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The object pool design pattern is used in several places in the standard classes of the .NET Framework. One example is the .NET Framework Data Provider for SQL Server. As SQL Server database connections can be slow to create, a pool of connections is maintained. Closing a connection does not actually relinquish the link to SQL Server.
The following is an example of a class with lazy initialization implemented in ActionScript: ... import java.util.Map; ... types. entrySet ()) ...
In Haskell, the polymorphic function map :: (a -> b) -> [a] -> [b] is generalized to a polytypic function fmap :: Functor f => (a -> b) -> f a -> f b, which applies to any type belonging the Functor type class. The type constructor of lists [] can be defined as an instance of the Functor type class using the map function from the previous example:
For example, the real projective space of dimension , where is a power of two, requires = for an embedding. However, this does not apply to immersions; for instance, R P 2 {\displaystyle \mathbb {R} \mathrm {P} ^{2}} can be immersed in R 3 {\displaystyle \mathbb {R} ^{3}} as is explicitly shown by Boy's surface —which has self-intersections.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.
This is an example of an endomorphism that is not an automorphism. In mathematics, an endomorphism is a morphism from a mathematical object to itself. An endomorphism that is also an isomorphism is an automorphism. For example, an endomorphism of a vector space V is a linear map f: V → V, and an endomorphism of a group G is a group ...
A bilinear map is a function: such that for all , the map (,) is a linear map from to , and for all , the map (,) is a linear map from to . In other words, when we hold the first entry of the bilinear map fixed while letting the second entry vary, the result is a linear operator, and similarly for when we hold the second entry fixed.
A map, sometimes referred to as a dictionary, consists of a key/value pair. The key is used to order the sequence, and the value is somehow associated with that key. For example, a map might contain keys representing every unique word in a text and values representing the number of times that word appears in the text.