New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions, not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new class of discrete diagonal representations. Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992.     

Extreme affine transformations

We classify the extreme points of the compact convex set of affine maps of IR ⁿ which map into itself the closed unit ball. This work is a preliminary step towards solving the problem of finding the extreme points of the compact convex set of affine maps of theN×N density matrices (dynamical maps of anN-level system) and forn=3 furnishes the solution of the problem in the simplest case of a two-level system.The bulk of this work was performed while the first author was visiting the Center for Particle Theory of the University of Texas at Austin under the partial support of the U.S.A.E.C. under contract ORO-(40-1) 3992. A travel grant under the Fulbright-Hays program is acknowledged.     

Gauge independence and unitarity in the Weinberg unified theory

We formulate the Weinberg theory with the help of the Lagrangian multiplier formalism. A new fictitious Lagrangian is obtained, which differs from the usual one. We show by explicit calculation that it restores unitarity and gauge independence of the theory.     

Time reversal for systems with internal symmetry

Wigner time reversal implemented by antiunitary transformations on the wavefunctions is to be refined if we are to deal with systems with internal symmetry. The necessary refinements are formulated. Application to a number of physical problems is made with some unexpected revelations about some popular models.This paper is presented in felicitation of Jean-Pierre Vigier with pleasant recollections of his infectious enthusiasm. This work is supported in part by DOE Grant No. DE-FG03-93ER40757. The authors thank Iwo Bialynicki-Birula and J. Bruce French for sharing their insights, and Luis J. Boya for discussions.     

Nilpotency of group ring units symmetric with respect to an involution

Let F be an infinite field of characteristic different from 2. Let G be a torsion group having an involution ∗, and consider the units of the group ring FG that are symmetric with respect to the induced involution. We classify the groups G such that these symmetric units satisfy a nilpotency identity (x₁,…,x_n)=1.     

MEASUREMENT OF INFRARED ABSORPTION COEFFICIENTS OF MOLTEN GLASSES

In this article, a method based on the "submerged mirror" technique to measure the absorption coefficient of molten glass is presented. Infrared light, which is modulated by Michelson's interferometeric setup, passes through the molten glass and is collected by a mercury-cadmium-telluride (MCT) or a silicon detector. The signal is processed by a Fourier transform infrared (FTIR) spectrometer to yield the spectral intensity of the infrared light. The processes are repeated with different thicknesses of molten glass layer. The spectral absorption coefficient is calculated from the apparent transmittance. Tests of the apparatus have been made with distilled water, for which the results agree well with existing data. Measurements were carried out for a number of calcia-alumina-silicate glasses at temperatures ranging from 1,200 to 1,300°C.     

One-pot Sonogashira coupling,hydroamination of alkyne and intramolecular CH arylation reactions toward the synthesis of indole-fused benzosultams

A one-pot Sonogashira coupling, hydroamination of alkyne and CH arylation reactions for the synthesis of indole-fused benzosultams are described. This method allows access to a variety of indole-fused seven membered benzosultams in good to excellent yields. The free indolyl nitrogen containing indole-fused benzosultams are also prepared by this method. The structures of the synthesized compounds are confirmed by single crystal XRD studies.     

Non-destructive assay technique for the determination of <Superscript>238</Superscript>U/<Superscript>232</Superscript>Th ratio in the mixed oxides of uranium and thorium using prompt gamma-ray neutron activation

A non-destructive assay technique based on prompt gamma-ray neutron activation analysis for the determination of ²³⁸U to ²³²Th ratio in the mixed oxide fuel materials has been established. The method uses closely spaced high energy gamma-rays in the region of 4000 keV to 4150 keV enabling it to be applied for samples of any geometry and thickness without having any correction for gamma-ray attenuations and detection efficiencies.