A first problem is whether it is possible to reduce the infinity inherent in the hierarchical account into a workable finite definition.
For more information about finite definitions, see Martinez 2001 and Gupta 2006.
The definition a finite number of targets requires the discretization of continuous property scores into a finite number of nominal or ordinal levels.
Here we adopt a simple finite difference definition for post rate given by post rate = (#posts − #posts(τ/2)) / (τ/2); of course, more robust rate estimates could be used.
One was a trivial definition for a finite language; it simply listed the finitely many true sentences.
The following statements offer an alternative definition for bisimulation, which is easily shown to be equivalent to the one presented in Definition 2.5 and is useful in the subsequent development: Definition 2.6: A finite partition Φ: S → P of the state space S of transition system T = (S, →, Y, h) naturally induces a quotient transition system T/~ = (P, →~, Y, h~) of T provided that.
It provides the definition of a finite state machine and explains the way a state machine is defined as a Mealy machine or a Moore machine.
In particular, we introduce a new definition of a finite chirp which is slightly more general than those that have been previously used.
By the definition of a finite element subspace, the finite element discretization of (9 - 11) is as follows: compute ( y h, u h ) ∈ V h × K h such that min u h ∈ K h { ∫ 0 T ( 1 2 ∥ y h − y 0 ∥ 2 + α 2 ∥ u h ∥ 2 ) } (17).
Definition 1.2 A finite collection of random variables X1, X2,..., X n is said to be NA if for every pair of disjoint subsets A1, A2 of {1, 2,..., n}, Cov f X i : i ∈ A 1, g X j : j ∈ A 2 ≤ 0, whenever f and g are coordinatewise nondecreasing such that this covariance exists.
Definition 1.2 A finite collection of random variables X1, X2,..., X m is said to be associated if Cov { f ( X 1, X 2, …, X m ), g ( X 1, X 2, …, X m ) } ≥ 0. for any two componentwise nondecreasing functions f, g on R m such that the covariance is defined.
