To study the fast-ion transport in a well controlled background plasma, a 3-cm diameter rf ion gun launches a pulsed, ,300 eV ribbon shaped argon ion beam parallel to or at 15° to the magnetic field in the Large Plasma Device sLAPDd fW. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 s1991dg at UCLA. The parallel energy of the beam is measured by...

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. ...

We show that depending on the direction of deformation of κ-Poincaré algebra (time-like, space-like, or light-like) the associated phase spaces of single particle in Doubly Special Relativity theories have the energy-momentum spaces of the form of de Sitter, anti-de Sitter, and flat space, respectively.

Specialised literature presents a number of models describing the function of the vocal folds. In most of those models an emphasis is placed on the effect of Bernoulli’s air underpressure during the air passage through the glottis. The author defines a principle of the vocal folds function with a working version name „principle of the compressed air bubble“. The paper deals with the experimenta...

Based upon previous studies on laws of large numbers for fuzzy, random, fuzzy random and random fuzzy variables, We go further to explore weak law of large numbers(WLLN) for hybrid variables comprising fuzzy random variables and random fuzzy variables. we mainly prove Chebyshev WLLN, Poisson WLLN, Bernoulli WLLN, Markov WLLN and Khintchin WLLN for hybrid variables based on chance measure.