Abstract Nano and micromechanical mass sensing using cantilever oscillators of different length-scales has been an established approach. The main principle underpinning this technique is the shift in resonance frequency caused by additional dynamic system. While object to be sensed useful information, some idea about shape would benefit. information may used make a distinction between two objec...

We investigate sums of products of Bernoulli numbers including poly-Bernoulli numbers. A relation among these sums and explicit expressions of sums of two and three products are given. As a corollary, we obtain fractional parts of sums of two and three products for negative indices.

In this paper we analyze the Beta-Bernoulli process from Bayesian nonparametrics using the framework of algebraic effects from programming language theory. Our analysis reveals the importance of abstract data types, and two types of program equations, called commutativity and discardability, in the study of the Beta-Bernoulli process. We develop an equational theory of terms that use the Beta-B...

is a well-known formula from classical analysis giving a relation between the finite sum of values of a function f , whose first m derivatives are absolutely integrable on [a, n], and its integral, for a,m, n ∈ N, a < n. This elementary formula appears often in introductory texts [2, 17], usually in reference to a particular application—Stirling’s asymptotic formula. However, general approaches...

The principal aim of this paper is to serve the numerical solution of an integralalgebraic equation (IAE) by using the Bernoulli polynomials and the residual correction method. After implementation of our scheme, the main problem would be transformed into a system of algebraic equations such that its solutions are the unknown Bernoulli coefficients. This method gives an analytic solution when t...

A new class of generalized Laguerre-based poly-Bernoulli polynomials are discussed with an attempt to generate new and interesting identities, some are in relation with Stirling number of the second kind. Different analytical means and generating function method is incorporated to derive implicit summation formulae and symmetry identities for generalized Laguerre poly-Bernoulli polynomials. It ...

For every countable group G, a family of isomorphism invariants for measurepreserving G-actions on probability spaces is defined. In the special case in which G is a countable sofic group, a special class of these invariants are computed exactly for Bernoulli systems over G. This leads to a complete classification of Bernoulli systems for many countable groups including all finitely generated l...

We introduce elliptic analogues to the Bernoulli ( resp. Euler) numbers and functions. The first aim of this paper is to state and prove that our elliptic Bernoulli and Euler functions satisfied Raabe’s formulas (cf. Theorems 3.1.1, 3.2.1). We define two kinds of elliptic Dedekind-Rademacher sums, in terms of values of our elliptic Bernoulli (resp. Euler) functions. The second aim of this paper...

We define a new percolation model by generalising the FK representation of the Ising model, and show that on the triangular lattice and at high temperatures, the critical point in the new model corresponds to the Ising model. Since the new model can be viewed as Bernoulli percolation on a random graph, our result makes an explicit connection between Ising percolation and critical Bernoulli perc...

A uniformly p-to-one endomorphism is a measure-preserving map with entropy log p which is almost everywhere p-to-one and for which the conditional expectation of each preimage is precisely 1/p. The standard example of this is a one-sided p-shift with uniform i.i.d. Bernoulli measure. We give a characterization of those uniformly finite-to-one endomorphisms conjugate to this standard example by ...