Convex function Convex function In mathematics, a real-valued function defined on an "n"-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set. For a twice differentiable function of a single variable, if the second derivative is always greater than or equal to
Compound refractive lens the order of meters, by using many lenses in series. To minimize the absorption the lens must be made from a material such as aluminium, beryllium, or lithium. CRLs were first demonstrated in the mid-1990s by a group of scientists at the ESRF. They drilled holes in an aluminium block, and achieved focusing in two dimensions. For X-rays a concave lens focuses the X-rays because the index of refraction is slightly below unity. In a CRL of this type the walls between the cylindrical holes act as concave lenses for X-rays traveling perpendicular to the axis of the drilled cylinders.