Density of the Set of Generators of Wavelet Systems

Given a function ψ in the affine (wavelet) system generated by ψ, associated to an invertible matrix a and a lattice Γ, is the collection of functions In this paper we prove that the set of functions generating affine systems that are a Riesz basis of ${\cal L}^2({\Bbb R}^d)$ is dense in We also prove that a stronger result is true for affine systems that are a frame of In this case we show that the generators associated to a fixed but arbitrary dilation are a dense set. Furthermore, we analyze the orthogonal case in which we prove that the set of generators of orthogonal (not necessarily complete) affine systems, that are compactly supported in frequency, are dense in the unit sphere of with the induced metric. As a byproduct we introduce the p-Grammian of a function and prove a convergence result of this Grammian as a function of the lattice. This result gives insight in the problem of oversampling of affine systems.     

Robert Vivian Pound and the Discovery of Nuclear Magnetic Resonance in Condensed Matter

This paper is based upon five interviews I conducted with Robert Vivian Pound in 2006–2007 and covers his childhood interest in radios, his time at the Massachusetts Institute of Technology Radiation Laboratory during the Second World War, his work on the discovery of nuclear magnetic resonance in condensed matter, his travels as a professor at Harvard University, and his social interactions with other physicists.     

A comparative theoretical study of dipeptide solvation in water

Molecular dynamics studies have been performed on the zwitterionic form of the dipeptide glycine-alanine in water, with focus on the solvation and electrostatic properties using a range of theoretical methods, from purely classical force fields, through mixed quantum mechanical/molecular mechanical simulations, to fully quantum mechanical Car-Parrinello calculations. The results of these studies show that the solvation pattern is similar for all methods used for most atoms in the dipeptide, but can differ substantially for some groups; namely the carboxy and aminoterminii, and the backbone amid NH group. This might have implications in other theoretical studies of peptides and proteins with charged -NH(3) (+) and -CO(2) (-) side chains solvated in water. Hybrid quantum mechanical/molecular mechanical simulations successfully reproduce the solvation patterns from the fully quantum mechanical simulations (PACS numbers: 87.14.Ee, 87.15.Aa, 87.15.He, 71.15.Pd).     

Acid-induced degradation of phosphorescent dopants for OLEDs and its application to the synthesis of tris-heteroleptic iridium(III) bis-cyclometalated complexes

Investigations of blue phosphorescent organic light emitting diodes (OLEDs) based on [Ir(2-(2,4-difluorophenyl)pyridine)(2)(picolinate)] (FIrPic) have pointed to the cleavage of the picolinate as a possible reason for device instability. We reproduced the loss of picolinate and acetylacetonate ancillary ligands in solution by the addition of Br?nsted or Lewis acids. When hydrochloric acid is added to a solution of a [Ir(C^N)(2)(X^O)] complex (C^N = 2-phenylpyridine (ppy) or 2-(2,4-difluorophenyl)pyridine (diFppy) and X^O = picolinate (pic) or acetylacetonate (acac)), the cleavage of the ancillary ligand results in the direct formation of the chloro-bridged iridium(III) dimer [{Ir(C^N)(2)(μ-Cl)}(2)]. When triflic acid or boron trifluoride are used, a source of chloride (here tetrabutylammonium chloride) is added to obtain the same chloro-bridged iridium(III) dimer. Then, we advantageously used this degradation reaction for the efficient synthesis of tris-heteroleptic cyclometalated iridium(III) complexes [Ir(C^N(1))(C^N(2))(L)], a family of cyclometalated complexes otherwise challenging to prepare. We used an iridium(I) complex, [{Ir(COD)(μ-Cl)}(2)], and a stoichiometric amount of two different C^N ligands (C^N(1) = ppy; C^N(2) = diFppy) as starting materials for the swift preparation of the chloro-bridged iridium(III) dimers. After reacting the mixture with acetylacetonate and subsequent purification, the tris-heteroleptic complex [Ir(ppy)(diFppy)(acac)] could be isolated with good yield from the crude containing as well the bis-heteroleptic complexes [Ir(ppy)(2)(acac)] and [Ir(diFppy)(2)(acac)]. Reaction of the tris-heteroleptic acac complex with hydrochloric acid gives pure heteroleptic chloro-bridged iridium dimer [{Ir(ppy)(diFppy)(μ-Cl)}(2)], which can be used as starting material for the preparation of a new tris-heteroleptic iridium(III) complex based on these two C^N ligands. Finally, we use DFT/LR-TDDFT to rationalize the impact of the two different C^N ligands on the observed photophysical and electrochemical properties.     

