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
Refracting telescope principles. The combination of an objective lens 1 and some type of eyepiece 2 is used to gather more light than the human eye is able to collect on its own, focus it 5, and present the viewer with a brighter, clearer, and magnified virtual image 6. The objective in a refracting telescope refracts or bends light. This refraction causes parallel light rays to converge at a focal point; while those not parallel converge upon a focal plane. The telescope converts a bundle of parallel rays to make an angle α, with the optical axis to a second parallel bundle