A ball is propelled through a random environment of obstacles oo which it rebounds with perfect reeection. What is the behaviour of the trajectory of the ball? We summarise known mathematical results concerning this model, which we calìstochastic pin-ball', and which is known also as a `Lorentz lattice gas' and a version of which is sometimes termed thèEhrenfest wind{tree model'. The rigorous t...

Although the sport of lacrosse has evolved dramatically over the last few decades and is presently the fastest growing team sport in the United States, the current specifications for balls date back to 1943. The purpose of this study was to see if various commercially available field lacrosse balls meet these specifications and to determine additional mechanical properties of the ball that may ...

This paper addresses questions of quasi-isometric rigidity and classification for fundamental groups of finite graphs of groups, under the assumption that the BassSerre tree of the graph of groups has finite depth. The main example of a finite depth graph of groups is one whose vertex and edge groups are coarse Poincare duality groups. The main theorem says that, under certain hypotheses, if G ...

The aim of the study was to determine if heart rate variability (HRV) showed any changes in patients with newly diagnosed epilepsy in comparison with controls. Sixty-five patients with epilepsy (38 males and 27 females), aged 30-50 years, who had never previously received treatment with antiepileptic drugs were eligible for inclusion in this study. Resting electrocardiogram (ECG) at spontaneous...

This paper investigates the control of a bouncing ball using Model Predictive Control. Bouncing ball is a benchmark problem for various rhythmic tasks such as juggling, walking, hopping and running. Humans develop intentions which may be perceived as our reference trajectory and tries to track it. The human brain optimizes the control effort needed to track its reference; this forms the central...

In the Bjorken limit of the present theory of deep inelastic scattering (DIS) the structure functions (up to anomalous dimensions and perturbative QCD corrections) are described by the parton model. However the current operator in the parton model does not properly commute with the representation operators corresponding to the Lorentz group, space reflection and time reversal. To investigate th...

A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators, to the anyon model with free phase space that is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is des...