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Given a set of functional dependencies , an Armstrong relation is a relation which satisfies all the functional dependencies in the closure + and only those dependencies. . Unfortunately, the minimum-size Armstrong relation for a given set of dependencies can have a size which is an exponential function of the number of attributes in the dependencies conside
[1]: 224–229 If attribute 1 is utility-independent of attribute 2, then the utility function for every value of attribute 2 is a linear transformation of the utility function for every other value of attribute 2. Hence it can be written as: (,) = + (,) when is a constant value for attribute 2. Similarly, If attribute 2 is utility-independent ...
The problem arises from attempts to account for the phenomenon of similarity or attribute agreement among things. [4] For example, grass and Granny Smith apples are similar or agree in attribute, namely in having the attribute of greenness. The issue is how to account for this sort of agreement in attribute among things.
U+0085: this is the only C1 control character accepted in both XML 1.0 and XML 1.1 (it is treated as whitespace or line-break in many contexts); U+00A0–U+D7FF, U+E000–U+FDCF, U+FDF0–U+FFFD: this includes all the other characters in the BMP, excluding all non-characters (such as surrogates);
In mathematics, the projective unitary group PU(n) is the quotient of the unitary group U(n) by the right multiplication of its center, U(1), embedded as scalars.Abstractly, it is the holomorphic isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space.
The above map U(n) to U(1) has a section: we can view U(1) as the subgroup of U(n) that are diagonal with e iθ in the upper left corner and 1 on the rest of the diagonal. Therefore U(n) is a semidirect product of U(1) with SU(n). The unitary group U(n) is not abelian for n > 1. The center of U(n) is the set of scalar matrices λI with λ ∈ U ...
In computer science, an attributed graph grammar is a class of graph grammar that associates vertices with a set of attributes and rewrites with functions on attributes. In the algebraic approach to graph grammars, they are usually formulated using the double-pushout approach or the single-pushout approach.
Definition 1. A unitary operator is a bounded linear operator U : H → H on a Hilbert space H that satisfies U*U = UU* = I, where U* is the adjoint of U, and I : H → H is the identity operator. The weaker condition U*U = I defines an isometry. The other weaker condition, UU* = I, defines a coisometry.