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In mathematics, the vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y , for each unique input, x . If a vertical line intersects a curve on an xy -plane more than once then for one value of x the curve has more than one value of y , and so, the curve does not ...
An introduction to categorical approaches to algebraic topology: the focus is on the algebra, and assumes a topological background. Ronald Brown "Topology and Groupoids" pdf available Gives an account of some categorical methods in topology, use the fundamental groupoid on a set of base points to give a generalisation of the Seifert-van Kampen ...
A cloze test (also cloze deletion test or occlusion test) is an exercise, test, or assessment in which a portion of text is masked and the participant is asked to fill in the masked portion of text. Cloze tests require the ability to understand the context and vocabulary in order to identify the correct language or part of speech that belongs ...
In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms f : X → Z and g : Y → Z with a common codomain.
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The numerical solution to the linear test equation decays to zero if | r(z) | < 1 with z = hλ. The set of such z is called the domain of absolute stability. In particular, the method is said to be absolute stable if all z with Re(z) < 0 are in the domain of absolute stability. The stability function of an explicit Runge–Kutta method is a ...
Let : be a smooth map between smooth manifolds and .Then there is an associated linear map from the space of 1-forms on (the linear space of sections of the cotangent bundle) to the space of 1-forms on .
Let (,) be a topological space; let () denote the Borel σ-algebra on , i.e. the smallest sigma algebra on that contains all open sets . Let be a measure on (, ()) Then the support (or spectrum) of is defined as the set of all points in for which every open neighbourhood of has positive measure: ():= {: (() >)}.
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