Related papers: Wheeling around Mazur rotations problem
In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic…
In this survey article, we present some panorama of groups acting on metric spaces of non-positive curvature. We introduce the main examples and their rigidity properties , we show the links between algebraic or analytic properties of the…
We deal with compact K\"ahler manifolds $M$ acted on by a compact Lie group $K$ of isometries, whose complexification $K^\C$ has exactly one open and one closed orbit in $M$. If the $K$-action is Hamiltonian, we obtain results on the…
This work explores the dynamic properties of test particles surrounding a distorted, deformed compact object. The astrophysical motivation was to choose such background, which could constitute a more reasonable model of a real situation…
The two-dimensional motion of an object on a moving rough horizontal plane is investigated. Two cases are studied: the plane having a translational acceleration, and a rotating plane. For the first case, the motions of a point particle and…
In classical mechanics, the 'geometry of motion' refers to a development to visualize the motion of freely spinning bodies. In this paper, such an approach of studying the rotational motion of axisymmetric variable mass systems is…
The problems related to nonlinear behavior of Regge trajectories (RT) and their renormalization group invariance are discussed.
We shed some light on the problem of determining the orbits of the braid group action on semiorthonormal bases of Mukai lattices as considered in \cite{GK04} and \cite{GO1}. We show that there is an algebraic (and in particular algorithmic)…
We introduce a new group action on set systems, constructed as a semidirect product of a permutation group and a group generated by twist and loop complementation operations on a single element. This action extends the ribbon group…
We introduce an invariant of a pair of commuting invertible matrices that we call the rotation index. We apply this invariant, together with the Milnor--Munkres--Novikov pairing, to the study of some questions about group actions of…
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity property. One class of examples is rotationally invariant…
In this paper the some questions of equivariant movability connected with substitution of acting group $G$ on closed subgroup $H$ and with transitions to spaces of $H$-orbits and $H$-fixed points spaces are investigated. In the special case…
We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…
We describe the kinematics, dynamics and also some energetic issues related to the Marta mouse motion when she walks on top of a horizontal bicycle wheel, which is free to rotate like a merry-to-go round, as presented recently by Paul…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
The action of the idempotent deformations on finite groups is discussed. This action is described in terms of the homological properties of groups. The orbits of finite simple groups are determined.
In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…
We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative…
We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…
We investigate the ballistic motion of electrons in III-V semiconductor quantum wells with Rashba spin-orbit coupling in a perpendicular magnetic field. Taking into account the full quantum dynamics of the problem, we explore the…