Exact regularity of Bergman,Szegö and Sobolev space projections in non pseudoconvex domains

Mathematische Zeitschrift -     

The Bergman kernel function: Explicit formulas and zeroes

We show how to compute the Bergman kernel functions of some special domains in a simple way. As an application of the explicit formulas, we show that the Bergman kernel functions of some convex domains, for instance the domain in defined by the inequality , have zeroes.

     

Synthesis of ionic polyurethanes with pyrene rings: Spectral properties and fluorescence quenching study

Hydrophilic ionic polyurethanes with 4‐chloromethylphenylcarbamoyl‐1‐oxymethylpyrene located on the quaternary ammonium structure from a polymer based on poly(ethylene glycol), isophorone diisocyanate, and N‐methyldiethanolamine were prepared by a quaternization reaction, in which the amount of pyrene covalently attached to the polymeric backbone ranged from 1.14 to 19.82 mmol of fluorophore/100 g of polymer. It was interesting to compare the photoluminescence of the pyrene polyurethane carrying a few mole percent of pyrene moieties with that of a third polymer resulting from its subsequent quaternization with benzyl chloride up to a concentration of ionic groups as in the latter (quaternization degree = 14.15%). The process of excimer formation between the pyrene molecules attached to the ionic polyurethane was investigated in tetrahydrofuran (THF), dimethylformamide, film, and THF/H₂O to illustrate the expected differences in the polymer behavior compared with that of the starting pyrene derivative. The formation of aggregates or core–shell micelles was sustained by the fluorescence data, which indicated the existence of pyrene units in the ground state of the molecule, giving rise thus to an explanation for the high excimer‐to‐monomer intensity ratio. The fluorescence decay of pyrene polyurethanes in the presence of various concentrations of nitrobenzene used as a quencher was analyzed too when the fluorescence quenching in the polymer solution normally followed Stern–Volmer kinetics. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 3945–3956, 2005     

Orthogonal and unitary tensor decomposition from an algebraic perspective

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. Those that do have attracted attention from theoretical computer science and scientific computing. We complement this existing body of literature with an algebro-geometric analysis of the set of orthogonally decomposable tensors.More specifically, we prove that they form a real-algebraic variety defined by polynomials of degree at most four. The exact degrees, and the corresponding polynomials, are different in each of three times two scenarios: ordinary, symmetric, or alternating tensors; and real-orthogonal versus complex-unitary. A key feature of our approach is a surprising connection between orthogonally decomposable tensors and semisimple algebras—associative in the ordinary and symmetric settings and of compact Lie type in the alternating setting.     

Core, shell, and surface-optimized dendrimers for blue light-emitting diodes

We present a novel core-shell-surface multifunctional structure for dendrimers using a blue fluorescent pyrene core with triphenylene dendrons and triphenylamine surface groups. We find efficient excitation energy transfer from the triphenylene shell to the pyrene core, substantially enhancing the quantum yield in solution and the solid state (4-fold) compared to dendrimers without a core emitter, while TPA groups facilitate the hole capturing and injection ability in the device applications. With a luminance of up to 1400 cd/m(2), a saturated blue emission CIE(xy) = (0.15, 0.17) and high operational stability, these dendrimers belong to the best reported fluorescence-based blue-emitting organic molecules.     

Iron-catalyzed intermolecular [2π+2π] cycloaddition

The bis(imino)pyridine iron dinitrogen compounds, ((iPr)PDI)Fe(N(2))(2) and [((Me)PDI)Fe(N(2))](2)(μ(2)-N(2)) ((R)PDI = 2,6-(2,6-R(2)-C(6)H(3)N═CMe)(2)C(5)H(3)N; R = (i)Pr, Me), promote the catalytic intermolecular [2π + 2π] cycloaddition of ethylene and butadiene to form vinylcyclobutane. Stoichiometric experiments resulted in isolation of a catalytically competent iron metallocycle intermediate, which was shown to undergo diene-induced C-C reductive elimination. Deuterium labeling experiments establish competitive cyclometalation of the bis(imino)pyridine aryl substituents during catalytic turnover.