Values of Tvµ and the Christoffel symbols for a line element of considerable generality

In the general theory of relativity the mechanical properties of any region of the universe are expressed by the energy-momentum tensor, Tvµ, which is itself calculable from the form of the line element, ds2 = gµvdxµdx4, applicable to that region. The expressions for Tvµ in the most general case, in which all the gµv are arbitrary functions of the four coordinates, x1, x2, x3, x4, are exceedingly complicated, but considerable simplification is introduced if it is assumed that gµv(µ ≠ v) = 0

Meteorological assessment of SRM exhaust products' environmental impact

The environmental impact of solid rocket motor (SRM) exhaust products discharged into the free air stream upon the launching of space vehicles that depend upon SRM boosters to obtain large thrust was assessed. The emission of Al2O3 to the troposphere from the SRMs in each Shuttle launch is considered. The Al2O3 appears as particles suitable for heterogeneous nucleation of hydrochloric acid which under frequently occurring atmospheric conditions may form a highly acidic rain capable of damaging property and crops and of impacting upon the health of human and animal populations. The cloud processes leading to the formation of acid rain and the concentration of the acid that then reaches the ground, and the atmospheric situations that lead to the production of cloud and rain at and near a launch site, and the prediction of weather conditions that may permit or prohibit a launch operation are studied

1956 survey of consumer finances: durable goods and housing

Consumer surveys ; Consumer goods ; Housing - Finance

Acid rain: Microphysical model

A microphysical model was used to simulate the case of a ground cloud without dilution by entrainment and without precipitation. The numerical integration techniques of the model are presented. The droplet size spectra versus time and the droplet molalities for each value of time are discussed

1956 survey of consumer finances: the financial position of consumers

Consumer surveys ; Consumer behavior

1957 survey of consumer finances: the financial position of consumers

Consumer surveys ; Consumers ; Income

PB4L school-wide evaluation: preliminary findings

Abstract: This report presents indicative findings from the first phase of an evaluation of Positive Behaviour for Learning: School-Wide (PB4L: School-Wide). The report discusses the implementation and short-term shifts for schools that began PB4L: School-Wide in 2010/11. The findings suggest that overall, PB4L: School-Wide is well-regarded in participating schools and is linked to a wide range of changes for schools, teachers, and students

Correlation of Automorphism Group Size and Topological Properties with Program-size Complexity Evaluations of Graphs and Complex Networks

We show that numerical approximations of Kolmogorov complexity (K) applied to graph adjacency matrices capture some group-theoretic and topological properties of graphs and empirical networks ranging from metabolic to social networks. That K and the size of the group of automorphisms of a graph are correlated opens up interesting connections to problems in computational geometry, and thus connects several measures and concepts from complexity science. We show that approximations of K characterise synthetic and natural networks by their generating mechanisms, assigning lower algorithmic randomness to complex network models (Watts-Strogatz and Barabasi-Albert networks) and high Kolmogorov complexity to (random) Erdos-Renyi graphs. We derive these results via two different Kolmogorov complexity approximation methods applied to the adjacency matrices of the graphs and networks. The methods used are the traditional lossless compression approach to Kolmogorov complexity, and a normalised version of a Block Decomposition Method (BDM) measure, based on algorithmic probability theory.Comment: 15 2-column pages, 20 figures. Forthcoming in Physica A: Statistical Mechanics and its Application