Sentence examples for essentially uniformly from inspiring English sources

In some cases, this complexity has given way to simplicity with the realization that certain key cell-cycle pathways are essentially uniformly deregulated in some cancer types, but by alternative mechanisms (see [ 23]).

In this paper, we shall assume that the sequence ({mathbf{f}_{epsilon_{k}}}_{k=1}^{infty}) is uniformly essentially bounded on ([0,T]).

From (27), we also see that ({hat{mathbf{z}}_{epsilon_{k}}}_{k=1}^{infty}) is uniformly essentially bounded on ([0,T]), i.e., uniformly bounded with respect to (| cdot|_{2}) on ([0,T]).

(32) Since the sequences ({mathbf{f}_{epsilon_{k}}}_{k=1}^{infty}) and ({mathbf{g}_{epsilon_{k}}}_{k=1}^{infty}) are uniformly essentially bounded on ([0,T]), from (4), we see that the sequence ({beta^_{epsilon_{k}}}_{k=1}^{infty}) is bounded, and the sequence ({mathbf{z}^_{epsilon_{k}}}_{k=1}^{infty}) is uniformly essentially bounded on ([0,T]).

It is clear that if the sequence ({mathbf{f}_{k}} _{k=1}^{infty}) is uniformly essentially bounded on ([0,T]), then it is also uniformly bounded on ([0,T]) with respect to (|cdot|_{2}), since (L^{infty}([0,T],mathbb{R})subset L^{2}([0,mathbb{R}{R})).

Since the sequence ({mathbf{f}_{epsilon_{k}}(t)}) is uniformly essentially bounded on ([0,T]), there exists a positive constant (widehat{tau}) such that (| f_{j,epsilon_{k}}| _{infty}leq widehat{tau}) for each j and k.

Given a sequence ({epsilon_{k}}_{k=1}^{infty}) in (mathbb {R}_setminus{0}) with (epsilon_{k}rightarrow0+) as (krightarrowinfty), suppose that the sequences ({mathbf{f}_{epsilon_{k}}}_{k=1}^{infty}) and ({mathbf{g}_{epsilon _{k}}}_{k=1}^{infty}) are uniformly essentially bounded on ([0,T]).

(27) Since the sequence ({mathbf{f}_{epsilon_{k}}(t)}) is uniformly essentially bounded on ([0,T]), there exists a positive constant (widehat{tau}) such that (| f_{j,epsilon_{k}}|_{infty}leqwidehat{tau}) for each j and k.

(37) Since the sequence ({mathbf{g}_{epsilon_{k}}}) is uniformly essentially bounded on ([0,T]), there exists a positive constant (widehat{zeta}) such that (| g_{i,epsilon_{k}}|_{infty}leqwidehat{zeta}) for each i and k.

Since the sequence ({mathbf{g}_{epsilon_{k}}}_{k=1}^{infty}) is uniformly essentially bounded, there exists a positive constant (widehat{zeta}) satisfying (| g_{i,epsilon_{k}}|_{infty}leqwidehat{zeta}) for each i and k.

Given a sequence ({epsilon_{k}}_{k=1}^{infty}) in (mathbb {R}_setminus{0}) with (epsilon_{k}rightarrow0+) as (krightarrowinfty), suppose that the sequences of functions ({mathbf{f}_{epsilon_{k}}}) and ({mathbf{g}_{epsilon_{k}}}) are uniformly essentially bounded on ([0,T]).