We propose two methods to find analytic periodic approximations intended for differential equations of Hill type. Here, we apply these methods on the simplest case of the Mathieu equation. The former has been inspired in the harmonic balance method and designed to find, making use on a given algebraic function, analytic approximations for the critical values and their corresponding periodic sol...

The inclusion of the linearized J2 effect in the Hill equations of relative motion gives greater insight into satellite formation flying dynamics, and the opportunity to investigate alternative feedback control strategies for the station keeping task. The work of Schweighart and Sedwick is verified and extended as time varying and analytical models are developed to incorporate the J2 perturbati...

In non-relativistic quantum mechanics, singular potentials in problems with spherical symmetry lead to a Schrödinger equation for stationary states with non-Fuchsian singularities both as r → 0 and as r → ∞. In the sixties, an analytic approach was developed for the investigation of scattering from such potentials, with emphasis on the polydromy of the wave function in the r-variable. The prese...

The relationship between extracellular Ca2+ concentration and EPSC amplitude was investigated at excitatory autapses on cultured hippocampal neurons. This relationship was steeply nonlinear, implicating the cooperative involvement of several Ca2+ ions in the release of each vesicle of transmitter. The cooperativity was estimated to be 3.1 using a power function fit and 3.3 using a Hill equation...

In cancer pharmacology (and many other areas), most dose-response curves are satisfactorily described by a classical Hill equation (i.e. 4 parameters logistical). Nevertheless, there are instances where the marked presence of more than one point of inflection, or the presence of combined agonist and antagonist effects, prevents straight-forward modelling of the data via a standard Hill equation...

Beginning in 1910, A. V. Hill performed careful experiments on the time course of heat production in isolated frog muscle. His research paralleled that of the German biochemist Otto Meyerhof, who measured the changes in muscle glycogen and lactate during contractions and recovery. For their work in discovering the distinction between aerobic and anaerobic metabolism, Hill and Meyerhof were join...