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...

In 1953 Casimir proposed a semiclassical model for the electron based on the concept that net inward radiation pressure from the electromagnetic vacuum fluctuations fields (as in the Casimir effect, generally) might play the role of Poincare stresses, compensating outward coulomb pressure to yield a stable configuration at small dimensions. Given that in scattering experiments the electron appe...

Consideration is given to a basic food chain model satisfying the trophic time diversification hypothesis which translates the model into a singularly perturbed system of three time scales. It is demonstrated that in some realistic system parameter region, the model has a unimodal or logistic-like Poincare return map when the singular parameter for the fastest variable is at the limiting value ...

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.