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Thus there exists at least one solution for the given problem in S by Theorem 3.4.

In consequence, there exists at least one solution for the given problem in S by Corollary 3.1.

In a simple statement, a PL is a network of related patterns which provides a step-by-step process to solve a given problem in a specific context.

We recall some basic concepts of fractional calculus and introduce the integral operator associated with the given problem in Sect. 2.

The basic idea of multistage generalized differential transform method (MsGDTM) is to apply the standard GDTM to the given problem in each sub-domain.

Two meta-heuristic algorithms of NSGAII and MOPSO were used to solve the given problem, in which the accuracy of the mathematical model and the proposed algorithms efficiency were assessed through numerical examples.

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Holly Eaton, a lawyer with the Texas Classroom Teachers Association, said that because of questions about the validity of evaluations based on test scores, and given problems in other states, there was no reason to overhaul the current framework.

The contribution of Streptococcus pneumoniae to childhood pneumonia has been difficult to define given problems in establishing the aetiology of paediatric lower respiratory tract infection [ 3].

What I find remarkable in this report is that the highest mean sentiment score is for Aubagio, a drug which many neurologists would have less enthusiasm for, given problems in its use in patients of childbearing age.

Positive deviance capitalises on a hugely energising fact: for any given problem, someone in the community will have already identified a solution.

This necessitates a data model that can be used to model any given problem instance in the form of a structured input language.

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