Sentence examples for under these hypotheses from inspiring English sources

Cohen, in 1963, showed that it is not provable under these hypotheses and hence is independent of the other axioms.

Under these hypotheses, the pressure field is slightly affected by the viscosity variation while dissipative effects are enhanced.

Under these hypotheses, and assuming that the vents will be placed on the boundary of the piece, the distance field from this boundary will provide useful information on the optimal position of injection nozzles.

Under these hypotheses existence and uniqueness of a solution follow from a fixed point argument as in [1].

Under these hypotheses, every bounded subset is weakly relatively compact (see [4]), which implies that (H1) is true.

Under these hypotheses, we will be able to approximate solutions in the sense of distributions to problem by a sequence of weak solutions to weak problems.

To test the significance of the observed s for the observed gene genealogy under each of these hypotheses, we generated null distributions for the test statistic by simulating 1,000 gene trees under a neutral coalescent process without migration under a null hypothesis of allopatric fragmentation and calculated s for each gene tree under each of our alternative population tree hypotheses [ 120].

Under these standard hypotheses on a and f, (3) admits a unique solution.

Under these two hypotheses and (4), the observation vector x v (nT) can be written as: H 1 : x v ( n T ) = μ s e j ϕ s a n s + b T v ( n T ) H 0 : x v ( n T ) = b T v ( n T ).

We constructed the distribution of the statistics to be tested under these null hypotheses using the software ms [27] (see supplementary File S1 for details).

Under these two hypotheses, the Ra peak was corrected by dividing by 1.7337.