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"
Crepuscular rays Crepuscular rays Crepuscular rays (more commonly known as sunbeams, sun rays, splintered light, or god rays), in atmospheric optics, are rays of sunlight that appear to radiate from the point in the sky where the Sun is located. Shining through openings in clouds (particularly stratocumulus) or between other objects, these columns of sunlit particulates are separated by darker cloud-shadowed volumes. Despite seeming to converge toward the light source, the rays are in fact near-parallel shafts of sunlight. Their apparent convergence is a perspective effect. This phenomenon mimics the way parallel railway lines or long hallways, for example, seem to seek