Kolmogorov studied the problem of whether a function of the parameter p of the Bernoulli distribution Bernoulli[p] has an unbiased estimator based on a sample X1, X2, . . . , Xn of size n and proved that exactly the polynomial functions of degree at most n can be estimated. For the geometric distribution Geometric[p], we prove that exactly the functions that are analytic at p = 1 have unbiased ...

An arbitrary-depth reduction theorem for the ‘convolution’ multiple L-values of Euler-Zagier type for a broad class of Dirichlet characters is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the monodromies of these functions and the parities of generating functions of generalized Bernoulli numbers. Some genera...

In this paper we study the reliability of calculations of the structural reliability. It compares the exact reliability expression within the Bernoulli-Euler column theory with its counterpart obtained via the finite difference expression in the buckling context.

Techniques for modeling hysteresis and material nonlinearities in magnetostrictive materials are presented. Hys-teresis in these materials is due to both the driving magnetic eld and stress relations within the material and is signiicant throughout most of the drive range of the material. Two characterizations are presented here. The rst model is posed in terms of Preisach operators and is pure...

A possibly unknown approach to the problem of finding the common term of a power series is considered. A direct formula for evaluating this common term has been obtained. This formula provides useful expressions for direct evaluation of the number of partitions of a nonnegative integer and the partitions themselves. These expressions permit easily to work with power series, evaluate nth derivat...

A new model for the interaction between the acoustic wave in an enclosed air cavity and the transversal motion of a flexible beam is proposed in this paper. This new boundary condition for the coupled wave and Euler-Bernoulli beam equations introduces sufficient damping of the energy of the system to gain uniform exponential stability. Careful physical justification of the boundary condition is...

This paper studies the regularity of an Euler–Bernoulli plate equation on a bounded domain of Rn, n ≥ 2, with partial Neumann control and collocated observation. It is shown that the system is not only well posed in the sense of D. Salamon but also regular in the sense of G. Weiss. It is also shown that the corresponding feedthrough operator is zero.

Using the finite difference calculus and differentiation, we obtain several new identities for Bernoulli and Euler polynomials; some extend Miki’s and Matiyasevich’s identities, while others generalize a symmetric relation observed by Woodcock and some results due to Sun.

We consider the following one-player game called Dundee. We are given a deck consisting of si cards of Value i, where i = 1, . . . , v, and an integer m ≤ s1 + · · · + sv. There are m rounds. In each round, the player names a number between 1 and v and draws a random card from the deck. The player loses if the named number coincides with the drawn value in at least one round. The famous Problem...

Let p be a fixed odd prime. Throughout this paper, Zp,Qp,Cp will, respectively, denote the ring of p-adic integers, the field of p-adic rational numbers, and the completion of algebraic closure of Qp. The p-adic absolute value | |p on Cp is normalized so that |p|p 1/p. Let Z>0 be the set of natural numbers and Z≥0 Z>0 ∪ {0}. As is well known, the Bernoulli polynomials Bn x are defined by the ge...