Sentence examples for given the continuity of from inspiring English sources

Given the continuity of, we have for some with.

Given the continuity of motion, there must be a precise instant in time, call it t, at which I leave the room.

Given the continuity of both ω and θ A, there are an uncountably infinite number of pairs that can be selected for notch filter design by Equation 16.

Given the continuities of the inner and outer NE membranes and within the NE-ER network [6], [29], the ER is the most likely area reservoir, especially during mitosis, with NE area acquisition likely accomplished via membrane redistribution within this network [1] [3], [30].

This gives the continuity of (D_{m}(c_{i})) and completes the proof of Theorem 1.3.

The first lemma gives the continuity of (lambda (c_{i})) on ((0,infty)).

Next result gives the continuity of (X_{cdot}^{v}) in (v_{cdot}in mathcal{U}).

The latter gives the continuity of blow-up with the self-diffusion rate since the solution without self-diffusion blows up.

In this paper, with the separated, real coupled and complex coupled BCs, we give the continuity of eigenvalues and eigenfunctions with respect to parameters.

Proof From (3.16) we have d ( f x, f y ) ≤ φ ( d ( x, y ) ) < d ( x, y ), which gives the continuity of f in b-metric space ( X, d ).

end{aligned}This gives the continuity of the function (frac{partial ^{2}{phi }}{partial x^{2}}), specially, begin{aligned} frac{partial ^{2}{phi }}{partial x^{2}}=0 quad text{ on }~Q_{0} end{aligned}thanks to (varepsilon >h).