Convex function than convex or strictly convex functions, since they are a smaller class. Like strictly convex functions, strongly convex functions have unique minima on compact sets. A uniformly convex function, with modulus formula_70, is a function that, for all "x", "y" in the domain and , satisfies where formula_70 is a function that is non-negative and vanishes only at 0. This is a generalization of the concept of strongly convex function; by taking formula_73 we recover the definition of strong convexity. Convex function In mathematics, a real-valued function defined on an "n"-dimensional interval is called convex (or convex downward or concave
Luneburg lens one side, and formula_14 only on the other: The parameter formula_19 is a constant for any given ray, but differs between rays passing at different distances from the centre of the lens. For rays passing through the centre, it is zero. In some special cases, such as for Maxwell's fish-eye, this first order equation can be further integrated to give a formula for formula_14 as a function or formula_13. In general it provides the relative rates of change of formula_14 and formula_13, which may be integrated numerically to follow the path of the ray through the lens. Luneburg lens A