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The advantage of the proposed methods is that the frequency equation for two rods coupled by translational springs can be established in terms of a determinant of 2-order for any number of translational springs and concentrated masses.
Proof The global existence of a unique strong solution to FBVP (1.1) and (2.1) can be established in terms of the short time existence carried out as in [7], the uniform a priori estimates and the analysis of regularities, which indeed follow from Lemmas 3.1-3.4 3.1-3.4
Again, these scenarios should and do include specific falsifiable hypotheses but the validity of the construct as a whole can only be established in terms of likelihood and only by synthesis of a multitude of evidence.
If the details can be worked out, the bond valence model would not only allow the constraints of a simulation to be established in terms of chemical concepts, but it would provide insights into the modeling process that are not available in other simulation techniques (section 12).
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The sufficient condition has been established in terms of LMIs.
The criteria are established in terms of linear matrix inequalities.
Then error bounds of generalized mixed variational inequalities are established in terms of residual vector.
Generalized correlations of the equation parameters are established in terms of Bondi's volume.
Local-asymptotic stability of the disease-free equilibrium is established in terms of Rv.
The delay-dependent condition is established in terms of matrix inequalities.
Sufficient conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimators.
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