Discrete Valuations Extend to Certain Algebras of Quantum Type

So-called “quantized” algebras are popular objects of study in non-commutative algebra. Usually such algebras are either positively graded Ore domains R with R ₀ = K a field and R = K[R ₁], R ₁ being a finite dimensional K vectorspace, or else filtered rings having a ring of forementioned type for its associated graded ring. We show that every discrete valuation of K extends to a valuation, in the sence of O. Schilling (cf. [S]), of the skewfield of fractions, Δ = Q_cl (R), of the Ore domain R (Proposition 2.3. and Corollary 2.8.). Such extension property has long been known to fail for finite dimensional skewfields over K; its validity in the case of several quantized algebras may be viewed as a consequence of the rigidity of their defining relations. Our result opens the door for a more arithmetical study of Δ e.g. in case K is a numberfield or an algebraic function field of a curve; for an application in this direction we refer to a first version of some divisor calculus started in [VW].     

Role of radicals in UV‐initiated postplasma grafting of poly‐ε‐caprolactone: An electron paramagnetic resonance study

Electron paramagnetic resonance (EPR) measurements were performed on poly‐ε‐caprolactone (PCL) films at different stages of the postplasma‐grafting process. PCL films prepared by solvent casting (SC) or electrospinning (ESP) yield very similar EPR spectra after Ar‐plasma treatment and subsequent exposure to air, but the EPR signal is much stronger in the PCL‐ESP films. The free radicals appear to be mainly, and possibly exclusively, oxygen centered. The radicals generated by UV irradiation in PCL‐ESP films were studied in situ with EPR, using a UV‐LED (λ = (285 ± 5) nm). Their EPR spectrum is distinctly different from the plasma‐induced signal, indicative of carbon‐centered radicals, and appears to be independent of the plasma pretreatment. UV‐induced homolytic splitting of (hydro)peroxide bonds was not observed. Both the plasma‐ and UV‐induced radicals decay at room temperature (RT), even in an inert atmosphere. This study demonstrates the potential of electrospun films and UV‐LEDs for the study of plasma‐ and UV‐generated free radicals with EPR in polyesters, and raises questions with respect to the validity of some generally accepted molecular mechanisms underpinning the postplasma grafting technique for polyesters. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2012     

Quasi-elementary <Emphasis Type="Italic">H</Emphasis>-Azumaya Algebras Arising from Generalized (Anti) Yetter-Drinfeld Modules

Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut _Hopf (H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H.     

Distortion of the Poisson Bracket by the Noncommutative Planck Constants

In this paper we introduce a kind of “noncommutative neighbourhood” of a semiclassical parameter corresponding to the Planck constant. This construction is defined as a certain filtered and graded algebra with an infinite number of generators indexed by planar binary leaf-labelled trees. The associated graded algebra (the classical shadow) is interpreted as a “distortion” of the algebra of classical observables of a physical system. It is proven that there exists a q-analogue of the Weyl quantization, where q is a matrix of formal variables, which induces a nontrivial noncommutative analogue of a Poisson bracket on the classical shadow.     

Lichens as biomonitors for the determination of polycyclic aromatic hydrocarbons (PAHs) in Caracas Valley,Venezuela

Biomonitoring of PAH air pollution using lichens was carried out. Sixteen PAHs were studied in 11 locations along the valley of Caracas (Venezuela). The results of this work indicate that 14 of the 16 analysed PAHs were highly accumulated into the lichen thalli of Pyxine coralligera Malme. PAH levels in the samples revealed that the several volatile PAHs (naphthalene, acenaphtylene, acenaphtene, and fluoranthene) have the highest levels in the majority of the studied locations. The fluoranthene/pyrene and phenantrene/antracene ratios suggested that the major sources of PAHs are anthropogenic, mainly associated with gasoline and diesel combustion (pyrolytic) and unburnt oil derivates (petrogenic). The total PAH concentrations obtained in the present study were in the range of 0.24 to 9.08?µg/g, similar to those reported by other works in European and Asian cities.