Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

Comparisons of pharynx, source, formant, and pressure characteristics in operatic and musical theatre singing

Belting, a vocal technique typically cultivated in musical theatre singing, differs timbrally from operatic singing in many interesting respects. The underlying phonatory differences have not been previously investigated in detail. Yet, belting is frequently associated with disturbances of voice function. Articulatory and phonatory characteristics are investigated in a female subject who is a professional singer (co-author JL) trained in both the operatic and belting styles and in an intermediate vocal technique (“mixed”). This article presents data obtained from this subject by video-fiberoptic observation of the pharynx, inverse filtering of airflow, and measurement of subglottal pressure. The results reveal that belting was characterized by very high subglottal pressures and sound levels, and apparently also by a comparatively high degree of glottal adduction. Comparisons with other investigations of related aspects of belting and operatic singing support the assumption that the data obtained from our subject are representative for these vocal techniques.     

Structure and Thermal Stability of La0.10WO3+y; A Hexagonal Tungsten Bronze Related Phase Formed at High Pressure

The structure and thermal stability of a hexagonal tungsten bronze (HTB) related compound, La_xWO_3+y with x≈0.10 and y≈0.15, has been studied by X-ray diffraction, thermal analysis, and electron microscopy. The structure was refined by the Rietveld method from X-ray powder diffractometer data of a La_0.10WO₃ sample prepared at T=1250°C and P=25 kbar, which consisted of two tungsten bronze related phases in 1:1 proportion. The unit cell dimensions are as follows: La_0.108WO_3+y (y≈0.16), a=7.40890(5), and c=3.79329(4) Å (HTB-related structure); La_0.091WO₃, a=3.82458(6) Å (cubic perovskite tungsten bronze (PTB) structure). The lanthanum atoms in La_0.108WO_3+y are located on the hexagonal axis and statistically distributed on two sites close to the tungsten atom plane. Thermal stability studies of the La_0.10WO₃ sample in an argon atmosphere under ambient pressure conditions revealed that the HTB-related compound is metastable, decomposing to the stable PTB-type structure and WO₃. It was also found from the TG experiments in argon and oxygen that additional oxygen atoms (y) are present in the structure, thus forming a lanthanum tungsten oxide of the above composition. The electron diffraction and microanalysis studies confirmed that crystals of the HTB- and PTB-type structures were formed, with a lanthanum content of x≈0.1.     

Diffusion-controlled vinyl polymerization. I. The gel effect

It is well known that the reaction rate and molecular weight of vinyl polymers can change markedly during the course of polymerization and that these changes are due to the influence of diffusion on the termination reaction. The chain length dependence of the termination rate constant has been considered in this work and has resulted in a general method of treating the polymerization kinetics and molecular weight distribution. This method is independent of the form of the chain length dependency and is capable of dealing with both disproportionation and recombination modes of termination. A specific model for the termination rate constant with chain length dependence is proposed and is based on free volume theory and entanglement coupling. Master curves for the characteristics of the reaction rate and molecular weight distribution are presented with the application of this model.     

Synthesis,Spectral and Magnetic Properties,and Crystal Structures of Copper(II) Pyridinecarboxylate Adducts with N‐Heterocyclic Ligands

Synthesis and characterization of seven new complexes [Cu(2‐MeSnic)₂(CH₃OH)]₂ (where 2‐MeSnic is 2‐methylthionicotinate), [Cu(2‐MeSnic)₂L₂]₂ (where L is pyridine — py, ethylnicotinate — Etnic and butylnicotinate — Bunic), [Cu(2‐MeSnic)₂L₂(H₂O)₂] (where L is py and nicotinamide — nia) and [Cu(2‐MeSnic)₂(N‐Menia)₂(H₂O)₂]·2H₂O (where N‐Menia is N‐methylnicotinamide) are reported. The characterization were based on elemental analysis, infrared, electronic and EPR spectra, and magnetic susceptibility measurements over a temperature range of 1.8 — 300 K or 70 — 300 K. Three complexes of different type were studied by X‐ray analysis. The molecule of [Cu(2‐MeSnic)₂(CH₃OH)]₂ has dimeric paddle‐wheel cage structure with a tetragonal pyramidal arrangement around Cu^II. The dimer results from the fact that carboxyl groups of four 2‐MeSnic anions function as bridging in a syn‐syn arrangement. On the other hand [Cu(2‐MeSnic)₂(py)₂]₂ forms dimers with hexacoordinated Cu^II atoms in highly distorted coordination octahedra, each with two oxygen atoms of bridging carboxyl groups in an anti‐anti arrangement of two 2‐MeSnic anions, with two oxygen atoms of one asymmetrically chelating 2‐MeSnic anion and with two nitrogen atoms of two pyridine ligands. The temperature independent EPR spectrum for this complex exhibits an axial signal which corresponds to almost isolated S = ¹/₂ magnetic ions. Magnetic data for the dimer show a weak antiferromagnetic interaction between the two metal ions with J = —0.65 cm^—1. The Cu^II atom in complex [Cu(2‐MeSnic)₂(py)₂(H₂O)₂] is hexacoordinated in an elongated centrosymmetrical tetragonal‐bipyramidal arrangement (4 + 2). Based on the molecular structure the electronic, infrared, electron paramagnetic resonance spectra and magnetic properties are discussed and stereochemistry as well as the mode of ligand coordination in new solid complexes under study have been determined.     

Aurophilicity-coordination interplay in the design of cyano-bridged nickel(II)-Gold(I) bimetallic assemblies: structural and computational studies of the gold(I)-gold(I) interactions

Two polymorphic cyano-bridged Au(I)-Ni(II) bimetallic complexes of formulas [Ni(en)2Au(CN)2][Au(CN)2] (1) and [Ni(en)2[Au(CN)2]2] (2) have been prepared from the 1:2 reaction between [Au(CN)2]- and either [Ni(en)2Cl2]Cl or [Ni(en)3]Cl2.2H2O, respectively. The structure of 1 consists of polymeric cationic chains of alternating [Au(CN)2]- and [Ni(en)2]2+ units running along the a axis and [Au(CN)2]- anions lying between the chains. The noncoordinated dicyanoaurate anions are aligned perpendicular to the ac plane and involved in aurophilic interactions with the bridging dicyanoaurate groups, ultimately leading to a 2D bimetallic grid. The structure of 2 consists of trinuclear molecules made of two [Au(CN)2]- anions linked to [Ni(en)2]2+ unit in trans configuration. Trinuclear units are joined by aurophilic interactions to form 1D zigzag chains. The magnetic properties of these compounds are strongly dominated by the local anisotropy of the octahedral Ni(II) ions, thus indicating that the magnetic exchange interaction mediated by dicyanoaurate bridging groups, if it exists, is very weak. To get insight into the electronic properties of the inter- and intramolecular interactions of the [Au(CN)2]- building blocks, the structures of different aggregates of dicyanogold units were optimized and then analyzed by making use of atoms-in-molecules (AIM) theory. Moreover, bond indices were calculated by methods based upon nonlinear population analysis.     

Challenges in predicting and controlling particle morphology in latices of commercial complexity

Independent, quantitative models for free energy associated with crosslinked seed latices, and monomer and surfactant at the polymer/water interface have been integrated into a predictive model for latex particle morphology. It has been found that very low levels of crosslinking are predicted to influence the particle morphology in a dramatic fashion. Free energy calculation also highlight the often critical role played by surfactant. Highly active surfactants tend to equalize the two polymer/water interfacial tensions and allow the polymer/water interfacial energy to significantly influence the particle morphology.