Sentence examples for especially there exist from inspiring English sources

Especially, there exist at least two radially symmetric positive solutions for 0 < λ < λ ∗.

Especially, there exist constants μ ≥ 1 and C such that ∫ B ( x, t r ) V ( y ) d y ≤ C t d μ ∫ B ( x, r ) V ( y ) d y (3).

Especially, there exist lots of papers focused on studying the following Kirchhoff-type equations: begin{cases} - (a+bint_{Omega} vert nabla uvert ^{2},mathrm {d}x )Delta u= f x,u quad mbox{in } Omega, u|_{partialOmega}=0, end{cases} (1.1) where f is a continuous function.

Especially, there exists a geologic boundary, forming an unconformity between conglomerate and anorthosite.

Especially since there exists the standard literary convention that there are only seven original stories and Shakespeare already told them all.

However, it is not always so efficient especially when there exist hot spot and network attacks in WSNs.

Thus, fault diagnosis of rotor system becomes more complicated and difficult, especially when there exist more faults than one in the system.

From the experimental results, we can conclude that MWPT-MWF is a suitable tool for denoising especially when there exist small targets in the HSI.

The results show that the responses from the former are much closer to the measured ones than those from the latter, especially when there exist some factors difficult to be considered in its theoretical model.

A life year in the far-off future is unlikely to be valued as much as one in a near future, especially when there exist the possibility of harm and other immediate costs due to the intervention.

In systematically analyzing such modified TASEP structures, in some cases a complementary PBN may be useful, especially since there exist tools for analyzing both the PBN and its deterministic counterpart, using semi-tensor product formulations, going beyond simulations.