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In this paper, we present the q-Lidstone polynomials which are q-Bernoulli generated by third Jackson q-Bessel function, based on Green’s function of a certain q-difference equation. Also, provide q-Fourier series expansions these and derive some results related to them.

When we toss a coin there are two outcomes and if the coin is fair, the two probabilities are equal. Consider the general case where the probability of heads is p0 and hence the probability of tails is 1−p0. This is the Bernoulli distribution where there are two outcomesX ∈ {0, 1}, and P{X = 1} = f(1) = p0 and P{X = 0} = f(0) = 1− p0 (3) When p0 = 1/2 we get the uniform distribution but with Be...

This article uses an active control dedicated to the positioning of subsea structures like flow lines. This kind of operation consists in connecting the bottom end of a very long pipeline to the wellhead, by dynamically modifying the pipeline top end position, which is linked to a Dynamically Positioned Vessel (DPV). Such long pipelines are usually called risers, because they are used to rise t...

Abstract This paper is concerned with the linear unbiased minimum variance estimation problem for discrete-time stochastic linear control systems with one-step random delay and inconsecutive packet dropout. A new model is developed to describe the phenomena of the one-step delay and inconsecutive packet dropout by employing a Bernoulli distributed stochastic variable. Based on the model, a recu...

We study a system coupling the incompressible Navier-Stokes equations in a 2D rectangular type domain with a damped Euler-Bernoulli beam equation, where the beam is a part of the upper boundary of the domain occupied by the fluid. Due to the deformation of the beam the fluid domain depends on time. We prove that this system is exponentially stabilizable, locally about the null solution, with an...

A class of nonlinear Schrödinger equations involving a triad of power law terms together with a de Broglie–Bohm potential is shown to admit symmetry reduction to a hybrid Ermakov–Painlevé II equation which is linked, in turn, to the integrable Painlevé XXXIV equation. A nonlinear Schrödinger encapsulation of a Korteweg-type capillary system is thereby used in the isolation of such a Ermakov–Pai...

Hurwitz found the Fourier expansion of the Bernoulli polynomials over a century ago. In general, Fourier analysis can be fruitfully employed to obtain properties of the Bernoulli polynomials and related functions in a simple manner. In addition, applying the technique of Möbius inversion from analytic number theory to Fourier expansions, we derive identities involving Bernoulli polynomials, Ber...

The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which used to solve Falkner-Skan equation. nonlinear differential equation converting a system equations solved using Mathematica®12, approximate solutions are obtained. efficiency these methods was studied by calculating maximum error remainder ( ), it found that their increases as increases. Moreover...