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     

Stochastic flows on the boundaries of SL(n,R)

Summary We study the asymptotic stability of the stochastic flows on a class of compact spaces induced by a diffusion process in SL(n, R) or GL(n, R). These compact spaces are called boundaries of SL(n, R), which include SO(n), the flag manifold, the sphereS ⁿ–1 and the Grassmannians. The one point motions of these flows are Brownian motions. For almost every, , we determine the set of stable points. This is a random open set whose complement has zero Lebesgue measure. The distance between any two points in the same component of this set tends to zero exponentially fast under the flow. The Lyapunov exponents at stable points are computed explicitly. We apply our results to a stochastic flow onS ⁿ–2 generated by a stochastic differential equation which exhibits some nice symmetry.Research supported in part by Hou Yin Dong Education Foundation of China On leave from Nankai University, Tianjin, China     

Properties of compact complex manifolds carrying closed positive currents

We show that a compact complex manifold is Moishezon if and only if it carries a strictly positive, integral (1, 1)-current. We then study holomorphic line bundles carrying singular hermitian metrics with semi-positive curvature currents, and we give some cases in which these line bundles are big. We use these cases to provide sufficient conditions for a compact complex manifold to be Moishezon in terms of the existence of certain semi-positive, integral (1,1)-currents. We also show that the intersection number of two closed semi-positive currents of complementary degrees on a compact complex manifold is positive when the intersection of their singular supports is contained in a Stein domain. The first author was partially supported by National Science Foundation Grant Nos. DMS-8922760 and DMS-9204273. The second author was partially supported by National Science Foundation Grant Nos. DMS-9001365 and DMS-9204037.     

Local analyticity for the [`(?)]\overline \partial -Neumann problem in completely decoupled pseudoconvex domains-Neumann problem in completely decoupled pseudoconvex domains

In this paper we prove local analyticity of solutions to the -Neumann problem up to the boundary of rigid, completely decoupled pseudoconvex domains with real-analytic boundary. These are domains that are locally of the form Imw > Σ |h _k (z _k )|² with eachh _k holomorphic and vanishing only at 0. As in those earlier papers, we use purelyL ² methods and must construct a special holomorphic vector fieldM and then use carefully balanced polynomials inM to localize high powers ofT = ∂/∂t effectively, wheret = Rew.     

Unique continuation theorems for the\bar \partial - Operator and applications

We formulate a unique continuation principle for the inhomogeneous Cauchy-Riemann equations near a boundary pointz ₀ of a smooth domain in complex euclidean space. The principle implies that the Bergman projection of a function supported away fromz ₀ cannot vanish to infinite order atz ₀ unless it vanishes identically. We prove that the principle holds in planar domains and in domains where the problem is known to be analytic hypoelliptic. We also demonstrate the relevance of such questions to mapping problems in several complex variables. The last section of the paper deals with unique continuation properties of the Szegő projection and kernel in planar domains. Research supported by NSF Grant DMS-8922810.     

Study on Electrochemiluminesce of Ru(bpy3)2+ Immobilized in a Titania Sol‐Gel Membrane

The immobilization of tris(2,2′‐bipyridyl)ruthenium(II), Ru(bpy)₃²⁺, at a glassy carbon electrode was achieved by entrapping the Ru(bpy)₃²⁺ in a vapor deposited titania sol‐gel membrane. The electrogenerated chemiluminescence (ECL) of the immobilized Ru(bpy)₃²⁺ was studied. The Ru(bpy)₃²⁺ modified electrode showed a fast ECL response to both oxalate and proline. The ECL intensity was linearly related to concentrations of oxalate and proline over the ranges from 20 to 700 μmol L^?1 and 20 to 600 μmol L^?1, respectively. The detection limits for oxalate and proline at 3σ were 5.0 μmol L^?1 and 4.0 μmol L^?1, respectively. This electrode possessed good precision and stability for oxalate and proline determinations. The electrogenerated chemiluminescence mechanism of proline system was discussed. This work provided a new way for the immobilization of Ru(bpy)₃²⁺ and the application of titania sol‐gel membrane in electrogenerated chemiluminescence.     

Extraction-spectrophotometric determination of iron with 2-(2′-benzothiazolylazo)-4,6-dimethylphenol

An extraction-spectrophotometric method for the determination of trace amounts of iron based on its extraction into chloroform with 2-(2-benzothiazolylazo)-4,6-dimethylphenol (BTADMP) from a pH 6.5 medium has been developed. The extracted 12 FeBTADMP complex species allow the determination of 4–30gmg of iron (=3.92×10⁴1·mol^–1·cm^–1 at 790 nm). The method is highly selective and has been applied to the determination of iron in polymineral-polyvitamin pharmaceutical products.     

Quantum chemistry study on B32 and B32H2–32

The structures of B32 and B₃₂H^2–₃₂ with I_h symmetry have been investigated by means of ab initio calculations at STO-3G level. The relationship between molecular orbitals of them has been analyzed and their bonding properties have been discussed. Then the possibility of their existence, as well as the similarity and difference between B₃₂ (B₃₂H^2–₃₂) and C₆₀ (C₆₀H₆₀) have been inferred.     

The blocking and structural properties of a Schiff base self-assembled monolayer on the surface of Au(111)

Electrochemistry and in situ electrochemical scanning tunneling microscopy (STM) were used to study the blocking and structural properties of Shiff base V-ape-V self-assembled monolayers (SAMs) on the surface of Au(111) in perchloric acid solution. The complex-plane impedance plots for the SAM covered Au(111) electrodes, with the redox couple of Fe(CN)₆^4–/3– present in solution, exhibit arc shapes, revealing that the electrochemical kinetics were controlled by the electron-transfer step. For bare Au(111), the electrode process was mass transport limited. The molecules adsorb on Au(111) with a flat-lying orientation and form a long-range well-defined adlayer. A new structure of was observed in the double-layer potential region. A structural model is proposed to interpret the molecular registry with Au(111) substrate.     

Generalized reinhardt domains

In this paper we investigate a class of Lie group actions on , the so-calledpolar actions, that naturally generalize the standard actions. For a domain invariant under such an action (i.e., a generalized Reinhardt domain) we characterize the invariant plurisubharmonic functions and determine the envelope of holomorphy in geometric terms. For a generalized Reinhardt domain containing the origin of we also compute its automorphism group. Supported in part by NSF Grant 8602020