Logarithmically concave function Logarithmically concave function In convex analysis, a non-negative function is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all and . If is strictly positive, this is equivalent to saying that the logarithm of the function, , is concave; that is, for all and . Examples of log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly, a function is log-convex if it satisfies the reverse inequality for all and . Log-concave distributions are necessary for a
Lens clock clock can be used if a dial thickness gauge is not available. To do this, the contact lens is placed concave side up on a table or other hard surface. The lens clock is then brought down on it such that the center prong contacts the lens as close to its center as possible, and the outer prongs rest on the table. The thickness of the lens is then the sagitta formula_4 in the formula above, and can be calculated from the optical power reading, if the distance between the outer prongs is known. Lens clock A lens clock is