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In model theory, a branch of mathematical logic, the diagram of a structure is a simple but powerful concept for proving useful properties of a theory, for example the amalgamation property and the joint embedding property, among others.
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The same structure can also be found in the Viterbi algorithm, used for finding the most likely sequence of hidden states. The butterfly diagram show a data-flow diagram connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT algorithm.
A cone with vertex N of a diagram D : J → C is a morphism from the constant diagram Δ(N) to D. The constant diagram is the diagram which sends every object of J to an object N of C and every morphism to the identity morphism on N. The limit of a diagram D is a universal cone to D. That is, a cone through which all other cones uniquely factor.
A similar but different notion to the amalgamation property is the joint embedding property. To see the difference, first consider the class K (or simply the set) containing three models with linear orders, L 1 of size one, L 2 of size two, and L 3 of size three. This class K has the joint embedding property because all three models can be ...
Template: Functions. ... Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Function; x ↦ f (x) History of the ...
Elements of kinematics diagrams include the frame, which is the frame of reference for all the moving components, as well as links (kinematic pairs), and joints. Primary Joints include pins, sliders and other elements that allow pure rotation or pure linear motion. Higher order joints also exist that allow a combination of rotation or linear ...
Flexibility in some joints can be increased to a certain degree by exercise, with stretching a common exercise component to maintain or improve flexibility. Limberness is the condition of having flexibility to a positive or superior degree, which is also spoken of as a person having flexibility or being flexible .
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