Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant

Summary This work is concerned with the existence and uniqueness of a class of semimartingale reflecting Brownian motions which live in the non-negative orthant of ^d . Loosely speaking, such a process has a semimartingale decomposition such that in the interior of the orthant the process behaves like a Brownian motion with a constant drift and covariance matrix, and at each of the (d-1)-dimensional faces that form the boundary of the orthant, the bounded variation part of the process increases in a given direction (constant for any particular face) so as to confine the process to the orthant. For historical reasons, this pushing at the boundary is called instantaneous reflection. In 1988, Reiman and Williams proved that a necessary condition for the existence of such a semimartingale reflecting Brownian motion (SRBM) is that the reflection matrix formed by the directions of reflection be completely-L. In this work we prove that condition is sufficient for the existence of an SRBM and that the SRBM is unique in law. It follows from the uniqueness that an SRBM defines a strong Markov process. Our results have potential application to the study of diffusions arising as approximations tomulti-class queueing networks.Research supported in part by NSF Grants DMS 8657483, 8722351 and 9023335, and a grant from AT&T Bell Labs. In addition, R.J. Williams was supported in part during the period of this research by an Alfred P. Sloan Research Fellowship     

Synthesis, structure, theoretical studies, and Ligand exchange reactions of monomeric, T-shaped arylpalladium(II) halide complexes with an additional, weak agostic interaction

A series of monomeric arylpalladium(II) complexes LPd(Ph)X (L = 1-AdPtBu2, PtBu3, or Ph5FcPtBu2 (Q-phos); X = Br, I, OTf) containing a single phosphine ligand have been prepared. Oxidative addition of aryl bromide or aryl iodide to bis-ligated palladium(0) complexes of bulky, trialkylphosphines or to Pd(dba)2 (dba = dibenzylidene acetone) in the presence of 1 equiv of phosphine produced the corresponding arylpalladium(II) complexes in good yields. In contrast, oxidative addition of phenyl chloride to the bis-ligated palladium(0) complexes did not produce arylpalladium(II) complexes. The oxidative addition of phenyl triflate to PdL2 (L = 1-AdPtBu2, PtBu3, or Q-phos) also did not form arylpalladium(II) complexes. The reaction of silver triflate with (1-AdPtBu2)Pd(Ph)Br furnished the corresponding arylpalladium(II) triflate in good yield. The oxidative addition of phenyl bromide and iodide to Pd(Q-phos)2 was faster than oxidative addition to Pd(1-AdPtBu2)2 or Pd(PtBu3)2. Several of the arylpalladium complexes were characterized by X-ray diffraction. All of the arylpalladium(II) complexes are T-shaped monomers. The phenyl ligand, which has the largest trans influence, is located trans to the open coordination site. The complexes appear to be stabilized by a weak agostic interaction of the metal with a ligand C-H bond positioned at the fourth-coordination site of the palladium center. The strength of the Pd.H bond, as assessed by tools of density functional theory, depended upon the donating properties of the ancillary ligands on palladium.     

A configuration interaction study of phosphine using bonded functions

A computational study is made of the effect of basis set upon the energy, properties and inversion barrier of the phosphine molecule. The calculations are performed at both the SCF and CI level. The flexibility of the double zeta basis is discussed in the light of the results.     

An automated procedure for the simultaneous determination of specific conductance and pH in natural water samples

An automated, continuous-flow system is utilized to determine specific conductance and pH simultaneously in natural waters. A direct electrometric procedure is used to determine values in the range pH 4–9. The specific conductance measurements are made with an electronically modified, commercially available conductivity meter interfaced to a separate module containing the readout control devices and printer. The system is designed to switch ranges automatically to accommodate optimum analysis of widely varying conductances ranging from a few μmhos cm^-1 to 15,000 μmho cm^-1. Thirty samples per hour can be analyzed. Comparison of manual and automated procedures for 40 samples showed that the average differences were 1.3% for specific conductance and 0.07 units for pH. The relative standard deviation for 25 replicate values for each of five samples was significantly less than 1% for the specific conductance determination; the standard deviation for the pH determination was ? 0.06 pH units.     

Intersequence cyclization in copolymers of N-vinyl carbamates

Monomer reactivity ratios determined for the copolymerization of tert-butyl N-vinylcarbamate (r_A = 0.55 ± 0.05) with phenyl N-vinylcarbamate (r_B = 2.08 ± 0.15) indicate that the monomer units are distributed randomly along the polymer chains. The following sequence of reactions was used to cause intersequence cyclization between tert-butyl N-vinylcarbamate and phenyl N-vinylcarbamate units in the copolymers. The extent of cyclization obtained was in accord with that expected for random copolymers.      

A new approach to intermolecular forces in non-bonding regions

A new method to compute intermolecular energies in non-bonding regions is presented. It is based on the assumption that in such regions molecules can be reviewed as the sum of distorted, possibly overlapping, and electron exchanging atoms. The intermolecular energy change at a given distance is due to the sum of the atomic energy changes caused by these distortions. The energy change of any particular atom is computed in a Hartree—Fock model in which the effect of the other atom is represented by an effective potential. This potential in turn is computed from a calculation at a slightly larger intermolecular distance of the potential seen by an external electron in the field of the “other” atom. This potential computed in the RPA approximation and involves the distorted Hartree—Fock orbitals of the other atom (computed in a similar manner to the above) and the RPA response function of the other distorted atom.     

Effects of molecular structure and environment on the photodimerization of substituted anthracenes

Photochemical and photophysical studies of a number of 9-substituted anthracene sandwich pairs in their corresponding photodimer crystal matrices have been carried out. Corresponding studies have also been made in methylcyclohexane matrices at 6 K. Photodimerization of the 9-methyl, 9-chloro and 9-cyano derivatives in the photodimer matrices occurs at 6 K with unit quantum yield. The presence of excimer fluorescence from sandwich pairs indicates the lack of a perfect topochemical orientation while activation processes, leading to photodimerization, involve molecular re-orientation from more stable ground state configurations which are achieved within the constraints imposed by the solvent or crystalline cage.