On the Hilbert Evolution Algebras of a Graph

Evolution algebras are a special class of nonassociative algebras exhibiting connections with various fields of mathematics. Hilbert evolution algebras generalize the concept in the framework of Hilbert spaces. This allows us to deal with a wide class of infinite-dimensional spaces. We study Hilbert evolution algebras associated to a graph. Inspired by the definitions of evolution algebras we define the Hilbert evolution algebra that is associated to a given graph and the Hilbert evolution algebra that is associated to the symmetric random walk on a graph. For a given graph, we provide the conditions for these structures to be or not to be isomorphic. Our definitions and results extend to the graphs with infinitely many vertices. We also develop a similar theory for the evolution algebras associated to finite graphs.

     

Influence of pH on the binding of diphenylmethylenepiperidines by 5-HT2B receptors in rat stomach fundus

Cyproheptadine is one of the compounds exhibiting the highest activity at 5-HT2B receptors. In a previous work we analysed the relevance of the amino group in diphenylmethylenepiperidines (DPMP), which are open cyproheptadine analogues. Only compounds containing N-H or N-methyl motifs, showed significant 5-HT2B activity. Surprisingly, the corresponding quaternary ammonium salt demonstrated a total lack of activity. Therefore, the question arises whether protonation favours the interaction of these compounds with 5-HT2B receptors. Consequently, we studied the protonation influence (by varying the pH of the medium) on the antagonism of serotonin by some cyproheptadine analogues in rat stomach fundus. The main results were: 1) N-protonation increases the activity of DPMPs. 2) Alkaline pH facilitates the occurrence of a non-surmountable antagonism. 3) The contrast between the activity of protonated DPMPs and the lack of activity of the corresponding quaternary ammonium cation, suggests either that the latter is prevented from acting by steric hindrance, or that the mechanism by which protonation may increase the activity depends not only on the charge of the proton, but also on its ability to form hydrogen bonds.     

Integration over the group space of SUq(2), Clebsch-Gordan coefficients, and related identities

We calculate the Clebsch-Gordan coefficients of SUq(2) by a Woronowicz integration over the group manifold and obtain a representation differing from that reached by working with theq-group algebra. These apparently different results must agree, however, and their equivalence implies aq-identity. On lettingq = 1, we shall obtain two results of different structures for the Clebsch-Gordan coefficients of SU(2) and their equivalence similarly implies an identity among the usual binomial coefficients. With the same approach, one may extend the Woronowicz integral of the product of two irreducible representations to products of many irreducible representations.     

Gauged Kac-Moody algebras

We construct a non-Abelian field theory by gauging a Kac-Moody algebra. One obtains an infinite tower of interacting vector fields and associated ghosts obeying slightly modified Feynman rules.     

The star exponential and path integrals on compact groups

Using the star exponential, a path integral is constructed for arbitrary compact Lie groups. This is a globalization of the results of Alcalde, Cadavid, and Nakashima, in which a path integral was constructed for SU(2) in terms of local coordinates. Also the phase factor encountered by Alcalde, Cadavid, and Nakashima is shown to be zero.     

Morphology evolution of Cu(2-x)S nanoparticles: from spheres to dodecahedrons

An oriented attachment and growth mechanism allows an accurate control of the size and morphology of Cu(2-x)S nanocrystals, from spheres and disks to tetradecahedrons and dodecahedrons. The synthesis conditions and the growth mechanism are detailed here.     

Cu2ZnGeSe4 nanocrystals: synthesis and thermoelectric properties

A synthetic route for producing Cu(2)ZnGeSe(4) nanocrystals with narrow size distributions and controlled composition is presented. These nanocrystals were used to produce densely packed nanomaterials by hot-pressing. From the characterization of the thermoelectric properties of these nanomaterials, Cu(2)ZnGeSe(4) is demonstrated to show excellent thermoelectric properties. A very preliminary adjustment of the nanocrystal composition has already resulted in a figure of merit of up to 0.55 at 450 °C.