We find Fourier expansions of Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. We give a very simple proof of them.

@ARTICLE{HeniklAT2012, author={J. Henikl and J. Schr\"ock and T. Meurer and A. Kugi}, title={{Infinit-dimensionaler Reglerentwurf f\"ur Euler-Bernoulli Balken mit Macro-Fibre Composite Aktoren}}, journal={at -Automatisierungstechnik}, year={2012}, volume={60}, number={1}, pages={10--19}, doi = {10.1524/auto.2012.0967}, url = {http://www.degruyter.com/view/j/auto.2012.60.issue-1/auto.2012.0967/a...

In this paper, we use the Stein-Chen method to determine a non-uniform bound for approximating the distribution of sums of dependent Bernoulli random variables by Poisson distribution. We give two formulas of non-uniform bounds and their applications.

Finite mixture models can be used in estimating complex, unknown probability distributions and also in clustering data. The parameters of the models form a complex representation and are not suitable for interpretation purposes as such. In this paper, we present a methodology to describe the finite mixture of multivariate Bernoulli distributions with a compact and understandable description. Fi...

In some distributions, such as the binomial distribution, the variance is determined by the mean. However, in practice, overdispersion is often observed where the variance is larger than that predicated by the mean, and underdispersion is sometimes observed where the variance is smaller. It is well known that overdispersion or underdispersion cannot be modeled for dichotomous responses having a...

We prove that two independent continuous-time simple random walks on the infinite open cluster of a Bernoulli bond percolation in the lattice Z meet each other infinitely many times. An application to the voter model is also discussed. 2000 MR subject classification: 60K

The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature meth...