Sentence examples for a scrambled set of from inspiring English sources

Then S is called a scrambled set of F if for any two distinct points (x,yin S), (i) (liminf_{ntoinfty}d(F^{n}(x),F^{n} y))=0);   (ii) (limsup_{ntoinfty}d(F^{n}(x),F^{n} y))>0).

Then S is called a scrambled set of f if for any two distinct points x, y ∈ S, (i) lim inf n → ∞ d ( f n ( x ), f n ( y ) ) = 0 ;   (ii) lim sup n → ∞ d ( f n ( x ), f n ( y ) ) > 0.  .

Then S is called a scrambled set of f if for any two distinct points x, y ∈ S, lim inf n → ∞ d ( f n ( x ), f n ( y ) ) = 0, lim sup n → ∞ d ( f n ( x ), f n ( y ) ) > 0. The map f is said to be chaotic in the sense of Li-Yorke if there exists an uncountable scrambled set S of f.

A set (Ssubseteq X) is said to be a scrambled set if for all (x,yin S), (xneq y), the ((x,y)) is a scrambled pair.

The map F is said to be chaotic in the sense of Li-Yorke if there exists an uncountable scrambled set S of F. (liminf_{ntoinfty}d(F^{n}(x),F^{n} y))=0); (limsup_{ntoinfty}d(F^{n}(x),F^{n} y))>0).

A TDS ((X,f)) is called Li-Yorke chaotic if it contains an uncountable scrambled set.

We find that a weakly mixing system always contains a dense uncountable scrambled set (see [9]).

By [9], we know that a weakly mixing system always contains a dense uncountable scrambled set.

We sorted the list by PFM score and then calculated the FDR as a function of the PFM score as the fraction of sequences exceeding the given cutoff that are members of the scrambled set.

Tyree's 32-yard catch of Eli Manning's pass from a desperate scramble set up a touchdown to beat the New England Patriots for the franchise's third Super Bowl.

Despite a critique of imperialism that reads like a scrambled "Heart of Darkness," passages set in the United States that recall a crazed reworking of Kafka's "Amerika," and even the war sections, with their echoes of "The Good Soldier Schweik," "Journey" is no political picaresque.