The phrase "and for the validity" is correct and usable in written English.
It can be used when discussing the importance or confirmation of something's legitimacy or accuracy.
Example: "The committee will review the documents and for the validity of the claims made, they will consult with experts."
Alternatives: "and regarding the validity" or "and concerning the validity".
According to these changes and for the validity of the extended model, all of the existing constraints are changed and four new constraints are added to the model.
Statistical power is an inherent part of empirical studies that employ significance testing and is essential for the planning of studies, for the interpretation of study results, and for the validity of study conclusions.
Lemma 4.4 (respectively, Lemma 4.2) implies that condition (1a) (respectively, condition (1b)) is sufficient for the existence and positivity of Green's functions g i (t, s), i = 1,..., n, of periodic problems (2.1), (2.2) and for the validity of relation (2.4).
Remark 1 Let us recall the well-known facts that for the validity of Theorem 1, it is necessary that a 1 < 0 and for the validity of Theorem 3, it is necessary that all characteristic values of the matrix A have negative real parts.
Forty one participants provided data for the self-reported participant reproducibility and for the validity assessment.
This is a prerequisite if measured dialysate concentrations are to immediately and consistently reflect the concentration of a solute in the medium outside the probe, and for the validity of calibration by the retrodialysis method [ 21].
Specifically, after receiving the invalid signal, the OCT slow-axis scanner steps back 10 B-scans and waits for the validity signal to become valid again.
It means that the condition (E_{1}and sufficient for the validity of (20).
In [7] the authors provide sharp conditions on the triple (Omega, rho ) and C for the validity of (2).
A random sample of 150 subjects from the claims was selected and used for the validity analysis of the algorithms.
The final KP Questionnaire (Bahasa Melayu) version on immunization was done and made ready for the validity and reliability study.
