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In mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the inverse image of any set of the form (,) is a convex set. For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints.
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.
A real image occurs at points where rays actually converge, whereas a virtual image occurs at points that rays appear to be diverging from. 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 ...
Such an image will be magnified. In contrast, an object placed in front of a converging lens or concave mirror at a position beyond the focal length produces a real image. Such an image will be magnified if the position of the object is within twice the focal length, or else the image will be reduced if the object is further than this distance.
The notion of convexity may be generalised to other objects, if certain properties of convexity are selected as axioms. Given a set X, a convexity over X is a collection 𝒞 of subsets of X satisfying the following axioms: [9] [10] [23] The empty set and X are in 𝒞; The intersection of any collection from 𝒞 is in 𝒞.
The following are among the properties of log-concave distributions: If a density is log-concave, so is its cumulative distribution function (CDF). If a multivariate density is log-concave, so is the marginal density over any subset of variables. The sum of two independent log-concave random variables is log-concave. This follows from the fact ...
Convex and Concave - a print by Escher in which many of the structure's features can be seen as both convex shapes and concave impressions. Convex body - a compact convex set in a Euclidean space whose interior is non-empty. Convex conjugate - a dual of a real functional in a vector space. Can be interpreted as an encoding of the convex hull of ...
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [ 3 ] [ 4 ] [ 5 ] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph ∪ {\displaystyle \cup } .