Sentence examples for the former expression from inspiring English sources
Using (4) in the former expression, we get S = prox γr ( S − γ ∇ f ( S ) ) (6).
If β > α, then the left-hand side of the former expression is increasing in κ, whereas the right-hand side is constant.
The former expression shows that Aristotle has his doubts about the connections between these philosophers and Pythagoras himself.
Substituting in a22 the steady-state condition (26), the former expression becomes: a22 = frac{partial_{dot{psi}}} {partial_{psi}} = frac{r + xi}{(1 - phi)} - frac{(2 - phi) (r + xi)}{phi - 1}.
Step-by-step derivation of (40) hinges on the characterization of E H w m ( x ) H w m ( y ) ∗ and E H w m ( x ) H w m ( y ) ∗ 2. The former expression is given by E H w m ( x ) H w m ( y ) ∗ = E ∑ n, i = 0 L h − 1 h [ n ] h ∗ [ i ] e − j w m x n e j w m y i, (41).
FUNC, the Sum Rule and the Product Rule, as restricted to one measurement context, trivially repeat these definitions, and there obviously is no point in testing, e.g., whether v(A·B) really equals v(A) v(B), if the former expression is defined by the latter.
The former, expressions of the Momoyama sensibility at its most lyrical, have been attributed to Unkoku Togan (the founder of the Unkoku school), while the latter are by his son Unkoku Toeki.
If it happens that GP finds expressions using a small number of variables with a better fitness value than the ones using all variables, the former expressions survive into the population, while the latter ones are extinguished.
A comparison between effectiveness factors predicted by approximate formulas to those given by the more accurate numerical solutions suggests that these former expressions underestimate the catalyst effectiveness and consequently are safe to employ for initial design estimates.
Most experts agree that microglia are virtually indistinguishable from peripheral macrophages; the only difference being a lower expression of the leucocyte tyrosine phosphatase CD45 in the former and expression of CCR2 (CC chemokine receptor 2) in infiltrating macrophages (Mizutani et al., 2012).
In the former, CD9 expression was evaluated in different types of brain tumours, and they concluded that CD9 expression in astrocytic tumours correlated with their malignancy and thus CD9 protein may have a different role in brain tumours than solid tumours elsewhere.
