The phrase "and subsequently applying" is correct and usable in written English.
It can be used when describing a sequence of actions where one action follows another, particularly in formal or academic contexts.
Example: "The researchers conducted a thorough analysis of the data, and subsequently applying their findings to improve the existing model."
Alternatives: "and then implementing" or "followed by applying".
We have extended this approach by recording the best solution in each iteration and subsequently applying these to a modified system.
Consistency between the Northcote Trevelyan recommendations and ongoing internal initiatives designed to ensure the competence of clerks recruited to undertake accounting work and subsequently applying for promotion to a higher grade is demonstrated.
The prediction of the flow behavior was made by first extrapolating shear and wall friction data and, subsequently, applying these extrapolation-based data as input variables to Jenike's hopper design method.
Expected wildfire mortality for large trees was calculated by building flame length mortality functions using the Forest Vegetation Simulator, and subsequently applying these functions to the burn probability outputs.
It could result from a re-specification of the entire system by explicit inclusion in the equations of the factors inducing cross-correlations among input-output technical coefficients, and subsequently applying computational methods that avoid simultaneity effects.
Time-activity curves were determined by drawing kidney, bladder, and whole-body regions-of-interest for each patient, and subsequently applying the calibration factor for conversion of counts to activity.
I took the National Rifle Association course, which I thoroughly enjoyed, and subsequently applied for a permit.
An established method for the matching of limiting solutions is reviewed and subsequently applied.
We demonstrate the method with a phantom object and subsequently apply it to resolving, in situ, the physicochemical states of a heterogeneous catalyst system.
The method was validated and subsequently applied to the analysis of 20 hair samples collected from MMT patients.
On the suggestion of her mother, she entered the civil service in Liverpool as a junior in 1980, and subsequently applied to join Margaret Thatcher's office in Downing Street, which she did in 1984.
