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The analytical expressions of the average intensity at any receiver plane are derived based on the extended Huygens-Fresnel principle.
For the Moran process and the Wright-Fisher process, we calculate the precise expressions of the average offer and the average demand under weak selection.
Based on the solution, explicit expressions of the average energy release rate for self-similar delamination growth are also given for the applied load as a function of the dimensions of the plate and the circular damage.
Approximate closed-form expressions of the average channel capacity will also be derived.
To summarize, the final expressions of the average BERs of the proposed adaptive relaying scheme for scenario 1 under i.n.d. and i.i.d.i.d
The expressions of the average factor graph degree distribution and an upper bound of the outage probability for random caching schemes are derived.
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Also an expression of the average growth of slip per loading cycle was empirically derived and recommended for design purposes.
A simplified expression of the average CHTC is then given as a function of the convective heat flux density (or the average temperature difference) and tested for building simulation purposes.
For anisotropic Coulomb's dry friction, in light of the non-smooth factors in both the internal control mode and external resistance, method of averaging is adopted to obtain an approximate expression of the average steady-state velocity when the stick slip motion is absent.
To summarize, all the expressions involved in the final expression of the average BER in (8) can be calculated analytically.
For the case P S (x)=α exp(−β x), we use the expression of the average SER in (11).
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