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Hence, for suitably large (lambda >0), we have (lambda +lambda _{1}>0) for (muin (-infty,bar{mu})).
This new algorithm uses several techniques to give an expected running time that scales linearly with the number p of processors for suitably large inputs (n>p2).
The curves a + , a − enclose the curve of Δ for suitably large N. Hence the closure interval is determined by solving a ± = 0, which gives an interval I ε, N : = [ a −, a + ].
The curves a + , a − trap the curve of Ω for suitably large N. Hence the closure interval is determined by solving a ± = 0, which gives an interval I ε, N : = [ a −, a + ].
A generalization of Kramers' law has been carried over to the infinite-dimensional case of SPDEs given by d U = [ Δ U − h ′ ( U ) ] d t + ϵ d W ( x, t ) (33). for U = U ( x, t ), x ∈ B ˜ ⊂ R, B ˜ a bounded interval, h ∈ C k ( R, R ) for suitably large k ∈ N and W ( x, t ) denotes space-time white noise and either Dirichlet or Neumann boundary conditions are used [4, 6, 7].
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This can then be used for the survey of suitably large samples that are representative of different subjects, and it should also be easy enough to carry out repeated mapping over time (i.e., monitoring of the spontaneous evolution of clinical cases or results obtained under given treatments).
Firstly, we investigate the bifurcation of positive solutions and derive the multiplicity result for γ suitably large.
To date, Confirmatory Factor Analysis of the Neck Disability Index has not been reported for a suitably large population study.
After a three-hour flight from Sydney to Cairns, and an hour-long flight to Lizard Island (so named by Captain Cook for its suitably large population of monitor lizards), I motored out to my new home for the next four days, joining 26 other passengers and 10 crew on the decks of the 37m-long Spirit of Freedom.
The lemma shows that the number of (H^{-1} z)) of a point z in tH^{-1} z{z:|z|
A simple and effective approach is to presolve this problem for a suitably large set of values of the channel gain and store the resulting tables of individual flow rates versus ; online we can interpolate between points in the table to find the (nearly) optimal policy.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com