This paper presents a method for under-approximating behavioural models with the guarantee that the abstract paths can be instantiated as executions of the models. This allows a model-based testing approach to operate on an abstraction of an infinite or very large behavioural model. We characterize the abstract transitions as may, must+ or must-. This allows us to benefit from Thomas Ball’s res...

existence of periodic solutions for non-linear third order autonomous differential equation (o.d.e.) has not been investigated to as large an extent as non-linear second order. the popular poincare-bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). this conclusion opens a way for further investigation.

the ball and beam system is one of the most popular laboratory setups for control education. in this paper, we design a fuzzy pd cascade controller for a ball and beam system using asexual reproduction optimization (aro) technique. the ball & beam system consists of a servo motor, a grooved beam, and a rolling ball. this system utilizes a servo motor to control ball’s position on the beam. chan...

A novel model for 3D soccer ball tracking is proposed, using multiple fixed cameras as input. The main problems are: successfully filtering false alarms, tracking through missing observations and estimating 3D positions from single or multiple camera inputs. The key innovation is to categorise all motion of the ball into four possible phases – rolling, flying, in possession, and out of play, an...

Closed timelike curves, along which an object can travel to its past, are interesting because they predicted by general relativity and yet need be reconciled with quantum mechanics. The authors consider a model of paradox where billiard ball two trajectories: one unperturbed the other it collide past.