Sentence examples similar to acap I from inspiring English sources

If in addition A is ergodic [10], (C(h)) can be estimated from the volume fraction of (Acap A_{-h}), i.e. C(h)=V_{V} Acap A_{-h}), where (A_{-h}={x-h |xin A}).

It is worth noticing that (Acap B neq emptyset), i.e., the two sets may share some articles, since in general each article cites and is cited by other articles.

Now, using Theorem 2.2, we see that T has a unique fixed point in (Acap B= {0 }), i.e., 0 is the unique fixed point of T. ([5], Example 2.13).

Throughout this paper, let ({A,B}) be a partition of the set (Lambda_{n}={1,2,ldots,n}), i.e., (Acup B=Lambda_{n}) and (Acap B=emptyset).

We conclude that ACAP-A and ACACAP-Bre not essential for establishing polarity and migration during chemotaxis.

A filter on X is a nonempty family of sets (mathcal{F}subset P X)) satisfying (i) (emptysetnotinmathcal{F}), (ii) (A, Bin{mathcal{F}} ) implies that (Acap B inmathcal{F}), and (iii) for any (Ain {mathcal{F}}) and (Bsupset A ), we have (Bin{mathcal{F}}).

The excellent Annapurna Conservation Area Project (Acap) asks tourists to dress and behave modestly.

(mu_{1}) is said to be equivalent to (mu_{2}) if there exist constants α and (beta>0) and a bounded interval I such that alphamu_{1}(A lebetamu_{)lebetamu_{1}(A) quadtext{for } Ain mathfrak{B} text{ satisfying } Acap I=emptyset.

For events A and B, (I(A)) denotes the indicator function of the event A, and (I(A,B =I Acap B)).

A is said to be weakly mixing if for any (kinmathbb{N}), any choice of nonempty open subsets (V_{1},ldots,V_{k},V_{k}) of A and nonempty open subsets (U_{1},U_{2},ldots,U_{k}) of X with (Acap U_{i}neqemptyset), (i=1,2,ldots,k), there exists an (minmathbb{N}) such that (f^{m}(V_{i} cap U_{i}neqemptyset) for (1leq ileq k).

Moreover, (zin Acap B).