Lower Bound for Convex Hull Area and Universal Cover Problems

In this paper, we provide a lower bound for an area of the convex hull of points and a rectangle in a plane. We then apply this estimate to establish a lower bound for a universal cover problem. We showed that a convex universal cover for a unit length curve has area at least 0.232239. In addition, we show that a convex universal cover for a unit closed curve has area at least 0.0879873.Comment: 12 pages, 9 figure

Radiation Damage and Recovery Properties of Common Plastics PEN (Polyethylene Naphthalate) and PET (Polyethylene Terephthalate) Using a 137Cs Gamma Ray Source Up To 1 MRad and 10 MRad

Polyethylene naphthalate (PEN) and polyethylene teraphthalate (PET) are cheap and common polyester plastics used throughout the world in the manufacturing of bottled drinks, containers for foodstuffs, and fibers used in clothing. These plastics are also known organic scintillators with very good scintillation properties. As particle physics experiments increase in energy and particle flux density, so does radiation exposure to detector materials. It is therefore important that scintillators be tested for radiation tolerance at these generally unheard of doses. We tested samples of PEN and PET using laser stimulated emission on separate tiles exposed to 1 MRad and 10 MRad gamma rays with a 137Cs source. PEN exposed to 1 MRad and 10 MRad emit 71.4% and 46.7% of the light of an undamaged tile, respectively, and maximally recover to 85.9% and 79.5% after 5 and 9 days, respectively. PET exposed to 1 MRad and 10 MRad emit 35.0% and 12.2% light, respectively, and maximally recover to 93.5% and 80.0% after 22 and 60 days, respectively

Wind-Tunnel Investigation at Subsonic and Supersonic Speeds of a Fighter Model Employing a Low-aspect-ratio Unswept Wing and a Horizontal Tail Mounted Well above the Wing Plane - Lateral and Directional Stability

The static lateral- and directional-stability characteristics of a high-speed fighter-type airplane, obtained from wind-tunnel tests of a model, are presented. The model consisted of a thin, unswept wing of aspect ratio 2.3 and taper ratio 0.385, a body, and a horizontal tail mounted in a high position on a vertical tail. Rolling-moment, yawing moment, and cross-wind-force coefficients are presented for a range of sideslip angles of -5 deg. to +5 deg, for Mach numbers of 0.90, 1.45, and 1.90. Data are presented which show the effects on the lateral and directional stability of: (1) component parts of the complete model, (2) modification of the empennage so as to provide different heights of the horizontal tail above the wing plane, (3) angle of attack, and (4) dihedral of the wing

Regular dissections of an infinite strip

AbstractIn the early 1970s, Bro. U. Alfred Brousseau asked for the number of regions formed in an infinite strip by the mn segments that join m equally spaced points on one edge to n equally spaced points on the other. Using projective duality, we express the number of points, segments, and regions formed by Brousseau's configuration in terms of the numbers Lk(m,n) of lines that meet an m × n lattice array in exactly k points

An Evaluation of the Principal\u27s Academies of Tennessee

The problem related to this study was to determine which components of the Tennessee Principal\u27s Administrator Academy are effective and which ineffective in influencing the principal\u27s performance. The purpose of this study was to evaluate the effects of the Principal\u27s Academy that influences the principal\u27s day-to-day job performance at the local school site. The study also attempted to determine if factors such as age, size of school, per pupil expenditure, number of teachers on the respondent\u27s staff, educational level, school setting, years in present position, years attending the academy had any effect on the administrator\u27s perceptions of the academy. Tennessee administrators were given the opportunity to respond to the questionnaire used to determine the effectiveness of the Principal\u27s Academy. Five research questions were answered, and seven hypotheses stated in null form were tested using the Kruskal-Wallis Anova for data involving more than two groups. The Mann-Whitney-Wilcoxan Rank Sum W Test was used to determine if there was any significant difference in the respondent\u27s perceptions of the academy as it related to the year they attended. All null hypotheses were retained except the hypothesis related to the year the respondents attended the academy. In years 1984 and 1985 there as a significant difference in the perceptions of the respondents; thus, the hypothesis was rejected. The key motivating factor other than to meet the state mandate of attendance is self-improvement. The collegiality and social network associated with the Principal\u27s Academy is valuable, and attending the Principal\u27s Academy is a factor in school administrators implementing school improvement strategies. Research should be conducted to develop an evaluation instrument that would be used to evaluate future principal\u27s academies

The relationship between risk and the respondent\u27s level of socialization in the military

The following thesis deals with a sensitive issue, namely the examination of risk-taking behaviors in a military context. Generally, it is agreed that certain decisions made by the military are considerably more vast and important (in terms of the sociopolitical, and moral ramifications) than decisions reached by non-military groups. In light of this agreement, any analysis of risk-taking behavior could be interpreted as threatening to the image of the military. Understanding the sensitivity of the central theme of the following thesis demands an understanding of the assumptions of the investigation. The two major assumptions of this work are: a) the military is not a mindless, thrill-seeking entity lacking in rational restraint, but the military socialization process does seem to elicit risk y behaviors from its members; and b) the military risk ethic is not necessarily any more dramatic than the civilian risk ethic, even though this relationship has not been tested in the literature of group behaviors. I am not, in other words, launching an attack on the rationality of military decision-making. With the above mentioned assumptions in mind, the analysis of socialization and risk in a military context will be developed throughout the following thesis

Biological and toxicological investigations of Chicago area navigation projects

unpublishednot peer reviewe