Elastic flows and gradient flows in planar curves form a vibrant area of research in geometric analysis, where curves evolve in time under rules dictated by an energy functional. Central to this ...

We can calculate the gradient of a tangent to a curve by differentiating. In order to find the equation of a tangent, we: Differentiate the equation of the curve Substitute the \(x\) value into the ...

Aim The goals of this study were to: (1) compare water conductivity and pH as proxy measures of mineral richness in relation to mollusc assemblages in fens, (2) examine the patterns of mollusc species ...

Below is the graph of a quadratic function, showing where the function is increasing and decreasing. If we draw in the tangents to the curve, you will notice that if the gradient of the tangent is ...

The occurrence and abundance of 12 canopy tree species from the moist tropical forests of West Africa have been studied in relation to a climatic gradient. We focused on environmental factors related ...