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There are many research topics [1, 2] in developing numerical methods for solving initial value problems (IVPs) described by frac{dphi}{dt} = fbigl t, phi(t bigr),quad t in[t_{0}, t_{f}];qquad phi(t_{0}) = phi_{0}, (1) where f has continuously bounded partial derivatives up to required order for the analysis of the developed numerical method.
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This paper deals with higher-order theories for the analysis of free vibration of beam structures.
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It is underlined, though, that the presence of a third-order interaction does not allow for the analysis of lower-order effects in the full model, given that these lower-order effects should not be interpreted as aggregate variable effects, but rather as contributions of particular effects to the magnitude of the third-order interaction, an issue that is often overlooked in related analyses.
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However, selecting the FrFT transform order for the proper analysis of multicomponent signals like speech is still debated.
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