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.

We consider a boundary value problem for the beam equation, in which the boundary conditions mean that the beam is embedded at one end and free at the other end. Some new estimates to the positive solutions to the boundary value problem are obtained. Some sufficient conditions for the existence of at least one positive solution for the boundary value problem are established. An example is given...

This study aimed to examine the effect of obstacles and age on walking time within a course (10 cm width) and on a balance beam in 158 preschool boys, aged 4 (47), 5 (50), and 6 (61) years. An obstacle 5 or 10 cm in height (depth, 11.5 cm and width, 23.5 cm) was placed at the halfway point of the course drawn on the floor and on the balance beam (200 cm in length, 10 cm in width and 30 cm in he...

The aim of this study is the investigation of the large amplitude deflection of an Euler-Bernoulli beam subjected to an axial load on a viscoelastic foundation with the strong damping. In order to achieve this purpose, the beam nonlinear frequency has been calculated by homotopy perturbation method (HPM) and Hamilton Approach (HA) and it was compared by the exact solutions for the different bou...

Previous work showed that every pair of nontrivial Bernoulli shifts over a fixed free group are orbit equivalent. In this paper, we prove that if G 1 , G 2 are nonabelian free groups of finite rank then every nontrivial Bernoulli shift over G 1 is stably orbit equivalent to every nontrivial Bernoulli shift over G 2. This answers a question of S. Popa.

The following result is proven. Let G 1 T 1 (X 1 , µ 1) and G 2 T 2 (X 2 , µ 2) be orbit-equivalent, essentially free, probability measure preserving actions of countable groups G 1 and G 2. Let H be any countable group. For i = 1, 2, let Γ i = G i * H be the free product. Then the actions of Γ 1 and Γ 2 coinduced from T 1 and T 2 are orbit-equivalent. As an application, it is shown that if Γ i...

Kalikow (1982) proved that the [T, T−1] transformation is not isomorphic to a Bernoulli shift. We show that the scenery factor of the [T,T−1] transformation is not isomorphic to a Bernoulli shift. Moreover, we show that it is not Kakutani equivalent to a Bernoulli shift.

The Polya’s Urn model is notable within statistics because it generalizes the binomial, hypergeometric, and beta-Bernoulli (beta-binomial) distributions through a single formula. In addition, Polya’s Urn is a multivariate distribution whose variables are exchangeable but not independent. This paper introduces basic probability and Bayesian concepts in order to prove these properties.

If k < n, can one express the majority of n bits as the majority of at most k majorities, each of at most k bits? We prove that such an expression is possible only if k & n = n. This improves on a bound proved by Kulikov and Podolskii [KP17], who showed that k & n. Our proof is based on ideas originating in discrepancy theory, as well as a strong concentration bound for sums of independent Bern...