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The analytical expressions for stress intensity factors at the central crack tip and the expression of the strain energy release rate have been derived for general loading.

Determination of suitable sample sizes for multilevel analyses is complex, in part because explicit formulas have not yet been derived for general models.

The following lemma has been derived for general max-tolerance graphs and applies also to c-max-tolerance graphs [ 9]: Lemma 1 The number of maximal cliques in (c- max-tolerance graphs is O(n).

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Common inductance equations are in general form and they are derived for general calculations.

The formulae for effective diffusion coefficients across interfaces between materials are derived for general polyhedral meshes.

Incremental harmonic balance (IHB) formulations are derived for general multiple degrees of freedom (d.o.f).o.f

Performance analysis is in Section "Performance analysis" where exact PEP is derived for general case and special case.

The analytical LS1 solutions are derived for general non-delaminated and delaminated multilayers and compared to 3D finite element solutions.

Mathematical expressions for the call forced termination probability and inter-cell handoff arrival rate are derived for general distributed CDT and unencumbered call interruption time.

In this section, the probability distributions of the CHTn and CHTh in CRCNs are derived for general distributions of both unencumbered service time and cell dwell times.

For perimeter control design, a set of sufficient conditions that guarantee the controllability, an important but yet untouched issue, are derived for general multi-region MFD systems.

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