Sentence examples for final expression for from inspiring English sources
The phrase "final expression for" is correct and usable in written English
It can be used when presenting a conclusive formula or result in a mathematical or scientific context. Example: "The final expression for the area of a circle is A = πr²."
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.
The final expression for the effluent profile is complex but can easily be evaluated in closed form, and we have confirmed this by comparison with numerical results.
Thus, a final expression for the current I, as a function of voltage V, ion concentration cb and temperature T is achieved and a qualitative comparison between theoretical and experimental data is made.
A mathematically accurate treatment of the experimental measurement of Young's modulus is also presented, yielding a final expression for E (I ω) as a function of the two measured entities, namely the acceleration of the base and the vertical displacement of an adequate point of the specimen.
The final expression for the objective function gradient includes only boundary integrals which can readily be calculated in both structured and unstructured grids; this is feasible in design problems where the objective function is either a boundary integral (pressure deviation along the solid walls) or a field integral (the entropy generation over the flow domain).
This is the final expression for (i) of (22).
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.
Their final expression of love for him was to cast their lots with him in Germany, where they formed the nucleus of four monasteries that served as centres of civilized Christian life.
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.
