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...

Several attempts have been made to give an objective definition of subjective probability. These attempts can be divided into two approaches. The first approach uses an a priori probability distribution over the set of interpretations of the language that we are using to describe information. The idea is to define such an a priori probability distribution using some general principles such as t...

General inequalities for the distribution of the longest success run in Bernoulli trials are found through a direct combinatorial analysis. Their employment allows the derivation of a new lower bound which can be used in the achievement of theoretical results.

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...