Probabilistic seismic hazard analysis of Nepal

Probabilistic seismic hazard analysis for Nepal has been carried out considering uniform density model. A detailed earthquake catalogue since 1255 A.D, within the rectangular area has been developed and historical earthquakes are plotted in the map of Nepal. Five hundred twenty eight numbers of areal sources are used within the study area to characterize the seismic sources. The completeness of the data has been checked by using Stepp's procedure. Seismicity in four regions of study area has been evaluated by defining 'a' and 'b' parameters of Gutenberg Richter recurrence relationship. Seismic hazard curve of Nepal for soft subsoil condition for 10% probability of exceedence in 50 years period i.e. for return period of 475 years has been plotted.

ON PROBABILTY DISTRIBUTION IN ASSOCIATION WITH A CERTAIN GENERALIZED HYPERGEOMETRIC FUNCTION

In the present paper, a probability function has been introduced in terms of the -function and its properties are studied. It is shown that the classical non-central distributions such as, non-central chi-square, non-central Student- , non-central and almost all classical central continuous distributions can be obtained as special cases of this general density function. This general density function is introduced with the hope that any density function, which can be represented in terms of any known special function as well as the density of the ratio of any two independent stochastic variables whose density functions can be represented in terms of any known special functions, is contained in as a special case. The properties of , discussed in this paper, include the characteristic function, moments, recurrence relationship among moments and the distribution function.

Stochastic Modeling of Density-Dependent Diploid Populations and the Extinction Vortex

We model and study the genetic evolution and conservation of a population of diploid hermaphroditic organisms, evolving continuously in time and subject to resource competition. In the absence of mutations, the population follows a three-type, nonlinear birth-and-death process, in which birth rates are designed to integrate Mendelian reproduction. We are interested in the long-term genetic behavior of the population (adaptive dynamics), and in particular we compute the fixation probability of a slightly nonneutral allele in the absence of mutations, which involves finding the unique subpolynomial solution of a nonlinear three-dimensional recurrence relationship. This equation is simplified to a one-dimensional relationship which is proved to admit exactly one bounded solution. Adding rare mutations and rescaling time, we study the successive mutation fixations in the population, which are given by the jumps of a limiting Markov process on the genotypes space. At this time scale, we prove that the fixation rate of deleterious mutations increases with the number of already fixed mutations, which creates a vicious circle called the extinction vortex.