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.

We generalize the notion of an Euler tour in a graph in the following way. An Euler family in a hypergraph is a family of closed walks that jointly traverse each edge of the hypergraph exactly once. An Euler tour thus corresponds to an Euler family with a single component. We provide necessary and sufficient conditions for the existence of an Euler family in an arbitrary hypergraph, and in part...

The Euler math fonts are suitable for math typesetting in conjunction with a variety of popular text fonts which do not provide math character sets of their own. Euler-VM is a set of virtual fonts based on Euler and Computer Modern, accompanied by a macro package for easy use with LATEX. 302 TUGboat, Volume 23 (2002), No. 3/4 The Euler math fonts “With Donald Knuth’s assistance and encouragemen...

A sliding mode control method is presented for Euler parameter command tracking of spacecraft maneuvers. Although only three Euler parameters are independent, desired closed-loop performance is specified on all four Euler parameters by way of four sliding surfaces in the Euler parameter error-error rate phase planes. The Euler parameters were chosen as the generalized coordinates for tracking t...

The main purpose of this paper is to present new q-extensions of Apostol’s type Euler polynomials using the fermionic p-adic integral on Zp. We define the q-λ-Euler polynomials and obtain the interpolation functions and the Hurwitz type zeta functions of these polynomials. We define qextensions of Apostol type’s Euler polynomials of higher order using the multivariate fermionic p-adic integral ...

One of the simplest and, at the same time, most important invariants of a topological space is the Euler characteristic. A generalization of the notion of the Euler characteristic to the equivariant setting, that is, to spaces with an action of a group (say, finite) is far from unique. An equivariant analogue of the Euler characteristic can be defined as an element of the ring of representation...

Nonlocally related systems for the Euler and Lagrange systems of twodimensional dynamical nonlinear elasticity are constructed. Using the continuity equation, i.e., conservation of mass of the Euler system to represent the density and Eulerian velocity components as the curl of a potential vector, one obtains the Euler potential system that is nonlocally related to the Euler system. It is shown...

Recently the new q-Euler numbers and polynomials related to Frobenius-Euler numbers and polynomials are constructed by Kim (see[3]). In this paper, we study the generalized q-Euler numbers and polynomials attached to χ related to the new q-Euler numbers and polynomials which is constructed in [3]. Finally, we will derive some interesting congruence on the generalized q-Euler numbers and polynom...

in this paper, the modified euler-bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. an explicit solution is derived for the buckling loads of microscaled euler beams considering surface effects. the size-dependent buckling behavior of the nanotube d...