The object of this paper is to introduce and study the properties unified Apostol-Bernoulli Apostol-Euler polynomials noted by $$\left\{ \mathfrak {V_{n}}(x;\lambda ;\mu )\right\} _{n \ge 0}$$ . We some arithmetic as their connection polynomials. Also, we give derivation integration representations Finally, use umbral calculus approach deduce symmetric identities.

The expected utility/subjective probability model of risk preferences and beliefs has long been the preeminent model of individual choice under conditions of uncertainty. It exhibits a tremendous flexibility in representing aspects of attitudes toward risk, has a well-developed analytical structure, and has been applied to the analysis of gambling, games of strategy, incomplete information, ins...

A special attention is paid to the motion of flexible links in a robotic configuration. The elastic deformation is a dynamic value which depends on the total dynamics of the robot system movements. The Euler-Bernoulli equation should be expanded according to the requirements of the motion complexity of elastic robotic systems. The EulerBernoulli equation (based on the existing laws of dynamics)...

In this study, an impact behavior of spherical striker on a double-walled carbon nanotube (DWCNT) is presented based on a three degree of freedom spring-mass model and the finite element (FE) simulations. The semi-analytical solution of the transverse impact of a striker on a DWCNT is investigated by using the elasticity nonlocal theory of Euler-Bernoulli (EBT) and Timoshenko (TBT) nanobeams. T...