Sentence examples for some time scales from inspiring English sources
By using the results in this paper, the problem can be considered on more irregular time scales including some time scales with (mu (t)rightarrow +infty ) as (trightarrow +infty ).
Note that the inversion of a Fourier transformation on some time scales was studied in [19, 20], but there is no inversion formula for an arbitrary time (space) scale.
When energy increases in supply, a population may grow [13], but energy supply may be approximately fixed over some time scales.
Then, X1 t) may blow up to infinity and X2 t) may go to zero at some time scales.
As given in [ 9], in the reaction network involving ∅→ S1, ∅→ S2, ∅→ S3, S1 + S2→ ∅, and S1 + S3→ ∅, convergence of the limit for the scaled species numbers may not be guaranteed at some time scales.
In what follows, Z i γ is a limit of the scaled species number of S i at some time scales depending on γ, and as γ gets larger the times are in the later stage.
In the light of these studies, let us introduce some time scale and measure theoretic notations.
Lemma 2.5 Let T be some time scale and f ( t, y ) = A ( t ) y + g ( t ), where A : T → B ( X ) and y, g : T → X.
Corollary 2.6 Let T be some time scale, f ( t, y ) = A ( t ) y + g ( t ) be the right-hand side of equation (2).
Suppose consumption (c(t)) takes place on some time scale (mathbb {T}_{c}), income (y(t)) arrives on a time scale (mathbb{T}_{y}), and assets/debts accrue on (mathbb{T}_{a}).
