Sentence examples for solutions implies that from inspiring English sources

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The great variety of geometric solutions implies that the final fold shape is adequate to distinguish among different folding mechanisms only in a limited suite of cases.

Thus, the method of lower and upper solutions implies that there exists a solution y satisfying (0

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We have also shown that DNA-bound FNR reacts more rapidly with O2 than FNR free in solution, implying that transcriptionally active FNR is the preferred target for reaction with O2.

The solutions imply that there is wide agreement on a number of starting principles concerning the integrity of radiology as a specialty and particularly the organizational integrity of all imaging services within the enterprise (hospital, multispecialty practice).

The lack of release in ultrapure water compared to buffered solutions implied that competing ligands other than water must be present in order to facilitate Cu release, which led us to further investigate Cu release as a function of competing ligand.

Theorem 2.4, (Janson and Tysk 2004, Theorem A.7), and the linearity of solutions imply that ((mathbf {x}_{0},dots, mathbf {x}_{k},mathbf {x} mapsto widetilde {v}_{k} t,mathbf {x}_{0},dots, mathbf {x}_{k},mathbf {x})) has at most polynomial growth, while the maximum principle in the form of (Janson and Tysk 2004, Theorem A.5) implies that (-widetilde {v}_{k}le v_{k}le widetilde {v}_{k}).

A suboptimal solution implies that more resources than really needed will be deployed.

As we discussed above, the absence of a trivial solution implies that all solutions will be strictly monotonic.

The nonnegativity of the model's solution implies that (limsup_{trightarrowinfty }s ( t ) leq M_{1}), where (M_{1}=frac{b}{bar{b} }).

Second, the non-degeneracy of the radial solution implies that any eigenvalue of (bar{L}^{1}_{u}) cannot be equal to zero.

A proportional relationship between the coupled diffusion coefficient and the proton concentration in solution implies that homogeneous electron transfer in the film is accompanied with proton transfer from the reduced sites to the oxidized sites of the polymer.

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