Specifically, the replicate data FAC 6J7 was subjected to a uniqueness filter against processed LC-HRMS data generated from a control group of strains containing empty vectors, as well as 13 other strains containing a variety of other FACs with unique genetic content.
Furthermore, the optimised mass layer should not be interpreted geophysically; it is only designed to replicate the external gravity field, so is subject to the problem of non-uniqueness of gravity inversion.
To prove (2.14) take the limit as in (2.20) Finally, to prove the uniqueness property of subject to (2.14) let us assume that there exists a quartic function which satisfies (2.14) Since and for all and from (2.14) it follows that.
To prove the uniqueness of the quadratic function subject to (2.4), let us assume that there exists a quadratic function which satisfies (1.5) and the inequality (2.4).
Finally, to prove the uniqueness of the cubic function subject to inequality (3.19), assume that there exists a cubic function which satisfies inequality (3.19).
Finally, to prove the uniqueness of the quadratic function subject to (3.4), assume that there exists a quadratic function which satisfies (3.4).
To prove the uniqueness of the quadratic function subject to (3.4), let us assume that there exists a quadratic function which satisfies (1.6) and inequality (3.4).
Finally, to prove the uniqueness of the quadratic mapping subject to (3.3), let us assume that there exists another quadratic mapping which satisfies (3.3).
Finally, to prove the uniqueness of the quartic mapping subject to let us assume that there exists a quartic mapping which satisfies (3.22).
Finally, to prove the uniqueness of the cubic mapping C subject to (2.2), let us assume that there exists another cubic mapping C ′ which satisfies (2.2).
