Sentence examples for the equality exactly from inspiring English sources
In general, the dimension, i.e., the number of basis functions is infinite in order to hold the equality exactly.
It may happen (and has been encountered for some of the channels randomly generated) that the optimal values of these Lagrange parameters are such that the equality is exactly met on some carriers (usually at most one).
The main criterion for Container attributes is that they can be compared for equality exactly as they are (i.e. without requiring any preprocessing such as normalization or canonicalization).
What is equality, exactly, and who shares in it?
Nor, he admits, does equality exactly "spring to mind as a keyword" in Freud, Klein or Lacan (though its absence may be revealing).
Since, by Watson-Crick base-pairing rules, we only have C-G/G-C and A-T/T-A pairs, this implies that APPROXIMATELY f_a = f_t and f_c = f_g Now, if we assume that the equalities hold exactly, then we have three constraints f_a+f_c+f_g+f_t = 1 f_a = f_t f_c = f_g and so we effectively have only 1 degree of freedom left (which is essentially GC-content).
Here again the case is less than compelling for at least two reasons: first, it is hard to pin down exactly how the equality argument is supposed to go, and second, we are still not sure about the content of Plato's theory of forms.
Note that the equalities (17) and (18) exactly coincide with the well-known Bernstein and Jackson inequalities in the form given in [[1], Section 7.2].
Using the equality condition in Theorem 1ii of Rosenberg and Jakobsson (2008), we can specify a set L of exactly ⌈(2 HT)−1⌉ allele frequencies whose sum of squares is HT.
The key simplification is that the nonlinear terms δ i d k =: z ik in (3) (the strong duality theorem equality) are exactly linearizable as follows: (4) 0 ≤ z ik ≤ δ i max d k (5) δ i − δ i max (1 − d k ) ≤ z ik ≤ δ i where δ i max is the upper bound for the dual variable δ i (chosen arbitrarily big in the implementation).
