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This, in turn, implies that the model admits a finite state bisimulation (Theorem 3).
This, in turn, implies that the model admits a finite state bisimilar abstraction (see Theorem 3).
We show that the stochastic model admits a nonnegative solution by using the Lyapunov function method.
First, we prove that the stochastic model admits a unique global positive solution.
We show that the model admits a unique global positive solution and study asymptotic moment properties of solutions.
This can happen even if the model admits a triangular identification and if the forecasts produced by the misspecified VAR are optimal.
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The resulting model admits an extremely rich variety of both hydrodynamic and reactive/diffusive instabilities that can be analyzed either numerically or analytically in various limiting parameter regimes.
The basic ideas of NetInf are also adopted in [15], of which the proposed model admits an additional constraint that the hidden network is a forest.
In the present work, we show that the new model admits an H-theorem and the numerical schemes which stem from the new model are more stable than the conventional LBM.
Therefore, while the two-patch cofactor-free model admits an exact solution, the additional non-linearity in the four-patch cofactor model makes mathematical analysis of the latter much more difficult.
Although this model admits all three possible fate outcomes, if we choose r = 0, we recover a process of invariant asymmetrical cell division in which each and every progenitor cell persists long-term.
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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