Schur-convex function if and only if formula_6 for all formula_7 holds for all 1≤"i"≠"j"≤"d". Schur-convex function In mathematics, a Schur-convex function, also known as S-convex, isotonic function and order-preserving function is a function formula_1 that for all formula_2 such that formula_3 is majorized by formula_4, one has that formula_5. Named after Issai Schur, Schur-convex functions are used in the study of majorization. Every function that is convex and symmetric is also Schur-convex. The opposite implication is not true, but all Schur-convex functions are symmetric (under permutations of the arguments). A function "f" is 'Schur-concave' if its negative, -"f", is Schur-convex. If "f"
Compound refractive lens Compound refractive lens A Compound refractive lens (CRL) is a series of individual lenses arranged in a linear array in order to achieve focusing of X-rays in the energy range of 5-40 keV. They are an alternative to the KB mirror. For all materials the refractive index for X-rays is close to 1, hence a single conventional lens for X-rays has an extremely long focal length (for practical lens sizes). In addition, X-rays attenuate as they pass through a material so that conventional lenses for X-rays have long been considered impractical. The CRL gets its reasonably short focal length, on