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.     

A discrete spectrum of solutions of the wave equation with strong cubic nonlinearity

The nonlinear wave equation, _tt –+³=0, has many solutions that are periodic in time and localized in space, all with infinte energies. The search for spherically symmetric solutions that are well represented by the simple approximation, (r, t)A(r) sin t, leads to a discrete spectrum of solutions{ _N (r, t; )}. The solutions are nonlinear wavepackets, and they can be regarded as particles. The asymptotic theory () of the motion of the guiding center of theNth wavepacket, in the presence of a specified potential, is characterized by an infinite mechanical mass and an infinte interaction mass, and they are compatible. The rest mass in the classical relativistic mechanics of guiding centers ism ₀ c ²= _N ; i.e. the spectrum { _N } determines a spectrum of Planck's constants.On leave (1972–73) Université de Paris VI, Département de Mécanique, 75 Paris 5^e, France.     

Cycloaddition reaction of quadricyclane and fluoroolefins

Reaction of quadricyclane (1) with fluoroolefins of different structure results in stereoselective formation of polyfluorinated exo-tricyclo[4.2.1.0^2,5]non-7-enes. The reaction of a mixture of trans/cis CF₃CFCFCF₃ with 1 is stereoselective and the resulting cycloadducts 7a, b preserve the original alkene stereochemistry. The relative rate constants of cycloaddition of a series of fluoroolefins to 1 under pseudo first-order conditions measured by kinetic NMR at 109 °C provide a kinetic scale of reactivities of the fluoroolefins in this reaction.These relative rate constants correlate well with the number of fluoroalkyl groups connected to the double bond, reaching a maximum for the tri-substituted olefin: CF₃CFCF₂:CF₃CFCFCF₃:(CF₃)₂CC(CF₃)₂:(CF₃)₂CCFC₂F₅ = 1:1.2-1.9:4:138.