Sentence examples for by using the separation from inspiring English sources
At first, the torsional response of the soil layer is solved by using the separation of variables technique.
Exact closed-form solutions are obtained for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method although it is difficult to solve them.
The governing equations describing the behaviour of the system are analyzed by using the separation of variables method and their solutions presented.
In their early paper, Liu and Xing obtained exact closed-form solutions for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method.
By using the separation of variables method and the derived method from Ferrari's method, the natural frequency equations and the critical flow velocity equations of pipeline conveying fluid with both ends supported are obtained in mathematical decoupling.
The nonlinear aircraft model with heavy cargo moving inside is derived by using the separation body method, which can describe the influence of the moving cargo on the aircraft attitude and altitude accurately.
The analytical formula of the unsteady temperature distribution is derived by using the separation-of-variables method and hence the maximum thermal stress attained at the surface of the FGM solid cylinder as well as its time of occurrence can be calculated.
Morphology control of various aromatic polyimides representative as poly(4,4′-oxydiphenylene pyromelliteimide) was examined by using the phase separation during solution polymerization.
By using the convex separation theorem, there exists such that, for all and, for all.
In this paper, we are interested in the approximation of a stochastic generalized Swift-Hohenberg equation with quadratic and cubic nonlinearity by using the natural separation of time-scales near a change of stability.
Total RNA was extracted from cells by using the phenol/chloroform separation method, as described in standard protocols (Trizol; Invitrogen Fischer Scientific, Illkirch, France) and then reverse-transcribed by using iScript cDNA Synthesis Kit (BioRad Marnes-la-Coquette, France).
