Sentence examples for with respect to the proof from inspiring English sources

Exact(4)

15 with respect to the proof of Theorem 15.

We provide the proof since there are some differences with respect to the proof of Theorem 1.

A study has been performed to assess the sensitivity of the LISA interferometer to motion of the spacecraft (SC) with respect to the proof mass.

It can be shown that and the constraints C1 and C2 are convex with respect to (the proof is given in appendix), and Slater's condition holds, so there is no duality gap, and the optimal solution is characterized by the Karush-Khun-Tucker conditions [13].

Similar(56)

These two mechanisms differ by their relative orientation of bistable mechanisms with respect to the central proof mass.

This subsection is devoted to the establishment of a Lipschitz continuous dependence property of the solution with respect to the data whose proof is based on a monotonicity property of the solution of (2.6) with respect to the source term and the boundary condition by which we first set out and demonstrate our result.

Therefore, this idea is a refinement with respect to the simplicity of the proof.

And various physical theories can be objectively compared with respect to the structure of the proofs they contain.

Therefore the sequence space V ϱ ( λ ; p, q ) is a Banach space, with respect to the Luxemburg norm, and the proof is complete.

With respect to the approach in [23], the proof in Appendix 1 is carried out asymptotically, that is, for M large enough to approximate E z as the outcome of a Gaussian random variables, and it leverages the hypothesis of a spatially sparse signal, i.e., a signal that is sparse in the canonical basis.

Then f is both a semistrictly G-preinvex and G-preinvex function with respect to the same η on K. Proof By Proposition 12 in [14], we know that f is G-preinvex on K.

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