Sentence examples for this assumption guarantees from inspiring English sources

Indeed, this assumption guarantees that exists a.e.

This assumption guarantees that ( overset{sim }{mathbf{w}}(k) ) is independent of both Ψ and X(k).

This assumption guarantees the existence and uniqueness of the exact solution (X t)) of equation (2.1), and, moreover, the solution (X t)) satisfies (sup_{0leq tleq T} mathbb{E}|X t)|^{2}<infty); see, e.g., [30] for more details.

This assumption guarantees that the embedding (H^{2}hookrightarrow L^{s}({mathbb{R}}^{N})) is compact for each (sin[2,frand2N}{N-4})) and obeys the coercivity condition: (V x toinfty) as (|x|toinfty).

It is well known that this assumption guarantees that the embedding (W^{1,2}(mathookrightarrowkrightarrow L^{p}(mathbb{R}^{3})) is compact for each (2le p<6).

This assumption guarantees (bigl[ {scriptsizebegin{matrix} M omega) & I cr -I & mathbf{0} end{matrix}} bigr]bigl( {scriptsizebegin{matrix} t cr y end{matrix}} bigr)+bigl( {scriptsizebegin{matrix} M omega l+q omega) cr u-lend{matrix}} bigr)) is monotone on (R^{2n}_) (see [16]).

Given this, Assumption 2 guarantees that for a sufficiently good idea, a self-employed agent will actively seek to hire workers.

The previous assumption guarantees that aliquots would always be measured within linear ranges.

where denotes the analytic semigroup having infinitesimal generator (note that Assumption guarantees that generates an analytic semigroup on ).

The last assumption guarantees that the measure (mucirctau^{-1}) defined for any (AinSigma) by the formula mucirctau^{-1}(A)=mubigl tau^{-1}(A)bigr) is absolutely continuous with respect to the measure μ (what is usually denoted by (mucirctau^{-1}llmu)).

This assumption is guaranteed if all the weak user data is ready at the beginning.