Sentence examples for using the notations of from inspiring English sources

An easier way was presented to derive the discrete multi-symplectic form formula from the discrete variational principle, using the notations of Poincaré-Cartan Poincaré-Cartan

Using the notations of (Upsilon_{t}) and (hat{z}_{t}) in the above inequality, we derive (hat{z}_{t}-z)^{top} Q z leqfrac{1}{2gammasigmaUpsilon_{t}}biglVert z-z^{0}bigrVert _{G}^{2},quadforall zin mathcal{Z}.

Then, we can write the dynamics of the asset processes using the notations of the previous section: d S^{i}_{t} = S^{i}_{t-}left(d M^{i}_t+alpha^{1}_{t} d leftlangle M^{i},M^{1} rightrangle _t+alpha^{2}_{t} d leftlangle M^{i},M^{2} rightrangle _{t}right) with begin{aligned} alpha^{1}_{t} & = 0 alpha^{2}_{t} & = {e^{-1}over left(e^{-1}-1right)^{2}} end{aligned} for all t≥0.

Using the notations of Section 4.1, we have: E e j 2 n = σ 0 2 + ∑ i, l M h ji h jl G il − 2 ∑ i, k M h ji w jk ∑ m = 1 N c km K i a km, b km + ∑ k, l M ∑ i, m N w jl w jk c li c km F lk a li, b li, a km, b km (89).

Using the notations of Fig. 10, with a wave propagating in the z direction, all the waves with a real α component will be measured.

Using the notations of stochastic simulation, the ODE model with the length of molecules is given by (18) d X d t = - k X 1 - L - X X (n - 1 ) q, d L d t = - k X.

Using the notation of calculus (which describes how things change, see here for more) the equation is: If dx/dt = x, find x.

Using the notation of Subsect.

Using the notation of Sect.

Using the notation of [6], let (gamma = beta bar {gamma }).

For instance, using the notation of Ding et al.