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Combining Theorems 2 and 3, we get a criterion of invertibility for Toeplitz operators.
In this theorem, we get a criterion of weak Poincaré inequality by integrability of hitting times and a local Poincaré inequality on a fixed subset for jump processes.
Computing the mean of the N log-likelihood functions expressed on each sensor, we get a criterion J ( u ) to provide an information about the nature of the processed samples J ( u ) = 1 N ∑ i = 1 N L i ( u ) (1) = - ( N s - u ) log ( π σ w 2 ) - 1 N σ w 2 ∑ i = 1 N ∑ m = u N s | y i ( m ) | 2 (2) (3) (12).
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In this paper, we get a criteria of weak Poincaré inequality by some integrability of hitting times for jump processes.
In this part we get a sufficient criterion for a point to be an extreme point or not, combining the generating function M and properties of both Orlicz spaces and Sobolev spaces.
So we wish that we can get a criteria parameter to identify the risk of spontaneous combustion more easily.
In this paper, we investigate SKC mappings to get a criterion to guarantee a fixed point, via extending the results proved by Karapınar and Tas into the class of CAT ( 0 ) spaces.
By also including r-proteins that are persistent according to our 90% cut off criterion we get a total of 45 r-proteins in our data set.
By Theorem 2, we can get a special existence criterion for Eq. (1).
According to the above analysis, we get similarity criteria based on the solid fluid coupling theory.
By analyzing the current tourist websites and personalized systems, we get some criteria to evaluate the ATRS.
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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