Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope γ − ε, where γ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we pro...

The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). In this work, an explicit finite-difference scheme for TFDE is presented. Discrete models of a non-Markovian random walk are generate for simulating random variables whose spatial probability density evolves...

Pollard’s rho algorithm, along with parallelized, vectorized, and negating variants, is the standard method to compute discrete logarithms in generic prime-order groups. This paper presents two reasons that Pollard’s rho algorithm is farther from optimality than generally believed. First, “higherdegree local anti-collisions” make the rho walk less random than the predictions made by the convent...

We consider Pollard’s rho method for discrete logarithm computation. Usually, in the analysis of its running time the assumption is made that a random walk in the underlying group is simulated. We show that this assumption does not hold for the walk originally suggested by Pollard: its performance is worse than in the random case. We study alternative walks that can be efficiently applied to co...

Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope γ − ε, where γ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we pro...

the purpose of this study is to identify parameters influence on the particle deposition within fin and tube heat exchanger of air-conditioning systems by cfd analysis. first the basic sketch of periodic geometry drawn and meshing operation including boundary conditions was performed. then the gas side properties and flow parameters were solved by ansys fluent 14.5 software. lagrangian equation...