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     

Crystal structure of (1rs, 14sr, 17rs, 18rs)-2,20-dioxa-17-methyltricyclo [16,3,0,0] heneicosa-15-ene-3,19,21-trione; a macrocyclic lac

An X-ray study of the major product of the intramolecular Diels-Alder reaction of the diene-anhydride (2) has confirmed it as being the desired cytochalasan analogue (3). In particular the cyclisation has been regioselective, and has taken place via the endo transition state to generate the adduct with the correct relative configurations at the four chiral centres. Details of the conformational geometry of (3) are discussed.     

Vibronic intensity borrowing. Deuterium effect and emission—absorption asymmetry of the S1---S0 transition in pyrene

The intensities of the vibrationally induced bands in the S₁---S₀ emission and absorption spectra of pyrene-h₁₀ and -d₁₀ are measured and analysed. Several new expressions are reported which relate the deuterium effect and emission—absorption asymmetry of induced spectra to the vibronic coupling mechanism.     

The accurate determination of cobalt: Gravimetric methods and in particular the phosphate method

Some gravimetric methods for determining cobalt have been examined in order to assess their value for the accurate determination of the metal. The electrolytic method was found to give high results (about 1.4%), and the anthranilate method slightly high results (0.2 – 0.3%). A modification of the phosphate method has been developed in which a former drawback, the solubility of CoNH₄PO₄·H₂O, has been overcome using a rapid spectrophotometric determination of residual cobalt. The final procedure developed has been found to give accurate results ( ±0.1 – 0.2%) and its use is recommended where this degree of accuracy is required.     

Theoretical aspects of a preparative continuous chromatograph

Summary Equipment which has been used or suggested for preparative scale chromatography is reviewed. Particular attention is paid to one form of equipment for continuous counter-current chromatography which employs a moving mechanical seal. The theoretical effects of practical operating conditions and the mode of operation of this equipment are discussed. The influence of these effects on polymer fractionation is also considered. A theoretical model, based on the equilibrium stage concept, is proposed for the simulation of continuous gel permeation chromatography of a binary feed on such an apparatus. Examples of the results obtained from the computer simulation are given.