Extreme value theory for singular measures

In this paper, we perform an analytical and numerical study of the extreme values of specific observables of dynamical systems possessing an invariant singular measure. Such observables are expressed as functions of the distance of the orbit of initial conditions with respect to a given point of the attractor. Using the block maxima approach, we show that the extremes are distributed according to the generalised extreme value distribution, where the parameters can be written as functions of the information dimension of the attractor. The numerical analysis is performed on a few low dimensional maps. For the Cantor ternary set and the Sierpinskij triangle, which can be constructed as iterated function systems, the inferred parameters show a very good agreement with the theoretical values. For strange attractors like those corresponding to the Lozi and He?non maps, a slower convergence to the generalised extreme value distribution is observed. Nevertheless, the results are in good statistical agreement with the theoretical estimates. It is apparent that the analysis of extremes allows for capturing fundamental information of the geometrical structure of the attractor of the underlying dynamical system, the basic reason being that the chosen observables act as magnifying glass in the neighborhood of the point from which the distance is computed.     

Gas phase reactions of the ion C5H5Fe+: A kinetic study

The kinetics of gas phase reactions of the ion C₅H₅Fe⁺ with oxygen (Me₂CO, Me₂O, MeOH, iso-propanol, H₂O) and nitrogen (NH₃, NH₂Me, NHMe₂, NMe₃) donor ligands have been studied by ion trap mass spectrometry. While in the literature reactions of the ion Fe⁺, with the same ligands, the principal reaction path involves fragmentation in almost all the reactions of the ion C₅H₅Fe⁺, formation of adduct ions is the major reaction path. The reactivity of these two ions is briefly compared in the ion trap conditions. Kinetic data for the ion C₅H₅Fe⁺ indicate that the reactions show a large range of efficiency and a linear correlation is found between the log of the reaction rate constants and the ionization energy of ligands with the same donor atom.     

Surfactant design for the 1,1,1,2-tetrafluoroethane-water interface: ab initio calculations and in situ high-pressure tensiometry

In situ high-pressure tensiometry and ab initio calculations were used to rationally design surfactants for the 1,1,1,2-tetrafluoroethane-water (HFA134a|W) interface. Nonbonded pair interaction (binding) energies (E(b)) of the complexes between HFA134a and candidate surfactant tails were used to quantify the HFA-philicity of selected moieties. The interaction between HFA134a and an ether-based tail was shown to be predominantly electrostatic in nature and much more favorable than that between HFA134a and a methyl-based fragment. The interfacial activity of (i) amphiphiles typically found in FDA-approved pressurized metered-dose inhaler (pMDI) formulations, (ii) a series of nonionic surfactants with methylene-based tails, and (iii) a series of nonionic surfactants with ether-based tails was investigated at the HFA134a|W interface using in situ tensiometry. This is the first time that the tension of the surfactant-modified HFA134a|W interface has been reported in the literature. The ether-based surfactants were shown to be very interfacially active, with tension decreasing by as much as 27 mN.m(-)(1). However, the methyl-based surfactants, including those from FDA-approved formulations, did not exhibit high activity at the HFA134a|W interface. These results are in direct agreement with the E(b) calculations. Significant differences in interfacial activity are noted for surfactants at the 2H,3H-perfluoropentane (HPFP)|water and HFA134a|W interfaces. Care should be taken, therefore, when results from the mimicking solvent (HPFP) are extrapolated to HFA134a-based systems. The results shown here are of relevance in the selection of surfactants capable of forming and stabilizing reverse aqueous aggregates in HFA-based pMDIs, which are promising formulations for the systemic delivery of biomolecules to and through the lungs.     

Multivariate optimization of a solid phase microextraction-headspace procedure for the determination of benzene, toluene, ethylbenzene and xylenes in effluent samples from a waste treatment plant

A method based on solid-phase microextraction (SPME) and gas chromatography with flame ionization detection (GC-FID) has been optimized for the determination of benzene, toluene, ethylbenzene and xylenes (BTEX) in water released from a waste treatment plant. The extraction step was optimized using fractional factorial and central composite designs including the following experimental factors: saline concentration; extraction time; desorption time; agitation velocity; headspace volume. A multiple function was used to describe the experimental conditions for simultaneous extraction of the compounds. The procedure, based on direct SPME at 50 degrees C, using a polydimethylsiloxane fiber, showed good linearity (r>0.997 over a concentration range 2-200 microg L(-1)) and repeatability (relative standard deviation (RSD)<4.23%) for all compounds, with limits of detection ranging from 0.05 to 0.28 microg L(-1), and limits of quantification ranging from 0.14 to 0.84 microg L(-1). Concentrations of the target compounds in these samples were between 145.8 and 1891 microg L(-1).     

X-ray and mössbauer studies of tricyclohexyltin(IV) halides. The crystal structures of (cyclo-C6H11)3SnX (X = F,Br and I)

The structures of tricyclohexyltin fluoride (I), bromide (II) and iodide (III) have been determined by X-ray analysis. Compound I crystallizes in the space group P2₁/m with a = 10.422(6), b = 17.238(9), c = 5.769(3) Å, β = 104.6(1)° and Z = 2. Compounds II and III crystallize in the space group Pcmn with a = 10.427(6), b = 16.914(9), c = 11.366(6) Å, Z = 4; and a = 10.400(6), b = 16.900(10), c = 11.400(4) Å, Z = 4, respectively. All three structures consist of discrete tetrahedral (cyclo-C₆H₁₁)₃SnX units.The temperature dependence of the Mössbauer resonance areas has been examined in order to obtain information about the relationship between chemical structure and lattice dynamics.     

Rejuvenating old computerized spectrometric instrumentation: discussion of two case histories

Computerized analytical instruments of late 70's and 80's are facing rapid technological obsolescence, although they are often retaining good analytical performances. Responsibility is to be attributed to the fast advance in computer technology, which is leaving little or no back-compatibility with old standards and data formats. Rejuvenation may be reached by simple hardware and software modifications, to allow data exchange with modern PC's and LIMS. Two typical case histories for spectrometric instrumentation of late 70's are then presented and discussed in a general fashion.     

Palladium-catalyzed reaction of aryl iodides with acetic anhydride. A carbon monoxide-free synthesis of acetophenones

[reaction: see text] The palladium-catalyzed reaction of aryl iodides with acetic anhydride provides a straightforward and experimentally simple carbon monoxide-free route to acetophenones. The reaction tolerates a wide range of functionalized aryl iodides. Acetophenones are isolated in excellent yield with a variety of neutral, slightly electron-rich, and slightly electron-poor aryl iodides, whereas moderate yields are obtained with aryl iodides containing strongly electron-withdrawing substituents.     

Reaction of CO2 with a Vanadium(II) Aryl Oxide: Synergistic Activation of CO2/Oxo Groups towards H‐Atom Radical Abstraction

Treatment of divalent (ONNO)V(TMEDA) ( 1 ; ONNO=[2,4‐Me₂‐2‐(OH)C₆H₂CH₂]₂N(CH₂)₂NMe₂) with CO₂ afforded [(ONNO)V]₂(μ‐OH)(μ‐formate) ( 2 ). Whereas the bridging hydroxo and formate groups both originated from CO₂, the H atoms present on the two residues were obtained through H‐atom radical abstraction from the solvent. DFT calculations revealed an initially linear CO₂ bonding mode, followed by deoxygenation, and highlighted a synergistic effect between the so‐formed oxo group and an additional bridging CO₂ residue in promoting radical behavior.