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The only difference between both problems is the scheduling parameter x qn which is discrete in DP 2 and continuous in (CP 2).
The wavelet function we used is "coiflets," which is discrete, near symmetric and has scaling functions with vanishing moments (Beylkin et al. 1991).
All of the variables are categorical except for schooling years, which is discrete and takes values between 0 (no education) and 24 (final year of graduate school completed), and age.
This is particularly exploited for the subgroup (Lambda ) of (Gamma ) which is discrete and assumed countable, so that the integral begin{aligned} int _Lambda varphi (lambda ) dm_Lambda (lambda ) = m_Lambda ({0}),sum _{lambda in Lambda } varphi (lambda ), end{aligned}where ( m_Lambda ({0})) is the (discrete) measure of ({0}).
M thus provides a continuous measure of eruption magnitude based on estimates of erupted mass; more common is the use of the Volcanic Explosivity Index (VEI), which is discrete and assigned on the basis of either erupted volume or eruption intensity (average mass eruption rate).
The proof of this proposition is based on convex optimization tools and is given in Appendix C. The intuition is that, at the convergence state, the iteration, which is discrete with respect to the spectrum allocation policy by construction, satisfies the KKT conditions which are both necessary and sufficient for optimality in convex optimization problems.
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The fiber orientations are taken as design variables which are discrete integer values between −90° and 90°.
These accessory genes are recognized as genomic islands (GEIs) which are discrete DNA segments between closely related strains of the same species.
Impulsive control of a chaotic system is ideal for designing digital control schemes where the control laws are generated by digital devices which are discrete in time.
Modern atomic theory tells us that in fact physical strings are composed of physical atoms, which are discrete entities, so eventually we will reach a point where we shift from string to something else.
Since the optimization parameters in PTS-AIC are the weighting factors which are discrete, the location of a particle has to be quantized to the nearest point in the constellation set before the objective function is evaluated.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com