Sentence examples for and hence the function from inspiring English sources

and hence the function is integrable over for each.

If f ∈ D, then U f ∈ Z and hence the function F f ∈ C 0 ∞ ( R ).

which implies that ϕ ∈ W p AA ( R ; R ) Open image in new window and hence, the function f + ϕ is Weyl pseudo almost automorphic.

So, h ( t + log b ) = − h ( t ) for all t ∈ R and hence the function h ( t ) is periodic with period 2 log b.

This implies that (varphi'(0)>0) and hence the function φ is increasing on ([0,x^]) and is decreasing on ([x^,1]), where (x^) is zero of (varphi') on ((0,1)); hence φ is non-negative on ([0,1]).

In biomedical applications, custom-tailored probiotic bacteria can be introduced into the human body to alter the composition and hence the function of the gut microbiota for disease treatment.

However, F j ( 1 ), G j ( 1 ) in (A3) may not be positive constants, and hence the functions f, g are more generic.

Despite the sequence homology and common association with mitotic regulatory events, the subcellular localization and signaling substrates differ, and hence the functions of Aurora A and Aurora B are essentially distinct [ 13].

This modulation is a possible mechanism used by T. crassiceps to modify the phenotype and hence the functions of human DCs, directing the balance toward immune suppression and allowing the survival of this parasite [ 60].

It is important to note that the signatures seen in the constitutive protein (and in some of the encoded isoforms) are totally lost in orphan isoforms and hence the functions associated with the constitutive protein are lost in the orphan isoforms.

These discoveries show that miRNAs and their targets are part of complex regulatory networks, for which a number of studies have been performed to reveal the effects of specific miRNAs on temporal and spacial expression of their target genes, and hence the functions of miRNAs.