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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A Feasibility Study of the Flare-Cylinder Configuration as a Reentry Body Shape for an Intermediate Range Ballistic Missile

A study has been made of a flare-cylinder configuration to investigate its feasibility as a reentry body of an intermediate range ballistic missile. Factors considered were heating, weight, stability, and impact velocity. A series of trajectories covering the possible range of weight-drag ratios were computed for simple truncated nose shapes of varying pointedness, and hence varying weight-drag ratios. Four trajectories were chosen for detailed temperature computation from among those trajectories estimated to be possible. Temperature calculations were made for both "conventional" (for example, copper, Inconel, and stainless steel) and "unconventional" (for example, beryllium and graphite) materials. Results of the computations showed that an impact Mach number of 0.5 was readily obtainable for a body constructed from conventional materials. A substantial increase in subsonic impact velocity above a Mach number of 0.5 was possible without exceeding material temperature limits. A weight saving of up to 134 pounds out of 822 was possible with unconventional materials. This saving represents 78 percent of the structural weight. Supersonic impact would require construction of the body from unconventional materials but appeared to be well within the range of attainability

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

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

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

A Bohmian approach to quantum fractals

A quantum fractal is a wavefunction with a real and an imaginary part continuous everywhere, but differentiable nowhere. This lack of differentiability has been used as an argument to deny the general validity of Bohmian mechanics (and other trajectory--based approaches) in providing a complete interpretation of quantum mechanics. Here, this assertion is overcome by means of a formal extension of Bohmian mechanics based on a limiting approach. Within this novel formulation, the particle dynamics is always satisfactorily described by a well defined equation of motion. In particular, in the case of guidance under quantum fractals, the corresponding trajectories will also be fractal.Comment: 19 pages, 3 figures (revised version