Algebras Whose Coxeter Polynomials are Products of Cyclotomic Polynomials

Let A be a finite dimensional algebra over an algebraically closed field k. Assume A is basic connected with n pairwise non-isomorphic simple modules. We consider the Coxeter transformation ? _A as the automorphism of the Grothendieck group K ₀(A) induced by the Auslander-Reiten translation τ in the derived category Der(modA) of the module category modA of finite dimensional left A-modules. We say that A is an algebra of cyclotomic type if the characteristic polynomial χ _A of ? _A is a product of cyclotomic polynomials. There are many examples of algebras of cyclotomic type in the representaton theory literature: hereditary algebras of Dynkin and extended Dynkin types, canonical algebras, some supercanonical and extended canonical algebras. Among other results, we show that: (a) algebras satisfying the fractional Calabi-Yau property have periodic Coxeter transformation and are, therefore, of cyclotomic type, and (b) algebras whose homological form h _A is non-negative are of cyclotomic type. For an algebra A of cyclotomic type we describe the shape of the Auslander-Reiten components of Der(modA).     

On the effect of friend feedbacks

Given ?? an (A,B)‐invariant subspace, we prove that the set of friend feedbacks is a linear variety, which can be considered as the direct sum of the feedbacks of the restriction to ?? and the co‐restriction to ??^⊥. In particular, when the natural controllability hypothesis hold, both pole assignments are simultaneously possible by means of a convenient friend feedback. Copyright © 2010 John Wiley & Sons, Ltd.     

On Anastassiou's Generalizations of the Ostrowski Inequality and Related Results

We provide a generalization of a recent result of Anastassiou related to thewell-known Ostrowski inequality, as well as some related results. Ourresults subsume, extend, and consolidate a number of known results.     

Nanostructuration of i-Al64Cu23Fe13 quasicrystals produced by arc-furnace

We have measured several Q values at JYFLTRAP for superallowed ?? decays that contribute to testing the Standard Model and candidate nuclei that one could use for the search of neutrinoless double-?? decay. These results play important roles in the research of fundamental physics that have scopes beyond Standard Model.     

Photocatalysis of Chloroform Decomposition by Hexachloroosmate(IV)

Hexachloroosmate(IV) effectively catalyzes the photodecomposition of chloroform in aerated solutions. The decomposition products are consistent with a mechanism in which excited state OsCl₆²⁻ reduces chloroform, rather than one involving photodissociation of chlorine atoms. Trace amounts of ethanol or water in the chloroform lead to photosubstitution to form OsCl₅(EtOH)⁻ or OsCl₅(H₂O)⁻, neither of which is photocatalytically active.     

Synthesis and characterization of a new semi-interpenetrating polymer network hydrogel obtained by gamma radiations

A new polyacrylic acid/polyhydroxybutyrate semi-interpenetrating polymer network hydrogel, the s-IPN/PAA-PHB, was prepared by a gamma radiation-induced polymerization. Thermal behavior was studied by thermogravimetric analysis (TG) and Differential scanning calorimetry (DSC), while the s-IPNs composition, FTIR spectra, and swelling kinetics were also determined. It was found that the DSC curve showed a melting point which is attributed to polyhydroxybutyrate. The TG curves showed various stages of degradation which are in correspondence of the presence of crosslinked polyacrylic acid and confirmed the higher thermal stability of the polymer network. The s-IPN/PAA-PHB composition was 10% of PHB and 90% of PAA. Moreover, the network reached approximately 600% of swelling in water, so it behaves like a superabsorbent hydrogel.     

Locally graded minimal non CC-groups arep-groups

The research of the two last authors has been supported by DGICYT (Spain) PS88-0085.