Minimum rank and zero forcing number for butterfly networks

The minimum rank of a simple graph $G$ is the smallest possible rank over all symmetric real matrices $A$ whose nonzero off-diagonal entries correspond to the edges of $G$. Using the zero forcing number, we prove that the minimum rank of the butterfly network is $\frac19\left[(3r+1)2^{r+1}-2(-1)^r\right]$ and that this is equal to the rank of its adjacency matrix

X-29A aircraft structural loads flight testing

The X-29A research and technology demonstrator aircraft has completed a highly successful multiphase flight test program. The primary research objective was to safely explore, evaluate, and validate a number of aerodynamic, structural, and flight control technologies, all highly integrated into the vehicle design. Most of these advanced technologies, particularly the forward-swept-wing platform, had a major impact on the structural design. Throughout the flight test program, structural loads clearance was an ongoing activity to provide a safe maneuvering envelope sufficient to accomplish the research objectives. An overview is presented of the technologies, flight test approach, key results, and lessons learned from the structural flight loads perspective. The overall design methodology was considered validated, but a number of structural load characteristics were either not adequately predicted or totally unanticipated prior to flight test. While conventional flight testing techniques were adequate to insure flight safety, advanced analysis tools played a key role in understanding some of the structural load characteristics, and in maximizing flight test productivity

A Survey of Analogs to Weak MgII Absorbers in the Present

We present the results of a survey of the analogs of weak MgII absorbers (rest frame equivalent width W(2796) < 0.3 A) at 0 < z < 0.3. Our sample consisted of 25 HST/STIS echelle quasar spectra (R = 45,000) which covered SiII 1260 and CII 1335 over this redshift range. Using those similar transitions as tracers of MgII facilitates a much larger survey, covering a redshift pathlength of g(z) = 5.3 for an equivalent width limit of MgII corresponding to W(2796) > 0.02 A, with 30% completeness for the weakest lines. We find the number of weak MgII absorber analogs with 0.02 < W(2796) < 0.3 to be dN/dz = 1.00 +/- 0.20 for 0 < z < 0.3. This value is consistent with cosmological evolution of the population. We consider the expected effect on observability of weak MgII absorbers of the decreasing intensity of the extragalactic background radiation eld from z~1 to z~0. Assuming that all the objects that produce absorption at z~1 are stable on a cosmological timescale, and that no new objects are created, we would expect dN/dz of 2-3 at z~0. About 30-50% of this z~0 population would be decendants of the parsec-scale structures that produce single-cloud, weak MgII absorbers at z~1. The other 50-70% would be lower density, kiloparsec-scale structures that produce CIV absorption, but not detectable low ionization absorption, at z~1. We conclude that at least one, and perhaps some fraction of both, of these populations has evolved away since z~1, in order to match the z~0 dN/dz measured in our survey. This would follow naturally for a population of transient structures whose generation is related to star-forming processes, whose rate has decreased since z~1.Comment: 45 pages, 12 figures, 7 tables ApJ accepte

Public Libraries and the Internet 2006

Examines the capability of public libraries to provide and sustain public access Internet services and resources that meet community needs, including serving as the first choice for content, resources, services, and technology infrastructure

Keys to building a profitable pasture-based dairy (2012)

"Agriculture.""Dairy grazing.""Dairy grazing publication series : This publication is one in a series about operating and managing a pasture-based dairy. Although these publications often refer to conditions in Missouri, many of the principles and concepts described may apply to operations throughout the United States. A list of the publications in this series is available online at http://extension.missouri.edu/m168."New 2/12/Web