Sum rules for charmed baryon masses

The measured masses of the three charge states of the charmed $\Sigma_c$ baryon are found to be in disagreement with a sum rule based on the quark model, but relying on no detailed assumptions about the form of the interaction. This poses a significant problem for the charmed baryon sector of the quark model. Other relations among charmed baryon masses are also discussed.Comment: 5 pages, latex, no figure

Time (in)dependence in general relativity

We clarify the conditions for Birkhoff's theorem, that is, time-independence in general relativity. We work primarily at the linearized level where guidance from electrodynamics is particularly useful. As a bonus, we also derive the equivalence principle. The basic time-independent solutions due to Schwarzschild and Kerr provide concrete illustrations of the theorem. Only familiarity with Maxwell's equations and tensor analysis is required.Comment: Revised version of originally titled "Kinder Kerr", to appear in American Journal of Physic

Indestructibility of compact spaces

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to $\omega_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba's "$\aleph_1$-Borel Conjecture" is equiconsistent with the existence of an inaccessible cardinal.Comment: 18 page

Numerical Analysis of an Elliptic-Parabolic Partial Differential Equation

G. Fichera [1] and other authors have investigated partial differential equations of the form [Eq. 1.1] in which the matrix (aij(x)) is required to be semidefinite. Equations of this type occur in the theory of random processes. A numerical analysis of some equations of this type has been by Cannon and Hill [9]. In this paper we consider a particular boundary value problem [Eq. 1.2] where we require [Eq. 1.3] and [Eq. 1.4]. A problem of this sort was discussed analytically by W. Fleming [2], but he did not obtain an explicit solution for T(x,0). The solution T(x,y) is related to a randomly-accelerated particle whose position ξ(t) satisfies the stochastic differential equation [Eq. 1.5] where w(t) is white Gaussian noise. If the initial position and velocity are ξ(0) = x and ξ'(0) = y, where |x| < 1, then T(x,y) is the expected value of the first time at which the position ξ(t) equals ±1. We obtain an analytic solution for T(x,y) in terms of hypergeometric functions and confluent hypergeometric functions. We use this analytic solution to test the validity of numerical methods which are applicable to general elliptic-parabolic equations (1.1). We show that, even though the truncation error for the difference equations does not tend to zero, nevertheless the difference methods give convergence of the difference methods. Each difference method requires the solution of a large number of simultaneous linear difference equations. We give iterative methods for solving these equations, and we prove that the iterations converge

The design of low cost structures for extensive ground arrays

The development of conceptual designs of solar array support structures and their foundations including considerations of the use of concrete, steel, aluminum, or timber are reported. Some cost trends were examined by varying selected parameters to determine optimum configurations. Detailed civil/structural design criteria were developed. Using these criteria, eight detailed designs for support structures and foundations were developed and cost estimates were made. As a result of the study wind was identified as the major loading experienced by these low height structures, whose arrays are likely to extend over large tracts of land. Proper wind load estimating is considered essential to developing realistic structural designs and achieving minimum cost support structures. Wind tunnel testing of a conceptual array field was undertaken and some of the resulting wind design criteria are presented. The SPS rectenna system designs may be less sensitive to wind load estimates, but consistent design criteria remain important