On Superalgebras of Matrices with Symmetry Properties

It is known that semi-magic square matrices form a 2-graded algebra or superalgebra with the even and odd subspaces under centre-point reflection symmetry as the two components. We show that other symmetries which have been studied for square matrices give rise to similar superalgebra structures, pointing to novel symmetry types in their complementary parts. In particular, this provides a unifying framework for the composite `most perfect square' symmetry and the related class of `reversible squares'; moreover, the semi-magic square algebra is identified as part of a 2-gradation of the general square matrix algebra. We derive explicit representation formulae for matrices of all symmetry types considered, which can be used to construct all such matrices.Comment: 25 page

Investigation of refractory composites for liquid rocket engines Final report, 1 Oct. 1969 - 31 Oct. 1970

Oxidation resistance and high temperature tests of rhenium, tungsten, hafnium, and tantalum matrix composites with iridium in oxygen, fluorine, and boron atmospheres for liquid propellant engine

Current activities at IITRI on high- temperature protective coatings

Heat resistant protective coatings for use in liquid propellant rocket engine

Jockey Falls, Injuries, and Fatalities Associated With Thoroughbred and Quarter Horse Racing in California, 2007-2011.

BackgroundDespite the popularity of the horse racing industry in the United States and the wide recognition that horse racing is one of the most hazardous occupations, little focused research into the prevention of falls by and injuries to jockeys has been conducted.PurposeTo describe the incidence rates and characteristics of falls and injuries to Thoroughbred and Quarter Horse racing jockeys in the state of California.Study designDescriptive epidemiology study.MethodsData on race-day falls and injuries were extracted from jockey accident reports submitted to the California Horse Racing Board from January 2007 to December 2011. Denominator data, number of jockey race rides, were obtained from commercial and industry databases. Jockey fall, injury, and fatality incidence rates and ratios in Thoroughbred and Quarter Horse flat races were estimated using Poisson regression. Characteristics of falls and injuries are described and compared.ResultsIn Thoroughbred races, 184 jockey injuries occurred from 360 reported jockey falls, 180,646 race rides, 23,500 races, and 3350 race meetings. In Quarter Horse races, 85 jockey injuries occurred from 145 jockey falls, 46,106 race rides, 6320 races, and 1053 race meetings. Jockey falls occurred at a rate of 1.99 falls per 1000 rides in Thoroughbred races, with 51% of falls resulting in jockey injury, and 3.14 falls per 1000 rides in Quarter Horse races, with 59% of falls resulting in jockey injury. The majority of falls occurred during a race, with catastrophic injury or sudden death of the horse reported as the most common cause in both Thoroughbred (29%) and Quarter Horse (44%) races. During the period studied, 1 jockey fatality resulted from a fall. Jockey fall rates were lower but injury rates were comparable to those reported internationally.ConclusionOn average, a licensed jockey in California can expect to have a fall every 502 rides in Thoroughbred races and every 318 rides in Quarter Horse races. While jockey fall rates were lower, injury rates were similar to those in other racing jurisdictions. The high proportion of jockey falls caused by horse fatalities should be further investigated

School Food Environments and Policies in U.S. Public Schools

Examines food environments in elementary, middle, and high schools based on seventeen factors, including foods and beverages offered, the availability of vending machines, and how they vary by grade level, location, and other school characteristics

Two hard spheres in a pore: Exact Statistical Mechanics for different shaped cavities

The Partition function of two Hard Spheres in a Hard Wall Pore is studied appealing to a graph representation. The exact evaluation of the canonical partition function, and the one-body distribution function, in three different shaped pores are achieved. The analyzed simple geometries are the cuboidal, cylindrical and ellipsoidal cavities. Results have been compared with two previously studied geometries, the spherical pore and the spherical pore with a hard core. The search of common features in the analytic structure of the partition functions in terms of their length parameters and their volumes, surface area, edges length and curvatures is addressed too. A general framework for the exact thermodynamic analysis of systems with few and many particles in terms of a set of thermodynamic measures is discussed. We found that an exact thermodynamic description is feasible based in the adoption of an adequate set of measures and the search of the free energy dependence on the adopted measure set. A relation similar to the Laplace equation for the fluid-vapor interface is obtained which express the equilibrium between magnitudes that in extended systems are intensive variables. This exact description is applied to study the thermodynamic behavior of the two Hard Spheres in a Hard Wall Pore for the analyzed different geometries. We obtain analytically the external work, the pressure on the wall, the pressure in the homogeneous zone, the wall-fluid surface tension, the line tension and other similar properties