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Detail of the chandelier and mirror from Jan van Eyck's 1434 Arnolfini Portrait, one of Hockney's key examples. In his book Secret Knowledge (2001), Hockney argues that early Renaissance artists such as Jan van Eyck and Lorenzo Lotto used concave mirrors; as evidence, he points to the chandelier in Van Eyck's Arnolfini Portrait, the ear in Van ...
Examples of real images include the image produced on a detector in the rear of a camera, and the image produced on an eyeball retina (the camera and eye focus light through an internal convex lens). In ray diagrams (such as the images on the right), real rays of light are always represented by full, solid lines; perceived or extrapolated rays ...
Every real-valued affine function, that is, each function of the form () = +, is simultaneously convex and concave. Every norm is a convex function, by the triangle inequality and positive homogeneity .
The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
A concave mirror, or converging mirror, has a reflecting surface that is recessed inward (away from the incident light). Concave mirrors reflect light inward to one focal point. They are used to focus light. Unlike convex mirrors, concave mirrors show different image types depending on the distance between the object and the mirror.
Based on a Robert Harris novel, the thriller "Conclave," starring Ralph Fiennes and Stanley Tucci, re-creates the secret process of electing a pope.
For example, the square of the gambler's fortune in the fair coin game is a submartingale (which also follows from the fact that X n 2 − n is a martingale). Similarly, a concave function of a martingale is a supermartingale.
That book is heavier than the dictionary. I could sleep forever. I have too much on my plate. Check out that mountain of books on my bedside table. The line at the grocery store was like Disney World.