In a recent paper, Guo, Mező, and Qi proved an identity representing the Bernoulli polynomials at non-negative integer points m in terms of the m-Stirling numbers of the second kind. In this note, using a new representation of the Bernoulli polynomials in the context of the Zeon algebra, we give an alternative proof of the aforementioned identity.

We show quenched large deviations for the simple random walk on percolation models with long-range correlations defined by Drewitz, Ráth and Sapozhnikov [3], which contain supercritical Bernoulli percolations, random interlacements, the vacant set of random interlacements and the level set of the Gaussian free field. Our result is an extension of Kubota’s result [8] for supercritical Bernoulli ...

and Applied Analysis 3 see 3, 4, 15, 16 . By 1.5 and 1.7 , the Witt’s formula for the q-Bernoulli numbers with weight α is given by ∫ Zp x qαdμq x β̃ α n,q , where n ∈ Z . 1.8 The q-Bernoulli polynomials with weight α are also defined by

We consider the exterior free boundary Bernoulli problem in the case of a rough given domain. An asymptotic analysis shows that the solution of the initial problem can be approximated by the solution of a non-rough Bernoulli problem at order 2. Numerical tests confirm these theoretical results.

Various types of graph statistics for Bernoulli graphs are represented as numerators of incomplete U-statistics. Asymptotic normality of these statistics is proved for Bernoulli graphs in which the edge probability is constant. In addition it is shown that subgraph counts asymptotically are linear functions of the number of edges in the graph. AMS Subject Classification: Primary 05C99; Secondar...

We present a new latent-variable model employing a Gaussian mixture integrated with a feature selection procedure (the Bernoulli part of the model) which together form a ”Latent Bernoulli-Gauss” distribution. The model is applied to MAP estimation, clustering, feature selection and collaborative filtering and fares favorably with the state-of-theart latent-variable models.

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number theoretical properties. A class of Euler-type polynomials is also presented. © 2007 Elsevier Inc. All rights reserved.

The billiard in a polygon is not always ergodic and never K-mixing or Bernoulli. Here we consider billiard tables by attaching disks to each vertex of an arbitrary simply connected, convex polygon. We show that the billiard on such a table is ergodic, K-mixing and Bernoulli.