The phrase "analysis using the third" is grammatically correct and can be used in written English.
It can be used in contexts where you are referring to a specific method or approach that involves a third element or variable in the analysis process.
Example: "The analysis using the third variable revealed significant insights that were previously overlooked."
Alternatives: "analysis employing the third" or "analysis with the third factor".
Adopting an ambient isothermal bulk modulus (210 GPa) obtained previously using the Brillouin scattering technique, analysis using the third-order Birch Murnaghan equation of state yielded pressure derivative KT0′=5.6 8), with zero-pressure volume of 263.9 2) Å3 for MgSiO3 akimotoite.
Traditional legal or constitutional analysis, using the first definition, has produced a huge body of literature on governmental structures, many of the specialized terms that are a part of the traditional vocabulary of political science, and several instructive classifying schemes.
A capacity (resistance) factor of 0.70 is also proposed based on a reliability analysis using the first order second moment (FOSM) method.
Soil types were separated with 100% accuracy and levels of organic carbon were separated with 96% accuracy by linear discriminant analysis using the first nine principal components.
Therefore, the results of 3D analysis using the first approach or 2D analysis similar to the three layers technique may be used to estimate the crack growth life of the repaired panels.
While the proposed flexible approach allows modifications of trial design, sample size, or statistical analysis using the first stage data, there is no need for a complete prespecification of the adaptation rule.
To ensure that these methods do in fact offer a benefit over a more basic approach, we compared them to an analysis using the first derivative.
The analysis using the first factor (di/dt) is conducted simultaneously with the step of decomposition, and a polarity (m l ) of the capacitive discharge current is compared with an allocated polarity (n l ) at any DC/DC converter (#l).
