Convex set polygon is sometimes called a concave polygon, and some sources more generally use the term "concave set" to mean a non-convex set, but most authorities prohibit this usage. The complement of a convex set, such as the epigraph of a concave function, is sometimes called a "reverse convex set", especially in the context of mathematical optimization. If is a convex set in -dimensional space, then for any collection of , , -dimensional vectors in , and for any nonnegative numbers such that , then one has: A vector of this type is known as a convex combination of . The
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.