Stereoselective Control by Face‐to‐Face Versus Edge‐to‐Face Aromatic Interactions: The Case of C3‐TiIV Amino Trialkolate Sulfoxidation Catalysts

The stereoselective oxidation of differently functionalised benzyl phenyl sulfides has been examined by using enantiopure Ti^IV trialkanolamine complexes. These complexes efficiently catalyse the sulfoxidation with good stereoselectivities. The data highlight the contribution to the stereoselectivity of steric effects and non‐covalent π–π interactions between the aromatic rings of the Ti^IV complex and those pertaining to the substrates. Enantiomeric excesses have been correlated with the electrostatic potential surfaces (EPS) of the reacting sulfides. The overall study leads to a mechanistic interpretation that explains the stereoselectivity of the system and dissects the role of aromatic and steric interactions in the stereoselective process.     

A semigroup characterization of well-posed linear control systems

We study the well-posedness of a linear control system Σ(A,B,C,D) with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^{p}$ and call it p-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on $\mathcal{X}^{p}$ . Our approach is based on the Laplace transform and Fourier multipliers. The results generalize and complement those of Curtain and Weiss (Int. Ser. Numer. Math. vol. 91. Birkhäuser, Basel, 1989), Staffans and Weiss (Trans. Am. Math. Soc. 354:3229–3262, 2002) and are illustrated by a heat equation with boundary control and point observation.     

On conditional extreme values of random vectors with polar representation

An effective approach for studying the asymptotics of bivariate random vectors is to search for the limits of conditional probabilities where the conditioning variable becomes large. In this context, elliptical and related distributions have been extensively investigated. A quite general model was presented by Fougères and Soulier (Limit conditional distributions for bivariate vectors with polar representation in Stochastic Models, 2010), who derived a conditional limit theorem for random vectors (X, Y) with a polar representation R · (u(T), v(T)), where R, T are stochastically independent and R is in the Gumbel max-domain of attraction. We reformulate their assumptions, such that they have a simpler structure, display more clearly the geometry of the curves (u(t), v(t)) and allow us to deduce interesting generalizations into two directions:

u has several global maxima instead of only one,

the curve (u(t), v(t)) is no longer differentiable, but forms a “cusp”.

The latter generalization yields results where only random norming leads to a non-degenerate limit statement. Ideas and results are elucidated by several figures.     

Chromium(VI) oxide oxidation of non‐ethoxylated and ethoxylated alcohols for determination by electrospray ionization mass spectrometry

A new derivatization procedure to increase the sensitivity of electrospray ionization mass spectrometry (ESI‐MS) to non‐ethoxylated and ethoxylated alcohols was investigated. The analytes were oxidized with chromium(VI) oxide and the resulting carboxylic and ethoxy‐carboxylic acids were isolated by extraction with ethyl acetate; the extracts were alkalinized and infused into the ESI‐MS system working in the negative‐ion mode. The yields of the combined oxidation‐extraction were ca. 100% for non‐ethoxylated fatty alcohols dissolved in acetone and they decreased moderately in samples containing increasing amounts of water (e.g., a 75% yield was obtained with 50% water). Ethoxylated alcohols with more than two ethylene oxide units resulted in yields of ca. 60%. Low limits of detection (LODs) were obtained when the procedure was applied to the analysis of body‐care products and cosmetics containing fatty alcohols, e.g., in a varicose‐vein cream, the LODs were 25 µg cetyl alcohol and 7.5 µg stearyl alcohol (detected as palmitic acid and stearic acid, respectively) per gram of sample. High molecular mass alcohols were also detected in seawater after pre‐concentration by solid‐phase extraction. Thus, the proposed method is particularly valuable for use in industrial samples having complex matrices and in environmental samples and it is competitive with other methods for the analysis of trace amounts of fatty alcohols. Copyright © 2010 John Wiley & Sons, Ltd.     

Dirac particles in a gravitational field

The semiclassical approximation for the Hamiltonian of Dirac particles interacting with an arbitrary gravitational field is investigated. The time dependence of the metric leads to new contributions to the in-band energy operator in comparison to previous works in the static case. In particular we find a new coupling term between the linear momentum and the spin, as well as couplings that contribute to the breaking of the particle–antiparticle symmetry.     

Nevanlinna counting function and Carleson function of analytic maps

We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.     

Bargaining among groups: an axiomatic viewpoint

We introduce a model of bargaining among groups, and characterize a family of solutions using a Consistency axiom and a few other invariance and monotonicity properties. For each solution in the family, there exists some constant α ≥ 0 such that the “bargaining power” of a group is proportional to c ^α , where c is the cardinality of the group.     

Polyethylenimine Functionalized with Dopamine: Characterization and Electrocatalytic Properties

We report the chemical modification of polyethylenimine (PEI) by functionalization with dopamine (Do) using glutaraldehyde (Glu) as a linker (PEI‐Glu‐Do). The new polymer was characterized by FT‐IR spectroscopy, by derivative UV‐vis spectroscopy, and Cyclic Voltammetry. The PEI‐Glu‐Do demonstrated to have an important electrocatalytic activity allowing an important decrease in the overvoltages for the oxidation of NADH and a significant increase in its oxidation peaks currents. Different ratios of PEI:Do were assayed and the best response was obtained using PEI : Glu : Do 1 : 2 : 1. The new polymer represents an interesting and promising alternative for the electrochemical quantification of NADH and other analytes of clinical interest, as well as for the development of new electrochemical (bio)sensors.