The phrase "alone provided that" is correct and usable in written English.
It can be used to indicate a condition that must be met for something to be true or valid, often in legal or formal contexts.
Example: "You may proceed with the project alone provided that you submit the necessary documentation first."
Alternatives: "only if" or "as long as".
However, the elastic effects can decrease (increase) the maximally unstable wavelength over that predicted by curvature effects alone provided that the rods are elastically stiffer (softer) than the surrounding matrix.
For simple modelling purposes in undrilled areas, the porosity may be considered to be controlled by depth alone, provided that 'present-day depths' are replaced by 'estimated maximum burial depths'.
The addition of a second risk model can lead to better overall performance than one risk model alone provided that the strategy is calibrated so that both risk models affect the optimal portfolio solution.
Our model further suggests that for R0 = 2.5 a local epidemic may be prevented by the use of non-pharmaceutical measures alone, provided that activation of measures is rapid and sustained.
Our experience with well-characterized deletions shows that this approach gives equivalent results to normalizing against controls alone, provided that samples with altered copy number are in the minority (data not shown).
The fiscal compact alone cannot provide that reason.
The emperor alone could provide that protection, since, as the embodiment of all the virtues, he possessed in perfection those qualities displayed only imperfectly by his individual subjects.
The Middle East alone can provide that supply.
Native myocardial T1 mapping proved to be superior to the EGEr technique and, alone, provided sensitivity comparable to that obtained with the established LLc (92 vs. 92 %, respectively) [19, 21].
That alone provided a new source for mining the Uncanny without feeling guilt or fear of an external authority.
Additionally, the inclusion of hypoxanthine alone provided better protection than that obtained with thymidine, thereby shifting the concentrations of metformin required to affect breast cancer cell growth by up to 19-fold at the IC30 level and up to 5-fold at the IC50 level.
