‎‎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 $h^2(l‎, ‎c^*) cong m(l)$‎...

In the present paper new criteria for classes of FP -injective and weakly quasi-Frobenius rings are given. Properties of both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we describe classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (resp. we...

Two mesoscopic SQUID rings which are far from each other, are considered. A source of twomode nonclassical microwaves irradiates the two rings with correlated photons. The Josephson currents are in this case quantum mechanical operators, and their expectation values with respect to the density matrix of the microwaves, yield the experimentally observed currents. Classically correlated (separabl...

The classes of FP -injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP -injective (weakly quasi-Frobenius...

We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a stable fixed state in arbitrarily large rings for a fixed coupling strength. This suggests that coherent behavior in networks of diffusively coupled systems m...

Quantum interference in coherent transport through single molecular rings may provide a mechanism to control the current in molecular electronics. We investigate its applicability, using a single-particle Green function method combined with ab initio electronic structure calculations. We find that the quantum interference effect (QIE) is strongly dependent on the interaction between molecular p...

In this paper we present a time-polynomial recognition algorithm for certain classes of circulant graphs. Our approach uses coherent configurations and Schur rings generated by circulant graphs for elucidating their symmetry properties and eventually finding a cyclic automorphism.

We present a formalization of coherent and strongly discrete rings in type theory. This is a fundamental structure in constructive algebra that represents rings in which it is possible to solve linear systems of equations. These structures have been instantiated with Bézout domains (for instance Z and k[x]) and Prüfer domains (generalization of Dedekind domains) so that we get certified algorit...

Background Intracardiac blood flow is known to influence cardiac development through transduction of endothelial shear forces. Vortex rings inside the left ventricle constitute a possible “blueprint” for cardiogenesis, the hemodynamic determinant of final cardiac shape. However, the relationship between the vortex ring and endocardium has previously not been quantified, and the influence of the...

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...