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A penalty formulation has been introduced to enforce positive concentrations in the presence of discontinuities.
For example, in magnetic resonance spectroscopy (MRS), the columns of the mixing matrix represent the positive concentrations of the source metabolites.
More specifically, it can be written as the noisy linear instantaneous mixing model described in Eq. 45, where is the MRS observation vector, is the source vector representing the statistically quasi-independent source metabolites, is the instrumental noise vector, and is the nonnegative mixing matrix containing the positive concentrations of the source metabolites.
:\frac{1}{v} = \frac{K_{M}}{V_\max [\mbox{S}]} + \frac{1}{V_\max} Naturally, no experimental values can be taken at negative 1/[S]; the lower limiting value 1/[S] = 0 (the y-intercept) corresponds to an infinite substrate concentration, where 1/v=1/Vmax as shown at the right; thus, the x-intercept is an extrapolation of the experimental data taken at positive concentrations.
■ Remark 5 In order to make sure the positive concentrations of gene regulation network in (19) or (20), the choice of designed kinetic parameter K k to solve LMI in (21) should guarantee the positive concentrations of gene networks.
Victims of violent death by accidents and homicide often show positive concentrations for alcohol and drugs [ 4, 26- 33].
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The interaction between anthraquinone concentration and corn treatment suggests a positive concentration-response for red-winged blackbirds.
Chemical kinetics conserves mass and renders nonnegative solutions; a good numerical simulation would ideally produce mass-balanced, positive concentration vectors.
The positive concentration gradient near the doublon root appears to be rapidly smeared out by back-diffusion in the solid, thus making difficult its quantification through experimental methods.
When the DGT devices are deployed in a water of low major cation concentrations (∑[cations]≤2×10−4 M), a steep negative concentration gradient of Na+ across the diffusive layer as well as small positive concentration gradients of the other cations develop.
In 4 days and 7 days treatment duration, 1 ml of A. niger extract was found to be most positive concentration for eliciting andrographolide compound.
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