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Hexatonic systems and dual groups in mathematical music theory [PDF]
Involve, a Journal of Mathematics, 2017 Motivated by the music-theoretical work of Richard Cohn and David Clampitt on late-nineteenth century harmony, we mathematically prove that the PL-group of a hexatonic cycle is dual (in the sense of Lewin) to its T/I-stabilizer. Our point of departure is Cohn's notions of maximal smoothness and hexatonic cycle, and the symmetry group of the 12-gon; we ...
Cameron Berry, Thomas M. Fiore
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GROUP THEORY FOR TEACHERS OF ELEMENTARY MATHEMATICS [PDF]
School Science and Mathematics, 1906 n ...
G. A. Miller
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Mathematical Crystallography and the Theory of Groups of Movements. By Harold Hilton, M.A. [PDF]
The Mathematical Gazette, 1904 xii, 262 p. :
Alfred Edwin Howard Tutton
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Group Theory: Mathematical Expression of Symmetry in Physics [PDF]
Symmetry, 2021 The present article reviews the multiple applications of group theory to the symmetry problems in physics. In classical physics, this concerns primarily relativity: Euclidean, Galilean, and Einsteinian (special). Going over to quantum mechanics, we first note that the basic principles imply that the state space of a quantum system has an intrinsic ...
Jean-Pierre Antoine
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Mathematical Modeling of Group Concurrency in Game Theory
Journal of Computational and Engineering Mathematics, 2015 The approach to an estimation of results of group "competitions" of intellectual agents is described. Petri-Markov models group "competition" are analyzed. Expressions for the determination of the probability density distribution and the participants or groups of participants win or lose "competition" are given.
Alexey Ivutin +2 more
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Development of the applied mathematics originating from the group theory of physical and mathematical problems [PDF]
, 1996 This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Group theoretical methods are a powerful tool both in their applications to mathematics and to physics. The broad goal of this project was to use such methods to develop the implications of group (symmetry)
James Benjamin Hyman +3 more
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Mathematics and group theory in music
, 2014 The purpose of this paper is to show through particular examples how group theory is used in music. The examples are chosen from the theoretical work and from the compositions of Olivier Messiaen (1908-1992), one of the most influential twentieth century composers and pedagogues. Messiaen consciously used mathematical concepts derived from symmetry and
Athanase Papadopoulos
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Group theory and biomolecular conformation: I. Mathematical and computational models [PDF]
Journal of Physics: Condensed Matter, 2010 Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational ...
Gregory S. Chirikjian
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Journal of Physics: Conference Series, 2020 Abstract The purpose of the article is to describe the IMTs’ identified mathematical connection between group theory and school mathematics curriculums in Indonesia. The data was gathered from the IMTs who involved in the Teachers Professional Training (TPT) program.
Agnita Siska Pramasdyahsari +2 more
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A Mathematical Theory of Interpersonal Interactions and Group Behavior
, 2018 Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these approaches transcend traditional studies of group decision making that focus on how individual preferences combine ...
Yaneer Bar‐Yam, Dávid Kántor
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