The phrase "and hence given" is not commonly used in written English and may sound awkward or unclear.
It can be used when explaining a conclusion or result that follows logically from a previous statement, but it is better to use clearer alternatives.
Example: "The data was analyzed thoroughly, and hence given the results, we can conclude that the hypothesis is valid."
Alternatives: "therefore provided" or "thus given".
Towards the novel's end, we find him sullen because jobless, and hence given to wearing 'the darkest shirts he owned, with pants that were charcoal black'.
Finally, optimal R i is set to maximize the objective function and, hence, given by (63).
If (a), P must be true, for if we suppose that P is false, since P says of itself that it is unprovable, "it is true that it is provable," and if it is provable, it must be true (which is a contradiction), and hence, given what P means or says, it is true that P is unprovable (which is a contradiction).
} int_{0}^{t}e^{ t-tau A} B mathbf{u}(tau),dtau in H,quadforall mathbf{u}in L^{ t-tau Ahrm{loc}} Bigl( [0, infty );U bigr), (1.3) in which the integral is well defined (and hence given initially) in ([ mathbf{u} tau) ] ').
Thus, our findings suggest that the genetic architecture is less complex in the case of FHB and, hence, given the same level of relatedness between training and test sets, can be more properly tackled to predict FHB than STB disease severity.
Given the binary, logistic link model developed below for association status given the functional data and the parameters α and β, odds(A s | F s ) = exp(α + F s β) and hence, given α and β 1 where F s β is the 'functional signature' of SNP s.
Merleau-Ponty wishes to begin in a dimension of experience which has not been "worked over, that offers us, all at once, pell-mell, both subject and object--both existence and essence--and, hence, gives philosophy resources to redefine them" (VI, 130).
Each gives its own account of interactions, and hence gives different meaning to the principle.
On the other hand, Steiner also speaks of the "sheer incapacity of the 'normal' mind to imagine and hence give active belief to the enormities of the circumstance".
Magazines, marriage books, and general sexual folklore reinforce these demanding ideals, which cannot always be met and hence give rise to anxiety, guilt, and feelings of inadequacy.
That might be a pity, but nevertheless you still get mostly unknown bands - local or not - that try to build up a fan base and hence give all their energy to satisfy the audience.
