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).     

Fatty Acid Carboxylate‐ and Anionic Surfactant‐Controlled Delivery Systems That Use Mesoporous Silica Supports

We report the preparation of a MCM‐41 mesoporous material that contains the dye [Ru(bipy)₃]Cl₂ (bipy=bipyridine) inside the mesopores and functionalised with suitable binding groups at the entrance of the pores. Solids S1 – S3 were obtained by the reaction of the mesoporous material with N‐methyl‐N′‐propyltrimethoxysilylimidazolium chloride, N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]thiourea, or N‐phenyl‐N′‐[3‐(trimethoxysilyl)propyl]urea, respectively. A study of the dye delivery of these systems in buffered water (pH 7.0, 2‐[4‐(2‐hydroxyethyl)piperazin‐1‐yl]ethanesulfonic acid (HEPES), 10^?3 mol dm^?3) in the presence of a family of carboxylate ions was carried out. In the interaction of the anions with the surface of the solids, the response depends on the characteristics of the binding groups (i.e., imidazolium, urea and thiourea) at the pore outlets and their specific interaction with the corresponding anion. The interaction of long‐chain carboxylate ions with the binding sites at the surface of the solids resulted in a remarkable inhibition of the delivery of the dye. This inhibition was observed clearly for the dodecanoate anion, whereas the octanoate, decanoate, cholate, deoxycholate, glycodeoxycholate and taurocholate anions induced a certain pore blockage that varied according to the solid studied. The interaction of smaller anions, such as acetate, butanoate, hexanoate and octanoate, with the solids had no effect on the dye release process. The possible use of the gating system for the chromo‐fluorogenic detection of anionic surfactants through selective dye delivery inhibition was also explored. Molecular dynamic simulations that use force‐field methods have been made to theoretically study the capping carboxylate mechanism. The calculations are in agreement with the experimental results, thus allowing a representation of the dye delivery inhibition in the presence of long‐chain carboxylate ions.     

Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

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.     

Development of a new reference material for the validation of molecular detection methods for microbiological analysis

The standard methodology used for the detection of bacteria in environmental samples and food is primarily based on bacterial growth on specific culture media and confirmation by biochemical and/or immunological tests of all presumptive colonies. However, this methodology presents a number of drawbacks, such as low sensitivity and specificity, and the long time needed to obtain results. For this reason, the implementation of molecular methods in diagnostic laboratories has increased over the past several years. Nevertheless, most of these newer methods have not been included in current legislation, and, in most of cases, they have not yet been normalized. In this sense, the availability of appropriate reference materials (RMs) can help to overcome these deficiencies. The aim of this study was to develop and validate, following ISO Guide 34, a new RM, in a tablet format, for the quantification of Legionella pneumophila and Salmonella spp. by quantitative PCR (qPCR). This new RM can be used as a work reference sample in internal quality control, in the organization of proficiency testing schemes (PTS), as well as for the validation of molecular methods based on qPCR.     

The chromatographic quantification of hydrophobicity using micellar mobile phases

Summary In micellar liquid chromatography (MLC), the hydrophobicity of a compound is the predominant factor in its retention and interaction with micelles. A non-linear empirical model can describe the dependence between the retention factor (logk) in MLC and the logarithm of partition coefficients octanol-water (logP). An algorithm based on such a model has been used to makelogP predictions. Retention data for series of neutral compounds eluted with different mobile phases and alkyl-bonded stationary phases have been used to test the predictive ability of the algorithm. The results of this approach are compared with those obtained from automatic computational software packages.     

Study of prehispanic wall paintings from Xochicalco, Mexico, using PIXE, XRD, SEM and FTIR

The characterization of samples of painted plasters obtained from the archaeological site of Xochicalco, in Central Mexico, is presented. Elemental concentrations of the painted layers were obtained by using proton induced X-ray emission (PIXE). The main crystalline structures of the samples are identified with the help of X-ray diffraction (XRD), while the microstructure is studied by scanning electron microscopy (SEM). The information resulting from the application of these three techniques is used to achieve more accurate values for the elemental concentrations. Additional data regarding organic components of the paintings was obtained through Fourier transform infrared spectrometry (FTIR). Although the latter results only provided reliable data on inorganic components, they help to clarify the results from XRD and confirm those of SEM.     

Variation Operators for Semigroups and Riesz Transforms on BMO in the Schrödinger Setting

In this paper we prove that the variation operators of the heat semigroup and the truncations of Riesz transforms associated to the Schrödinger operator are bounded on a suitable BMO type space.