A Theorem of Ludwig Revisited

Using a recent result of Busch and Gudder, we reconsider a theorem of Ludwig which allows one to identify a class of effect automorphisms as the symmetry transformations in quantum mechanics.     

Physico-Chemical Investigation on the Interaction Between Ochratoxin A and Heptakis-2,6-di-O-Methyl-β-Cyclodextrin

Journal of Solution Chemistry - The interaction of ochratoxin A (OTA) with heptakis-2,6-di-O-methyl-β-cyclodextrin (DIMEB) in aqueous solutions at two different pHs (3.5 and 9.5) was studied...     

Analysis of glycerophospho‐ and sphingolipids by CE

Glycerophospholipids are amphiphilic molecules possessing polar head groups with a glycerol backbone and nonpolar variable long‐chain fatty acids. Numerous molecular species are found in a single class of glycerophospholipid, conferring to these lipids a high structural diversity. They are major components of biological membranes and participate in important activities involving cell signaling and substrate transport. Sphingolipids consist of long‐chain bases linked by an amide bond to a fatty acid and via the terminal hydroxyl group to complex carbohydrate or phosphorus moieties, constituting a complex family of compounds that also present an enormous structural variability. As important component of neuronal membranes, sphingolipids contribute to cellular diversity and functions and are associated with several neurodegenerative disorders. Moreover, they were studied in several foods due to their sensorial, reological, and antioxidant characteristics. In this work, the most relevant information available on glycerophospholipid and sphingolipid analysis by CE is reviewed. CE is a very promising analytical technique in polar lipid analysis, which provides high efficiency, relatively high resolution, and enormous versatility and requires small amounts of sample and solvent. MEKC and NACE methodologies have been developed as the most useful alternatives for these analyses by CE. Very interesting LODs have been achieved enabling the application of CE to the determination of glycerophospholipids and sphingolipids in several food and biological matrices.     

Theoretical investigation of the adsorption of methanol on the (110) surface of γ-alumina

The adsorption of methanol on the (110) surface of γ-alumina was investigated using both ab initio and density functional theory quantum chemical methods. A [Al₃O₉H₁₀]⁺ cluster model comprising one tetrahedral and two octahedral aluminum cations were used to describe the surface and the mechanism of adsorption of methanol. This has allowed us to rationalize the stable structures of adsorbate and the mode of bonding. The IR frequency shifts between the gas phase and the adsorbed species were also calculated and they exhibit good agreement with experiment.     

Vanadium(III) Complexes with Picolinic Acid and Dipicolinic Acid in Aqueous Solution

The complex species formed in aqueous solution (25 ^∘C, I = 3.0 mol-dm⁻³ KCl ionic medium) between V³⁺ cation and the ligands: picolinic acid (Hpic, HL) and dipicolinic acid (H₂dipic, H₂L), have been studied potentiometrically and by spectrophotometric measurements. The application of the least-squares computer program LETAGROP to the experimental emf (H) data, taking into account the hydrolytic species of V³⁺ ion, indicates that under the employed experimental conditions, the formation of the complexes [VL]²⁺, [V(OH)L]⁺, [VL₂]⁺, [VL₃], [V₂OL₄] with picolinic acid and the complexes [VL]⁺, [V(OH)L], [V(OH)₂L]⁻, [V(HL)(L)], and [VL₂]⁻ with dipicolinic acid were observed. The stability constants of the complexes formed were determined by potentiometric measurements, and spectrophotometric measurements were done in order to perform a qualitative characterization of the complexes formed in aqueous solution.     

Iodidomesityltellurium(II) iodidotrimesitylditellurium(II)(Te—Te)

In the title compound, C₉H₁₁ITe·C₂₇H₃₃ITe₂ or (Mes)TeI·(Mes₂Te)TeI(Mes) (Mes is mesityl or 2,4,6‐trimethylphenyl), a strong Te...I interaction of 3.3157 (9) Å links the Te atom of an iodidomesityltellurium(II) moiety, (Mes)TeI, and an I atom of the iodidotrimesitylditellurium(II) unit, (Mes₂Te)TeI(Mes). Further weak Te...I contacts of 4.0818 (9) Å give rise to one‐dimensional chains along the b axis in the crystal structure. An intramolecular C—H...π(arene) interaction is present in the (TeMes₂)TeI(Mes) moiety, with a C...Cg distance of 3.497 (9) Å and a C—H...Cg angle of 142° (where Cg is the centroid of a mesityl ring of the Mes₂Te moiety).     

Optimal Rates for the Regularized Least-Squares Algorithm

We develop a theoretical analysis of the performance of the regularized least-square algorithm on a reproducing kernel Hilbert space in the supervised learning setting. The presented results hold in the general framework of vector-valued functions; therefore they can be applied to multitask problems. In particular, we observe that the concept of effective dimension plays a central role in the definition of a criterion for the choice of the regularization parameter as a function of the number of samples. Moreover, a complete minimax analysis of the problem is described, showing that the convergence rates obtained by regularized least-squares estimators are indeed optimal over a suitable class of priors defined by the considered kernel. Finally, we give an improved lower rate result describing worst asymptotic behavior on individual probability measures rather than over classes of priors.