The Derivative as a Function.
Figure 1 shows the role of the density derivative as a function of T. Hence we consider the coefficient of thermal expansion αP = −(∂ ln ρ/∂T P = −V−1 ∂S/∂P T, representing the entropy and volume cross-correlations 〈δSδV〉 to be αP = 〈δSδV〉/kBTV.
For these two parts, simple general explicit formulae are derived, which contain only the initial concentration and height variables, the interface height and its derivative as a function of time.
The changes in the photophysical properties of two novel, yellow-green emitting pH chemosensors namely a 1,8-naphthalimide dye and its condensed heterocyclic derivative, as a function of pH were investigated in water/ethanol.
Figure 3 shows the simulation for a different constant fractional-order derivative as a function of t for a fixed value of x = 0.8. Figure 1 Numerical solution of the main problem for ρ ( x, t ) = 1 + sin ( x t ), where ( x, t ) ∈ [ − 1, 1 ] × [ 0, t ].
This notation is shorter than Leibniz notation, and is helpful when looking at the derivative as a function.
The latter notation generalizes to yield the notation f (n) for the nth derivative of f – this notation is most useful when we wish to talk about the derivative as being a function itself, as in this case the Leibniz notation can become cumbersome.
Tissue samples were homogenized (50 mg/mL) in Locke's buffer (120 mM NaCl, 2.5 mM KCl, 5 mM NaHCO3, 6 mM g-glucose, 1 mM CaCl2, and 10 mM HEPES, pH 7.4) and incubated for 20 min at room temperature with 10 mM H2DCFDA (Molecular Probes Inc .. Production of the fluorescent derivative DCF as a function of time (min) was measured using a microplate reader (Perkin Elmer Life Science, Monza, Italy).
The ratio of this anisotropic derivative to the isotropic derivative, when plotted as a function of position and depth shows prominent differences in both the sign and the magnitude of the sensitivities, especially for steep dips and for strongly anisotropic rocks.
The free radical polymerization behavior of three norbornadiene derivatives was studied as a function of their structure.
