Quantization of Poisson-Lie groups and applications

LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ^∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.     

Relativistic calculations of coalescing binary neutron stars

We have designed and tested a new relativistic Lagrangian hydrodynamics code, which treats gravity in the conformally flat approximation to general relativity. We have tested the resulting code extensively, finding that it performs well for calculations of equilibrium single-star models, collapsing relativistic dust clouds, and quasi-circular orbits of equilibrium solutions. By adding a radiation reaction treatment, we compute the full evolution of a coalescing binary neutron star system. We find that the amount of mass ejected from the system, much less than a per cent, is greatly reduced by the inclusion of relativistic gravitation. The gravity wave energy spectrum shows a clear divergence away from the Newtonian point-mass form, consistent with the form derived from relativistic quasi-equilibrium fluid sequences.     

High-accuracy surface position sensor based on a two-lens system

Two optical lenses are used to compose a surface position measuring system. A measurand is positioned near the front focal point of the first lens. At the output end of the other lens, a beam splitter is used to split the beam into two paths. One photodetector is positioned before the focal point of the lens in one path and another after the focal point in the other so that the intensities falling onto the two detectors can be adjusted to be equal when the first lens is in focus. This device provides a compact and high-accuracy surface sensor. In this paper, the design and experimental study of the sensor system is described. It is shown that such a sensor embodiment can lead to a resolution of 1 μm.     

On Non-simple Marked Point Processes

Simple point processes are often characterized by their associated compensators or conditional intensities. Non-simple point processes are not uniquely determined by their conditional intensity and compensator, so instead one may identify with the point process its associated simple point process and corresponding conditional intensity, on an expanded mark space. Some relations between the conditional intensity on the expanded mark space and the ordinary conditional intensity are investigated here, and some classes of separable non-simple processes are presented. Transformations into simple point processes, involving thinning and rescaling, are presented.     

On Torsion of Prismatic Bodies

The method of decaying residual solution is applied to obtain an approximate interior solution for the torsion of slender prismatic elastic bodies under different end conditions. The approximate solution is generally accurate up to terms that are exponentially small in the length-to-cross-sectional-width ratio. For stress end conditions, the result is identical to the classical Saint-Venant torsion solution. Similar types of simple solutions, not known previously, are obtained for different types of mixed end conditions. For displacement conditions at both ends, the corresponding Saint-Venant type result requires an accurate solution of a canonical problem for a semi-infinite prismatic body that is to be obtained once and for all. The solution of the canonical problem is elementary for a circular cross section. The approximate interior solution in that case is identical to the known exact interior solution.     

Linear programming based analysis of marginal cost pricing in electric utility capacity expansion

This paper concerns methods for discretizing and approximating the annual load duration curve in the context of a linear programming model and its interpretation in electric utility expansion planning. The emphasis is upon the interpretation of the linear programming dual variables and their relationship with classical results of peak load pricing. In particular, for capacity planning in which one can choose from a diverse number of technological alternatives, we support the work of Wenders by precisely characterizing how off-peak periods bear partial responsibility of the capacity cost.     

Perturbation and Asymptotic Solutions for Problems in the Theory of Urban Land Rent

Simple but accurate approximate solutions for R. M. Solow's theory of urban land rent with congest cost of transportation are obtained by perturbation and asymptotic methods. Only the case of an absentee landlord is discussed though the techniques used can be modified in a straightforward manner to handle the more interesting (and mathematically more complicated) case of municipal ownership. Solow's model is also extended to have expenditures for housing and space as separate items in the budget equation. This extension eliminates the ambiguity in the value for the fraction of income after travel cost spent on ground rent, without affecting the structure of the mathematical problems associated with Solow's original theory.     

Classical and quantum theories of radiation damping in ferromagnetic and antiferromagnetic resonance

Both classical and quantum theories of radiation damping in ferromagnetic and antiferromagnetic resonance relaxation are given. Effects of demagnetization and anisotropy, that is, of elliptical classical precession, are included. In the classical theory a phenomenological approach to ferromagnetic resonance relaxation by means of the Landau-Lifshitz equation is also presented. In the quantum theory, the magnon-photon interaction Hamiltonian is derived, and the radiation-damped linewidth is obtained by computing the transition matrix element and also the one-magnon self energy. As noted long ago by Einstein, each photon is emitted in a random but specific direction, and only on average does the quantum radiation pattern reproduce the classical. To first order, however, this reproduction is shown to be exact, correcting a recent calculation by Shrivastava.