Completion of a half linearly cyclically ordered group

2002 ◽  
Vol 22 (1) ◽  
pp. 5
Author(s):  
Stefan Cernak
Keyword(s):  
Ordered Group ◽  
Cyclically Ordered Group

Completion of a cyclically ordered group

1987 ◽  
Vol 37 (1) ◽  
pp. 157-174 ◽  
Author(s):  
Štefan Černák ◽  
Ján Jakubík
Keyword(s):  
Ordered Group ◽  
Cyclically Ordered Group

Sequential convergences on cyclically ordered groups without Urysohn’s axiom

2008 ◽  
Vol 58 (6) ◽  
Author(s):  
Ján Jakubík
Keyword(s):  
Cyclic Order ◽  
Ordered Group ◽  
Group Operation ◽  
Partially Ordered ◽  
Ordered Groups ◽  
Brouwerian Lattice ◽  
Cyclically Ordered Group

AbstractIn this paper we investigate sequential convergences on a cyclically ordered group G which are compatible with the group operation and with the relation of cyclic order; we do not assume the validity of the Urysohn’s axiom. The system convG of convergences under consideration is partially ordered by means of the set-theoretical inclusion. We prove that convG is a Brouwerian lattice.

scholarly journals Cyclically ordered group and C *-dynamical system

2019 ◽  
Vol 1280 ◽  
pp. 022043
Author(s):  
I Yusnitha ◽  
R Rosjanuardi ◽  
S M Gozali
Keyword(s):  
Dynamical System ◽  
Ordered Group ◽  
Cyclically Ordered Group

Torsion Radicals and Torsion Classes of Cyclically Ordered Groups

2015 ◽  
Vol 65 (2) ◽  
Author(s):  
Jan Jákubík ◽  
Judita Lihoyá
Keyword(s):  
Proper Class ◽  
Ordered Sets ◽  
Ordered Group ◽  
Completely Distributive ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Complete Completely Distributive Lattice ◽  
Cyclically Ordered Group ◽  
Completely Distributive Lattice ◽  
Torsion Radical

AbstractThe notion of torsion radical of cyclically ordered groups is defined analogously as in the case of lattice ordered groups. We denote by T the collection of all torsion radicals of cyclically ordered groups. For τ1, τ2 ∈ T, we put τ1 ∈ τ2 if τ1(G) □ τ2(G) for each cyclically ordered group G. We show that T is a proper class; nevertheless, we apply for T the usual terminology of the theory of partially ordered sets. We prove that T is a complete completely distributive lattice. The analogous result fails to be valid for torsion radicals of lattice ordered groups. Further, we deal with products of torsion classes of cyclically ordered groups.

The absolute convexity of certain subgroups of an ordered group

1968 ◽  
Vol 7 (2) ◽  
pp. 82-85
Author(s):  
V. M. Kopytov ◽  
I. I. Mamaev
Keyword(s):  
Ordered Group ◽  
The Absolute

scholarly journals Congruences on bicyclic extensions of a linearly ordered group

2020 ◽  
Vol 15 (2) ◽  
pp. 61-80
Author(s):  
Oleg Gutik ◽  
Dušan Pagon ◽  
Kateryna Pavlyk
Keyword(s):  
Positive Cone ◽  
Inverse Semigroups ◽  
Green’S Relations ◽  
Ordered Group ◽  
Green's Relations ◽  
Linearly Ordered Group

In the paper we study inverse semigroups B(G), B^+(G), \overline{B}(G) and \overline{B}^+(G) which are generated by partial monotone injective translations of a positive cone of a linearly ordered group G. We describe Green’s relations on the semigroups B(G), B^+(G), \overline{B}(G) and \overline{B}^+(G), their bands and show that they are simple, and moreover, the semigroups B(G) and B^+(G) are bisimple. We show that for a commutative linearly ordered group G all non-trivial congruences on the semigroup B(G) (and B^+(G)) are group congruences if and only if the group G is archimedean. Also we describe the structure of group congruences on the semigroups B(G), B^+(G), \overline{B}(G) and \overline{B}^+(G).

scholarly journals APPLICATION OF THE LENNARD-JONES POTENTIAL IN MODELLING ROBOT MOTION

2019 ◽  
Vol 9 (4) ◽  
pp. 14-17
Author(s):  
Piotr Wójcicki ◽  
Tomasz Zientarski
Keyword(s):  
Interaction Strength ◽  
Robot Motion ◽  
Lennard Jones Potential ◽  
Ordered Group ◽  
Jones Potential ◽  
Lennard Jones ◽  
Optimal Value ◽  
Potential Impact ◽  
Moving Groups ◽  
Dynamics Simulations

The article proposes a method of controlling the movement of a group of robots with a model used to describe the interatomic interactions. Molecular dynamics simulations were carried out in a system consisting of a moving groups of robots and fixed obstacles. Both the obstacles and the group of robots consisted of uniform spherical objects. Interactions between the objects are described using the Lennard-Jones potential. During the simulation, an ordered group of robots was released at a constant initial velocity towards the obstacles. The objects’ mutual behaviour was modelled only by changing the value of the interaction strength of the potential. The computer simulations showed that it is possible to find the optimal value of the potential impact parameters that enable the implementation of the assumed robotic behaviour scenarios. Three possible variants of behaviour were obtained: stopping, dispersing and avoiding an obstacle by a group of robots.

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