Let L (u, a), oo < u < + oo denote the Fourier-Stieltjes transform, 00 f eluoda(x), of a distribution function u(x), oo < x < + co . Thus if 00 /3(x) is the distribution function which is 0, J, 1 according as x -1 < x ,< 1, 1 < x, then L (u,,8) = cos u ; and so, if b is a positive constant, cos (u/b) is the transform of the distribution function /3(bx) . Hence, if a is a positive constant, the ...

A The chaos hierarchy 12 A.1 Ergodicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.2 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 A.3 K Systems (Kolmogorov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 A.4 B-Systems (Bernoulli) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The paper deals with the mechanical behavior of a micro-beam bonded with two piezoelectric layers. The micro-beam is suspended over a fixed substrate and undergoes the both piezoelectric and electrostatic actuation. The piezoelectric layers are poled through the thickness and equipped with surface electrodes. The equation governing the micro-beam deflection under electrostatic pressure is deriv...

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is ad...

We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urbański [23]. We extend their results to the overlapping region and also consider some extensions and generalizations.

We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)= ∑∞ n=1(qn(s−1)/[n]s), 0< q < 1, s ∈ C. In this paper, we give q-Bernoulli numbers which can be viewed as interpolation of the above q-analogue of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative integers. Also, we will treat some...

We prove the hyperbolicity, ergodicity and thus the Bernoulli property of two hard balls in one of the following four polygons: the square, the equilateral triangle, the 45 − 45 − 90◦ triangle or the 30− 60− 90◦ triangle.

*Correspondence: [email protected] College of Science, China University of Petroleum (East China), Qingdao, Shandong 266555, People’s Republic of China Abstract In this paper, we reduce a linear d-dimensional beam equation with an x-periodic and t-quasi-periodic potential for most values of the frequency vector via the KAM theorem. We focus on the measure estimates of small divisor conditions and ...

We describe a new algorithm that computes the nth Bernoulli number in n4/3+o(1) bit operations. This improves on previous algorithms that had complexity n2+o(1).