Dirac to obtain an equation of motion for a particle which is in a representation of the braid group and should describe alternative statistics. A formulation invariant under general reparametrization is given by means of a curved fractional superline.

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Carvalho, Rozana Neves Guimarães de, Renato Matos da Silva, Carlos Freitas Lisboa, and Solange Gonçalves Belchior. "Participação no Comitê Estudantil na Associação Brasileira de Enfermagem: relato de experiência." Research, Society and Development 11, no. 10 (2022): e520111033314. http://dx.doi.org/10.33448/rsd-v11i10.33314.

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Objetivo: Relatar a experiência da participação de membros ativos e inativos do Comitê Estudantil na Associação Brasileira de Enfermagem-seção Rio de Janeiro (COEST ABEn-RJ). Método: Trata-se de um estudo reflexivo utilizando-se de relato de experiência, desenvolvido por um ex-integrante e integrante atual do COEST- ABen-RJ. Resultado e discussão: Participar de um Movimento Estudantil representativo da Enfermagem é entender e analisar todo o contexto de ideias no qual determinado grupo está inserido. O COEST é o meio de comunicação mais eficiente entre os estudantes de enfermagem de todos os n

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Liu, Ziming. "Composing group action to permutation representation." Theoretical and Natural Science 9, no. 1 (2023): 30–37. http://dx.doi.org/10.54254/2753-8818/9/20240708.

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A mapping that satisfies two specific axioms provides a common notion of group action. A homomorphism translating from a group to a symmetric group of a certain set can also be used to describe group action. Therefore, any example of the group actions can be stated based on the second equivalent definition, such as the regular action, natural matrix action, coset action, and Z^2 acting on R^2, etc. It is necessary to examine the concepts of the orbit and stabilizer of a group in order to reveal the orbit-stabilizer theorem. After the preparatory work, the orbit-stabilizer theorem can be proved

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MANSSUR, L. R. U., R. PORTUGAL, and B. F. SVAITER. "GROUP-THEORETIC APPROACH FOR SYMBOLIC TENSOR MANIPULATION." International Journal of Modern Physics C 13, no. 07 (2002): 859–79. http://dx.doi.org/10.1142/s0129183102004571.

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We describe how Computational Group Theory provides tools for manipulating indexed objects (tensors, spinors, and so on) in explicit index notation. In particular, we present algorithms that put tensors with free and dummy indices obeying permutation symmetries into the canonical form. The method is based on algorithms for determining canonical double coset representatives of subgroups of the symmetric group. The complexity of the algorithms is polynomial on the number of indices in practical applications and allows one to address the simplification of tensor expressions with hundreds of indic

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Olson, R. J. M., and J. M. Pasachoff. "Historical Comets Over Bavaria: The Nuremberg Chronicle and Broadsides." International Astronomical Union Colloquium 116, no. 2 (1991): 1309–41. http://dx.doi.org/10.1017/s0252921100012914.

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Abstract.The first widely distributed printed comet images appear in the Nuremberg Chronicle, whose Latin edition appeared in 1493, followed closely by a German edition. In the first section, we begin our consideration with the comet image that has frequently been cited as a representation of the A.D. 684 apparition of Comet P/Halley. To better understand this image, we present a thorough survey of the 13 comet images that appear in the Chronicle, all reproduced from four woodblocks, representing 14 apparitions between A.D. 471 and A.D. 1472. In the second part, we present an analysis of the u

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