We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

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...

The Polya’s Urn model is notable within statistics because it generalizes the binomial, hypergeometric, and beta-Bernoulli (beta-binomial) distributions through a single formula. In addition, Polya’s Urn is a multivariate distribution whose variables are exchangeable but not independent. This paper introduces basic probability and Bayesian concepts in order to prove these properties.

If k < n, can one express the majority of n bits as the majority of at most k majorities, each of at most k bits? We prove that such an expression is possible only if k & n = n. This improves on a bound proved by Kulikov and Podolskii [KP17], who showed that k & n. Our proof is based on ideas originating in discrepancy theory, as well as a strong concentration bound for sums of independent Bern...

Several attempts have been made to give an objective definition of subjective probability. These attempts can be divided into two approaches. The first approach uses an a priori probability distribution over the set of interpretations of the language that we are using to describe information. The idea is to define such an a priori probability distribution using some general principles such as t...

General inequalities for the distribution of the longest success run in Bernoulli trials are found through a direct combinatorial analysis. Their employment allows the derivation of a new lower bound which can be used in the achievement of theoretical results.

Let X1,X2, . . . ,Xn be independent Bernoulli random variables with P(Xj = 1) = 1 − P(Xj = 0)= pj and let Sn := X1 +X2 + ···+Xn. Sn is called a Poisson binomial random variable and it is well known that the distribution of a Poisson binomial random variable can be approximated by the standard normal distribution. In this paper, we use Taylor’s formula to improve the approximation by adding some...