Almost Invariant Half-Spaces of Operators on Banach Spaces

We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on an infinite-dimensional Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators on ℓ_p (1 ≤ p < ∞) or c₀.     

Ligand‐site exchange in intramolecular complexes of silicon: substituent effects

The intramolecular complexes containing coordination bonds Si←N or Si←O are distinguished for their stereochemical nonrigidity resulting in interconversion between isomers, that is, ligand‐site exchange. The influence of the substituents bound to the silicon atom on the free energies of activation for ligand exchange ΔG^≠ of specific interest is poorly understood. In this work, the literature data on substituent influence on the energies ΔG^≠ for 13 series of the complexes have been considered, using the correlation analysis. On the basis of the obedience of the energies ΔG^≠ to the linear free energy relationship, it has been established for the first time that the ΔG^≠ values depend not only on the inductive and resonance effects but also on the polarizability and steric effects of substituents. The reason for the occurrence of the polarizability effect is the appearance of excess charges on Si and N (or O) atoms as a result of intramolecular coordination consisting in the charge transfer from the donor center (N or O atom) to the acceptor one (Si atom). In some series the contribution of the polarizability or steric effect to the overall change in ΔG^≠ because of the influence of substituents is a maximum. An understanding of these effects may give a better insight into the mechanism of nucleophilic substitution, involving organoelement compounds. Copyright © 2012 John Wiley & Sons, Ltd.     

Dichloromethane as solvent and reagent: a case study of photoinduced reactions in mixed phosphonium‐iodonium ylide

Several years ago the photoinduced reaction of mixed phosphonium‐iodonium ylides ( 1 ) with acetylenes ( 2 ) to give λ⁵‐phosphinolines ( 3 ) and substituted furans ( 4 ) was described. This reaction is one‐pot, metal‐free synthesis of heterocycles 3 and 4 with the yields of 40% to 80%. The reaction proceeds only in dichloromethane (DCM) at the high ylide concentrations (>0.01 mol/L). The product analysis by ³¹P NMR, electrospray ionization mass spectrometry, UV‐vis spectrophotometry, and the dynamic light scattering study of the self‐aggregation of the ylide in DCM showed a dual role of the solvent in the photoinduced reactions of mixed phosphonium‐iodonium ylide: (i) at the low ylide concentrations (<0.01 mol/L), the conjugated photoinitiation of the chain reaction in DCM results in the formation of chlorine‐containing products and (ii) at the high ylide concentrations (>0.01 mol/L), the photolysis mechanism is determined by self‐organization of the ylide molecules to give large stable aggregates in DCM, in which the target heterocycles are synthesized. Two important issues follow from the study. First, the annulation reaction between mixed phosphonium‐iodonium ylide and acetylenes occurs only when the reactive intermediates are in close proximity to one other, and, second, DCM is not inert reagent in reactions occurring with participation of radicals and in one form or another can participate in photoinduced radical reactions of various solutes.     

Benzo[b]Furan in the Povarov Reaction

The Povarov-type condensation of ethyl 2-(arylimino)acetates, 1-aryl-2-aryliminoethanones or N-benzylideneanilines with benzo[b]-furan affords 5,6,6a,11b-tetrahydrobenzofuro[2,3-c]quinolines and/or related benzofuro[2,3-c]quinolines.     

A comment on the emission from the Galactic Center as seen by the Fermi telescope

In the recent paper of Hooper and Goodenough (2010) [10] it was reported that γ-ray emission from the Galactic Center region contains an excess compared to the contributions from the large-scale diffuse emission and known point sources. This excess was argued to be consistent with a signal from annihilation of Dark Matter with a power law density profile. We reanalyze the Fermi data and find instead that it is consistent with the “standard model” of diffuse emission and of known point sources. The main reason for the discrepancy with the interpretation of Hooper and Goodenough (2010) [10] is different (as compared to the previous works) spectrum of the point source at the Galactic Center assumed by Hooper and Goodenough (2010) [10]. We discuss possible reasons for such an interpretation.     

Organometallic synthesis and electrophoretic characterization of high-quality ZnS:Mn/ZnS core/shell nanoparticles for bioanalytical applications

A novel and facile preparation method for colloidal ZnS nanoparticles doped with Mn²⁺ is introduced, using a simple one pot heating process followed by a capping procedure for saturation of the surface bound doping atoms to increase the nanoparticles’ stability and photoluminescence quantum yield. The particles were transferred into water with a standard ligand exchange method and investigated by means of laser Doppler electrophoresis, agarose gel electrophoresis, and isotachophoresis. Correspondence: Alexey Merkulov, Freiburg Materials Research Centre (FMF), University of Freiburg, Stefan-Meier-Strasse 21, D-79104 Freiburg, Germany