We investigate Fourier expansions for the Apostol-Bernoulli and Apostol-Euler polynomials using the Lipschitz summation formula and obtain their integral representations. We give some explicit formulas at rational arguments for these polynomials in terms of the Hurwitz zeta function. We also derive the integral representations for the classical Bernoulli and Euler polynomials and related known ...

the dynamic response of the railway under accelerated moving load using dynamic green function is presented in this paper. for this purpose, an exact and direct modeling technique is introduced for the railway modeling as the damped euler-bernoulli beam on the partial winkler foundation with arbitrary boundary conditions subjected to the moving load. the effects of the elastic coefficient of wi...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

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...

We consider the billiard flow of elastically colliding hard balls on the flat ν-torus (ν 2), and prove that no singularity manifold can even locally coincide with a manifold describing future non-hyperbolicity of the trajectories. As a corollary, we obtain the ergodicity (actually the Bernoulli mixing property) of all such systems, i.e. the verification of the Boltzmann–Sinai ergodic hypothesis...

Harsanyi [4, 5] develops expected utility theory of von Neumann and Morgenstern [21] to provide two formalizations of utilitarianism. Weymark [22, 23] refers to these results as Harsanyi’s Aggregation and Impartial Observer Theorems. In this paper, we are concerned only with Aggregation Theorem. Sen [6] argues that von Neumann-Morgenstern expected utility theory is an ordinal theory and, theref...

<p>A physics-informed machine learning model, in the form of a multi-output Gaussian process, is formulated using Euler-Bernoulli beam equation. Given appropriate datasets, model can be used to regress analytical value structure’s bending stiffness, interpolate responses, and make probabilistic inferences on latent physical quantities. The developed applied numerically simulated cantileve...