Sentence examples for completed derivation from inspiring English sources

Only Liu et al. (2011), Wang et al. (2013), Song et al. (2013), and Cui et al. (2015) in China proposed the exponential and binomial equations for the relation between the ratio of oil and water permeability and the water saturation, completed derivation of exponential, binomial, and inverse-proportion water drive curves, which have some limitations in prediction accuracy.

Zhang (1998) completed derivation of water drive curve that is applied widely in the oilfields.

Chen (1985 , 1993 1994, 1995, 2000) and Yu and Jin (1995), Yu (1999a, 2000) completed theoretical derivation of formulas for type A, B, C, D, and other water drive curves based on oil water flow in the porous medium.

For a complete derivation see [4].

(The complete derivation of the model is in Appendix 2).

The complete derivation is illustrated on an edge-preserving optical flow estimator and on image restoration.

Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation.

The complete derivation of the required mathematical models is reported in the paper.

The complete derivation of the DDM-based response sensitivity algorithm is presented.

The hyperplasticity and continuous hyperplasticity formulations enable complete derivation of thermodynamically admissible constitutive models.

A complete derivation of the closed-form linear theory dispersion relation for the instability is presented.