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.     

Infrared laser induced energy transfer studies in S18O2

Vibrational energy transfer has been studied in S¹⁸O₂, following pumping of the symmetric stretch (ν₁) by a Q-switched CO₂ laser. Fluorescence from the asymmetric stretch (ν₃) is monitored as a function of time following the laser pulse. This fluorescence rises with a rate constant of 74 ± 10 ms^?1 torr^?1, and then decays with a rate constant of 3.6 ± 0.1 ms^?1 torr^?1 for the S¹⁸O₂ itself. The effect of rare gases on the rise and fall rates was also studied. The results agree well with those on S¹⁶O₂ and are consistent with a double V-V picture in which the excitation is distributed rapidly between the stretches, but is shared with the bend much more slowly. This produces molecules in which the stretches are much “hotter” than the bend, giving rise to possibilities of laser action on the stretch-to-bend transitions and mode-selective vibrational enhancement of chemical reactions. Also, new results have been derived on the kinetics of V-V processes in mixtures. V-V transfer in various isotopic mixtures of SO₂ has been studied and the kinetic analysis indicates that S¹⁸O₂ and S¹⁶O₂ exhibit the same V-V rates.     

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.     

Birefringence changes in vertebrate striated muscle.

The changes in birefringence in the rigor to relax transition of single Triton-extracted rabbit psoas muscle fibers have been investigated. The total birefringence of rigor muscle fibers was dependent on sarcomere length and ranged from (1.46 +/- 0.08) X 10(-3) to (1.60 +/- 0.06) X 10(-3) at sarcomere lengths from 2.70 mum to 3.40 mum. An increase in total birefringence was measured dependent on sarcomere length when 55 single fibers were relaxed from the rigor state with Mg-ATP. Pyrophosphate relaxation produced a smaller increase in retardation when compared to Mg-ATP. The expected change in intrinsic birefringence during the rigor to relax transition was calculated assuming a hinge function of the subfragment 2 moiety of myosin. The changes in birefringence during isometric contraction and relaxation have been discussed in relation to possible structural changes.     

Highly substituted pyridines via tethered imine-enamine (TIE) methodology

A tethered imine-enamine methodology has been developed for the direct conversion of 1,2,4-triazines into highly substituted pyridines via the inverse electron demand Diels-Alder reaction which avoids the need for a discrete aromatisation step. This TIE methodology has also been applied in one pot reaction cascades involving 1,2,4-triazines and utilising MnO(2)-mediated tandem oxidation processes (TOPs).