Canonical Model (other)
Canonical model may refer to: *Canonical model, a design pattern used to communicate between different data formats * Canonical ring in mathematics * in modal logic * Relative canonical model in mathematics See also * Canonical ensemble In statistical mechanics, a canonical ensemble is the statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. The system can exchange energy with the hea ...

Canonical Model
A canonical model is a design pattern used to communicate between different data formats. Essentially: create a data model which is a superset of all the others ("canonical"), and create a "translator" module or layer to/from which all existing modules exchange data with other modules. The canonical model acts as a middleman. Each model now only needs to know how to communicate with the canonical model and doesn't need to know the implementation details of the other modules. Details A form of enterprise application integration, it is intended to reduce costs and standardize on agreed data definitions associated with integrating business systems. A canonical model is any model that is canonical in nature, meaning a model that is in the simplest form possible based on a standard enterprise application integration (EAI) solution. Most organizations also adopt a set of standards for message structure and content (message payload). The desire for consistent message payload resul ...
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Canonical Ring
In mathematics, the pluricanonical ring of an algebraic variety ''V'' (which is nonsingular), or of a complex manifold, is the graded ring :R(V,K)=R(V,K_V) \, of sections of powers of the canonical bundle ''K''. Its ''n''th graded component (for n\geq 0) is: :R_n := H^0(V, K^n),\ that is, the space of sections of the ''n''-th tensor product ''K''''n'' of the canonical bundle ''K''. The 0th graded component R_0 is sections of the trivial bundle, and is one-dimensional as ''V'' is projective. The projective variety defined by this graded ring is called the canonical model of ''V'', and the dimension of the canonical model is called the Kodaira dimension of ''V''. One can define an analogous ring for any line bundle ''L'' over ''V''; the analogous dimension is called the Iitaka dimension. A line bundle is called big if the Iitaka dimension equals the dimension of the variety. Properties Birational invariance The canonical ring and therefore likewise the Kodaira dimension is a b ...
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Relative Canonical Model
In the mathematical field of algebraic geometry, the relative canonical model of a singular variety of a mathematical object where X is a particular canonical variety that maps to X, which simplifies the structure. Description The precise definition is: If f:Y\to X is a resolution define the adjunction sequence to be the sequence of subsheaves f_*\omega_Y^; if \omega_X is invertible f_*\omega_Y^=I_n\omega_X^ where I_n is the higher adjunction ideal. Problem. Is \oplus_n f_*\omega_Y^ finitely generated? If this is true then Proj \oplus_n f_*\omega_Y^ \to X is called the ''relative canonical model'' of Y, or the ''canonical blow-up'' of X. Some basic properties were as follows: The relative canonical model was independent of the choice of resolution. Some integer multiple r of the canonical divisor of the relative canonical model was Cartier and the number of exceptional components where this agrees with the same multiple of the canonical divisor of Y is also independ ...
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