The value of models and modelling to traditional scientific research is well documented (Black 1962). Models are important in scientific research both in formulating hypotheses to be tested and in describing scientific phenomena (Gilbert, J. 1995). In the past decade the value of models and modelling to science education has been increasingly recognized among the science education reform moveme...

In Andean lakes a distinctive assemblage of large mixotrophic ciliates (>80 μm), dominated by the peritrich Ophrydium naumanni Pejler and the heterotrich Stentor araucanus Foissner & Wölfl, has been previously reported (Wölfl, 1995; Modenutti, 1997; Queimaliños et al., 1999; Modenutti et al., 2000). These two species have been found only in large, deep ultra-oligotrophic lakes (area >5 km2, Zma...

An extended Landau-Lifshitz-Gilbert (LLG) equation is introduced to describe the dynamics of inhomogeneous magnetization in a current-carrying wire. The coefficients of all the terms in this equation are calculated quantum-mechanically for a simple model which includes impurity scattering. This is done by comparing the energies and lifetimes of a spin wave calculated from the LLG equation and f...

For an optimal control problem with fixed initial state and constraints on admissible controls we propose new second-order necessary optimality conditions using second-order tangents to the set of controls. In the absence of constraints on controls, our conditions are stronger than those of Gilbert and Bernstein (1983). Then, we investigate optimal control problems with fixed initial state and ...