The Poisson binomial distribution is the distribution of the sum of independent and non-identical random indicators. Each indicator follows a Bernoulli distribution with individual success probability. When all success probabilities are equal, the Poisson binomial distribution is a binomial distribution. The Poisson binomial distribution has many applications in different areas such as reliabil...

A widely used electrostatics model in the biomolecular modeling community, the nonlinear Poisson–Boltzmann equation, along with its finite element approximation, are analyzed in this paper. A regularized Poisson–Boltzmann equation is introduced as an auxiliary problem, making it possible to study the original nonlinear equation with delta distribution sources. A priori error estimates for the f...

Approximative properties of the Taylor-Abel-Poisson linear summation method Fourier series are considered for functions several variables, periodic with respect to hexagonal domain, in integral metric. In particular, direct and inverse theorems proved terms approximations by means K-functionals generated radial derivatives. Bernstein type inequalities L1-norm derivatives arbitrary order Poisson...