Biconvex Shell
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Biconvex Shell
Biconvex may refer to: * Biconvex bipartite graph * Biconvex lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ... * Biconvex optimization {{disambig ...
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Convex Bipartite Graph
In the mathematical field of graph theory, a convex bipartite graph is a bipartite graph with specific properties. A bipartite graph, (''U'' ∪ ''V'', ''E''), is said to be convex over the vertex set ''U'' if ''U'' can be enumerated such that for all ''v'' ∈ ''V'' the vertices adjacent to ''v'' are consecutive. Convexity over ''V'' is defined analogously. A bipartite graph (''U'' ∪ ''V'', ''E'') that is convex over both ''U'' and ''V'' is said to be biconvex or doubly convex. Formal definition Let ''G'' = (''U'' ∪ ''V'', ''E'') be a bipartite graph, i.e., the vertex set is ''U'' ∪ ''V'' where ''U'' ∩ ''V'' = ∅. Let ''N''''G''(''v'') denote the neighborhood of a vertex ''v'' ∈ ''V''. The graph ''G'' is convex over ''U'' if and only if there exists a bijective In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invert ...
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Lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), usually arranged along a common axis. Lenses are made from materials such as glass or plastic, and are ground and polished or molded to a desired shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called lenses, such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses. Lenses are used in various imaging devices like telescopes, binoculars and cameras. They are also used as visual aids in glasses to correct defects of vision such as myopia and hypermetropia. History The word ''lens'' comes from '' lēns'', the Latin name of the lentil (a seed of a lentil plant), b ...
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