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In 2004, by introducing the explicit finite difference (EFD) method to calculate the volume force, Kupershtokh developed a single-component Lattice Boltzmann model (LBM) (Kupershtokh and Medvedev 2006; Kupershtokh et al. 2009; Kupershtokh 2010).
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We propose an alternative approach, by introducing the idea of an instance decomposition to obtain an explicit intermediate goal state which allows an effective application of PDBs.
Explicit algorithms for estimating moment statistics of arbitrary order are derived, by introducing the generalized difference equation of Fokker-Planck type for the probability distribution function.
We begin by introducing the replicator dynamics.
Motivated and inspired by the idea of Zhang et al. [6] and Saeidi [7], we introduce the explicit viscosity iterative process by Meir-Keeler type contraction in a smooth Banach space.
Thus, to improve the convergence speed, we propose a new setting about social coefficient by introducing an explicit selection pressure, in which each particle decides its search direction toward the personal memory or swarm memory.
If the subRiemannian structure is equiregular, as an original contribution of this paper, in Theorem 3.10 we also present a quantitative version of this result, by introducing an explicit quasi-norms equivalent to (d_epsilon ).
Dependencies among neighboring genomic locations may be better reflected by introducing an explicit self-transition probability.
Designers must take care not to lose the benefit of natural and implicit interaction by introducing explicit interface controls that may be useful only occasionally.
Since the employment of the gradient-based reliability techniques is very much limited due to the some degree of numerical noise introduced by the explicit dynamic algorithm used to perform sheet stamping simulation the method of adaptive Monte Carlo simulations were chosen for reliability assessment.
Motivated by this result, we introduce the following explicit general iterative scheme: { x 1 ∈ H, F ( u n, y ) + 1 r n 〈 y − u n, u n − x n 〉 ≥ 0, ∀ y ∈ H, x n + 1 = P C [ α n γ f ( x n ) + ( I − α n A ) W n u n ], ∀ n ∈ N, (1.16).
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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