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In Section 4, the higher-order integrability of the approximation solution and the variational solution associated to (1.3) are obtained.
The existence and uniqueness of the solution associated to the initial condition is ensured by the existence-uniqueness theorem.
Based on the finite element method a starting point corresponding to a non-linear solution associated to a given frequency and amplitude of excitation is computed.
We use symmetrization techniques to derive the regularity in Lorentz spaces or to consider the radial solution associated to the increasing radial rearrangement function ˜f of f.
On the other hand, the solution associated to the upper bound (UB) overestimates the QoS constraint and, thus, the performance in term of EGP are always satisfied, although at the price of spending more power than the strictly required one.
Genetic algorithms use selection, mutation and cross-over operations to transform a random initial population into a new one, with the aim of improving the fitness of a solution associated to the objective function [17].
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Other option is to choose solutions associated to the greatest scores.
Since the goal is to satisfy the mutation testing criterion, solutions associated to the best scores are analyzed.
end{aligned} (36 Thus, we have identified the complete quantum solutions associated to the DNS in the transformed system.
But, as the model is of hyperbolic type and the run of the characteristics crucially depend on the physical parameters, the existence regimes of the stationary solutions associated to certain boundary conditions turn out to be limited.
The main goal of this article is to identify, classify, organize and quantify the main security concerns and solutions associated to cloud computing, helping in the task of pinpointing the concerns that remain unanswered.
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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