On approximation of affine Baire-one functions

It is known (G. Choquet, G. Mokobodzki) that a Baire-one affine function on a compact convex set satisfies the barycentric formula and can be expressed as a pointwise limit of a sequence of continuous affine functions. Moreover, the space of Baire-one affine functions is uniformly closed. The aim of this paper is to discuss to what extent analogous properties are true in the context of general function spaces. In particular, we investigate the function spaceH(U), consisting of the functions continuous on the closure of a bounded open setU⊂ℝ ^m and harmonic onU, which has been extensively studied in potential theory. We demonstrate that the barycentric formula does not hold for the spaceB ₁ ^b (H(U)) of bounded functions which are pointwise limits of functions from the spaceH(U) and thatB ₁ ^b (H(U)) is not uniformly closed. On the other hand, every Baire-oneH(U)-affine function (in particular a solution of the generalized Dirichlet problem for continuous boundary data) is a pointwise limit of a bounded sequence of functions belonging toH(U). It turns out that such a situation always occurs for simplicial spaces whereas it is not the case for general function spaces. The paper provides several characterizations of those Baire-one functions which can be approximated pointwise by bounded sequences of elements of a given function space. Research supported in part by grants GA ČR No. 201/00/0767 from the Grant Agency of the Czech Republic, GA UK 165/99 from the Grant Agency of Charles University, and in part by grant number MSM 113200007 from the Czech Ministry of Education.     

Alternative charge stabilisation and a changing reactivity of 1,3,5-triazine based starburst compounds as studied by in situ ESR/UV–vis–NIR spectroelectrochemistry

The role of the chemical structure in an alternative charge stabilisation and a changing reactivity of star-shaped compounds with a central triazine ring linked to aryl groups like thiophene, furan or ethylenedioxythiophene synthesized by a Stille cross-coupling procedure, is followed by spectroelectrochemical measurements. While cathodic reduction leads to stable anion radicals with a delocalised spin on the central triazine moiety, dimerisation and oligomerisation occurs upon anodic oxidation. The stability of the charged states in the polymer film increased substantially using an EDOT (3,4-ethylenedioxythiophene) side group. The location of the charged states on the molecules has been proved by computations. These star-shaped molecules are excellent model structures for studies of the competition of dimerisation and oligomerisation processes based on the variation of the electron and spin distribution in the molecules.     

Applying Unconventional Spectroscopies to the Single-Molecule Magnets,Co(PPh3)2X2 (X=Cl,Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃)₂X₂ ( Co-X ; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X , showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.     

Oxidation of heterocyclic nitrogen Ylids to nitro heterocycles. Comparison of a sulfilimine and a phosphine imine

Oxidation of 3-amino-4-(4-chlorophenyl)furazan ( 1 ) with peroxytrifluoroacetic acid (ptfa) gave azoxy(4-chlorophenylfurazan) ( 6 ) as the major product along with a small amount of 3-(4-chlorophenyl)-4-nitrofurazan ( 5 ). The dimethylsulfilimine 2 derived from 1 gave near quantitative yields of 5 when subjected to oxidation with either ptfa or m-chloroperoxybenzoic acid (mcpba). In contrast, both the trioctylphosphine imine 3 and the triphenylphosphine imine 4 derived from 1 were oxidized by mcpba to give 6 as the exclusive product.     

Elektrolyse, Polarographie

Ohne Zusammenfassung     

Effects of fuel blending on first stage and overall ignition processes

The effects of blending ratio on mixtures of an alcohol-to-jet (ATJ) fuel and a conventional petroleum-derived fuel on first stage ignition and overall ignition delay are examined at engine-relevant ambient conditions. Experiments are conducted in a high-temperature pressure vessel that maintains a small flow of dry air at the desired temperature (825 K and 900 K) and pressure (6 MPa and 9 MPa) for fuel injections from a custom single-hole, axially-oriented injector, representing medium (7.5 mg) and high (10 mg) engine loading. Formaldehyde, imaged using planar laser-induced fluorescence, is measured at discrete time steps throughout the first and second stage ignition process and is used as a marker of unburned short-chain hydrocarbons formed after the initial breakdown of the fuel. The formaldehyde images are used to calculate the first stage ignition delay for each ambient and fuel loading condition. Chemiluminescence imaging of excited hydroxyl radical at 75 kHz is used to determine the overall ignition delay. At all conditions, increased volume fraction of ATJ resulted in longer, but non-linearly increasing, overall ignition delay. Across all of the blends, first stage ignition delay accounted for about 15% of the increase in overall ignition delay compared to the military's aviation kerosene, F-24, which is Jet A with additives, while extended first stage ignition duration accounted for 85% of the increase. It is observed that blends consisting of 0–60% by volume of the low cetane number ATJ fuel produced nearly identical first stage ignition delays. These results will inform the development of ignition models that can capture the non-linear effects of fuel blending on ignition processes.     

A first‐order system least‐squares finite element method for the Poisson‐Boltzmann equation

The Poisson‐Boltzmann equation is an important tool in modeling solvent in biomolecular systems. In this article, we focus on numerical approximations to the electrostatic potential expressed in the regularized linear Poisson‐Boltzmann equation. We expose the flux directly through a first‐order system form of the equation. Using this formulation, we propose a system that yields a tractable least‐squares finite element formulation and establish theory to support this approach. The least‐squares finite element approximation naturally provides an a posteriori error estimator and we present numerical evidence in support of the method. The computational results highlight optimality in the case of adaptive mesh refinement for a variety of molecular configurations. In particular, we show promising performance for the Born ion, Fasciculin 1, methanol, and a dipole, which highlights robustness of our approach. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Critical parameters in a supported liquid membrane extraction technique for ionizable organic compounds with a stagnant acceptor phase

The reviews cover important critical parameters that are often optimized in a supported liquid membrane extraction technique in both flat sheet and hollow fibre designs for ionizable organic molecules. Understanding of these parameters can enable one to predict the behavior of the compound before hand and thus reduce the number of optimization experiments. Moreover, less number of experiments can be also generated using statistical techniques which are now becoming more commonly used. Supported liquid membrane extraction optimal parameters such as the conditions of the pH of the acceptor and donor phases should easily be fixed from the pKa values of the compounds. Other parameters, including the polarity of the compound can help to predict the partitioning into the membrane and the behavior of the compound. The influence of parameters such as temperature on the mass transfer in supported liquid membrane depends on the design of the module, experimental design and type of mass transfer controlling the extraction process.