The linlog approximation expresses the reaction rates as proportional to the enzyme concentrations and to a linear function of the logarithms of internal and external metabolite concentrations.
That work also contains accurate approximations (expressed as ratios of integers) to the square roots of 3 and several large numbers.
In this section we examine the validity of the approximations expressed by formulas (16) and (21) for the surface impedance Zp given exactly by Eq. (4).
The total bond energy within the harmonic approximation is expressed as E B = 6 N k 2 a / 2 − r CC 2 + 8 N k ' 2 a 3 4 − r MC 2, Open image in new window (6).
In a PF the target density p(x t |y1 t) is approximated by a particle mixture, containing N particles x t ( i ) i = 1 N and their corresponding importance weights w t ( i ) i = 1 N. Thus, the approximation is expressed as p x t | y 1 : t ≈ ∑ i = 1 N w t ( i ) δ x t - x t ( i ) (9).
In one variable, the fact that the derivative is the best linear approximation is expressed by the fact that it is the limit of difference quotients.
In the quantum mechanical formulation of eq 5.6, the concept of time scale separation underlying the adiabatic approximation is expressed by the neglect of the electronic wave function derivatives with respect to the nuclear coordinates (note that Pα = −iℏ∇α).
These approximations are expressed in terms of physical and geometrical properties of the bodies such as the entire charge, the location of the center of charge, and the pseudo-inertia tensor about the center of charge of the clusters.
Their simplest approximation can be expressed as an approximate sampling variance of the estimate of heritability as 2/[(N − 1 var] ≈ 2/(N var. This expression is the same as our special cases h 2 → 0 and All λ i → 1.
