BACKGROUND The assessment of the severity of aortic valve stenosis is done by either invasive catheterization or non-invasive Doppler Echocardiography in conjunction with the simplified Bernoulli equation. The catheter measurement is generally considered more accurate, but the procedure is also more likely to have dangerous complications. OBJECTIVE The focus here is on examining computational...

Geometrically simple Bernoulli generators are constructed for certain ergodic endomorphisms of solenoids. An arbitrary ergodic solenoidal group automorphism is obtained as the limit of a sequence of such Bernoulli factors and hence, by a theorem of D. S. Ornstein, must be measuretheoretically isomorphic to a Bernoulli shift. In his survey paper [6], B. Weiss stated that, using Y. Katznelson's m...

In the wake of D. Ornstein's proof five years ago that Bernoulli shifts with the same entropy are isomorphic came a flood of new results concerned in one way or another with Bernoulli shifts. Perhaps most surprising has been the discovery that so many of the classical examples of ergodic theory, as well as many "physical" systems, are isomorphic to Bernoulli shifts. We shall not discuss this as...

We present a relationship between the generalized hyperharmonic numbers and poly-Bernoulli polynomials, motivated from connections harmonic Bernoulli numbers. This yields numerous identities for hyper-sums several congruences.

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