Real image (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays of light are represented by dashed lines. A real image occurs where rays converge, whereas a virtual image occurs where rays only "appear" to converge. Real images can be produced by concave mirrors and converging lenses, only if the object is placed further away from the mirror/lens than the focal point and this real image is inverted. As the object approaches the focal point the image approaches infinity, and when the object passes the focal point the image
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