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This paper develops one such approximation method by examining the effect of cluster sampling on the covariance and correlation matrices of sample distribution functions based on a superpopulation model.
One such approximation is the assumption of uniform total gas pressure across the anode.
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One such stochastic approximation would be to test if a change in a single bound (corresponding to a single trial) improves the noisy estimate of the reward rate, that is, if f (θ n ) > f (θ n − 1 ) + ε, where only a single element (i.e., bound) is changed between θ n − 1 and θ n, and ε is zero-mean symmetric random noise.
In this work, in the finite element framework, we consider one special such approximation, namely, the element-wise Schur complement.
The basic idea here is to approximate the noncommuting Lie algebra with a commuting one, such that the approximation error is minimum.
In the framework of such approximation, one can neglect the electron hole interaction energy.
Based on our findings, such approximation or estimation could be carried out in patients with either no comorbidities (i.e., primary insomnia) or in patients with one or more comorbidities (i.e., secondary insomnia).
We may avoid such approximation by using a less stringent one.
One such constraint is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand.
Molecular mechanics(243) is one such method which employs empirical potential energy functions and uses a number of approximations to provide a simpler model to simulate the conformational and dynamical properties of molecular systems.
The same-sex marriage ban prohibited the government from creating any such approximation.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com