A relativistic generalization of the rational Calogero model is obtained by using deformation a gauging matrix system with extra semi-dynamical variables. The Hamiltonian this derived imposing gauge fixing conditions and eliminating degrees freedom. integrability proposed proved.

Hybrid systems are dynamic systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid ...

stability and safety analysis of dams is a subject which has been studied in recent years by several researchers. researchers have used various methods and models for studying the stability of the dam. several methods are proposed for the analysis of earth dams under earthquakes. some of these methods are viscoelastic methods and semi static methods. each of these methods can be used as an appr...

We present a numerical study of a one-dimensional version of the Burridge-Knopoff model [16] of N-site chain of spring-blocks with stick-slip dynamics. Our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. It is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

We employ the relative category to develop relations between Wa\.zewski pair $(N,E)$ and Morse decomposition of maximal invariant set in $\ol{N\sm E}$ for infinite-dimensional dynamical systems. Via these relations, we can detect connecting trajectories sets obtain a dynamical-system version critical point theorem with category.

We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n + m) log n) size for n sites and m barriers. They support O(m) barrier insertions and O(n) site deletions in O((m + n) polylog (mn)) total time, an...

We show that Ribet sections are the only obstruction to the validity of the relative Manin-Mumford conjecture for one dimensional families of semi-abelian surfaces. Applications include special cases of the Zilber-Pink conjecture for curves in a mixed Shimura variety of dimension four, as well as the study of polynomial Pell equations with non-separable discriminants.