Trajectory-based solution of the nonadiabatic quantum dynamics equations: an on-the-fly approach for molecular dynamics simulations

The non-relativistic quantum dynamics of nuclei and electrons is solved within the framework of quantum hydrodynamics using the adiabatic representation of the electronic states. An on-the-fly trajectory-based nonadiabatic molecular dynamics algorithm is derived, which is also able to capture nuclear quantum effects that are missing in the traditional trajectory surface hopping approach based on the independent trajectory approximation. The use of correlated trajectories produces quantum dynamics, which is in principle exact and computationally very efficient. The method is first tested on a series of model potentials and then applied to study the molecular collision of H with H(2) using on-the-fly TDDFT potential energy surfaces and nonadiabatic coupling vectors.     

Thermolytic carbonates for potential 5'-hydroxyl protection of deoxyribonucleosides

Thermolytic groups structurally related to well-studied heat-sensitive phosphate/thiophosphate protecting groups have been evaluated for 5'-hydroxyl protection of deoxyribonucleosides as carbonates and for potential use in solid-phase oligonucleotide synthesis. The spatial arrangement of selected functional groups forming an asymmetric nucleosidic 5'-O-carbonic acid ester has been designed to enable heat-induced cyclodecarbonation reactions, which would result in the release of carbon dioxide and the generation of a nucleosidic 5'-hydroxyl group. The nucleosidic 5'-O-carbonates 3-8, 10-15, and 19-21 were prepared and were isolated in yields ranging from 45 to 83%. Thermolytic deprotection of these carbonates is preferably performed in aqueous organic solvent at 90 degrees C under near neutral conditions. The rates of carbonate deprotection are dependent on the nucleophilicity of the functional group involved in the postulated cyclodecarbonation reaction and on solvent polarity. Deprotection kinetics increase according to the following order: 4 < 5 < 10 < 6 < 12 < 7 < 13 < 8 < 14 congruent with 19-21 and CCl4 < dioxane < MeCN < t-BuOH < MeCN:phosphate buffer (3:1 v/v, pH 7.0) < EtOH:phosphate buffer (1:1 v/v, pH 7.0). Complete thermolytic deprotection of carbonates 7, 8, 13, and 14 is achieved within 20 min to 2 h under optimal conditions in phosphate buffer-MeCN. The 2-(2-pyridyl)amino-1-phenylethyl and 2-[N-methyl-N-(2-pyridyl)]aminoethyl groups are particularly promising for 5'-hydroxyl protection of deoxyribonucleosides as thermolytic carbonates.     

Photochemische Cycloadditionen von 3-Phenyl-2H-azirinen an Carbonsäurechloride. 35. Mitteilung über Photoreaktionen

Irradiation of 2, 3-diphenyl-2H-azirine ( 1a ) and 1-azido-1-phenyl-propene, the precursor of 2-methyl-3-phenyl-2H-azirine ( 1b ), in benzene, with a high pressure mercury lamp (pyrex filter) in the presence of acid chlorides yields the oxazoles 5a–d (Scheme 2). Photolysis of 2, 2-dimethyl-3-phenyl-2H-azirine ( 1c ) under the same conditions gives after methanolysis the 5-methoxy-2, 2-dimethyl-4-phenyl-3-oxazolines 7a, b, d , while hydrolysis of the reaction mixture leads to the formation of the 1, 2-diketones 8a, c, d (Scheme 4). The suggested reaction path for all these reactions is a 1, 3-dipolar cycloaddition of the photochemically generated benzonitrilemethylides 2 to the carbonyl double bond of the acid chlorides to give the intermediates 4 , followed by either elimination of hydrogen chloride or solvolysis (Schemes 2 and 4). Irradiation of 1c in the presence of acetic acid anhydride leads via the intermediate 9 to the 5-hydroxy-3-oxazoline 10 and the 5-methylidene-3-oxazoline 11 (Scheme 5).     

Eine Methode zur Isolierung und Bestimmung von Kreatin und Glykocyamin im Urin

Ohne Zusammenfassung