Sentence examples for there exists a time from inspiring English sources

Due to the integrability of (1.5), we conclude that for any small constant, there exists a time such that (2.17).

So there exists a time (t_{l+1}) such that (Vert boldsymbol{x}(t) Vert _{infty }^{ underline{boldsymbol{upsilon }}}leq delta^{l+1}beta Vert boldsymbol{x}(0) Vert _{ infty }^{underline{boldsymbol{upsilon }}}).

Moreover, for the particular price trajectory S, there exists a time T 0 at which one can make the strictly positive profit (V^{mathbf {S}}_{boldsymbol {xi }}(T_{0})>0}.

So there exists a time T, such that when t > T, ∫ − ∞ q ( x 0, t ) e ξ y ( ξ, t ) d ξ > 0. This completes the proof for Case 4. Remark 3.2 Scrutinizing the proof, we find that the condition of ρ 0 ( x ) guarantees that Claim 3 holds.

Secondly now assume that (u_{i}(t)) is oscillatory about (tilde{M}_{i}) for (tgeq T_{1}^), that is, there exists a time sequence ({t_{n}}) such that (tau< t_{i}

Assume the following conditions hold: (1) (S t)) has a bounded absorbing set (Bsubset H), i.e., for any bounded set (Asubset H) there exists a time (t_{A} >0) such that (S t)varphiin B), (forallvarphiin A) and (t>t_{A}),   (2) (S t)) is uniformly compact, i.e., for any bounded set (U subset H) and some (T > 0) sufficiently large, the set (overline {bigcup_{tgeq T}S t)U}) is compact in H.  .

For example, the phase of the reverberant speech (varPhi _{r_{i}}) could be different from the phase of reconstructed signal (varPhi _{s_{i}}), because for a spectrogram-like matrix in the time-frequency domain, it is not guaranteed there exists a time-domain signal whose STFT is equal to that matrix [25].

Then by virtue of Proposition 3.1, there exist a time T* ∈ (0, T) and a unique strong solution (ρ δ, u δ, w δ ) in [0, T * ] × Ω to the problem (1 -(4) with the initial data replaced by ( ρ 0 δ, u 0 δ, w 0 δ ).

where J=N M is the dimension of received data, and there exists a time-consuming eigen decomposition of MSMB at the beginning of this algorithm.

We need only to prove that there exist a time scale T 0 and a function A from T 0 to B ( X ) with V ( A ) ⊆ M such that equation (1) either has no solution or has at least two solutions on  T 0. Take A 0 ∈ M ∖ U, then there exists λ > 0 such that − λ ∈ σ ( A 0 ).

Whether there exist a time interval for which the cross-feeding genotype does better than the non-cross feeding genotype (X t)>Xc(t)) depends on a range of assumptions regarding the nature of the trade-off between the cost of cooperation and the benefit to the recipient, the initial population densities as well as the values of the intrinsic growth rates and/or the benefit of cross-feeding.