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When satisfied, this condition guarantees existence of an interpolating surface.
However, it guarantees existence of enough paths connecting the information source to the sink so that all the traffic can be transmitted to the sink.
In this section we show that Theorem 2.1 guarantees existence of solutions to some cases of (4.1) not covered by the existence results in [6, 7].
We note that in all the above mentioned cases, the main conclusion is drawn using ([1], Theorem 2.6), which guarantees existence as well as equality of components of the coupled fixed point.
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In a few very important cases, noncentralization is given support through the constitutionally guaranteed existence of different systems of law in the constituent polities.
We determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions.
This constraint is regularized by including a compact and linear operator S to guarantee existence of solutions.
This is the minimal framework to guarantee existence of the minimizers at each step, and to get estimates as in (2.11) providing the existence of a limit curve.
In 1986, Turinici [21] gave an initial result for guaranteeing existence of fixed points by involving a new algebraic structure: a partial order on the metric space.
In this framework standard deterministic analysis for e.g. guaranteeing existence and uniqueness of solutions can be applied pathwise; see for example [26], Chap. 1.
Because you're important, it guarantees your existence.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com