Tseng and Wang [24] proposed a modification equation based on the Preston equation in chemical-mechanical polishing; Nanz [25] considered the bending of pad and flow of slurry into the Preston equation to obtain a new polishing formula.
Two theorems have been obtained, which have demonstrated that the properties of Galilean invariance from a modification equation, can serve as the positive constrain condition for general conservative finite difference schemes.
In a similar manner, one can define associational-RR modification (see equations A5 and A6).
Another example is the definition of R 0,k =0, which differs from the inverse of Equation 5 only by a factor in the exponential function, or Equation 13, which is not a mere modification of Equation 6, but an extension.
An appropriate modification of Equation 29 is given as a linear quadratic Verhulst equation: dx ( t ) = x ( t ) ( λ - x ( t ) ) dt, Open image in new window (30).
Therefore, with modification in Equation 6, this trend is reversed to satisfy the characteristics of the micro-crack.
With modification, FN Equation 1 can be used to describe the linear relationship between ln(J/E 2) and 1/E, i.e., ln ( J E 2 ) = − B ϕ 3 2 β − 1 E + ln ( A ϕ − 1 β 2 ) (1).
Our theoretical model emerged from modifications of equations that have been used to describe the formation of peak levels of BMP signaling along the dorsal midline in Drosophila (Eldar et al., 2002).
We have used a modification to equation 2 in Fay and Wu [ 14] to convert this to an estimate of heterozygosity within Holstein to compare this result with the estimated heterozygosity from equation 3. Hence, Holstein heterozygosity was estimated as (4) where dI is the polymorphism rate at noncoding sites estimated from MacEachern et al. [ 20] and n = the number of chromosomes sampled.
We compute a weighted harmonic mean based on the theoretical variance of in the two time periods, using a simple modification of Equation 3 to compute the weights: (A4) This variance applies specifically to the LD method, but for lack of quantitative information regarding precision of the ABC method we use it for the combined LDN e + O ne S amp estimates as well.
