Sentence examples for changing of variables from inspiring English sources

Then, by changing of variables (Pi^{-1}: hat{Omega}rightarrowOmega) and Lemma 3.2, one has (mathbf {u}_{epsilon}in H^{2}(hat{Omega})), which implies that T is a compact mapping from (H^{1}) into (H^{1}).

Then system (1) by changing of variables u =  x +  y, z =  z is reduced to 2-component Malthusian system (M1) with respect to u,  z - variables.

By the changing of variables μ and u in (1), the above problem reduces to a study of the solutions in a neighborhood of the point ((0,0)).

For the integral on the right hand side of the above inequality, by changing of variable, we can get (2.19).

For the integral on the right hand side of the above inequality, by changing of variable and noting that,, we can get (3.7).

Indeed, after changing of variable s r = ξ, the last integral can be written as u ( x ) = C + ∫ 0 r w ξ d ξ.

Then by changing of the variables, we see that mathcal{M}_{Omega,alpha}{vec{f}_{epsilon}} y)= epsilon^{-alpha }mathcal{M}_{Omega,alpha}{vec{f}} epsilon y).

If you aren't familiar with pricing optimisation software, it helps companies accurately define the price of goods across a vast and constantly changing spectrum of variables.

From its beginning in 2005, to its current incentive and penalty phases, the value based purchasing program has had a changing constellation of variables measured, and now rewarded or penalized.

Taken together these findings emphasise that monitors tracking beat-to-beat CO benefit from frequent calibrations during changing loading conditions or changes of variables potentially influencing the underlying calculation algorithm, such as IAH.

However, it does not consider in-depth analysis into the infectiousness of the virus or the impact of changing environmental variables and conditions, such as change in device susceptibility.