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In Books IV to VII Diophantus extends basic methods such as those outlined above to problems of higher degrees that can be reduced to a binomial equation of the first- or second-degree.
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Moreover, formula 3, which characterizes the relation between K ro/K rw and S w at ultra-high water cut stage, has higher precision than formula 1 for medium high water cut stage and the binomial equation of K ro/K rw and S w for the ultra-high water cut from reference Song et al. (2013).
Only Liu et al. (2011), Wang et al. (2013), Song et al. (2013), and Cui et al. (2015) in China proposed the exponential and binomial equations for the relation between the ratio of oil and water permeability and the water saturation, completed derivation of exponential, binomial, and inverse-proportion water drive curves, which have some limitations in prediction accuracy.
The equilibrium distribution, calculated using the binomial equation, also changes because it is based on the relative starting concentration of peak 1.
Expected genotype proportions were obtained using allele frequencies observed in the controls and the binomial equation [47].
Thus, the distribution of the random variable R defined in the preceding section is the function of i = 0, 1,…, n given in the binomial equation.
The contents of the three missing books of the Arithmetica can be surmised from the introduction, where, after saying that the reduction of a problem should "if possible" conclude with a binomial equation, Diophantus adds that he will "later on" treat the case of a trinomial equation a promise not fulfilled in the extant part.
We derived the risk equation using a binomial equation and standard HIV modeling techniques [ 50, 51].
Write the equation of the perpendicular bisector.
Since not all SNPs are biallelic, binomial expansions of the equation were used to compute expected values.
Selection, mutation and migration occur according to the deterministic recurrence equation (1) where (2) (3) Drift is included by binomial sampling of the infinite population.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com