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for all u between u L and u R; this is called the entropy condition, or Condition E. Oleinik has shown that weak solutions satisfying Condition E are uniquely determined by their initial data.
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Subsequently, a major review including approximately 335 cases of bacterial EE was published in 2003 [11], and the authors have recently updated their initial data by accommodating further reports [13].
The numerical schemes we employ are conservative (see e.g., Leveque 1992), and therefore preserve the value of the rest mass to the one determined by the initial data.
np.empty one may use the global_shape keyword argument: If the data type is specified neither implicitly by some initial data nor explicitly via dtype, distributed_data_object uses float as a default19.
Since the receiver can estimate the channel gain of all the users (either by receiving known pilots or by using initial data received), the receiver can use successive cancellation decoding strategy to decode all the users.
Since the receiver can estimate the channel gain of all the users (either by receiving known pilots or by using initial data received), the receiver can use successive decoding strategy to decode all the users.
Our constructive theory does not provide a wave selection principle; however, by varying initial data in direct numerical simulations we were able to find solutions in excellent agreement with the theoretical predictions up to some maximal value of Δ.
When (trightarrow0), the solution (46) of the Cauchy problem (5 - 6) is bounded by the initial data biglVert u x,t) bigrVert _{L^{p}(R)} leq biglVert u x,0) bigrVert _{L^{p}(R)}, quad xin R, pgeq1.
In the case k r = 0, f = 1, the total number of receptors is conserved by (46)–(52), and so determined by the initial data imposed, not by the Eqs.
In the case of the conventional SOM, the initial vectorial data are set at a random value, but this results in a final map which is changed by each initial data set.
Thus, as argued by us, initial data from pilot studies should be scrutinised with the most accurate statistical correction (Bocci and Loupakis, 2011), and efforts should be made to validate the preliminary data with randomised, prospective phase III clinical trials.
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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