Second-order phase transitions include the ferromagnetic phase transition observed in materials such as iron, where the magnetization (which is the

first derivative of the free energy with respect to the applied magnetic field) increases continuously from zero as the temperature is lowered below a critical temperature called the Curie temperature (the temperature at which the material lose its permanent magnetic properties, to be replaced by the magnetic properties induced by the external magnetic field).

(a)

First derivative of storage modulus of COC/EOC blend and COC/EOC/MWCNT nanocomposites prepared by different orders of feedings.

Generating Functions,

First Derivative, and Taylor's Formula.

With the continuity of the spline and their

first derivatives at x (i = 2,3, ..., m), we can get

Yet, it is known from Calculus [20] that if [B.sup.2] - 3AC [less than or equal to] 0 this function will have no local extrema over its domain of definition and therefore, except (2) and (3), no additional conditions can be set regarding the

first derivative of [v.sub.i] (r).

The

first derivative, or the gradient function of the quadratic function, would follow the number pattern illustrated by the increasing difference between the outputs whereas the second derivative would follow the pattern represented by the constant difference between the difference of the difference of the outputs.

However, as there are no boundary conditions given for the

first derivative, we must solve this in the typical manner of interpolating the unknown function and obtaining the

first derivative values through differentiation of the result.

PCA Applied on Combined

First Derivative FT-NIR and Micro-Raman Spectra.

(c)

First derivative spectra of the XAES KVV showing the D parameter estimated as 22 eV.

The

first derivative spectrum was recorded and the absorbance values were plotted against concentrations to obtain the calibration curves.

The

first derivative of the Hat wavelet functions is square integrable.

"

First derivative + SNV" was chosen for wheat bran and corn flour, while "SNV" was chosen for rosin powder.