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     

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.     

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.     

Obtaining partial widths from siegert wavefunctions

It is shown that a simple expression for the partial widths in a multichannel decay problem can be readily obtained from a Siegert wavefunction.