The phrase "are obtained by utilizing" is correct and usable in written English.
It can be used in contexts where you want to describe the process of acquiring something through the use of a particular method or resource.
Example: "The results of the experiment are obtained by utilizing advanced statistical analysis techniques."
Alternatives: "are acquired through" or "are achieved by using".
The analytical conditions for synchronization of the systems are obtained by utilizing Laplace transform.
For practicability, the channel temporal and spatial correlations are considered and the channel estimate and its error covariance are obtained by utilizing the outdated channel state information.
Sufficient conditions for the solvability of the two problems are obtained by utilizing a Lyapunov functional together with the linear matrix inequality (LMI) approach.
The reflection and transmission coefficients are obtained by utilizing two possible sets of boundary conditions, for a specific model and there values corresponding to two boundary conditions are also compared graphically.
The knowledge about the influencing quantities and parameters is expressed by their degree of belief, i.e. appropriate probability density functions that usually are obtained by utilizing the principle of maximum information entropy and the Bayes theorem.
Dispersion equations of Love waves in double porosity medium are obtained by utilizing the usual assumption of Love waves in elastic solid with the coupling mass coefficient ρ23 and coupling permeability term k(12) being equal to zero.
The closed-form solution of dynamic frequency and electrostatic voltage is obtained by utilizing the homotopy perturbation method (HPM).
By solving the RCB, the positioning information in three dimensions is obtained by utilizing a linear equation.
Experimental data in the form of rate of oxygen uptake were obtained by utilizing a stirred cell.
The dynamic structural response is obtained by utilizing an appropriate modal technique referring to the response spectrum defined by the Italian code.
All freezing rates studied were obtained by utilizing a custom-made apparatus and were then indirectly related to conventional vial freeze-drying.
