A DIHEDRAL GROUP CODE OVER THE UNITARY TRI-DIMENSIONAL SPHERE S2

Jorge Pedraza Arpasi

doi:10.17654/ms130020165

Center of Mass Theorem and the Separation of Variables for Two-Body System on a Three-Dimensional Sphere

Nonlinear Phenomena in Complex Systems ◽

10.33581/1561-4085-2020-23-3-306-311 ◽

2020 ◽

Vol 23 (3) ◽

pp. 306-311

Author(s):

Yu. Kurochkin ◽

Dz. Shoukavy ◽

I. Boyarina

Keyword(s):

Constant Curvature ◽

Jacobi Equation ◽

Separation Of Variables ◽

Center Of Mass ◽

Three Dimensional ◽

Relative Distance ◽

Dimensional Sphere ◽

Body System ◽

Spaces Of Constant Curvature ◽

Hamilton Jacobi Equation

The immobility of the center of mass in spaces of constant curvature is postulated based on its definition obtained in [1]. The system of two particles which interact through a potential depending only on the distance between particles on a three-dimensional sphere is considered. The Hamilton-Jacobi equation is formulated and its solutions and trajectory equations are found. It was established that the reduced mass of the system depends on the relative distance.

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EXCITON INSULATOR STATES IN MATERIALS WITH â€˜MEXICAN HATâ€™ BAND STRUCTURE DISPERSION AND IN GRAPHENE

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v11i1.6947 ◽

2015 ◽

Vol 11 (1) ◽

pp. 2927-2949

Author(s):

Lyubov E. Lokot

Keyword(s):

Band Structure ◽

Three Dimensional ◽

Dimensional Sphere ◽

Electron Hole ◽

Dinger Equation ◽

Fermi Sphere ◽

Zinc Blende ◽

Bulk Gan ◽

Structure Dispersion ◽

Excitonic States

In the paper a theoretical study the both the quantized energies of excitonic states and their wave functions in grapheneand in materials with "Mexican hat" band structure dispersion as well as in zinc-blende GaN is presented. An integral twodimensionalSchrÃ¶dinger equation of the electron-hole pairing for a particles with electron-hole symmetry of reflection isexactly solved. The solutions of SchrÃ¶dinger equation in momentum space in studied materials by projection the twodimensionalspace of momentum on the three-dimensional sphere are found exactly. We analytically solve an integral twodimensionalSchrÃ¶dinger equation of the electron-hole pairing for particles with electron-hole symmetry of reflection. Instudied materials the electron-hole pairing leads to the exciton insulator states. Quantized spectral series and lightabsorption rates of the excitonic states which distribute in valence cone are found exactly. If the electron and hole areseparated, their energy is higher than if they are paired. The particle-hole symmetry of Dirac equation of layered materialsallows perfect pairing between electron Fermi sphere and hole Fermi sphere in the valence cone and conduction cone andhence driving the Cooper instability. The solutions of Coulomb problem of electron-hole pair does not depend from a widthof band gap of graphene. It means the absolute compliance with the cyclic geometry of diagrams at justification of theequation of motion for a microscopic dipole of graphene where >1 s r . The absorption spectrums for the zinc-blendeGaN/(Al,Ga)N quantum well as well as for the zinc-blende bulk GaN are presented. Comparison with availableexperimental data shows good agreement.

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Redefining Forro as a marker of identity: Language contact as a driving force for language maintenance among Santomeans in Portugal

Multilingua ◽

10.1515/multi-2020-0082 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Marie-Eve Bouchard

Keyword(s):

Language Contact ◽

Language Maintenance ◽

Attitudes And Beliefs ◽

Speech Community ◽

Group Code ◽

Community Members ◽

Sao Tome And Principe ◽

Semistructured Interviews ◽

Changing Attitudes

AbstractIn São Tomé and Príncipe, the language shift toward Portuguese is resulting in the endangerment of the native creoles of the island. These languages have been considered of low value in Santomean society since the mid-twentieth century. But when Santomeans are members of a diaspora, their perceptions of these languages, especially Forro, change in terms of value and identity-marking. It is possible to observe such changes among the Santomeans who learn Forro when they are abroad, who use it as an in-group code, and start to value it more. In this article, I address the role of language contact in the maintenance and expansion of Forro. I investigate the mechanisms of language maintenance by focusing on the shifts in community members’ attitudes and beliefs regarding their languages, as a result of contact. The changing attitudes and beliefs have led to a redefinition of the role of Forro in the speech community. This qualitative study is based on semistructured interviews conducted on São Tomé Island and in Portugal. Findings suggest that the change in value attributed to Forro by Santomeans as a result of contact contribute to the valorization of the language.

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Some characterizatsion of coprime graph of dihedral group D 2n

Journal of Physics Conference Series ◽

10.1088/1742-6596/1722/1/012051 ◽

2021 ◽

Vol 1722 ◽

pp. 012051

Author(s):

A G Syarifudin ◽

Nurhabibah ◽

D P Malik ◽

I G A W Wardhana

Keyword(s):

Dihedral Group ◽

Group D

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Continuous Maps from Spheres Converging to Boundaries of Convex Hulls

Forum of Mathematics Sigma ◽

10.1017/fms.2021.10 ◽

2021 ◽

Vol 9 ◽

Author(s):

Joseph Malkoun ◽

Peter J. Olver

Keyword(s):

Convex Hull ◽

Convex Geometry ◽

Gauss Map ◽

Parameter Family ◽

Convex Hulls ◽

Dimensional Sphere ◽

Continuous Maps ◽

Dimensional Boundary

Abstract Given n distinct points $\mathbf {x}_1, \ldots , \mathbf {x}_n$ in $\mathbb {R}^d$ , let K denote their convex hull, which we assume to be d-dimensional, and $B = \partial K $ its $(d-1)$ -dimensional boundary. We construct an explicit, easily computable one-parameter family of continuous maps $\mathbf {f}_{\varepsilon } \colon \mathbb {S}^{d-1} \to K$ which, for $\varepsilon> 0$ , are defined on the $(d-1)$ -dimensional sphere, and whose images $\mathbf {f}_{\varepsilon }({\mathbb {S}^{d-1}})$ are codimension $1$ submanifolds contained in the interior of K. Moreover, as the parameter $\varepsilon $ goes to $0^+$ , the images $\mathbf {f}_{\varepsilon } ({\mathbb {S}^{d-1}})$ converge, as sets, to the boundary B of the convex hull. We prove this theorem using techniques from convex geometry of (spherical) polytopes and set-valued homology. We further establish an interesting relationship with the Gauss map of the polytope B, appropriately defined. Several computer plots illustrating these results are included.

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