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The condition 3 > q > 1 assures that f ( u m ) defined above is nonnegative.
Then Theorem 1 assures that there exists a feedback gain matrix K so that systems (3.11) and (3.12) realize the synchronization.
Assumption 1 assures the stationarity of { ε t ( i ) }, i ∈ E. Assumption 2 and Assumption 3 guarantee the Markov property of { Y t }.
Brouwer's theorem follows from Lefschetz because a manifold M homeomorphic to the unit ball has H k ( M ) and is trivial for k > 0 so that L ( T ) = 1 assures the existence of a fixed point.
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Low PANI/Pd ratio (mainly ≪ 1) assured the predominating contribution of electrodeposition process as compared to possible chemical deposition.
Such considerations would include (1) Assuring an accurate diagnosis of autism before proceeding with any investigation.
In general, an overall rating of 8 assures admission, though they are sometimes rejected while 5's are admitted.
After 7... Nf6, Topalov could have retreated his bishop to h4, but that wastes time, whereas 8 Bf6 Qf6 9 Bb5 c6 10 Bd3 assures White of a lead in development.
"His quartet," Schumann added of the F minor Piano Quartet (Op. 6), "assures for him an immortal place in the history of music".
Luckily, as F1 assures us, he was not of an age, but for all time, so perhaps there's no hurry.
The condition (H.1) assures that ( left| (S tright. left. +h -S t))phi (0)right| le 2MVert phi (0)Vert,) then, by the Lebesgue dominated theorem, we conclude that first item begin{aligned} lim _{hrightarrow 0}E |I_{1}(h)|^{p}=0.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com