The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with combinatorial techniques. Here we illustrate that a wider context may be considered and show some structural restrictions on the group.

‎we consider two commutativity ratios $pr(g)$ and $f(g)$ in a finite group $g$‎ ‎and examine the properties of $g$ when these ratios are `large'‎. ‎we show that‎ ‎if $pr(g) > frac{7}{24}$‎, ‎then $g$ is metabelian and we give threshold‎ ‎results in the cases where $g$ is insoluble and $g'$ is nilpotent‎. ‎we also‎ ‎show that if $f(g) > frac{1}{2}$‎, ‎then $f(g) = frac{n+1}{2n}$‎, ‎for some‎ ‎na...

A peptide NTH-18 was synthesized in which a N-terminal helix is stabilised by two crossed disulfide bonds to a C-terminal extension. The design was inspired by the structure of the neurotoxic peptide apamin, which has previously been used to stabilise helices in miniature enzymes. CD- and NMR-spectroscopy indicated that NTH-18 adopted a fold similar to that found in apamin. However, the arrange...

Concurrency control schemes for object-oriented database systems (OODBSs) used in the area of performance-critical applications should increase the degree of concurrency and decrease locking overhead in order to offer maximum performance. However, most commercially available OODBSs use conventional concurrency control schemes that never exploit the rich semantics of object-oriented data model, ...

In this work we present a new sampling-based “black box” inference approach for learning the behaviors of a library component. As an application, we focus on the problem of automatically learning commutativity specifications of data structures. This is a very challenging problem, yet important, as commutativity specifications are fundamental to program analysis, concurrency control and even low...

We show, using the no–disentanglement theorem, that to teleport (exactly) any set of non–commuting states (i.e., a set containing at least two non–commuting states), it is necessary to have an entangled channel. We further show that to teleport any set of commuting states it is sufficient to have a classically correlated channel. Using this result we provide a simple proof of the fact that any ...

We give a simple characterization for a nonassociative algebra A, having characteristic 6= 2, to be commutative. Namely, A is commutative if and only if it is exible with a commuting set of generators. A counterexample shows that characteristic 6= 2 is necessary. Both the characterization and the counterexample were discovered using the computer algebra system in [2].

We consider the following condition (*) on an associative ring R : (*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy) = (xy)n(x,y) for some positive integer n(x,y) > 1. Commutativity and structure are established for Artinian rings R satisfying (*), and a counterexample is given for nonArtinian rings. The results generalize...