Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points

We consider Toeplitz operators with piecewise continuous symbols and singular integral operators with piecewise continuous coefficients onL ^p (,w) where 1<p<,w is a Muckenhoupt weight and belongs to a large class of Carleson curves. This class includes curves with corners and cusps as well as curves that look locally like two logarithmic spirals scrolling up at the same point. Our main result says that the essential spectrum of a Toeplitz operator is obtained from the essential range of its symbol by joining the endpoints of each jump by a certain spiralic horn, which may degenerate to a usual horn, a logarithmic spiral, a circular arc or a line segment if the curve and the weightw behave sufficiently well at the point where the symbol has a jump. This result implies a symbol calculus for the closed algebra of singular integral operators with piecewise continuous coefficients onL ^p (,w).Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer of the Krupp Foundation.     

A variational principle for transition and density matrices and approximations to the equations-of-motion

A general variational principle for transition and density matrices is proposed. The principle is closely related to Rowe's variational treatment of the equations-of-motion method. It permits the simultaneous construction of coupled approximations for two eigenstates, and it is a straightforward extension of the usual variational method.     

Determination of tetrahydrocannabinolic acid—carrier protein conjugate by matrix-assisted laser desorption/ionization mass spectrometry and antibody formation

In order to form the monoclonal antibody against tetrahydrocannabinolic acid (THCA), THCA was coupled with bovine serum albumin (BSA) or human serum albumin (HSA) using β-alanine as a linker or without β-alanine to produce individual antigen conjugates. The number of haptens contained in the antigen conjugates was determined by matrix-assisted laser desorption ionization mass spectrometry using BSA or HSA as an internal standard. The formation of monoclonal antibody is also discussed.     

Study of the electronic structure of radicals by the CI method

Results are presented which were obtained in the -electronic approximation for the ground state properties of the benzyl radical (total energy, distribution of the electronic and spin density) by the CI method on closed and open shell SCF orbitals taking into account all singly and some doubly excited configurations. Some of the singly excited configurations which in the first order perturbation theory do not interact with the ground state configuration contribute to the ground state more than some of those which interact with the latter. Certain doubly excited configurations contribute more than some singly ones. The consideration of all singly excited configurations leads to a lower ground state energy if the closed shell orbitals are used compared with the open shell ones. The former bring about the non-uniform electron density distribution becoming more smooth as the set of the basis configurations becomes larger. The spin density distribution strongly depends on the number of the configurations as well as on the orbitals used for their construction. The computation of the benzyl radical done by Hinchliffe by the CI method on open shell orbitals is believed to be wrong.

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Zusammenfassung Rechnungen im Rahmen der -Elektronen-NÄherung für den Grundzustand des Benzyl-Radikals (Gesamtenergie, Verteilung von Elektronen- und Spin-Dichte) mittels des SCF-CI-Verfahrens für geschlossene und offene Schalen unter Einschlu\ aller einfach und einiger zweifach angeregten Konfigurationen werden mitgeteilt. Dabei zeigt sich, da\ einfach angeregte Konfigurationen, die in der Störungsrechnung erster Ordnung nicht mit der Grundfiguration kombinieren, zum Grundzustand mehr als solche, die kombinieren, beitragen.Zusammenfassung Die Berücksichtigung aller einfach angeregten Konfigurationen führt zu einer niedrigeren Grundzustandsenergie, wenn die Einteilchenfunktionen, die sich für geschlossene Schalen ergeben, an Stelle derer für offene Schalen verwendet werden. Erstere führen zu ungleichförmiger Verteilung der Elektronendichte, die um so mehr geglÄttet ist, je grö\er die Anzahl der Konfigurationen wird. Die Verteilung der Spin-Dichte hÄngt stark von der Anzahl der Konfigurationen wie auch von den benutzten Orbitalen ab. Die Berechnung des Benzyl-Radikals von Hinchliffe mittels des CI-Verfahrens für offene Schalen wird als unrichtig angesehen.

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Résumé Propriétés de l'état fondamental du radical benzyle (énergie totale, distribution des densités électroniques et de spin) dans l'approximation par la méthode d'I.C. sur les orbitales SCF des couches complètes et incomplètes avec introduction de toutes les configurations monoexcitées et de certaines configurations diexcitées. Certaines configurations monoexcitées qui n'intéragissent pas avec la configuration fondamentale au premier ordre de la théorie des perturbations apportent à l'état fondamental une contribution plus élevée que certains de ceux qui interagissent à ce stade là. Certaines configurations diexcitées ont une contribution plus forte que certaines monoexcitées. Si l'on tient compte de toutes les configurations monoexcitées, on obtient une énergie plus basse en utilisant les orbitales des couches complètes et non celles des couches ouvertes. On obtient ainsi une distribution électronique dont la non uniformité va en s'affaiblissant lorsque la base de configurations s'élargit. La distribution de densité de spin dépend fortement du nombre de configurations employé ainsi que des orbitales utilisées. Le calcul d'I.C. d'Hinchliffe sur le radical benzyle à l'aide des orbitales des couches ouvertes semble faux.

