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The Milnor–Thurston kneading theory is a mathematical theory which analyzes the iterates of piecewise monotone mappings of an interval into itself. The emphasis is on understanding the properties of the mapping that are invariant under topological conjugacy.
The term natural mapping comes from proper and natural arrangements for the relations between controls and their movements to the outcome from such action into the world. The real function of natural mappings is to reduce the need for any information from a user’s memory to perform a task.
These maps are quasisymmetric, although they are a much narrower subclass of quasisymmetric maps. For example, while a general quasisymmetric map in the complex plane could map the real line to a set of Hausdorff dimension strictly greater than one, a δ-monotone will always map the real line to a rotated graph of a Lipschitz function L:ℝ → ...
In order theory, a branch of mathematics, an order embedding is a special kind of monotone function, which provides a way to include one partially ordered set into another. Like Galois connections , order embeddings constitute a notion which is strictly weaker than the concept of an order isomorphism .
The locality property of the Hilbert curve has also been used to design algorithms for exploring regions with mobile robots [6] [7] and indexing geospatial location data. [ 8 ] In an algorithm called Riemersma dithering, grayscale photographs can be converted to a dithered black-and-white image using thresholding, with the leftover amount from ...
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.
In design space approximation, one is not interested in finding the optimal parameter vector, but rather in the global behavior of the system. Here the surrogate is tuned to mimic the underlying model as closely as needed over the complete design space. Such surrogates are a useful, cheap way to gain insight into the global behavior of the system.
For example, if is a field, then for every vector space over we have a "natural" injective linear map from the vector space into its double dual. These maps are "natural" in the following sense: the double dual operation is a functor, and the maps are the components of a natural transformation from the identity functor to the double dual functor.