The structure of equivalent 3-separations in a 3-connected matroid

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The structure of 3-connected matroids of path width three

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Asymptotic analysis of a system of algebraic equations arising in dislocation theory

The system of algebraic equations given by\ud \ud $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$\ud \ud appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole.\ud \ud We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n -> ∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment but, up to corrections of logarithmic order, it also leads to a differential equation.\ud \ud The continuum approximation is only valid for i not too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem

The pioneer projects: Economical exploration of the solar system

The interplanetary Pioneer missions are reviewed in terms of management implications and cost control. The responsibilities, organizational structure, and management practices of the Pioneer Projects are presented. The lines of authority and areas of responsibility of the principal organizational elements supporting the Pioneer missions are identified, and the methods employed for maintaining effective and timely interactions among these elements are indicated. The technical and administrative functions of the various organizational elements of the Pioneer Project Office at Ames Research Center are described in terms of their management responsibilities and interactions with other elements of the Project Office and with external organizations having Pioneer Project responsibilities. The management and control of activities prior to and during the hardware procurement phase are described to indicate the basis for obtaining visibility of the technical progress, utilization of resources, and cost performance of the contractors and other institutions supporting the Pioneer projects

Fork-decompositions of matroids

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On matroids of branch-width three

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Investigation of the feasibility of CARS measurements in scramjet combustion

Results are presented of analytical and experimental investigations to determine the feasibility of using coherent anti-Stokes Raman Spectroscopy (CARS) to measure temperature and species concentration in supersonic combustion experiments. The CARS spectra of H2O, O2 and H2 were measured in laboratory flames. Computer code calculated spectra agree very well with the measured spectra. Temperature, and O2 and H2 concentration profiles have been determined from CARS spectra in a laboratory H2 air flat diffusion flame. Temperature measurements agree with radiation corrected thermocouple measurements within 5 to 10 percent, depending on species concentration. The feasibility of measuring O2 concentrations up to 10 percent, from the spectral shape was demonstrated. H2 concentrations determined from CARS intensities agree with spontaneous Raman measurements within a factor of two. Finally, a conceptual design was formulated for diagnostics in the Langley Research Center scramjet combustion facility

Perturbation expansions for a class of singular potentials

Harrell's modified perturbation theory [Ann. Phys. 105, 379-406 (1977)] is applied and extended to obtain non-power perturbation expansions for a class of singular Hamiltonians H = -D^2 + x^2 + A/x^2 + lambda/x^alpha, (A\geq 0, alpha > 2), known as generalized spiked harmonic oscillators. The perturbation expansions developed here are valid for small values of the coupling lambda > 0, and they extend the results which Harrell obtained for the spiked harmonic oscillator A = 0. Formulas for the the excited-states are also developed.Comment: 23 page

Assessment of Thematic Mapper band-to-band registration by the block correlation method

Rectangular blocks of pixels from one band image were statistically correlated against blocks centered on identical pixels from a second band image. The block pairs were shifted in pixel increments both vertically and horizontally with respect to each other and the correlation coefficient to the maximum correlation was taken as the best estimate of registration error for each block pair. For the band combinations of the Arkansas scene studied, the misregistration of TM spectral bands within the noncooled focal plane lie well within the 0.2 pixel target specification. Misregistration between the middle IR bands is well within this specification also. The thermal IR band has an apparent misregistration with TM band 7 of approximately 3 pixels in each direction. The TM band 3 has a misregistration of approximately 0.2 pixel in the across-scan direction and 0.5 pixel in the along-scan direction, with both TM bands 5 and 7

Spiked oscillators: exact solution

A procedure to obtain the eigenenergies and eigenfunctions of a quantum spiked oscillator is presented. The originality of the method lies in an adequate use of asymptotic expansions of Wronskians of algebraic solutions of the Schroedinger equation. The procedure is applied to three familiar examples of spiked oscillators