Sentence examples for periodic that from inspiring English sources

Suppose that a nonconstant meromorphic function f is periodic, that is, f ( z + η ) = f ( z ) for nonzero complex number η.

Then x is a fixed point for g, and the orbit of x is periodic, that is, X H 1 π ( x ) ( x ) = x, where π ( x ) is the period of x.

({t^{j}_{i} = t_{i+j} - t_{i}}), (jinmathbb{Z}), is equipotentially almost periodic, that is, for any (varepsilon> 0), there exists a relatively dense set (Q_{varepsilon}) of (mathbb{R}) such that for each (tauin Q_{varepsilon}) there is an integer (q inmathbb{Z}) such that (|t_{i+q}-t_{i}-tau| < varepsilon) for all (i inmathbb{Z}).

{ t i j = t i + j − t i }, i ∈ Z, j = 0, ± 1, ± 2, …  , are equipotentially almost periodic; that is, for any ϵ > 0, there exists a relatively dense set Q ϵ of R such that for each τ ∈ Q ϵ, there is an integer q ∈ Z such that | t i + q − t i − τ | < ϵ for all i ∈ Z.

We always study periodic or almost periodic problems assuming that the time scale (mathbb{T}) is periodic, that is, we always suppose the functions that describe the status of the object are periodic or almost periodic on periodic time scales (i.e., the status of the object is the same or almost the same after an accurately chosen interval; see [14] and its references).

(H3) A(n) is pseudo almost periodic and F (n, n + s) is pseudo almost periodic, that is F n, n + s) = F1(n, n + s) + F0(n, n + s), where F1(n, n + s) satisfies almost periodicity in (H30) and F0(n, n + s) satisfies lim r → ∞ 1 2 r ∑ n = - r r F 0 ( n, n + s ) | = 0 uniformly for s ∈ Z-.

Throughout this paper, the time scale T is assumed to be ω-periodic, that is, (forall tinmathbb{T}) implies (t+omegainmathbb{T}) and (mu(t+omega)=mu(t)).

We assume that (A t)) is an (N times N) real continuous matrix function defined on (mathbb{R}) and T-periodic, that is, (A(t+T) = A t)) for all (t inmathbb{R}).

He received periodic grants that indicate that he was in favour at court under Edward VI and Mary.

It wasn't just the periodic table that had to be revised.

Some may be bioluminescent or form periodic blooms that may colour water yellow or red.