We undertake a case study of two series of nonclassical Zariski geometries. We show that these geometries can be realised as representations of certain noncommutative C∗-algebras and introduce a natural limit construction which for each of the two series produces a classical U(1)-gauge field over a 2-dimensional Riemann surface.

Errors are found in example problems from Henri Poincaré’s paper “Mémoire sur les courbes définies par une équation différentielle.” Examples four and five from chapter seven and examples one, two, and three from chapter nine do not have the limit cycles at infinity predicted by Poincaré. Instead they have fixed points at every point at infinity. In order to understand the errors made by Poinca...

Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the MichaelisMenten equation (Porter & Trager, 1977). When used in conjunction with the modified form of the direct linear plot (Cornish-Bowden & Eisenthal, 1978), they prove to be more robust than least-squares confidence limits. In circumstances where the least-squares as...

Separatrix cycles for a planar quadratic vector field are studied. The results obtained are used to show that in any bounded region of the plane a quadratic vector field has at most a finite number of limit cycles.

software with confidence limits and Bayes (predicted value) calculations.

Per vehicle crash involvement rates were compared for otherwise identical vehicle models with and without electronic stability control (ESC) systems. ESC was found to affect single-vehicle crashes to a greater extent than multiple-vehicle crashes, and crashes with fatal injuries to a greater extent than less severe crashes. Based on all police-reported crashes in 7 states over 2 years, ESC redu...

Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems, are extended to continuous piecewise– linear differential systems. Then we obtain new results on the existence and uniqueness of limit cycles for systems with three linearity zones and without symmetry. We also reprove existing results of systems with two linearity zones giving shorter and ...