On Uniform Boundedness and Uniform Asymptotics for Orthogonal Polynomials on the Unit Circle

The known conditions due to G. Baxter, Ya. L. Geronimus, and B. L. Golinskii which guarantee the uniform boundedness and/or uniform asymptotic representation for orthonormal polynomials on the unit circle are under consideration. We show that these conditions are in general not necessary. We discuss the relation between the orthonormal polynomials on the unit circle, the best approximations, and absolutely convergent Fourier series.     

Fluctuation measurements in a supersonic boundary layer implying in-situ calibration of the hot-wire anemometer

A calibration technique for the constant-temperature hot-wire anemometer is presented, which is based on traversing the probe through the boundary layer of a flat plate while simultaneously performing fluctuation measurements. The free stream Mach number was M = 2.54, and the Reynolds number Re_d, based on wire diameter, ranged from 9 to 23. A comparison of the sensitivity values obtained with the aid of such a calibration procedure — under the condition of neglecting low temperature loadings (t<0.6) — agrees well with sensitivities determined with free-stream data-The use of a modified transfer function for correcting the power spectra of flow perturbations revealed a conformity of wide parts of the corrected spectra with the Kolmogorov decay. The fluctuation levels of total temperature and mass flux were computed for the boundary layer of a flat plate. This work was presented at the International Conference on the Methods of Aerophysical Research ICMAR 2007, which was held in Novosibirsk on 5–10 February 2007.     

Reducing system of parameters and the Cohen-Macaulay property

Let R be a local ring and let (x ₁, …, x _r) be part of a system of parameters of a finitely generated R-module M, where r < dim_R M. We will show that if (y ₁, …, y _r) is part of a reducing system of parameters of M with (y ₁, …, y _r) M = (x ₁, …, x _r) M then (x ₁, …, x _r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V _R(x ₁, …, x _r) with dim_R R/P = dim_R M − r the localization M _P of M at P is an r-dimensional Cohen-Macaulay module over R _P. Furthermore, we will show that M is a Cohen-Macaulay module iff y _d is a non zero divisor on M/(y ₁, …, y _d−1) M, where (y ₁, …, y _d) is a reducing system of parameters of M (d:= dim_R M).     

Mechanism of the thermal decomposition of nitrates from graphite furnace mass spectrometry studies

A basically new mechanism of the thermal decomposition of solids is proposed to explain the mass spectral observations of gaseous molecules of CoO, CuO, Cu₂O, NiO, PbO and Mg(OH)₂ during the low-temperature decomposition of the anhydrous and hydrated nitrates of these metals. The mechanism consists of two stages: congruent gasification of all reaction products irrespective of their saturated vapor pressure and subsequent condensation of the low-volatility species (oxides and hydroxides). The partial pressures of these species at the appearance temperatures calculated from this theory for the first stage of the process (1–50 mPa) are in agreement with the detection limits of the quadrupole mass spectrometers used in these experiments. The proposed mechanism is supported by other available data obtained by thermal analysis.     

Confinement of electrons and ions in a combined trap with the potential for antihydrogen production

Experiments with electrons and ions in a combined trap are reported. The unique capability to confine particles with opposite charge and very different mass simultaneously in the same spatial region makes the combined trap a promising device for future synthesis of antihydrogen.     

A one‐dimensional CdII coordination polymer: catena‐poly[cadmium(II)‐bis(μ‐6‐methylpicolinato)]

In the title compound, [Cd(C₇H₆NO₂)₂]_n, the Cd^II ion has a distorted octahedral geometry. The 6‐methylpyridine‐2‐carboxylate anions are perpendicular to one another and act as bidentate and bridging ligands. Two carboxylate O atoms bridge the Cd^II ions, forming centrosymmetric dinuclear units. These units are further connected via carboxylate O atoms into a one‐dimensional polymeric chain which extends in the [100] direction.     

Generalized resolvent matrices and spaces of analytic functions

We introduce triplet spaces for symmetric relations with defect index (1, 1) in a Pontryagin space. Representations of Pontryagin spaces by spaces of vector-valued analytic functions are investigated. These concepts are used to study 2×2-matrix valued analytic functions which satisfy a certain kernel condition.     

Electron screening in backward elastic scattering

Abstact: The elastic scattering cross sections, σ (E,θ), for the systems He+Ta and He+W have been measured at θ_lab=165° and E _lab=76.1 keV to 3.988 MeV using targets with a thickness of a few atomic layers. The results are smaller than the results given by the Rutherford scattering law, σ_R(E,θ), due to the effects of electron screening and can be described by σ(E,θ)/σ_R(E,θ)=(1+U_e/E)⁻¹, where U _e is an atomic screening potential energy. The deduced average value, U _e=28 ± 3 keV, is consistent with the Moliére- and Lenz-Jensen-models as well as electron binding energies. Received: 25 May 1998