KMS condition in a Schrödinger picture of the dynamics

Given the C¹-algebra $\text{A}$ of observables, the KMS condition is formulated in terms of the time evolution α¹_t of a set $\text{S}$₀ ? $\text{S}$($\text{A}$) of “physical” states subject to certain natural conditions. α¹_t need not be defined by an automorphism group of $\text{A}$. It is shown that, for a KMS state ω, α¹_t induces a 1-automorphism α^ω_t of the von Neumann algebra π_ω($\text{A}$)″ generated by the representation π_ω belonging to ω.     

Use of borohydride reduction in the separation of estrogen carbonyls

The chromatographic behavior of the estrogen carbonyls, equilenin, equilin, and estrone, and their respective sodium borohydride reduction products has been studied. The separation of the 17 alpha-hydroxy reduced compounds is superior to the separations achieved for the parent carbonyls using both reversed-phase and normal-phase systems. The reductions appear quantitative by the chromatographic systems used but other work indicates that a small quantity of 17 alpha-hydroxy isomer is produced. The separations developed here have been used in the identification of 9-dehydroestrone, an impurity in estrone, and in the identification of the estrogens in a commercial aqueous suspension of estrogenic substances.     

A CASSCF-CI study of the coordination of ethylene with iron

Summary Complete active space SCF, CASSCF, and contracted CI calculations have been performed on the -bonded complex between ethylene and an iron atom. An extended basis set of the ANO type was used, which included polarization functions on all centers. The results indicate an attractive interaction between Fe ⁵ F(d⁷s) and ethylene, with an estimated binding energy of 14 kcal/mol. The low spin complex arising from Fe ³ F(d⁷s) was found to be bound with 18 kcal/mol. Both these potential minima are, however, above the ground state of the iron atom. It is concluded that the interaction between atomic ground state iron and ethylene is not of the normal -bonded type, but is dominated by dispersion forces. A preliminary study showed this interaction to be almost isotropic, with no preferred site for the iron atom.     

Primal-Dual Interior-Point Algorithms for Semidefinite Optimization Based on a Simple Kernel Function

Interior-point methods (IPMs) for semidefinite optimization (SDO) have been studied intensively, due to their polynomial complexity and practical efficiency. Recently, J. Peng et al. introduced so-called self-regular kernel (and barrier) functions and designed primal-dual interior-point algorithms based on self-regular proximities for linear optimization (LO) problems. They also extended the approach for LO to SDO. In this paper we present a primal-dual interior-point algorithm for SDO problems based on a simple kernel function which was first presented at the Proceedings of Industrial Symposium and Optimization Day, Australia, November 2002; the function is not self-regular. We derive the complexity analysis for algorithms based on this kernel function, both with large- and small-updates. The complexity bounds are and , respectively, which are as good as those in the linear case. Mathematics Subject Classifications (2000) 90C22, 90C31.     

New classes of domains with explicit Bergman kernel

We introduce two classes of egg type domains, built on general bounded sym-metric domains, for which we obtain the Bergman kernel in explicit formulas. As an aux-iliary tool, we compute the integral of complex powers of the generic norm on a boundedsymmetric domains using the well-known integral of Selberg. This generalizes matrix in-tegrals of Hua and leads to a special polynomial with integer or half-integer coefficientsattached to each irreducible bounded symmetric domain.     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

High-conversion-efficiency, diode-pumped continuous-wave Raman laser

We demonstrate a diode-pumped cw Raman laser in H(2) with photon-conversion efficiency of (66+/-8)%. Pumped by an injection-locked diode laser at 792 nm, the Stokes laser produces a peak output power of ~16mW at 1180 nm. Accompanying the high Stokes power are deviations from the existing theory, which are believed to be caused by the thermal-lensing effect of the Raman gas.     

Widely tunable continuous-wave Raman laser in diatomic hydrogen pumped by an external-cavity diode laser

What is to the authors' knowledge the first experimental demonstration of a nonresonant cw Raman laser pumped by a tunable external-cavity diode laser (ECDL) is presented. The ECDL is phase-frequency locked to a high-finesse Raman laser cavity containing diatomic hydrogen (H(2)) by the Pound-Drever-Hall locking technique. The Stokes lasing threshold occurs at a pump power of 400 +/- 30 muW, and a maximum photon conversion efficiency of 12.0 +/- 1.3% is achieved at 1.6 mW of pump power. A 40-nm tuning range of the cw Stokes emission, 1174-1214 nm, is obtained by tuning of the wavelength of the ECDL pump source.