Second order parallel algorithms for piecewise smooth displacement kernels

Second order parallel algorithms for Fredholm integral equations with piecewise smooth displacement kernels are derived. One is based on a difference scheme of Runge-Kutta type for an unusual partial differential equations for continuous functions of two variables. The other is based on the trapezoidal quadrature rule applied to a modified integral equations. It is found that the Runge-Kutta type algorithm exhibits certain advantages.The work of these authors was supported in part by the NSF Grant DMS-9007030The work of this author was supported in part by a grant from the National Science and Engineering Research Council of Canada     

An existence and monotonicity theorem for the discrete algebraic matrix Riccati equation

Maximal hermitian solutions of the discrete algebraic matrix Riccati equation play an important role in least squares optimal control problems for discrete linear systems. We prove an existence and comparison theorem concerning maximal hermitian solutions. This theorem is inspired by known results for the algebraic Riccati equation arising in the least squares optimal control problem in continuous linear systems.     

Quantitation of trace components in liquid process streams by direct liquid sampling mass spectrometry

This paper describes the development of a liquid sampling approach for trace analysis by electron impact ionization magnetic sector mass spectrometry, with no chromatographic separation. Development of a liquid sample introduction interface based on the principle of Programmable Temperature Vaporizing (PTV) GC injection is shown. A univariate procedure for the analysis of trace (mg kg(-1)) propanoic acid in acetic acid was developed. Results from the laboratory-based analysis of acetic acid are presented and compared with conventional GC analysis. The detection limit was 16 mg l(-1) and the speed of analysis was employed to acquire 30 scans per minute thus reducing the confidence intervals of the results and potentially allowing production plants to run much closer to sales specifications. For the analysis of more complex samples where the analytes contained no unique ions, multivariate analysis was employed and up to three scans per minute were acquired. Results from the analysis of an ester for six trace impurities are shown. Calibration was by partial least squares regression. The detection limits for these components were 20-30 mg kg(-1), well within the required product specifications. The system proved to be robust and easy to operate, with analyses being carried out over a period of several months requiring no maintenance of the spectrometer and only cleaning of the injection liner of the PTV injector on a monthly basis.     

Acetyl nitrate nitrations in [bmpy][N(Tf)2] and [bmpy][OTf], and the recycling of ionic liquids

In this work we have examined the nitration by acetyl nitrate of a range of activated and deactivated aromatic substrates in two ionic liquids and compared the results to the same reaction in dichloromethane. Both ionic liquids are stable to the reaction conditions, and in both ionic liquids the yields of reaction are higher after unit time than the same reactions in dichloromethane, although the regioselectivity is little affected by solvent choice. This result gives further support to the suggestion that in the ionic liquid, acetyl nitrate dissociates to give the nitronium ion, and that this is the effective nitrating agent here. However, it is shown that [bmpy][N(Tf)(2)] is a better solvent for aromatic nitration than [bmpy][OTf]. This is due to the ease of formation of nitronium ion in the former ionic liquid, and is consistent with the fact that [bmpy][N(Tf)(2)] is a weaker hydrogen bond acceptor solvent than [bmpy][OTf]. Finally, a method by which [bmpy][N(Tf)(2)] may be recovered and reused for aromatic nitration has been demonstrated.     

Nucleophilicity in ionic liquids. 3. Anion effects on halide nucleophilicity in a series of 1-butyl-3-methylimidazolium ionic liquids

We have continued the study of halide nucleophilicity in ionic liquids, concentrating on the effect of changing the anion ([BF(4)](-), [PF(6)](-), [SbF(6)](-), [OTf](-), and [N(Tf)(2)](-)) when the cation is [bmim](+) (where bmim = 1-butyl-3-methylimidazolium). It was found that the nucleophilicities of all the halides were lower in all of the ionic liquids than in dichloromethane. Changing the anion affected the order of halide nucleophilicity, e.g., in [bmim][BF(4)] the order of nucleophilicity was Cl(-)>Br(-)>I(-) while in [bmim][N(Tf)(2)] the order was Cl(-)相似文献   

AIB induced chemical reactions at surfaces detected by SIMS

Secondary ion mass spectrometry (SIMS) has been used to detect the reactions induced by active ion bombardment (AIB) of N⁺₂ on surfaces of pyrolytic graphite and a (100) Si crystal. The SIMS spectra exhibit ions of CN^?, HCN^?, H_nC₂N^?(n = 2, 3, 4), HN^?, and SiN^?, indicating that reactions take place with the graphite and silicon as well as adsorbed hydrogen on the surfaces.     

Intra- and intermolecular N-H...F-C hydrogen-bonding interactions in amine adducts of tris(pentafluorophenyl)borane and -alane

The reaction between B(C(6)F(5))(3) and NH(3)(g) in light petroleum yielded the solvated adduct H(3)N.B(C(6)F(5))(3).NH(3). Treatment with a second equivalent of B(C(6)F(5))(3) afforded H(3)N.B(C(6)F(5))(3). Attempts to prepare the analogous alane adduct were unsuccessful and resulted in protolysis. Related compounds of the form R'R' 'N(H).M(C(6)F(5))(3) were synthesized from M(C(6)F(5))(3) and the corresponding primary and secondary amines (M = B, Al; R' = H, Me, CH(2)Ph; R' ' = Me, CH(2)Ph, CH(Me)(Ph); R'R' ' = cyclo-C(5)H(10)). The solid-state structures of 13 new compounds have been elucidated by single-crystal X-ray diffraction and are discussed. Each of the borane adducts has a significant bifurcated intramolecular hydrogen bond between an amino hydrogen and two o-fluorines, while N-H...F-C interactions in the alane adducts are weaker and more variable. (19)F NMR studies demonstrate that the borane adducts retain the bifurcated C-F...H...F-C hydrogen bond in solution. Compounds of the type R'R' 'N(H).M(C(6)F(5))(3) conform to Etter's rules for the prediction of hydrogen-bonding interactions.