in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

‎Let $G$ be a finite non-abelian group with center $Z(G)$‎. ‎The non-commuting graph of $G$ is a simple undirected graph whose vertex set is $Gsetminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy ne yx$‎. ‎In this paper‎, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups‎..

Extending the work of del-Castillo-Negrete, Greene, and Morrison @Physica D 91, 1 ~1996!; 100, 311 ~1997!# on the standard nontwist map, the breakup of an invariant torus with winding number equal to the inverse golden mean squared is studied. Improved numerical techniques provide the greater accuracy that is needed for this case. The new results are interpreted within the renormalization group...

De nition 3.1. Let X be a complex manifold. A holomorphic vector bundle of rank k over E is a complex manifold E and a holomorphic map : E ! X such that makes E ! X into a complex vector bundle of rank k, and E admits holomorphic trivializations, i.e. there’s an open cover U of X trivializing E such that for each U 2 U, there’s a biholomorphic map ' : EjU ! U C commuting with projection to U th...

A geometric interpretation of the duality between two real forms of the complex trigonometric Ruijsenaars-Schneider model is presented. The phase spaces of the models in duality are realized as two different gauge slices in the same inverse image of the moment map defining a suitable symplectic reduction of the standard Heisenberg double of U(n). The collections of commuting Hamiltonians of the...

We invoke some ideas from finite geometry to map bijectively 135 heptads of mutually commuting three-qubit observables into 135 symmetric four-qubit ones. After labeling the elements of the former set in terms of a seven-dimensional Clifford algebra, we present the bijective map and most pronounced actions of the associated symplectic group on both sets in explicit forms. This formalism is then...

let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...

We investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space. Let X be a compact metric space. First we show the following. If τ : X → X is an expansive onto continuous map with the pseudo-orbit tracing property (POTP) and if there is a topologically mixing continuous map φ : X → X with τφ = φτ , then τ is topologically mixing. If...

We discuss the canonical structure of a class of integrable quantum mappings, i.e. iterative canonical transformations that can be interpreted as a discrete dynamical system. As particular examples we consider quantum map-pings associated with the lattice analogues of the KdV and MKdV equations. These mappings possess a non-ultralocal quantum Yang-Baxter structure leading to the existence of co...

SINCE the appearance of Enflo's negative solution to the approximation problem [3], only a few positive general results on the approximation properties have been obtained. However, it is shown in [2] that any separable Banach space with the metric approximation property (M.A.P.) has the commuting metric approximation property. More precisely, if X has (MAP) there exists a sequence {Rn} of finit...