Quasidiagonal Solutions of the Yang–Baxter Equation, Quantum Groups and Quantum Super Groups

This paper answers a few questions about algebraic aspects of bialgebras, associated with the family of solutions of the quantum Yang–Baxter equation in Acta Appl. Math. 41 (1995), pp. 57–98. We describe the relations of the bialgebras associated with these solutions and the standard deformations of GL_n and of the supergroup GL(m|n). We also show how the existence of zero divisors in some of these algebras are related to the combinatorics of their related matrix, providing a necessary and sufficient condition for the bialgebras to be a domain. We consider their Poincaré series, and we provide a Hopf algebra structure to quotients of these bialgebras in an explicit way. We discuss the problems involved with the lift of the Hopf algebra structure, working only by localization.     

When is a Cleft Extension H-Azumaya?

We show which H ^op -cleft extensions of k for a dual quasi-triangular Hopf algebra (H, r) are H-Azumaya. The result is given in terms of bijectivity of a map defined in terms of the universal r-form r and the 2-cocycle σ, generalizing a well-known result for the commutative and co-commutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).Presented by A. Verschoren     

Photoelectron spectroscopic studies of some alkoxy phenalenones

The Hel (21.22 eV) vapor phase photoelectron spectra of 1-phenalenone and its 9-substituted OH, OMe, OEt and O n-Bu derivatives have been measured. The low ionization potential regions show characteristic bands arising from π_cc and n_o orbitals and their interactions. The assignments are based on data from SPINDO calculations as well as correlations based on a composite-molecule approach. An apparent variation in intramolecular H-bonding in the OH and OMe compounds is explained in terms of Me steric interactions.     

13C NMR Study of the Natural Glycosides Vicine and Convicine

¹³C NMR parameters have been obtained for vicine and convicine in DMSO, D₂O/DMSO and D₂O. Complete assignment of the spectra has been achieved. Interpretation of spin-lattice relaxation rates and heteronu-clear NOES has yielded evidence of intramolecular structuring in the case of vicine and not in that of ronvirine and also of a complex network of solute-solvent interactions.     

Absolute dipole oscillator strengths for photoabsorption,photoionization and ionic photofragmentation processes in HBr

Absolute dipole oscillator strengths (cross section) have been obtained for valence shell photoabsorption (7–100eV) and a variety of partial photoionization (11–40 eV) processes in gaseous HBr. Partial dipole oscillator strengths are reported for the formation of the X²Π, A²Σ⁺ and B²Σ electronic state of HBr⁺ as well as the respective photoelectron branching ratios. The photoelectron binding energy spectra show clear evidence of many-body effects in photoionization to the B²Σ state of HBr⁺ with the ionization oscillator strength divided over many bands as predicted by many-body Green's function calculations. Partial dipole oscillator strengths are also reported for molecular ion formation as well as for all dissociative ionization processes. The measurements have been made by the dipole (e,e) (e,2e) and (e,e + ion) methods, which respectively provide quantitative measurements of photoabsorption, photoelectron spectroscopy and photoionization mass spectrometry at continuously tuneable energies. The measurements of dipole oscillator strengths for production of electronic states of HBr⁺ are combined with those for molecular and dissociative photoionization. These, considered together with the ionization and appearance potentials, provide a quantitative dipole breakdown picture for the ionic photofragmentation pathways of HBr in the energy region up to 40 eV.     

On the q -Convolution on the Line

The investigation of a q -analogue of the convolution on the line, started in conjunction with Koornwinder, is continued, with special attention to the approximation of functions by means of the convolution. A new space of functions that forms an increasing chain of algebras (with respect to the q -convolution), depending on a parameter s>0 , is constructed. For a special value of the parameter the corresponding algebra is commutative and unital, and is shown to be the quotient of an algebra studied in a previous paper modulo the kernel of a q -analogue of the Fourier transform. This result has an analytic interpretation in terms of analytic functions, whose q -moments have a (fast) decreasing behavior and allows the extension of Koornwinder's inversion formula for the q -Fourier transform. A few results on the invertibility of functions with respect to the q -convolution are also obtained and they are applied to the solution of certain simple linear q -difference equations with polynomial coefficients.     

Evaluation of tea tree oil quality and ascaridole: A deep study by means of chiral and multi heart-cuts multidimensional gas chromatography system coupled to mass spectrometry detection

The natural-like assessment of essential oils is a demanding task due to the growing trend toward adulterations. Usually chiral chromatography was used for this purpose due to the capability of assessing stereospecificity which is directly related to the enzymatic pathways of each plant species. On the other hand, the quality of an essential oil involves also the evaluation of its oxidative state, mainly connected with the age and storage conditions. In fact, some modifications in the chemical profile of the oil can occur if not properly preserved. Alterations of the components due to oxidative reactions lead to the formation of peroxides, endoperoxides and epoxides, such as ascaridole and 1,2,4-trihydroxymenthane, usually present in very low amount, formed by the oxidation of terpinen-4-ol and α-terpinene, respectively. Therefore, in the present research, the quality of Australian Tea Tree oil (Melaleuca alternifolia (Maiden & Betche) Cheel, Myrtaceae) was investigated by means of a multi heart-cut multidimensional gas chromatographic system coupled to a mass spectrometer detector and by conventional enantio-GC. The MDGC system allowed the complete separation of the compounds of interest transferred from the first column to a second dimension based on a different separation mechanism. The MS detector at the end of the second column provided the identification of the peaks with high similarity values because of their high purities after the multidimensional separation. Method validation was carried out, in order to use this procedure for routine application, monitoring the repeatability of 1D retention times and 2D peak areas, LoD and LoQ. Finally, enantiomeric ratios for chiral compounds were established to support quality data obtained.     

Multidimensional liquid chromatography for the determination of chiral coumarins and furocoumarins in Citrus essential oils

In this work the enantiomeric distribution of chiral coumarins (meranzin and epoxyaurapten), and furocoumarins (oxypeucedanin, byakangelicol, and epoxybergamottin) in different Citrus essential oils (lemon, lime, grapefruit, and bitter orange) was determined by means of a heart-cutting multidimensional-liquid chromatography (MD-LC) system, equipped with a microsilica column in the first dimension in a combination to a cellulosic-based chiral column used in the second dimension. The normal phase-liquid chromatography-liquid chromatography (NP-LC-LC) instrumentation was equipped with a photodiode array detector and a multiport valve as interface. For method optimization and the determination of absolute configuration, natural compounds were isolated and racemic mixture was synthesized. The NP-LC-LC/PDA (where PDA is photodiode array) method provided a good baseline separation of chiral coumarins (meranzin and epoxyaurapten) and furocoumarins (epoxybergamottin and byakangelicol) present in cold-pressed Citrus essential oils without any sample pretreatment. Results obtained showed that for all the chiral compounds present in Citrus essential oils analyzed, there is always a clear prevalence of one of the two enantiomers, and do not appear influenced by the different geographical origin of the oils.     

On the subgroup structure of the full Brauer group of Sweedler Hopf algebra

We introduce a three-parameter family of two-dimensional algebras representing elements in the Brauer group BQ(k,H ₄) of Sweedler Hopf algebra H ₄ over a field k. They allow us to describe the mutual intersection of the subgroups arising from a quasitriangular or coquasitriangular structure. We also define a new subgroup of BQ(k,H ₄) and construct an exact sequence relating it to the Brauer group of Nichols 8-dimensional Hopf algebra with respect to the quasitriangular structure attached to the 2 × 2-matrix with 1 in the (1, 2)-entry and zero elsewhere.