BACKGROUND Transvalvular peak pressure drops are routinely assessed noninvasively by echocardiography using the Bernoulli principle. However, the Bernoulli principle relies on several approximations that may not be appropriate, including that the majority of the pressure drop is because of the spatial acceleration of the blood flow, and the ejection jet is a single streamline (single peak veloc...

“Bernoulli” levitation is the basis of many popular counter-intuitive physics demonstrations. However, few of these lend themselves to a quantitative description without recourse to computational fluid dynamics. Levitation of a flat plate is the exception, and we present here a straightforward analysis which illustrates several principles of fluid mechanics in a pedagogically useful way.

We review several occurrences of poly-Bernoulli numbers in various contexts, and discuss in particular some aspects of relations of poly-Bernoulli numbers and special values of certain zeta functions, notably multiple zeta values.

In this paper, we study three types of sums of products of ordered Bell and poly-Bernoulli functions and derive their Fourier series expansion. In addition, we express those functions in terms of Bernoulli functions.

In this paper we consider a discrete version of the Bernoulli convolution problem traditionally studied via functional analysis. We develop an algorithm which bounds the Bernoulli sequences, and we give a significant improvement on the best known bound.

By using q-integration, we will give some integral equation which are related to the Barnes’ multiple Bernoulli numbers. The object of this paper is to give explicit q-integral’s formulae which are related to Barnes’ multiple q-Bernoulli polynomials. §

PrQcedures are exhibited and analyzed for converting a sequence of iid Bernoulli variables with unknown mean p into a Bernoulli variable with mean 1/2. The efficiency of several procedures is studied.