Sentence examples for mappings as defined from inspiring English sources

The uncertainties derived by the individual character of the agents in election situations are described with the help of fuzzy random mappings, as defined by Huang [10].

Theorem 3.2 Let E and K be as defined above, T i ( i ∈ I ) be N asymptotically pseudo-contractive mappings as defined above and satisfying condition ( C ¯ ) and { α n } be a sequence of real numbers as in Lemma  3.1.

Let (S,T Crightarrow C) be two further generalized hybrid mappings, as defined in (1.3), which satisfy (alpha+beta +gamma +deltageq0), (varepsilongeq0) and either (alpha+beta>0) or (alpha +gamma>0).

Let H be a real Hilbert space, and let C be a nonempty subset of H. Let (S,T Crightarrow C) be two further generalized hybrid mappings as defined in (1.3) which satisfy (alpha+beta +gamma +deltageq0), (varepsilongeq0) and either (alpha+beta>0) or (alpha +gamma>0).

Theorem 3.3 Let E and K be as defined above, and let T i ( i ∈ I ) be N asymptotically pseudo-contractive mappings as defined above such that one of the mappings in { T i } i = 1 N is semicompact, and let { α n } be a sequence of real numbers as in Lemma  3.1.

By putting α 1 j = λ j and α 2 j = 0, for all j = 1, 2, …, N, we see that the S-mapping reduces to the K-mapping as defined in Definition 2.2.

For the sake of simplicity, we take the same parameters (alpha,beta,gamma,delta,varepsiloninmathbb{R}) for the two further generalized hybrid mappings S, T as defined in (1.3).

Here we take a fundamentally different approach, discounting the names of regions and instead comparing their definitions as spatial entities in an effort to provide more precise quantitative mappings between anatomical entities as defined by different atlases.

Definition 1.1 Let the sets X, E and F and the mappings S and T be as defined above.

These include the long-range interaction networks in protein structure [ 44], the metabolic network of E. coli as defined by atomic mappings [ 45], the KSHV PPI network [ 46], the global network of Avian Influenza outbreaks [ 47], the sequence-based chemoinformatics threshold networks for drug target [ 48], and the network for phenolic secondary metabolism of T. cacao [ 49].

Let X, E, and F be the sets and the mappings S, T, η, and h be as defined above.