If \ mathbf { b } ( \ boldsymbol \ theta ) is the identity function, then the distribution is said to be in canonical form ( or " natural form " ).
32.
The canonical Gaussian cylinder set measure on an infinite-dimensional Hilbert space can never be a " bona fide " measure; equivalently, the identity function on such a space cannot be " & gamma; "-radonifying.
33.
If the random variable is itself real-valued, then moments of the variable itself can be taken, which are equivalent to moments of the identity function f ( X ) = X of the random variable.
34.
In fact, the NULL cipher does not perform any encryption ( i . e . the encryption algorithm functions as the identity function, and copies the input stream to the output stream without any changes ).
35.
Where " n " ?" n " matrices are used to represent linear transformations from an " n "-dimensional vector space to itself, " I n " represents the identity function, regardless of the basis.
36.
SWIFT focuses on extending identity functions and federation to the network while addressing usability and privacy concerns and leverages identity technology as a key to integrate service and transport infrastructures for the benefit of users and the providers.
37.
In general, the intersection number of the graph of a function with the diagonal may be computed using homology via the Lefschetz fixed point theorem; the self-intersection of the diagonal is the special case of the identity function.
38.
Let I be the identity function on R . Let j be the function on R such that j ( x ) = 1 / x for each nonzero number x, and j ( 0 ) = 0.
39.
Since the notion of functions acting on a set always includes the notion of an identity function, which when applied to the set does nothing, a transformation semigroup can be made into a monoid by adding the identity function.
40.
Since the notion of functions acting on a set always includes the notion of an identity function, which when applied to the set does nothing, a transformation semigroup can be made into a monoid by adding the identity function.
