The separating mechanisms occuring in a class of Poincar6 halfmaps that is induced by the flow of a saddle-focus are described quantitatively. The “critical spiral” is calculated explicitly inside the domain of the map. A complete hierarchy, consisting of three different types of separating mechanisms, is demonstrated. It is characterized in terms of the properties of the critical spiral, as it...

We propose and rigorously analyze two randomized algorithms to factor univariate polynomials over finite fields using rank 2 Drinfeld modules. The first algorithm estimates the degree of an irreducible factor of a polynomial from Euler-Poincare characteristics of random Drinfeld modules. Knowledge of a factor degree allows one to rapidly extract all factors of that degree. As a consequence, the...

A novel manner of one-legged bipedal locomotion (i.e., ballistic flip) is proposed in this paper. A flip is composed of three sequential stages: stance phase, flight phase and touchdown. During the stance phase, the two objectives of control, constant locomotive speed and taking off at the end of stance phase, are achieved via a control algorithm based on nonlinear feedback linearization. The f...

It is well known that the particles with the value of spin more than two arise naturally when quantizing such classical objects as the relativistic oscillator [1], string [2] or discrete string [3,4]. The challenging problem for these kinds of theories is to construct the lagrangian description both for free and for interacting particles with the higher spins. In order to kill ghosts and all ot...

For a Poincare-Einstein manifold under certain restrictions, X. Chen, M. Lai and F. Wang [Adv. Math. 343 (2019), pp. 16–35] proved sharp inequality relating Yamabe invariants. We show that the is true without any restriction.