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The simplicity and compactness of the boundary integral expression derived make it much less difficult to analytically tackle Eshelby's piezoelectric problem for a large variety of non-elliptical inclusions.
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Numerical techniques are often the unique viable option for computing these designs since to tackle analytically the problem results impracticable in most of cases.
The solution of (43) is hard to tackle analytically.
The latter is, however, difficult to tackle analytically for time-varying channels.
The reserved subcarriers approach is one of the simplest and oldest and most well-known approach in literature but at the same time one the analytically hardest to tackle.
The comparatively small number of papers on problems involving derivative-dependent nonlinear terms shows that problems of this type are more difficult to tackle analytically, we note, however, that numerical methods are more developed for this type of problems, see for example [20 25].
A relatively small number of papers on problems involving derivative-dependent nonlinearities indicates that problems of this type are more difficult to tackle analytically; we note, however, that numerical methods are more developed for this type of problems; see, for example, [23 28].
A number of authors have tackled this problem analytically using various approximations (e.g. Zakamska et al. 2008; Lyubarsky 2009; Lyubarsky 2010; Kohler and Begelman 2012).
We tackle this problem by analytically computing the set of all values of K at which system (1) admits a Hopf bifurcation.
It also affects the related issue of the classification of discontinuous functions and analytically representable functions of real variables, tackled by the French semi-intuitionists Borel, Baire and Lebesgue.
Nevertheless, we can hardly tackle with the KKT conditions analytically of the intractable problem in this paper.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com