To estimate ( varDelta {E}_{sigma Rightarrow {sigma}^{hbox^i ), the angular momentum matrix elements are considered.
Due to symmetry property of the atomic orbitals, only a few angular momentum matrix elements between the d orbitals are nonzero: 〈xz|L z |yz〉, 〈x 2−y 2|L z |xy〉, 〈z 2|L x |yz〉, 〈xy|L x |xz〉, and 〈x 2−y 2|L x |yz〉 (bra and ket can be exchanged).
An angular distance matrix Δ is calculated by minimizing the objective function (Equation 5), where δ ij is the angular distance and d ij is the original distance (stored in D) between gene sets i and j.
The angular distortive matrices are calculated for the bcc → fcc, bcc → hcp and fcc → hcp transitions, and for fcc → fcc mechanical twinning.
The testing of the model was based on the use of two kinds of widely accepted statistical texture quantities: five texture features determined by the co-occurrence matrix (angular second moment, contrast, correlation, inverse difference moment, entropy), and four statistical texture features determined after the wavelet transformation (mean, standard deviation, energy, entropy).
Space-fixed, total angular momentum, transition matrices are required as input.
Notwithstanding the findings, other factors such as matrix size, angular response, and color functionality should further be taken into consideration.
GLCM, grey-level co-occurrence matrix; ASM, Angular Second Moment; IDM, Inverse Difference Moment.
We calculated nuclear texture features using variables of the gray-level co-occurrence matrix (second angular moment, entropy, energy, peak prominence, standard deviation, cluster shade, and cluster prominence) as well as Shannon's entropy of the gray level histogram and the fractal dimension according to Sarkar.
