Elastic constants of lithium thallium tartrate measured by Brillouin scattering

All components of the elastic stiffness tensor of lithium thallium tartrate at room temperature have been measured by Brillouin scattering techniques using two different scattering configurations. Refractive indices have been determined independently by optical measurement. The results are compared with previous work on lithium thallium tartrate and lithium ammonium tartrate.     

Optimal Control Problems for a Class of Semilinear Multisolution Elliptic Equations

We study the optimal control problem for a class of elliptic problems that may possess multiple solutions. We obtain necessary conditions for optimal control by constructing a related parabolic problem and using known results for the parabolic problem.     

Generalized Lamé Operators

We introduce a class of multidimensional Schrödinger operators with elliptic potential which generalize the classical Lamé operator to higher dimensions. One natural example is the Calogero–Moser operator, others are related to the root systems and their deformations. We conjecture that these operators are algebraically integrable, which is a proper generalization of the finite-gap property of the Lamé operator. Using earlier results of Braverman, Etingof and Gaitsgory, we prove this under additional assumption of the usual, Liouville integrability. In particular, this proves the Chalykh–Veselov conjecture for the elliptic Calogero–Moser problem for all root systems. We also establish algebraic integrability in all known two-dimensional cases. A general procedure for calculating the Bloch eigenfunctions is explained. It is worked out in detail for two specific examples: one is related to the B₂ case, another one is a certain deformation of the A₂ case. In these two cases we also obtain similar results for the discrete versions of these problems, related to the difference operators of Macdonald–Ruijsenaars type.On leave of absence from: Advanced Education and Science Centre, Moscow State University, Moscow 119899, Russia     

Melvin universe as a limit of the C-metric

It is demonstrated that the Melvin universe representing the spacetime with a strong ‘homogeneous’ electric field can by obtained from the spacetime of two accelerated charged black holes by a suitable limiting procedure. The behavior of various invariantly defined geometrical quantities in this limit is also studied.     

A leader-follower model and analysis for a two-stage network of oligopolies

This paper is concerned with the existence, uniqueness and computation of leader-follower equilibrium solutions for an industry involved with two major stages of production. We assume that there exists one set of firms performing the first stage of production, which produces a semi-finished product. This semi-finished product is converted to a final good by a second set of firms performing the second stage of production. Furthermore, also competing in the final product market is a third set of firms, which are vertically integrated through the two stages of production and which are assumed to lead the second set of firms by explicitly considering the reaction or response of these latter firms to their own outputs. We model such an industry as a two-stage network of oligopolies, and define equilibrium solutions based on assumed market structures. Our analysis examines the existence and uniqueness of such equilibrium solutions, characterizes the nature of the production strategies of the various firms at an equilibrium, and prescribes algorithms to compute such solutions. This provides the machinery required to perform sensitivity analyses for studying the effects of various mergers or integrations on individual firm profits, and on the industry outputs and prices at equilibrium. The presentation is self-contained, and does not necessarily require any significant prior preparation in economic theory on the part of the reader.This paper is based on work done for the Minerals and Mining Resources Research Institute, under the sponsorship of the Bureau of Mines, Department of the Interior.     

The anisotropy of fluorescence in ring units

The time dependence of the anisotropy of fluorescence after an impulsive excitation in the ring unit (resembling the B850 ring of the purple bacterium Rhodopseudomonas acidophila) is calculated. Fast fluctuations of the environment are simulated by dynamic disorder and slow fluctuations by static disorder. Both types of disorder are taken into account simultaneously. Without dynamic disorder modest degrees of static disorder are sufficient to cause the experimentally found initial drop of the anisotropy on a sub-100 fs time scale. Two different models of the spectral density J(ω) of phonons have been often used in the literature to describe influence of the bath. The spectral density J(ω) enters the non-Markovian dynamical equations for the one exciton density matrix (entering the time dependence of the anisotropy of fluorescence). The spectral density J(ω) with high-energy tail leads to faster anisotropy decay.     

Reaction of [60]fullerene with CF3COOHal affords an unusual 1,3-dioxolano-[60]fullerene

Reaction of C₆₀ with acyl hypohalogenites CF₃COOBr or CF₃COOI in the presence of water affords an orthoester-type 1,3-dioxolanofullerene in 40-50% yield. This method cannot be applied for the synthesis of 1,3-dioxolanofullerenes bearing aryl- or alkyl-groups since they undergo non-selective halogenation under the reaction conditions.     

Compatibility and generalised conditional symmetries

It is shown that the determining equations for generalised conditional symmetries (GCSs) of order n, of an evolution equation of arbitrary order, can be found as a consequence of compatibility with an nth-order invariant surface condition. The compatibility technique is demonstrated on a second-order nonlinear diffusion–convection equation with absorption and used to find new GCSs of a linear diffusion equation with nonlinear source.     

Hartree–Fock versus quantum Monte Carlo study of persistent current in a one-dimensional ring with single scatterer

We calculate the persistent current of interacting spinless electrons in a one-dimensional ring containing a single δ barrier. We use the self-consistent Hartree–Fock method and the quantum Monte Carlo method which gives fully correlated solutions. Our Hartree–Fock method treats the non-local Fock term in a local approximation and also exactly (if the ring is not too large). Treating the Fock term exactly we attempt to support our previous Hartree–Fock result obtained in the local approximation, in particular the persistent current behaving like I∝L^-1-α, where L is the ring length and α>0 is the power depending only on the electron–electron interaction. Finally, we use the Hartree–Fock solutions as an input for our quantum Monte Carlo calculation. The Monte Carlo results exhibit only small quantitative differences from the Hartree–Fock results.     

Analysis of Selected Macrocyclic Antibiotics by HPTLC with Non-Aqueous Binary Mobile Phases

JPC – Journal of Planar Chromatography – Modern TLC - The retention behavior of selected macrocyclic antibiotics (ery-thromycin, troleandomycin, tylosin, vancomycin, rifamycin B, and...