Spin physics at RHIC: Present and future

In 2001–2002 the relativistic heavy-ion collider (RHIC) at the Brookhaven National Laboratory (BNL) was first commissioned for polarized proton collisions. Polarized protons were injected into the RHIC, accelerated to 100 GeV, stored and the two beams were made to collide in four interaction regions. I will review the progress made by the RHIC spin program, followed by the physics goals for the next few years. After that I will present a brief overview of a proposal to build a high intensity polarized electron/positron beam facility at BNL which would enable deep inelastic scattering (DIS) experiments to be pursued at BNL by its collisions with the RHIC hadron beams.     

EDA Complexes of 2,3-Dichloro-1,4-naphthoquinone with Some Substituted Anilines

Summary. Electron donor-acceptor (EDA) complexes of several substituted anilines with the -acceptor 2,3-dichloro-1,4-naphthoquinone (DClNQ) in chloroform, dichloromethane, and 1,2-dichloroethane were studied by a spectrophotometric method. Experimental data has been shown to confirm the 1:2 stoichiometry of the acceptor-donor in spite of the apparent linearity of the Benesi-Hildebrand plot for a 1:1 complex. The calculated values of oscillator strengths, transition moments, and thermodynamic parameters confirms the 1:2 (A:D) stoichiometry of the complexes. The formation constants and molar absorptivities for these AD₂ complexes have been evaluated. The stoichiometry was unaffected by the variation of the temperature over a small interval and also by the change in polarity of the solvent. The order of the donor strength followed the sequence: N-benzylaniline>p-chloroaniline>m-chloroaniline>o-chloroaniline.Present address: Materials Research Centre, Indian Institute of Science, Bangalore-12, India     

EDA Complexes of 2,3-Dichloro-1,4-naphthoquinone with Some Substituted Anilines

Electron donor-acceptor (EDA) complexes of several substituted anilines with the -acceptor 2,3-dichloro-1,4-naphthoquinone (DClNQ) in chloroform, dichloromethane, and 1,2-dichloroethane were studied by a spectrophotometric method. Experimental data has been shown to confirm the 1:2 stoichiometry of the acceptor-donor in spite of the apparent linearity of the Benesi-Hildebrand plot for a 1:1 complex. The calculated values of oscillator strengths, transition moments, and thermodynamic parameters confirms the 1:2 (A:D) stoichiometry of the complexes. The formation constants and molar absorptivities for these AD₂ complexes have been evaluated. The stoichiometry was unaffected by the variation of the temperature over a small interval and also by the change in polarity of the solvent. The order of the donor strength followed the sequence: N-benzylaniline>p-chloroaniline>m-chloroaniline>o-chloroaniline.     

Null infinity,the BMS group and infrared issues

There has been a recent resurgence of interest in the structure of the gravitational field at null infinity, sparked by new results on soft charges and infrared issues related to the S matrix theory in perturbative quantum gravity. We summarize these developments and put them in the broader context of research in the relativity community that dates back to several decades. In keeping with intent of this series, this overview is addressed to gravitational scientists who are not experts in this specific area.     

Weak convergence to a Markov process: The martingale approach

Summary In this article, we obtain some sufficient conditions for weak convergence of a sequence of processes {X _n } toX, whenX arises as a solution to a well posed martingale problem. These conditions are tailored for application to the case when the state space for the processesX _n ,X is infinite dimensional. The usefulness of these conditions is illustrated by deriving Donsker's invariance principle for Hilbert space valued random variables. Also, continuous dependence of Hilbert space valued diffusions on diffusion and drift coefficients is proved.Research supported by National Board for Higher Mathematics, Bombay, IndiaPart of the work was done at University of California, Santa Barbara, USA     

A generalization of tensor calculus and its applications to physics

Penrose's abstract index notation and axiomatic introduction of covariant derivatives in tensor calculus is generalized to fields with internal degrees of freedom. The result provides, in particular, an intrinsic formulation of gauge theories without the use of bundles.Work supported in part by the NSF Contract No. PHY-80-08155 and a grant from the Research and Equipment Fund, Syracuse University.Supported in part by Crédits Ministériels, Tranche de Type C.     

On the existence of solutions to Einstein's equation with non-zero Bondi news

It is shown that theC-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, , is a 2-sphere. This structure of is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuumC-metric represents the gravitational field of two accelerating black-holes.