The cost function (15) is differentiated with respect to each of the three variables and set to 0. For each frequency bin k ∂ J m + 1 ∂ W k m + 1 = 2 W k m + 1 − W k m * − λ * S k m X k m + 2 α k W k * m + 1 W k m + 1 2 − C k z = 0 (16) ∂ J m + 1 ∂ λ * = D k m − S k m W k m + 1 X k m = 0 (17) ∂ J m + 1 ∂ α max, k = W k m + 1 2 − C k 2 z = 0. (18).
Then, the Lagrange function is differentiated with respect to each unknown and equated by zero trying to find a solution to that unknown in terms of the Lagrange multiplier.
They cannot be differentiated with certainty from each other because of border effacement.
This method finds the estimators of parameters that maximize the likelihood function: (5) l β = ∏ i = 1 n π x i y i 1 - π x i 1 - y i The log likelihood of (5) is defined as (6) L β = ln l β = ∑ i = 1 n y i ln π x i + 1 - y i 1 - π x i To find the maximum likelihood estimators, L is differentiated with respect to each parameter, and then the resulting terms are set as equal to zero.
In actively dividing differentiated cells, with each cell division, a small amount of DNA is necessarily lost at each chromosome end, resulting in ever-shorter telomeres and altered telomere structure, eventually leading to the cessation of cellular proliferation (Blackburn 2000; Weinert and Timiras 2003).
The set of differential equations is differentiated with respect to the boundary condition chosen and the resulting partial differential equations are solved by a finite-difference method.
After being differentiated with respect to hemisphere (left and right), each of the side variables was tested for gender and age effect.
Except for the same two varieties (Aboudja and Ahimon), the genotypes specific to each variety were clearly differentiated with a minimum of eight mutations.
At each locus, three genotypes were differentiated, with an expected BC1S3 segregation ratio of 0.71875 : 0.0625 : 0.21875 for homozygous recipient (i.e. Barke), heterozygous and homozygous donor genotypes, respectively.
Pre-osteoblastic MC3T3-E1 cells were plated on each implant disk (40,000 cells/disk) and were differentiated with mineralization medium for 12 days.
