The likes of Robert Byrd, Howard Baker, Bob Dole, George Mitchell, Mark Hatfield, and Ted Kennedy simply have not been appropriately replaced.
For the energetic equivalence rule, the average resource use rate or metabolic rate of individual plants, Q, should be more appropriately replaced by photosynthetic biomass, ML.
Having somebody spend time with a member of Congress is very different than having somebody go downstairs and see that they were appropriately replacing a torn carpet.
Again, this approach extends to the more general case of uniformly elliptic second order partial differential operators (mathcal {L}) by appropriately replacing in (1.10)–(1.14) the fundamental solution (E_n^{(0)} z;x-y)) for the Helmholtz operator (-Delta -z) in ({mathbb {R}}^n) by the fundamental solution (E_n z; x-y)) of (mathcal {L}- z) in ({mathbb {R}}^n).
New START appropriately replaces the START treaty, which took effect in 1991 but expired last year.
To initiate regeneration, stem cells must sense an injury, proliferate and differentiate appropriately, and replace the missing organs (Poss, 2010).
A beautifully weighted, subtly curving McCann free‑kick concluded matters as, appropriately, brilliant sunshine replaced the cloud and rain which, possibly in sympathy with Ferguson Sr, had earlier shrouded the ground.
But with calls for his resignation and his future in doubt at the time of going to press, he drops out of this year's MediaGuardian 100 entirely, replaced, appropriately perhaps, by his boss.
For example, in ϕx, in which both variables are free, each variable must be replaced appropriately if a proposition of the form in question (such as "Socrates is wise") is to be obtained; but in (∃x)ϕx, in which x is bound, it is necessary only to replace ϕ by a predicate in order to obtain a complete proposition (e.g., replacing ϕ by "is wise" yields the proposition "Something is wise").
This implies that the heterogeneous features can all be replaced by appropriately kernel matrices.
Finally, when ordinal categorical variables appeared in any of the predictor sets, they were replaced with appropriately chosen ordinal dummy variables.
