A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD o...

This paper describes a revision of the Hill-type muscle model so that it will describe the chemo-mechanical energy conversion process (energetic) and the internal-element stiffness variation (viscoelastic) during a skeletal muscle isometric force twitch contraction. The derivation of this energetic-viscoelastic model is described by a first-order linear ordinary differential equation with const...

A new approach has been developed to study binding of a ligand to a macromolecule based on the diffusion process. In terms of the Fick's first law, the concentration of free ligand in the presence of a protein can be determined by the measurement of those ligands which are diffused out. This method is applied to the study of binding of methyl-orange to lysozyme in phosphate buffer of pH 6.2, at...

In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous cells, whose proliferation is controled by growth factors diffusing in the extracellular medium and binding to the cell surface. We extend the results on the e...

Pharmacology started to develop into a real quantitative science in 1909, when A.V. Hill derived the Langmuir equation in the course of his studies on nicotine and curare. A history of the developments since then shows both brilliant insights and missed opportunities. It also shows that much remains to be done. There is still no mathematical description that can describe quantitatively the acti...

Inulosucrases catalyze transfer of a fructose moiety from sucrose to a water molecule (hydrolysis) or to an acceptor molecule (transferase), yielding inulin. Bacterial inulin production is rare and a biochemical analysis of inulosucrase enzymes has not been reported. Here we report biochemical characteristics of a purified recombinant inulosucrase enzyme from Lactobacillus reuteri. It displayed...