     

Sonochemical synthesis of cerium oxide nanoparticles-effect of additives and quantum size effect

Cerium oxide (CeO(2)) nanoparticles were prepared sonochemically, by using cerium nitrate and azodicarbonamide as starting materials, and ethylenediamine or tetraalkylammonium hydroxide as additives. The additives have a strong effect on the particle size and particle size distribution. CeO(2) nanoparticles with small particle size and narrow particle size distribution are obtained with the addition of additives; while highly agglomerated CeO(2) nanoparticles are obtained in the absence of additives. Monodispersed CeO(2) nanoparticles with a mean particle size of ca. 3.3 nm are obtained when tetramethylammonium hydroxide (TMAOH) is used as the additive and the molar ratio of cerium nitrate/azodicarbonamine/TMAOH is 1/1/1. Blue shifts of the absorption peak and the absorption edges of the products are observed in the UV-Vis absorption spectra as a result of the quantum size effect. The samples have been characterized using powder XRD, TEM, DLS, and absorption spectra.     

Comparison of the hole mobility in undoped and boron-doped polycrystalline CVD diamond films

The drift mobility of nonequilibrium holes injected in undoped polycrystalline diamond films was determined, by a transit-time technique, as ca. 10⁻³ cm²/(V s). This hole mobility is three orders of magnitude lower than the “equilibrium” mobility in boron-doped diamond films [0.1–1 cm²/(V s)], determined from the films' dc conductivity. This difference is explained by the effect of a nonequilibrium charge carrier trapping during the carrier transport in polycrystalline diamond. Received: 3 December 1997 / Accepted: 9 April 1998     

Manipulation of the magnetic properties of magnetite-silica nanocomposite materials by controlled Stober synthesis

The paper describes the synthesis and characterization of the magnetic properties of magnetite/silica nanocomposites using a modified Stober method. Magnetite nanoparticles averaging 8-10 nm in diameter and stabilized with oleic acid in toluene were used as the magnetic component of the nanocomposites. SQUID magnetic measurements and ferromagnetic resonance spectroscopy measurements were performed at each stage of the synthesis to understand the properties of the formed composites. Changes of blocking temperature in ZFC/FC SQUID curves correlated with corresponding changes of the resonance field in the ferromagnetic spectra of the sample at each stage of formation. The paper concludes that it is possible to manipulate the magnetic properties of silica/magnetite composite materials by controlling their surface properties and silica coating thickness.     

Intramolecular dynamics of 1,2,3-trifluorobenzene radical anions as studied by OD ESR and quantum-chemical methods

Ab initio UMP2, RMP2, DFT/UB3LYP, and CBS-QB3 calculations have shown that the adiabatic potential energy surface (PES) of the 1,2,3-trifluorobenzene radical anion is a pseudorotation surface formed by nonplanar stationary structures. The low (approximately 2-4 kcal/mol) energy barriers in the path of pseudorotation imply manifestations of spectral exchange in the ESR spectra of this radical anion. The optically detected ESR of radical ion pairs was used to obtain the ESR spectrum of 1,2,3-trifluorobenzene radical anion in liquid squalane solution and to study temperature variations in the spectrum over the range of 243-325 K. The spectrum is a doublet of triplets with hfc constants of a(F(2)) = 29 mT and a(2F(1,3)) = 7.6 mT at T = 243 K. The experimental hfc constants are temperature-dependent. Calculations of the temperature dependence of hfc constants in the framework of the model of classical nuclei motion along the pseudorotation coordinate reproduce well the experimental data.     

Remarks on the process of homogeneous carbonylation of rhodium compounds by N,N-dimethylformamide

Reductive carbonylation of rhodium(III) chloride complexes, commercial RhCl₃ · nH₂O neutralized with BaCO₃, (Me₂NH₂)₂[RhCl₅(DMF)], (PPh₄)[RhCl₄(H₂O)₂], RhCl₃(DMF)₃, RhCl₃(CH₃CN)₃, RhCl₃(CH₃CN)₂(DMF), [Rh(CO)₂Cl₃]₂, and rhodium(I) complex, Rh(PPh₃)₃Cl, by N,N-dimethylformamide (DMF) is studied. The data obtained support the conception of direct carbonyl group transfer from DMF molecule to the Rh metal center. The mechanistic scheme of carbonylation process is refined and discussed with regard of new experimental results.     

Receptors for tetrahedral oxyanions

This review covers the field of anion recognition from the perspective of tetrahedral oxyanion recognition. The bulk of the attention is devoted to metal-free systems that are able to effect the recognition, binding or transport of phosphate and sulfate. Particular emphasis is devoted to design criteria that allow for discrimination and selectivity. In this context, a variety of recognition motifs are discussed and, within each receptor class, general paradigms that allow for the construction of receptor systems with high affinity and specificity are noted.