Characterization of TcCl4 and β-TcCl3 by X-ray absorption fine structure spectroscopy

Technetium tetrachloride and β-TcCl₃, synthesized from the reaction of Tc metal and Cl_2(g) in sealed tubes, were characterized by X-ray absorption fine structure spectroscopy. Extended X-ray absorption fine structure (EXAFS) spectroscopy measurements are in good agreement with the X-ray diffraction structures of the two compounds. For TcCl₄, the absorbing Tc atom is surrounded by Cl atoms at 2.34(2) Å and Tc atoms at 3.66(4) Å. For β-TcCl₃, the absorbing Tc atom is surrounded by Cl atoms at 2.40(2) Å and Tc atoms at 2.81(3), 3.66(4) and 5.71(6) Å. EXAFS spectroscopy indicates that the TcCl₄ and β-TcCl₃ samples obtained by sealed tube reactions are single phase. The X-ray absorption near edge structure spectra of TcCl₄ and β-TcCl₃ were recorded; the positions of the Tc K-edges of β-TcCl₃ (21,050.5 eV) and TcCl₄ (21,053.0 eV) are compared to the ones measured for α-TcCl₃ (21,051.0 eV) and TcCl₂ (21,048.8 eV). A correlation between the positions of the Tc K-edges and the oxidation state of the Tc atom in technetium binary chlorides was determined.     

On Rescaled Poisson Processes and the Brownian Bridge

The process obtained by rescaling a homogeneous Poisson process by the maximum likelihood estimate of its intensity is shown to have surprisingly strong self-correcting behavior. Formulas for the conditional intensity and moments of the rescaled Poisson process are derived, and its behavior is demonstrated using simulations. Relationships to the Brownian bridge are explored, and implications for point process residual analysis are discussed.     

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.     

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.     

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.     

Highly diastereoselective synthesis of vicinal quaternary and tertiary stereocenters using the iodo-aldol cyclization

The intramolecular iodo-aldol cyclization of alpha-substituted enoate aldehydes and ketones is described. Using prochiral starting materials, the reaction produces hetero- and carbocycles containing quaternary centers adjacent to secondary or tertiary centers. The reactions occur in good yields and are highly selective for the trans-products, having the hydroxyl and iodomethyl groups on opposite faces of the ring system.