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...

We study a coupled fluid-structure system. The structure corresponds to a part of the boundary of a domain containing an incompressible viscous fluid. The structure displacement is modeled by a damped beam equation. We prove the existence of strong solutions to our system for small data and the existence of local strong solutions for any initial data.

Remark added May 1997 This paper was a preliminary version of the paper \Some harmonic analysis questions suggested by Anderson-Bernoulli models" by the same authors. It is being posted here because setion 5 contains proofs of some minor results which are stated but not proved in the paper submitted for publication. Speci ̄cally, Proposition 4.8 in the version submitted is proved di®erently here...

An ordinary block design has v points, blocks of size k, and each of the ( v 2 ) unordered pairs of points is contained in a common number λ of blocks. In 2007, Sarvate and Beam introduced a variation where rather than covering all pairs a constant number of times, one wishes to cover all pairs a different number of times. It is of greatest interest when these pair frequencies form an interval ...

not only provides an elegant formula for evaluating ζ(2n), but it also tells us of the arithmetical nature of ζ(2n). In contrast, we know very little about ζ(2n + 1). One of the major achievements in number theory in the past half-century is R. Apéry’s proof that ζ(3) is irrational [2], but for n ≥ 2, the arithmetical nature of ζ(2n+ 1) remains open. Ramanujan made many beautiful and elegant di...

In this paper, we study some supercongruences involving multiple harmonic sums by using Bernoulli numbers. Our main theorem generalizes previous results by many different authors and confirms a conjecture by the authors and their collaborators. In the proof, we will need not only the ordinary multiple harmonic sums in which the indices are ordered, but also some variant forms in which the indic...

In classical Bernoulli processes, it is assumed that a single Bernoulli experiment can be described by a precise and precisely known probability distribution. However, both of these assumptions can be relaxed. A first approach, often used in sensitivity analysis, is to drop only the second assumption: one assumes the existence of a precise distribution, but has insufficient resources to determi...

Consider a nite alphabet with a probability distribution p. We study the probability (p) of obtaining a palindrome in a nite time by independent draws. Using a Mahler equation for an associated generating function, we give a closed form expression for (p). Moreover we describe completely the cases where (p) has value less than 1, in connection with the singularities of the generating function. ...