a ~ opt k ( i ) = R k − 1 ( i ) P k ( i ) (9). is found by differentiating J k (i) with respect to a ~ k ( i ), setting the derivative to zero, and solving for a ~ k ( i ), where.
where (boldsymbol {M}_{n,i,j}=frac {partial boldsymbol {K}_{n}}{partial A_{n}(i,j }), which is found by differentiating (12) with respect to A n (i,j); hence, begin{array}{*{20}l} boldsymbol{M}_{n,i,j} &= boldsymbol{F}_{n} boldsymbol{S}_{n,i,j} boldsymbol{X}_{n}^{H} boldsymbol{R}_{n}^{-1}. end{array} (18).
Here, (boldsymbol {q}_{n,i,j}=frac {partial boldsymbol {hat {h}}_{n}}{partial A_{n}(i,j }) and is found by differentiating (13) with respect to A n (i,j), such that begin{array}{*{20}l} boldsymbol{q}_{n,i,j} &= boldsymbol{F}_{n} left(boldsymbol{A}_{n} boldsymbol{q}_{n-1,i,j} + boldsymbol{Gamma}_{i,j} boldsymbol{hat{h}}_{n-1}right) + boldsymbol{M}_{n,i,j} boldsymbol{e}_{n}.
A general expression for Young's modulus was found by differentiating the polynomial equation of the engineering stress-strain curve with respect to strain.
The deviation time point is found by differentiating s(t), and then scaling it to get the cosine of s(t), which is then 90 degree phase shifted to get ŝ(t).
According to the Department of Defense call for proposals, these spent shells are also liable to be found by locals around the training facilities, who may be unable to differentiate the training rounds from tactical rounds.
These can be found from the GF by differentiating with respect to the corresponding ω i and evaluating at ω i ¯ → 0. All distributions have a discontinuity at T 1 and at multiples of T 1 corresponding to varying numbers of coalescences occurring within the bottleneck.
As in the previous case (KOW), PC1 was found to differentiate the ILs by solubility.
Nevertheless, the pattern we described must be differentiated by other conditions in which PAS-positive material can be found in the apical portion of enterocytes.
The diagnostic horizons, properties and materials used by the WRB to differentiate between Reference Soil Groups are described hereafter in Tables 2, 3 and 4; their full definitions can be found in Annex 2 to this text.
