Sentence examples for the final expression for from inspiring English sources

In particular, firstly we present the mechanical model, later we perform the shape derivative of the corresponding cost function and, finally, we calculate the final expression for the topological derivative using the Topological-Shape Sensitivity Method and results from classical asymptotic analysis around spherical cavities.

This is the final expression for (i) of (22).

The final expression for routing overhead model is given below: (11).

Integrating the previous equation, the final expression for PEP of the proposed scheme is extracted: (21).

The final expression for the signal-to-interference ratio in (34) contains the term (35).

For sake of brevity, the final expression for probability of each category is given with brief description of the expression.

The final expressions for complex impedance contain contributions of the bulk film, interfacial charge-transfer resistances and (in contact with solution(s)) bulk solution.

By using this lemma and the results of [5], we can express the final expression of the average BER for the considered asynchronous and nonlinear FBMC-based multi-cellular network as follows: {begin{aligned} text{BER}_{Av}&= frac{3}{4}-frac{3}{4sqrt{pi}} intlimits_{0}^{infty} frac{e^{-z(1+5b)}}{sqrt{z}} prod_{k=1}^{K} left| I_{L_{k}} left(1+ fra_{d a_{d} varepsilon_{k})}{SNR_{eta_{k}}} right)right.

The integrations in (28) carried out the final expressions of the rigidities are for convenience presented in Appendix 2. The local equilibrium equations are expressed in terms of the displacement functions by substituting (27) into Eqs.

The Fourier transform is then applied on each overlapping time frame individually, and the final expression values for each timepoint are calculated using a weighted average for each time frame, where higher weights are used for expression values near the center of each time frame (Additional file 1: Figure S1B).

By inserting (21) and (22) into (20), one obtains the final expression (18) for the probability of successful transmission on the link.