We give an exact solution for the complete distribution of component sizes in random networks with arbitrary degree distributions. The solution tells us the probability that a randomly chosen node belongs to a component of size s for any s . We apply our results to networks with the three most commonly studied degree distributions-Poisson, exponential, and power-law-as well as to the calculatio...

An analysis has been presented of the effect of elastic foundation and uniform in-plane peripheral loading on the natural frequencies and mode shapes of circular plates of varying thickness exhibiting bi-directional functionally graded characteristics, on the basis of first order shear deformation theory. The material properties of the plate are varying following a power-law in both the radial ...

In this thesis, starting from a schematic mode-coupling model, the dynamics and the ow behavior of colloidal dispersions under stationary shearing close to the glass transition is analyzed. Both analytical and numerical methods are applied. The most important control parameters of the model are the shear rate and the separation parameter measuring the distance from the glass transition point. A...

A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mix...

The evolutionary origin of general statistics in a biochemical reaction network is studied here to explain the power-law distribution of reaction links and the power-law distribution of chemical abundance. Using cell models with catalytic reaction networks, we have confirmed that the power-law distribution for the abundance of chemicals emerges by the selection of cells with higher growth rates...

The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter α ∈]0, 1[. Using extensive numerical simulations of large web networks, with a special accent on British University networks, we determine numerically and analytically the universal features of PageRank vector at its emergence when α → 1. The whole network...

In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law dist...

The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah Alzaatreh studied the best linear unbiased estimators for location scale parameters three-parameter model. same authors also propose a shift-invariant Hill estimator unknown shape parameter. In this work, we new estimation method We deriv...

We derive a dual-primal recursive algorithm based on the Fenchel duality framework, extending Dykstra’s successive projections and Csiszar’s I-projections schemes, to handle Tsallis MaxEnt. The Tsallis entropy Sq(p) is a one-parameter extension of Shannon’s entropyH(p) in the sense that Sq→1(p) = H(p). The solution of the Tsallis MaxEnt falls under a q-deformed Gibbs distribution which is a pow...

In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated ...