scholarly journals Rotations in the Space of Split Octonions

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Merab Gogberashvili
Keyword(s):  
Direct Product ◽  
Lorentz Group ◽  
Classical Limit ◽  
Exceptional Group ◽  
Geometrical Application ◽  
Split Octonions

The geometrical application of split octonions is considered. The new representation of products of the basis units of split octonionic having David's star shape (instead of the Fano triangle) is presented. It is shown that active and passive transformations of coordinates in octonionic “eight-space” are not equivalent. The group of passive transformations that leave invariant the pseudonorm of split octonions isSO(4,4), while active rotations are done by the direct product ofO(3,4)-boosts and real noncompact form of the exceptional groupG2. In classical limit, these transformations reduce to the standard Lorentz group.

On non-compact groups. II. Representations of the 2+1 Lorentz group

1965 ◽  
Vol 287 (1411) ◽  
pp. 532-548 ◽  
Keyword(s):  
Hilbert Space ◽  
Direct Product ◽  
Lorentz Group ◽  
Complex Number ◽  
Algebraic Method ◽  
Unitary Representations ◽  
Compact Groups ◽  
Matrix Elements ◽  
Linear Representations ◽  
The Matrix

A simple algebraic method based on multispinors with a complex number of indices is used to obtain the linear (and unitary) representations of non-com pact groups. The method is illustrated in the case of the 2+1 Lorentz group. All linear representations of this group, their various realizations in Hilbert space as well as the matrix elements of finite transformations have been found. The problem of reduction of the direct product is also briefly discussed.

II. Non adiabatic theory of collisions in a radiative field. Semi-classical limit : Ar + O case

1989 ◽  
Vol 50 (10) ◽  
pp. 1195-1208 ◽  
Author(s):  
A. Spielfiedel ◽  
E. Roueff ◽  
N. Feautrier
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory

Non adiabatic theory of collisions in a radiative field. Semi-classical limit

1988 ◽  
Vol 49 (11) ◽  
pp. 1911-1923 ◽  
Author(s):  
N. Feautrier ◽  
E. Roueff ◽  
A. Spielfiedel
Keyword(s):  
Classical Limit ◽  
Adiabatic Theory

Equitable Total Coloring of Direct Product of Path and Cycle

2019 ◽  
Vol 10 (7) ◽  
pp. 1476-1481
Author(s):  
S. Moidheen Aliyar ◽  
S. Manimaran ◽  
K. Manikandan
Keyword(s):  
Direct Product ◽  
Total Coloring

Sport and nationalism in the Republic of North Macedonia

Focaal ◽  
2019 ◽  
pp. 1-13
Author(s):  
Vasiliki P. Neofotistos
Keyword(s):  
Direct Product ◽  
Nation Building ◽  
National History ◽  
Sports Teams ◽  
The Balkans ◽  
The North ◽  
Political Forces ◽  
The Republic

Using the Republic of North Macedonia as a case study, this article analyzes the processes through which national sports teams’ losing performance acquires a broad social and political significance. I explore claims to sporting victory as a direct product of political forces in countries located at the bottom of the global hierarchy that participate in a wider system of coercive rule, frequently referred to as empire. I also analyze how public celebrations of claimed sporting victories are intertwined with nation-building efforts, especially toward the global legitimization of a particular version of national history and heritage. The North Macedonia case provides a fruitful lens through which we can better understand unfolding sociopolitical developments, whereby imaginings of the global interlock with local interests and needs, in the Balkans and beyond.

On the g-hypergroupoids associated with g-hypergraphs

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4819-4831 ◽  
Author(s):  
Mehdi Farshi ◽  
Bijan Davvaz ◽  
Saeed Mirvakili
Keyword(s):  
Direct Product ◽  
Fundamental Relation ◽  
Join Space ◽  
Commutative Hypergroup ◽  
Regular Relation

In this paper, we associate a partial g-hypergroupoid with a given g-hypergraph and analyze the properties of this hyperstructure. We prove that a g-hypergroupoid may be a commutative hypergroup without being a join space. Next, we define diagonal direct product of g-hypergroupoids. Further, we construct a sequence of g-hypergroupoids and investigate some relationships between it?s terms. Also, we study the quotient of a g-hypergroupoid by defining a regular relation. Finally, we describe fundamental relation of an Hv-semigroup as a g-hypergroupoid.

scholarly journals Semi-Classical Localisation Properties of Quantum Oscillators on a Noncommutative Configuration Space

2015 ◽  
Vol 22 (04) ◽  
pp. 1550021 ◽  
Author(s):  
Fabio Benatti ◽  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Configuration Space ◽  
Classical Limit ◽  
Coherent States ◽  
Point Of View ◽  
Quantum Mechanical ◽  
Wigner Functions ◽  
Quantum Mechanical Oscillators ◽  
Mechanical Oscillators ◽  
Space Noncommutativity

When dealing with the classical limit of two quantum mechanical oscillators on a noncommutative configuration space, the limits corresponding to the removal of configuration-space noncommutativity and position-momentum noncommutativity do not commute. We address this behaviour from the point of view of the phase-space localisation properties of the Wigner functions of coherent states under the two limits.

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