We investigate second order half-linear Euler type difference equations whose coefficients have mean values. We show that these equations are conditionally oscillatory and we explicitly identify the corresponding oscillation constants given by the coefficients. Our results generalize the known ones concerning equations with positive constant, periodic, or (asymptotically) almost periodic coeffi...

Let φ denote Euler’s phi function. For a fixed odd prime q we investigate the first and second order terms of the asymptotic series expansion for the number of n 6 x such that q ∤ φ(n). Part of the analysis involves a careful study of the Euler-Kronecker constants for cyclotomic fields. In particular, we show that the Hardy-Littlewood conjecture about counts of prime k-tuples and a conjecture o...

Structure constants of the su(N) (N odd) Lie algebras converge when N goes to infinity to the structure constants of the Lie algebra sdiff(T 2) of the group of area-preserving diffeomorphisms of a 2D torus. Thus Zeitlin and others hypothesized that solutions of the Euler equations associated with su(N) algebras converge to solutions of the Euler equations of incompressible fluid dynamics on a 2...

This article presents a new beam model that employs recursive derivation procedure enables the user to set order of governing differential equations as an input parameter, without need for ad hoc assumptions or methodologies. novel system kinematic variables, section constants, and functions facilitate development higher-order models retain clear philosophical link classical such Euler–Bernoull...