This paper is about a type of quantitative density closed geodesics and orthogeodesics on complete finite-area hyperbolic surfaces. The main results are upper bounds the length shortest geodesic doubly truncated orthogeodesic that $\varepsilon$-dense given compact set surface.

In this paper the recently developed semi-analytic method to solve the free-surface wave interaction with a thin elastic plate is extended to the case of a plate of finite thickness. The method used is based on the reformulation of the differential-integral equation for this problem. The thickness of the plate is chosen such that the elastic behavior of the plate can be described by means of th...