«3-Fluorisopren» (2-Fluor-3-methyl-1,3-butadien) und einige heterosubstituierte Abkömmlinge

‘3-Fluoroisoprene’ (2-Fluoro-3-methyl-1,3-butadiene) and Some Hetero-substituted Derivatives Thereof The readily accessible 1-chloro-1-fluoro-2-iodomethyl-2-methylcyclopropane undergoes zinc-promoted ring-cleavage yielding 2-fluoro-3-methyl-1, 3-butadiene (‘3-fluoroisoprene’) in almost quantitative yield. Alternatively the iodine atom may be replaced by electron-attracting groups such as cyano, benzenesulfonyl or triphenylphosphonio. Ring-opening of the resulting derivatives can then be brought about by various bases and leads to substituted fluorodienes. - The chemical reactivity of ‘3-fluoroisoprene’ has been studied in some detail. For example, it was found to add bromine at temperatures below 0° under kinetic control and to afford mainly the 1,4-adduct having the (Z)-configuration besides smaller quantities of the 1,2- and 3,4-adduct. At room temperature this mixture slowly undergoes a transformation yielding, as the sole products, both stereoisomeric 1, 4-adducts in a 1:1 ratio.     

Formation of solvated ions in the atmospheric interface of an electrospray ionization triple-quadrupole mass spectrometer

A simple method capable of generating and investigating various solvent clusters and solvated ions was developed. The technique opens a door to studying these complexes on commercially available instruments. Formation of the desired solvated ion in the gas phase was achieved by introducing the appropriate volatile solvent vapour into the curtain gas stream. Capabilities of the technique are illustrated by generating alkali, alkaline earth and transition metal cations solvated by various volatile compounds such as water, methanol and acetonitrile. Depending on the ligands and on the experimental conditions, clusters of 2-100 molecules may be observed. Isotope labelling suggests that these are formed by a re-solvation process in the curtain gas region.     

The acidity of chloro-substituted benzenes: a comparison of gas phase, ab initio, and kinetic data

The deprotonation energies of benzene, chlorobenzene, all di-, tri-, tetrachlorobenzenes, and pentachlorobenzene have been determined in the gas phase using a Fourier transform ion cyclotron resonance mass spectrometer. The values measured differ only slightly, though significantly, from the corresponding data for oligofluorobenzenes. The heavier halogen acidifies orthopositions slightly less and meta-positions slightly more than fluorine does. Moreover, the contributions of three or more chloro substituents are not perfectly additive. In fact the accumulation attenuates the contributions somewhat. Quantum chemical calculations at the MP2/6-311+G* level reproduce the gas-phase acidities fairly well, but reveal special effects when extended to experimentally not observable benzenides carrying the halogens at anion-remote positions. Competition experiments have been performed to assess the relative reactivity of nine oligochlorobenzenes towards sec-butyllithium in tetrahydrofuran at -100 degrees C. An almost exact linear correlation between logarithmic rates and gas-phase acidities has been found.     

Uptake of magnetic nanoparticles into cells for cell tracking

A challenge for future applications in nanotechnology is the functional integration of nano-sized materials into cellular structures. Here we investigated superparamagnetic Fe₃O₄ iron oxide nanoparticles coated with a lipid bilayer for uptake into cells and for targeting subcellular compartments. It was found that magnetic nanoparticles (MNPs) are effectively taken up into cells and make cells acquire magnetic activity. Biotin-conjugated MNPs were further functionalized by binding of the fluorescent tag streptavidin–fluorescein isothiocyanate (FITC) and, following uptake into cells, shown to confer magnetic activity and fluorescence labeling. Such FITC-MNPs were localized in the lysosomal compartment of cells which suggests a receptor-mediated uptake mechanism.     

Shearlet coorbit spaces and associated Banach frames

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.     

A Multidimensional Generalization of Shukla's 8ψ8 Summation

   Abstract. We give an r -dimensional generalization of H. S. Shukla's very-well-poised ₈ ψ ₈ summation formula. We work in the setting of multiple basic hypergeometric series very-well-poised over the root system A _r-1 or, equivalently, the unitary group U(r) . Our proof, which is already new in the one-dimensional case, utilizes an A _r-1 nonterminating very-well-poised ₆ φ ₅ summation by S. C. Milne, a partial fraction decomposition, and analytic continuation.     

Elliptic Solutions of Dynamical Lucas Sequences

We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences which defines the non-commutative (or abstract) Fibonacci polynomials introduced by Johann Cigler. If the non-commuting variables are specialized to be elliptic-commuting variables the abstract Fibonacci polynomials become non-commutative elliptic Fibonacci polynomials. Some properties we derive for these include their explicit expansion in terms of normalized monomials and a non-commutative elliptic Euler–Cassini identity.     

Parabolic Molecules

Anisotropic decompositions using representation systems based on parabolic scaling such as curvelets or shearlets have recently attracted significant attention due to the fact that they were shown to provide optimally sparse approximations of functions exhibiting singularities on lower dimensional embedded manifolds. The literature now contains various direct proofs of this fact and of related sparse approximation results. However, it seems quite cumbersome to prove such a canon of results for each system separately, while many of the systems exhibit certain similarities. In this paper, with the introduction of the notion of parabolic molecules, we aim to provide a comprehensive framework which includes customarily employed representation systems based on parabolic scaling such as curvelets and shearlets. It is shown that pairs of parabolic molecules have the fundamental property to be almost orthogonal in a particular sense. This result is then applied to analyze parabolic molecules with respect to their ability to sparsely approximate data governed by anisotropic features. For this, the concept of sparsity equivalence is introduced which is shown to allow the identification of a large class of parabolic molecules providing the same sparse approximation results as curvelets and shearlets. Finally, as another application, smoothness spaces associated with parabolic molecules are introduced providing a general theoretical approach which even leads to novel results for, for instance, compactly supported shearlets.     

A generalization of Gram–Schmidt orthogonalization generating all Parseval frames

Given an arbitrary finite sequence of vectors in a finite-dimensional Hilbert space, we describe an algorithm, which computes a Parseval frame for the subspace generated by the input vectors while preserving redundancy exactly. We further investigate several of its properties. Finally, we apply the algorithm to several numerical examples.      

Pertraction through liquid membranes

A survey of liquid membranes and related transport mechanisms is presented. Possibilities and advantages of application of pertraction as a separation and concentration operation are discussed. Pertraction into emulsions is analyzed from the process point of view in more detail. A further development of this operation will be connected with a better understanding of interphase phenomena.