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We extend traditional directed graphs to generalized directed graphs, making them capable of representing function structures as graphs.
Let f be its representing function.
We call f the representing function of σ.
Let σ be a connection with representing function f.
Let g be the representing function of the transpose of σ.
Let σ be a connection with representing function f and associated measure μ.
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We propose a functional concept ontology which provides a rich vocabulary representing functions together with clear definitions grounded on behavior.
[Schröder 95] describes a basis of second-generation wavelets adapted for representing functions on a sphere.
The "cross-product" of these sets of functions is now suitable for representing functions defined on a pair of hemispheres.
[Schröder 95] Schröder, P. and Sweldens, W. "Spherical Wavelets: Efficiently Representing Functions on the Sphere", Siggraph 1995.
Square waves make the system well suited for detecting and representing functions with discontinuities.
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