A sinc-collocation method for initial value problems

A collocation procedure is developed for the initial value problem , , using the globally defined sinc basis functions. It is shown that this sinc procedure converges to the solution at an exponential rate, i.e., where and basis functions are used in the expansion. Problems on the domains and are used to illustrate the implementation and accuracy of the procedure.

     

A fully integrated high-throughput screening methodology for the discovery of new polyolefin catalysts: discovery of a new class of high temperature single-site group (IV) copolymerization catalysts

For the first time, new catalysts for olefin polymerization have been discovered through the application of fully integrated high-throughput primary and secondary screening techniques supported by rapid polymer characterization methods. Microscale 1-octene primary screening polymerization experiments combining arrays of ligands with reactive metal complexes M(CH(2)Ph)(4) (M = Zr, Hf) and multiple activation conditions represent a new high-throughput technique for discovering novel group (IV) polymerization catalysts. The primary screening methods described here have been validated using a commercially relevant polyolefin catalyst, and implemented rapidly to discover the new amide-ether based hafnium catalyst [eta(2)-(N,O)[bond](2-MeO[bond]C(6)H(4))(2,4,6-Me(3)C(6)H(2))N]Hf(CH(2)Ph)(3) (1), which is capable of polymerizing 1-octene to high conversion. The molecular structure of 1 has been determined by X-ray diffraction. Larger scale secondary screening experiments performed on a focused 96-member amine-ether library demonstrated the versatile high temperature ethylene-1-octene copolymerization capabilities of this catalyst class, and led to significant performance improvements over the initial primary screening discovery. Conventional one gallon batch reactor copolymerizations performed using selected amide-ether hafnium compounds confirmed the performance features of this new catalyst class, serving to fully validate the experimental results from the high-throughput approaches described herein.     

AB initio MO LCAO UHF calculations of magnetic hyperfine interactions in π-radicals. Isotropic and anisotropic couplings of ·CH3, ·NH3+, ·C2H5 and ·N2H4+

A series of π-electron radicals have been investigated with ab initio methods, using the unrestricted Hartree-Fock approximation. The geometries have been partially optimized, and magnetic hyperfine coupling constants have been evaluated. For the dipolar hyperfine couplings, the results obtained are in fair agreement with experiment, whereas the isotropic coupling constants show greater deviations. These values are also shown to be sensitive to annihilation of the quartet contamination of the wavefunction.     

Ab initio MO LCAO UHF calculations of magnetic hyperfine interactions in σ radicals. Isotropic and anisotropic couplings of NO2 and CO2−

The magnetic hyperfine coupling constants in NO₂ and CO₂^? have been computed by an initio methods. Spin annihilation is found to be essential in order to obtain useful results for the dipolar couplings, but has much less influence on the isotropic couplings. The electric quadrupole coupling constants have also been evaluated, and are in good agreement with available experimental data.     

A discrete sampling inversion scheme for the heat equation

Summary We present a simple and extremely accurate procedure for approximating initial temperature for the heat equation on the line using a discrete time and spatial sampling. The procedure is based on the sinc expansion which for functions in a particular class yields a uniform exponential error bound with exponent depending on the number of spatial sample locations chosen. Further the temperature need only be sampled at one and the same temporal value for each of the spatial sampling points. ForN spatial sample points, the approximation is reduced to solving a linear system with a (2N+1)×(2N+1) coefficient matrix. This matrix is a symmetric centrosymmetric Toeplitz matrix and hence can be determined by computing only 2N+1 values using quadratures.Supported in part by a grant from the Texas State Advanced Research ProgramSupported by NSF MONTS grant #ISP8011449Supported in part by grants from NSA, NASA and TATRP     

Flame atomic absorption analysis for selenium after electrochemical preconcentration

Selenium(IV) is determined in the presence of 3.5% sodium chloride by electrochemical preconcentration on a platinum spiral, prior to flame atomic absorption analysis. The electrodeposition is carried out in the presence of hydrazine dihydrochloride to prevent the generation of chlorine at the counter electrode; chlorine oxidizes selenium(IV) to the non-reducible selenium(VI) ion. A detection limit of 5 ppb and an electrolysis efficiency of 10% were obtained for a 25-ml sample and a 5-min electrolysis time. The absolute detection limit was 10 ng.     

Atomic absorption spectrometry of selenium in an argon-hydrogen flame after electrochemical preconcentration

Different methods of atomization of selenium from a platinum wire filament are described, including electrothermal heating of the filament and atomlzation in an argon-hydrogen flame. A combination of these approaches proved to give the best sensitivity and detection limit. The selenium was preconcentrated on the filament by electrolysis prior to the atomic absorption measurements to eliminate chemical interferences and improve the sensitivity of the method. The detection limit was 0.5 μg l^-1 for a 5-min electrolysis, and 0.2 μg l^-1 when the electrolysis time was 30 min.     

Production of slow singly charged fragments in 200 GeV/c hadron nucleus interactions

Measurements of slow, singly charged fragments in the target rapidity region have been performed for proton and pion induced reactions with various nuclei at 200 GeV/c. Multiplicity, angular and energy distributions are examined and used to study the effects of rescattering in the nuclear medium. Data are compared to a geometric cascade model and to simulations with the VENUS 3.11 and the FRITIOF 1.7 Monte Carlo codes.     

Determination of reactor neutron spectra with multicomponent activation detectors

A procedure is described for the functional fitting of reactor neutron spectra with C/Eⁿ and fission spectra. The method is applied to multicomponent activation detector measurements in a Triga research reactor. In multicomponent detectors a mixture of several detector materials is irradiated as a single unit and measured simultaneously for all reaction products with a Ge(Li) gamma ray spectrometer.