The phrase "and hence define" is correct and usable in written English.
It can be used when you want to indicate that something follows logically from what has been previously stated, leading to a definition or clarification.
Example: "The results of the experiment were conclusive, and hence define the parameters for future research."
Alternatives: "and thus establish" or "and therefore specify".
It is, however always possible to measure, and hence define, the size of this change in a subsequent measurement of the final momentum with arbitrary precision.
end{aligned}In fact, under the given assumption (fin mathcal S), Eq. (1.10) holds for all (xin mathbb {R}), since both series are uniformly convergent, at least on compact subsets of (mathbb {R}), and hence define continuous functions.
Our recent data suggest that the new flagellum could participate to basal body migration and hence define its own positioning.
Amino acids surrounding phosphorylation sites direct kinase binding and hence define kinase-substrate specificity.
Astrocytes control tissue equilibrium and hence define the homoeostasis and function of the CNS (central nervous system).
Thus, inhibition of PRC2 by specific histone modifications could be used as an alternative mechanism to limit sites of activity and hence define patterns of occupancy of PcG complexes.
This successful designed engineering led us to identify two naturally occurring and oppositely oriented VKOR homologues from the hyperthermophile Aeropyrum pernix that promote oxidative protein folding in the periplasm or cytoplasm, respectively, and hence defines the probable route for disulfide bond formation in the cytoplasm of hyperthermophiles.
For finite-dimensional Lie algebras, the Baker Campbell–Hausdorff series always has a non-zero radius of convergence and, hence, defines a local Lie group.
This is an important need because TADR is intimately related to flow length and area (e.g., Walker 1973; Malin 1980; Pinkerton and Wilson 1994; Calvari and Pinkerton 1998; Murray and Stevens 2000; Harris and Rowland 2009), and hence defines the potential for a lava flow to enter vulnerable areas to cause damage.
If (h3) holds, using the aforementioned construction we can find w 1 such that L w 1 = 1 and w 1 ( 0 ) = 0. Now, w 2 : = w 1 − 1 / ( a 0 + b 0 ) satisfies L w 2 = 0. Observe that the second part of condition (h2) is precisely w 2 ( t 0 ) ≠ 0, and hence, defining w = u ¯ + c − u ¯ ( t 0 ) w 2 ( t 0 ) w 2 we see that w is a solution of problem (2.1).
Only paired end reads were used because they were derived from a 300-bp library and, hence, defined more precisely the junction boundaries.
