Coordination complexes of acetylenic phosphines and diphosphines

The reactions of π-cyclopentadienylnickel carbonyl dimer with 3,3,3-trimethylpropynyldiphenylphosphine and phenylethynyldiphenylphosphine are described. The products have been characterized by elemental and mass spectral analysis, infrared and NMR spectroscopy. An acetylene bridged complex (π-C₅H₅Ni)₂Ph₂PC₂-t-Bu, containing an uncoordinated phosphorus atom, has been prepared. The complex can be oxidized to the phosphine oxide derivative (π-C₅H₅Ni)₂Ph₂P(O)C₂-t-Bu and converted to the phosphonium salts with methyl iodide or ethyl bromide. These are the first reported π-complexes of phosphonium salts. The complex (π-C₅H₅Ni)₂Ph₂PC₂-t-Bu forms the novel mixed metal derivative [PdCl₂][(π-C₅H₅Ni)₂Ph₂PC₂-t-Bu]₂ from bis(benzonitrile)-palladium dichloride. The dicarbonyl complexes Ni(CO)₂(Ph₂PC₂R)₂ (R  t-Bu, Ph), the phosphine oxide complex (π-C₅H₅Ni)₂(Ph₂P(O)C₂Ph) and the trinuclear nickel carbonyl derivative Ni(CO)₃[(π-C₅H₅Ni)₂Ph₂PC₂Ph] are described.     

Experimental measurement and prediction of hydrate forming conditions in the nitrogen-propane-water system

Experimental data on initial hydrate formation conditions have been obtained for the nitrogen-propane-water system in the L₁HG, L₁L₂H, and L₁L₂HG regions, where L₁ is the water rich liquid phase, L₂ is the hydrocarbon rich liquid phase, H is the hydrate and the G is the vapor phase. The measurements covered a range of temperatures from about 275 to 293 K and pressures from about 0.3 to 17.0 MPa. The concentrations covered for the L₁HG region extended from 0.94 to 75.0 mole percent propane in the gas phase, and for the L₁L₂H region they extended from 83.1 to 99.0 mole percent in the condensed liquid phase. Four-phase measurements were made at concentrations of propane from 18.1 to 71.1 mole percent in the gas phase.The experimental data were used to find a fitted binary interaction parameter for predicting hydrate formation in systems containing nitrogen and propane.     

On solving a D.C. programming problem by a sequence of linear programs

We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in ⁿ . This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation.     

A simple reliable approximation for isotropic intermolecular forces. A critical test using HH(3Σu+) as a model

A simple semi-empirical approximation for the exchange energy (E_x), coupled with a tractable representation of the Coulomb energy (E_C), has been found to yield very accurate results for the isotropic part of the interaction energy (E_int = E_x + E_C) between two closed shell systems. The expression for E_int is based on the knowledge of the first order Coulomb energy and the first three terms in the asymptotic long range expansion of the second order Coulomb energy for the interaction and contains but one adjustable parameter which occurs in E_x. The usefulness of this approach for evaluating E_int is tested critically by using the non-bonded H(1s)H(1s) (³Σ_u⁺) interaction as a model (accurate values of the total interaction energy, the exchange energy, and various orders of Coulomb energies, are available for a wide range of R for this system). The results obtained for both E_int and (dE_int/dR) are inremarkable agreement with the exact results of Kotos and Wolniewicz for R > 3 a_o. Since the law of corresponding states for inert gas pairs holds equally well for the HH(³Σ_u⁺) interaction, our analysis of this simple system yields valuable information on the reliability of the approach for other van der Waals dimers.     

Spectral Analysis for HSS Preconditioners

In this paper,we are interested in HSS preconditioners for saddle point lin- ear systems with a nonzero(2,2)-th block.We study an approximation of the spectra of HSS preconditioned matrices and use these results to illustrate and explain the spectra obtained from numerical examples,where the previous spectral analysis of HSS precon- ditioned matrices does not cover.