Examples of the application of the confluent hypergeometric functions in miscellaneous areas of the theoretical physics are presented. It is suggested these functions to be utilized as a universal means for solution of a large number of problems, leading to: cylindrical, incomplete gamma, Coulomb wave, Airy, Kelvin, Bateman, Weber’s parabolic cylinder, logarithmic-integral and exponential integ...

We characterize, under some technical assumptions and up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. Our method is based on differential equations and the obtained measures are particular Beta distributions. We actually recover the free Meixner family of probability distributions so that our met...

This paper analyzes arrival flight track data at Chicago (ORD) and Atlanta (ATL) airports. We investigate distributions of vertical and lateral position at different distances from the runway threshold in instrument meteorological conditions (IMC) and visual meteorological conditions (VMC). In IMC, the observed standard deviations at different distances are similar between the two airports. The...

Coordination can greatly improve the efficiency of anti-predatory vigilance scans by increasing predator detection for a constant proportion of time spent vigilant. However, it has been rarely found in nature and most studies have detected or assumed independent scanning by group members. In this study, we analysed the functional consequences of the coordinated alternation of vigilance scanning...

1 Last two lectures ¯ probability spaces ¯ probability measure ¯ random variables and stochastic processes ¯ distribution functions ¯ independence ¯ conditional probability ¯ memoriless property of geometric and exponential distributions ¯ expectation ¯ conditional expectation (double expectation) ¯ mean-square estimation 1

The concentration of a drug in the circulatory system is studied under two different elimination strategies. The first strategy--geometric elimination--is the classical one which assumes a constant elimination rate per cycle. The second strategy--Poisson elimination--assumes that the elimination rate changes during the process of elimination. The problem studied here is to find a relationship b...

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.

The shear constitutive model of the slip zone soil can be used to quantitatively describe relationship between stress and displacement, which is great significance for analysis deformation mechanism stability evaluation landslides. conventional models were usually proposed based on statistical damage theory with Weibull distribution function, widely in field rock material. However, there are di...