The Riemann Surface of a Static Dispersion Model and Regge Trajectories

The S-matrix in the static limit of a dispersion relation is a matrix of a finite order N of meromorphic functions of energy $\omega$ in the plane with cuts $(-\infty,-1],[+1,+\infty)$. In the elastic case it reduces to N functions $S_{i}(\omega)$ connected by the crossing symmetry matrix A. The scattering of a neutral pseodoscalar meson with an arbitrary angular momentum l at a source with spin 1/2 is considered (N=2). The Regge trajectories of this model are explicitly found.Comment: 5 pages, LaTe

On Geometry of Flat Complete Strictly Causal Lorentzian Manifolds

A flat complete causal Lorentzian manifold is called {\it strictly causal} if the past and the future of each its point are closed near this point. We consider strictly causal manifolds with unipotent holonomy groups and assign to a manifold of this type four nonnegative integers (a signature) and a parabola in the cone of positive definite matrices. Two manifolds are equivalent if and only if their signatures coincides and the corresponding parabolas are equal (up to a suitable automorphism of the cone and an affine change of variable). Also, we give necessary and sufficient conditions, which distinguish parabolas of this type among all parabolas in the cone.Comment: The exposition is revised (no essential change in the content). The paper is publishe

Modeling of liquid flow in surface discontinuities

Polymer composite and metallic materials have found wide application in various industries such as aviation, rocket, car manufacturing, ship manufacturing, etc. Many design elements need permanent quality control. Ensuring high quality and reliability of products is impossible without effective nondestructive testing methods. One of these methods is penetrant testing using penetrating substances based on liquid penetration into defect cavities. In this paper, we propose a model of liquid flow to determine the rates of filling the defect cavities with various materials and, based on this, to choose optimal control modes