Jacobson introduced the concept of K-rings, continuing the investigation of Kaplansky and Herstein into the commutativity of rings. In this note we focus on the ring-theoretic properties of K-rings. We first construct basic examples of K-rings to be handled easily. It is shown that a semiprime K-ring of bounded index of nilpotency is a commutative domain. It is proved that if R is a prime K-rin...

We report on a heterocircuit [2]catenane in which a reversible half-rotation of one ring about the other can be induced, and locked in place, by switching the coordination of the interlocked rings between Pd(II) and Co(III).

Here we describe the design, assembly and characterisation of different structurally stable and highly polyvalent DNA catenanes. We synthesized a series of different catenated DNA nanostructures, among them symmetric ones containing two 126 or 168 base-pair rings, non-symmetric ones with a 126 and a 168 base-pair ring, and a [3]catenane containing three 126 base-pair rings. Reversible and quant...

We investigate parallelizable schemes for simulating dynamics of conservative systems admitting a decomposition into weakly coupled subsystems. A new method, related to Reversible Averaging [20], is introduced for constrained and unconstrained dynamics. Stability issues are discussed.

‎‎we exhibit an explicit construction for the second cohomology group‎ ‎$h^2(l‎, ‎a)$ for a lie ring $l$ and a trivial $l$-module $a$‎. ‎we show how the elements of $h^2(l‎, ‎a)$ correspond one-to-one to the‎ ‎equivalence classes of central extensions of $l$ by $a$‎, ‎where $a$‎ ‎now is considered as an abelian lie ring‎. ‎for a finite lie‎ ‎ring $l$ we also show that $h^2(l‎, ‎c^*) cong m(l)$‎...

The Pt(ii) dithiolene complex of a tetrathiafulvalene diphosphine ligand exhibits two reversible redox systems at close potentials, localized on the weakly interacting TTF (tetrathiafulvalene) and Pt(dmit) moieties.

A mechanism for the validity of a local version of the fluctuation theorem, uniform in the system size, is discussed for a reversible chain of weakly coupled Anosov systems.

A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the associated mass-action system. Furthermore, an index formula is given for the set of equilibria in a given stoichiometric compatibility class.

We study the conductance of mesoscopic graphene rings in the presence of a perpendicular magnetic field by means of numerical calculations based on a tight-binding model. First, we consider the magnetoconductance of such rings and observe the Aharonov–Bohm effect. We investigate different regimes of the magnetic flux up to the quantum Hall regime, where the Aharonov–Bohm oscillations are suppre...

We study the conductance of mesoscopic graphene rings in the presence of a perpendicular magnetic field by means of numerical calculations based on a tightbinding model. First, we consider the magnetoconductance of such rings and observe the Aharonov-Bohm effect. We investigate different regimes of the magnetic flux up to the quantum Hall regime, where the Aharonov-Bohm oscillations are suppres...