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The graded modulus of elasticity of the plate is assumed to vary through the thickness and is found experimentally by means of nano-indentation technique and also estimated mathematically by a mathematical model originally proposed by Tamura, Tomota and Ozawa (TTO model).
This may be estimated mathematically, with varying degrees of sophistication.
SH coefficients have no obvious physical significance because they are estimated mathematically by the least-squares method.
Structure change for materials with the same composition and different initial particle size (BHA/glass) can be estimated mathematically using relations for permeability coefficients: {k}_1/{k}_2={varTheta_{mathrm{op}_1timeses {left({d}_{mathrm{av}1}right)}^2times {delta}_2timesTheta_{leftrm{dp}}}_{mathrm{av}2}rightmathrm{av}2}right)}^2times {delta}_{mathrm{av}2}right
Figure 4 shows that the probability of ototoxicity can be reliably estimated mathematically as a function of each of these 3 parameters.
Such an approach allows complex sampling designs, for which probability statistics cannot be estimated mathematically, to be simulated and run repeatedly to generate evidence for decision-making.
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The oxygen distribution in various bio-hybrid systems composed of cellular tissue on an artificial scaffold was estimated by mathematically modeling the oxygen consumption and diffusion.
The complete in vivo resorption time within 3 6 months for α-CSH/ACP (60/40) was mathematically estimated by an extrapolation method.
We introduced surface molar solubilization ratio (MSRs) for sorbed micelles of surfactant and mathematically estimated using effectiveness factor and available carbon fraction of activated carbon after surfactant sorption.
Figure 1 shows that the mathematically estimated error of coefficient does not contain the estimates of the CHAOS-2 model.
We want it acknowledged that many of us can and will live beyond mathematically estimated standard deviations on a computer's spread sheet.
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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