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The familiar 1/ r distance dependence for the NOE cross-relaxation rate typically invokes the assumption of an isolated pair of nuclear spins in the absence of internal motion.
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The next result does not require that (T_{n}0 = 0), (forall n in mathbf{Z}_{0 +}) while it invokes the assumptions that ({ T_{n} } _{ to}^{ to} T^) and that (T^) satisfies a ϕ-contractive condition like (3.18a).
Again invoking the assumption of independent hops, we obtain.
The retained methodology allows to presume the joint probability density function of the two scalar fields without invoking the assumption of statistical independence between them.
gusts, extremal distributions are often used to fit the annual maximum value obtained from available records, invoking the assumption of stationarity and statistical independence.
In this approach, a subset of link gains is measured, and then we invoke the assumption of smooth spatial variations to infer all other path gains via interpolation.
The two-phase mass transport in the anode and cathode porous regions is formulated based on the classical multiphase flow in porous media without invoking the assumption of constant gas pressure in the unsaturated porous medium flow theory.
Bootstrap analysis is a nonparametric resampling technique that does not invoke the assumption of normality of the sampling distribution [ 36– 36].
Furthermore, linear free energy relationships that invoke physicochemical models of the relationship between the amount of PCB sorbed and free aqueous concentrations invoke the assumption of thermodynamic equilibrium.
Once again, we invoked the assumption of a constant annual survival rate and used a 3% discount rate to determine the total costs of CHF therapy for a 5-year period, as required by our model.
The purposes of this work are: (i) to develop a simple model to predict the rate of gas generation by the depressurization method when decomposition occurs deep inside the hydrate zone, and (ii) to compare the results with a corresponding model that invokes the sharp-interface assumption.
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