On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Differential inhibition of postnatal brain,spinal cord and body growth by a growth hormone antagonist

Background  

Growth hormone (GH) plays an incompletely understood role in the development of the central nervous system (CNS). In this study, we use transgenic mice expressing a growth hormone antagonist (GHA) to explore the role of GH in regulating postnatal brain, spinal cord and body growth into adulthood. The GHA transgene encodes a protein that inhibits the binding of GH to its receptor, specifically antagonizing the trophic effects of endogenous GH.     

Boerhaave’s Mineral Chemistry and Its Influence on Eighteenth-Century Pharmacy in the Netherlands and England

In the eighteenth century, the use of mineral or fossil substances was relatively common in European medicine and pharmacy. However, this period also saw profound changes in ideas about the nomenclature, chemistry, and curative properties of minerals. Jonathan Simon has recently argued that an increasing orientation towards the mineral kingdom and the chemical transformation of minerals, and a rise in the number of mineral preparations demanded of the pharmacist, were characteristic for eighteenth-century chemistry within pharmacy. Yet in the Netherlands, and to a certain extent in England, another pattern is visible: although there certainly was an interest in the mineral kingdom and the chemical transformation of nonorganic materials, nothing suggests that this resulted in a strong increase in the demand for mineral-based pharmaceutical preparations – rather the contrary. Unlike English and French eighteenth-century pharmacy, Dutch pharmacy and its relation to academic medicine and chemistry have hardly received attention from historians of science thus far. This paper aims to fill that gap and argues that Herman Boerhaave’s (1668–1738) view on mineral medicine was crucial in the development of a certain wariness of “mineral medicine” in the eighteenth-century Netherlands and England, especially among apothecaries.     

Transfer measurements for the Ti+Ni systems at near barrier energies

Large enhancements have been observed in the sub-barrier fusion cross sections for Ti+Ni systems in our previous studies. Coupled channel calculations incorporating couplings to 2⁺ and 3⁻ states failed to explain these enhancements completely. A possibilty of transfer channels contributing to the residual enhancements had been suggested. In order to investigate the role of relevant transfer channels, measurements of one- and two-nucleon transfer were carried out for ^46,48Ti+⁶¹Ni systems. The present paper gives the results of these studies.     

Microstructural studies on degradation of interface between LSM–YSZ cathode and YSZ electrolyte in SOFCs

The changes in the cathode/electrolyte interface microstructure have been studied on anode-supported technological solid oxide fuel cells (SOFCs) that were subjected to long-term (1500 h) testing at 750 °C under high electrical loading (a current density of 0.75 A/cm²). These cells exhibit different cathode degradation rates depending on, among others, the composition of the cathode gas, being significantly smaller in oxygen than in air. FE-SEM and high resolution analytical TEM were applied for characterization of the interface on a submicron- and nano-scale. The interface degradation has been identified as the loss of LSM coverage and the loss of three-phase-boundary (TPB) length. Firstly, the degradation is caused by the size reduction of the individual LSM/YSZ electrolyte contact points (areas) that are initially of 100–200 nm in diameter. Quantitative microstructure evaluation shows that in the cell tested in air this mechanism contributes to an estimated overall reduction in the LSM coverage and the TPB length by 50 and 30%, respectively. For the cell tested in oxygen the corresponding values are 10 and 4%. Secondly, in the cell tested in air the LSM coverage and the TPB length appear to decrease further due to the more pronounced formation of insulating zirconate phases that are present locally and preferably in LSM/YSZ electrolyte contact areas. The effects of the cathode gas on the interface degradation are discussed considering the change of oxygen activity at the interface, possible changes in the Mn diffusion pattern as well as the LSM/YSZ reactivity. Finally, based on thermodynamic calculations a T–p(O₂) diagram predicting the safe and risky operation conditions in terms of the zirconate formation is presented and compared with the experimental observations.