We give a complete classification of the phase portraits in Poincare´ disk for cubic polynomial systemsx˙=1−x−axy2,y˙=−by+axy2, R2 according with values its two parameters and b. These differential systems correspond to Gray-Scott model. Moreover we provide bifurcation diagram parameter plane (a,b) these systems.

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on Moyal plane. The Drinfeld twist, which plays a key mathematical role in this construction, is then applied to case discrete groups, with view geons gravity. Poincare-twisted can also be study CMB anisotropies, corrections power spectrum are used put constraints spacetime noncommutativity....

Recently we have shown that (3+1)-dimensional expanding universe appears dynamically and uniquely from the Lorentzian version of the IIB matrix model, which is considered as a nonperturbative formulation of superstring theory. Similarly, it is possible that the Standard Model appears uniquely at the electroweak scale from the same model at late times. In order to pursue such a possibility, we d...

For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M, N ; f) of continuous maps homotopic to f : M → N . We will show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f , denoted Λf,f , equals zero. Since Λf,f is equal to ...

The spring-driven ball-type check valve is one of the most important components of hydraulic systems: it controls the position of the ball and prevents backward flow. To simplify the structure, the spring must be eliminated, and to accomplish this, the flow pattern and the behavior of the check ball in L-shaped pipe must be determined. In this paper, we present a full-scale model of a check bal...

A mathematical model is developed for a mobile robot with three ball-wheels. The resulting model turns out to be a Chaplygin system, which allows the dynamics equations and the kinematic constraints to be integrated separately. The system is driven by six actuators: one actuator connected to one roller of each wheel, and three more actuators controlling the orientation of the ball-carriers with...

Two control schemes have been hypothesized for the manual interception of fast visual targets. In the model-free on-line control, extrapolation of target motion is based on continuous visual information, without resorting to physical models. In the model-based control, instead, a prior model of target motion predicts the future spatiotemporal trajectory. To distinguish between the two hypothese...

In this note we consider a method of generating functions for systems with constraints and, as an example, we prove that the billiard mappings for billiards on the Euclidean space, sphere, and the Lobachevsky space are sympletic. Further, by taking a quadratic generating function we get the skew-hodograph mapping introduced by Moser and Veselov, which relates the ellipsoidal billiards in the Eu...

We suggest to use " minimal " choice of quantum gravity theory, that is the quantum field theory, in which space-time is seen as Rie-mannian space and metrics (or vierbein field) is the dynamical variable. We then suggest to use the simplest acceptable action, that is the squared curvature action. The correspondent model is renor-malizable, has the correct classical limit and can be explored us...

We propose a model-based reinforcement learning algorithm for biped walking in which the robot learns to appropriately place the swing leg. This decision is based on a learned model of the Poincare map of the periodic walking pattern. The model maps from a state at the middle of a step and foot placement to a state at next middle of a step. We also modify the desired walking cycle frequency bas...