Here we consider some non-autonomous ordinary differential equations of order n and present some results and theorems on the existence of periodic solutions for them, which are sufficient conditions, section 1. Also we include generalizations of these results to vector differential equations and examinations of some practical examples by numerical simulation, section 2. For some special cases t...

Most Irish traditional folk dance music contains two musical themes; the tune begins with one musical theme which is usually repeated, then progresses to another theme with similar musical structure and motives, which is usually also repeated. The first section is typically called the A section while the second is called the B section. Our goal is to understand, at a quantitative level, the mus...

So far we have assumed that a plastic hinge forms if the bending moment in a critical cross section reaches the plastic limit value, M0. We have tacitly neglected the effect of the other internal forces on the formation of the yield hinge. This effect, however, can be appreciable, for example in multi-storey frames or frames with a large horizontal thrust where the axial forces are large. So, w...

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of afluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid...

The objective of this investigation is to derive closed-form partial-wave series expansions for the extrinsic and intrinsic acoustical scattering, extinction and absorption cross-sections of afluid viscous cylindrical particle of arbitrary geometrical cross-section, located nearby a flat rigid boundary. Plane progressive waves with arbitrary incidence angle are considered in a non-viscous fluid...

In this paper we improve the estimate obtained by Lu-Pan on the value of the upper critical field HC3(κ) for a cylindrical superconductor with cross section Ω being an arbitrary 2-dimensional smooth bounded domain. We also show that, when a homogeneous magnetic field is applied along the axis of the cylinder with magnitude of the field close to HC3 , superconductivity nucleates first at the sur...

The differential theory of diffraction by arbitrary cross-section cylindrical objects is developed for the most general case of an incident field with a wave vector outside the cross-section plane of the object. The fast Fourier factorization technique recently developed for studying gratings is generalized to anisotropic and/or inhomogeneous media described in cylindrical coordinates; thus the...