First, the buckling problem is analytically addressed, by solving the so-called bifurcation equation in a 3D framework.
A problem with the conventional method for obtaining volume fraction of binder is analytically addressed in terms of error sensitivity.
The investigated work analytically addresses the diffraction of horizontally polarised shear wave by a rigid strip in a pre-stressed transversely isotropic poroelastic infinite medium.
In order to understand how Melan Koiter method works for such materials, the evolution of the structure's response until the stabilization of the plastic strain ('shakedown') or the asymptotic dissipative behavior ('alternating plasticity' or 'ratcheting') is analytically addressed and the Bree diagram is then constructed.
The stability of coatings with regard to the intended use has to be analytically addressed as well.
Over the past several decades, computation has become an essential component of most branches of scientific inquiry, making it possible to test hypotheses and scenarios that would be difficult to address analytically or experimentally.
Yet, neither the transnational nor the assimilation frame of analysis address, analytically or empirically, how premigration experiences impact on immigrant adaptation and transnational engagement.
This is relatively straightforward to address analytically as when m = 0, Equation 68 reduces to P (0, t ) = | G o v e r a l l | z = 0, which in the notation above is simply: (73) ζ ≡ P (0, t ) = (B ′ D ′ ) m 0, where we introduce the notation ζ for fixation probability for later brevity.
Then, clinical importance can be addressed as a qualitative question: "Is the difference clinically important?" This question is addressed analytically via a comparison of effect sizes to an effect size predefined as clinically important.
