Sentence examples for by using these equations from inspiring English sources

By using these equations, the large amplitude vibration of a simply supported rectangular plate is investigated.

We compare MTBF estimates obtained by using these equations to estimates gathered from comprehensive simulation analysis, and show that error terms are not insignificant.

By using these equations and response surfaces, it is possible to assess radial displacements around the face and to construct the longitudinal deformation profile of a circular opening with different diameters excavated in weak rock mass under different stress conditions.

By using these equations, we derive some derivative formulas for these numbers and polynomials.

By using these equations, we find many properties of q-Eulerian polynomials and numbers.

Since FDEs have memory, nonlocal relations in space and time, complex phenomena can be modeled by using these equations.

By using these functional equations and differential equations, we derive some identities associated with special polynomials and partial Hecke-type operators.

The advantage of the proposed method is that DS-d PI/PID settings could be expediently sought by simple calculations using these equations without any tedious design.

It is possible to predict rheological properties of blends using these equations by TG-DTG method by comparing real rheological properties of rubber compounds to those predicted by both calibration curves to test the accuracy of the thermogravimetric method.

By using these determined binary parameters, both equations predicted the specific volumes of the polymer blends with anisole to average absolute deviations of better than 0.13%.

The equation: By using these numbers, I found the odds of a New York victory to be 66.9 percent.