Disruption of the three-body gravitational systems: Lifetime statistics

We investigate statistics of the decay process in the equal-mass three-body problem with randomized initial conditions. Contrary to earlier expectations of similarity with "radioactive decay", the lifetime distributions obtained in our numerical experiments turn out to be heavy-tailed, i.e. the tails are not exponential, but algebraic. The computed power-law index for the differential distribution is within the narrow range, approximately from -1.7 to -1.4, depending on the virial coefficient. Possible applications of our results to studies of the dynamics of triple stars known to be at the edge of disruption are considered.Comment: 13 pages, 2 tables, 3 figure

Calculation of aggregate loss distributions

Estimation of the operational risk capital under the Loss Distribution Approach requires evaluation of aggregate (compound) loss distributions which is one of the classic problems in risk theory. Closed-form solutions are not available for the distributions typically used in operational risk. However with modern computer processing power, these distributions can be calculated virtually exactly using numerical methods. This paper reviews numerical algorithms that can be successfully used to calculate the aggregate loss distributions. In particular Monte Carlo, Panjer recursion and Fourier transformation methods are presented and compared. Also, several closed-form approximations based on moment matching and asymptotic result for heavy-tailed distributions are reviewed

The surface abundance and stratigraphy of lunar rocks from data about their albedo

The data pf ground-based studies and surveys of the lunar surface by the Zond and Apollo spacecraft have been used to construct an albedo map covering 80 percent of the lunar sphere. Statistical analysis of the distribution of areas with various albedos shows several types of lunar surface. Comparison of albedo data for maria and continental areas with the results of geochemical orbital surveys allows the identification of the types of surface with known types of lunar rock. The aluminum/silcon and magnesium/silicon ratios as measured by the geochemical experiments on the Apollo 15 and Apollo 16 spacecraft were used as an indication of the chemical composition of the rock. The relationship of the relative aluminum content to the age of crystalline rocks allows a direct dependence to be constructed between the mean albedo of areas and the age of the rocks of which they are composed