In this paper, we study some ring theoretic properties of the amalgamated duplication ring $Rbowtie I$ of a commutative Noetherian ring $R$ along an ideal $I$ of $R$ which was introduced by D'Anna and Fontana. Indeed, it is determined that when $Rbowtie I$ satisfies Serre's conditions $(R_n)$ and $(S_n)$, and when is a normal ring, a generalized Cohen-Macaulay ring and finally a filter ring.

After recalling briefly the main properties of the amalgamated duplication of a ring R along an ideal I , denoted by R1 I [5], we restrict our attention to the study of the properties of R1 I , when I is a multiplicative canonical ideal of R [9]. In particular, we study when every regular fractional ideal of R1I is divisorial.

A generalized-statistics variational principle for source separation is formulated by recourse to Tsallis’ entropy subjected to the additive duality and employing constraints described by normal averages. The variational principle is amalgamated with Hopfield-like learning rules resulting in an unsupervised learning model. The update rules are formulated with the aid of q-deformed calculus. Num...

Gold nanostars (AuNSt) amalgamated with mercury ions (Hg 2+ ) results in reduced SERS performance whilst their enzyme-mimicking capability is not deteriorated, thus providing a basis for Hg detection inverse sensitivity.

In the paper we prove the convergence of the method of feasible directions for the case of quasi-concave constraining functions. These results were already published but in a shorter form and amalgamated with a stochastic programming problem. Here we give a detailed and a more general treatment of the earlier results.

We prove that the amalgamated free product of two free groups of rank two over a common cyclic subgroup, admits an amenable, faithful, transitive action on an infinite countable set. We also show that any finite index subgroup admits such an action, which applies for example to surface groups and fundamental groups of surface bundles over S.

We study the geometry of compact Lorentzian manifolds that admit a somewhere timelike Killing vector field, and whose isometry group has infinitely many connected components. Up to a finite cover, such manifolds are products (or amalgamated products) of a flat Lorentzian torus and a compact Riemannian (resp., lightlike) manifold.

The Bianchi groups are a family of discrete subgroups of PSL2(C) which have group theoretic descriptions as amalgamated products and HNN extensions. Using Bass-Serre theory, we show how the cohomology of these two constructions relates to the cohomology of their pieces. We then apply these results to calculate the mod-2 cohomology ring for various Bianchi groups.

It is shown that the compressed word problem for an HNNextension 〈H, t | tat = φ(a)(a ∈ A)〉 with A finite is polynomial time Turing-reducible to the compressed word problem for the base group H . An analogous result for amalgamated free products is shown as well.

In this paper we study residual solvability of the amalgamated product of two finitely generated free groups, in the case of doubles. We find conditions where this kind of structure is residually solvable, and show that in general this is not the case. However this kind of structure is always meta-residually-solvable.