Precise measurements of the longitudinal profiles of ion beams with ∼10 ps temporal resolution became available with the help of a Bunch Shape Monitor (BSM) developed and used at the INR. A number of BSMs have been developed, fabricated at the INR and tested with a beam at several laboratories during last 3 years. The upgraded BSM-Bunch Length and Velocity Detector (BLVD)-can measure not only l...

Here, and in a sequel, we invoke the invariant spin field to provide an in–depth study of spin motion at and near low order orbital resonances in a simple model for the effects of vertical betatron motion in a storage ring with Siberian Snakes. This leads to a clear understanding, within the model, of the behaviour of the beam polarisation at and near so–called snake resonances in proton storag...

The efficiency and robustness of reliability methods are two important factors in the first-order reliability method (FORM). The conjugate choice control (CCC) and directional chaos control method (DCC) are developed to improve the robustness and efficiency of the FORM formula using the stability transformation method. In this paper, the CCC and DCC methods are applied for the reliability analy...

This paper presents exact solutions for the nonlinear bending problem, buckling loads, and postbuckling configurations of a perfect an imperfect bioinspired helicoidal composite beam with linear rotation angle. The is embedded on elastic medium, which modeled by two foundation parameters. integro-differential governing equation system derived based Euler–Bernoulli hypothesis, von Kármán strain,...

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

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.

A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lamé operator.

We introduce and investigate the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials by means of a suitable theirs generating polynomials. We establish several interesting properties of these polynomials. Also, we gave some propositions two theorems and one corollary.

In this paper we derive a general combinatorial identity in terms of polynomials with dual sequences of coefficients. Moreover, combinatorial identities involving Bernoulli and Euler polynomials are deduced. Also, various other known identities are obtained as particular cases.