Number of irreducible polynomials and pairs of relatively prime polynomials in several variables over finite fields

We discuss several enumerative results for irreducible polynomials of a given degree and pairs of relatively prime polynomials of given degrees in several variables over finite fields. Two notions of degree, the total degree and the vector degree, are considered. We show that the number of irreducibles can be computed recursively by degree and that the number of relatively prime pairs can be expressed in terms of the number of irreducibles. We also obtain asymptotic formulas for the number of irreducibles and the number of relatively prime pairs. The asymptotic formulas for the number of irreducibles generalize and improve several previous results by Carlitz, Cohen and Bodin.     

Elastic and inelastic scattering in silicon using Mössbauer diffraction

The Mossbauer diffraction instrument at the Missouri University Research Reactor has been used to measure the elastic and inelastic contributions to the 444 Bragg reflection in dynamic silicon at room temperature. These measurements used the 46.5-keV gamma rays from high intensity¹⁸³Ta sources cooled to liquid nitrogen temperature. The main feature of this study compared to similar measurements on silicon is the significantly improved momentum space resolution. ΔQ values of 0.011 Å^?1 and 0.11 Å^?1 were measured for the transverse and longitudinal directions, respectively.     

Asymmetry parameters in183W and182W using mice detection with a crystal monochromator

Using exceptionally high intensity Mössbauer sources (～ 1–100 Ci) of¹⁸²Ta and¹⁸³Ta, we have measured the Mössbauer effect for the 46.5 and 99.1 keV transitions of¹⁸³W and the 100.1 keV transition of¹⁸²W. Using a microfoil internal conversion electron (MICE) /1/ detector capable of operation at low temperatures, and a LiF crystal monochromator, we obtain effects of nearly 600% for the 46.5 keV transition and 3 1/2% and 6% for the other two cases, while standard transmission measurements typically yield much smaller signal-to-background ratios. With this technique we have measured the asymmetry term in the conversion electron spectra. To our present level of accuracy the results are in agreement with theoretical calculations of interference parameters /2/. Our results do not agree with earlier measurements /3/ on this transition, which are grossly at variance with theoretical calculations of the interference parameter.     

Selective Homogeneous Palladium(0)-Catalyzed Hydrogenation of Alkynes to (Z)-Alkenes

Zero-valent palladium precatalysts containing rigid bidentate bis(arylimino)acenaphthene ligands (shown schematically) facilitate the highly stereoselective homogeneous catalytic hydrogenation of alkynes to (Z)-alkenes. Internal, terminal, aryl-substituted, and cyclic alkynes are suitable substrates, as are some enynes, which are chemoselectively hydrogenated to dienes. E=CO(2)Me; R(1), R(2)=4-OCH(3), 4-CH(3), 2,6-(CH(3))(2).     

Three-dimensional orientational colocalization of individual donor--acceptor pairs

We report on the determination of the three-dimensional orientation of the donor and acceptor transition dipoles in individual fluorescence resonance energy transfer (FRET) pairs by means of scanning optical microscopy with annular illumination. Knowledge of the mutual orientation of the donor and acceptor dipole is mandatory for reliable distance determination based on FRET efficiency measurements. In our model system perylenediimide as the donor and terryelenediimide as the acceptor are coupled via a stiff p-terphenyl linker. The absorption dipoles of the donor and acceptor are selectively addressed by the 488 nm and 647 line of an Ar/Kr mixed gas laser, respectively. A clear deviation from collinearity is observed with a distribution of misalignment angles peaked around 22 degrees.     

The influence of molecular gases and analytes on excitation mechanisms in atmospheric microwave sustained argon plasmas

The effect of introducing molecular compounds into argon plasmas has been studied using an expanding microwave induced plasma at atmospheric pressure. Besides the use of optical emission spectroscopy (OES), also the time dependent behavior of line intensities during power interruptions has been studied. From the measurements it is found that even an injection of small amounts of molecular compounds (> 0.5%) leads to important changes in excitation mechanisms in the plasma. It is also found that in the recombination zone downstream in the plasma an excitation mechanism which is independent of the electron density, e.g. excitation transfer from metastables or Penning ionization, must be responsible for the excitation of analytes. Received: 12 February 1998 / Revised: 14 April 1998 / Accepted: 17 April 1998     

The determination of nitrogen in nitrocellulose

A method for the determination of nitrogen in nitrocellulose has been developed. The sample is dissolved in concentrated sulphuric acid and a salicylic acid solution is added. The nitrosalicylic acid formed is reduced at room temperature with an excess of titanous chloride solution and the excess is estimated by titration with ferric alum. Statistically designed experiments were used to establish the conditions necessary for accurate results. The procedure is more rapid than the usual nitrometer method and gives results of high precision; e.g. on a mean result of about 13.8% nitrogen, the standard deviation is 0.014.