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The closed-form solution, relating the cell geometry with the characteristic impedance Zc, is possible only for the simplest "canonical" transmission line transverse cross-sections.
The approach exploits a new closed-form solution relating settling height and time for a very simple functional form of the settling flux.
UF models under respectively low- and high-concentration polarization are used to interpret some experimental results on protein solution relating to effects on rotation speed or centrifugal acceleration, centrifugation time (for spintube), filtrate viscosity, and feed solute concentration.
An analytical solution relating the mass flow rate to the film thickness and other flow parameters have been developed for the general case of gas liquid two-phase annular flow in a horizontal pipe line for power-law fluids.
For example, an analytical solution relating Tr and the normalized crack depth (h/λ, h is the depth of a surface-breaking crack) was given by Achenbach and his colleagues (Achenbach et al. 1980; Angel and Achenbach 1984; Mendelsohn et al. 1980).
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In another work (now lost) Apollonius solved the problem of cube duplication by conics (a solution related in some way to that given by Menaechmus); further, a solution of the problem of angle trisection given by Pappus may have come from Apollonius or been influenced by his work.
The discretization form is the approximate numerical solution related to (4).
We, therefore, propose a method that searches for an efficient solution related to a Pareto-optimum.
A simple analytic solution relates the average stress rotation over a given rupture area to the ratio between the earthquake stress drop and the differential stress.
A simple and elegant solution related to PNNs is the enhanced probabilistic neural networks (EPNNs), whose idea is to consider only the samples that fall in a neighborhood of given a training sample to estimate its probability density function.
Since global stability is guaranteed under some deviation of the current solution related to the limiting one, which is considered as nominal, the stability is robust against such errors for certain tolerance margins.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com