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The hardness distribution was determined using an analytical relation between effective strain and hardness.
The analytical relation between the EO flow rate and the ion concentration was determined and exhibited exponential decay characteristics.
An explicit analytical relation between the sum-correlation function and the outage probability is still an open problem.
Assuming that the evaporation of volatiles occurs and that the expansion of the vapor accelerates solid dust grains, we obtain an analytical relation between Dp and r.
By explicitly incorporating the carrier sense threshold and the transmit power into our analysis, we derive an analytical relation between MAC throughput and system parameters.
Then, the analytical relation between RQD and discontinuity frequency that may be derived, provided that discontinuity sets follow the negative exponential model, is validated against simulation data.
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Finally, analytical relations between the thermodynamic and phase field parameters are found and verified for these simulations.
Analytical relations between the isentropic efficiency and the flow coefficient, the work coefficient, the flow angles and the degree of reaction of the compressor stage are obtained.
We determine analytical relations between fracture toughness and the parameters governing bulk hysteresis, and quantitatively predict the reduction in fracture toughness due to pre-stretch.
Finally, analytical relations between the sink and source terms of the breakage or aggregation of the PBE were derived and discussed, highlighting interesting features of the PBE model.
To describe correctly the energy balance of the considered dynamical processes, we used analytical relations between the rate of wave energy dissipation and wave acceleration for nonzero vertical gradients of the mean wind.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com