We next describe algorithmically how to obtain a sequence of tree pairs--which is important to mathematically state Hill et al's conjecture--by decomposing two rooted binary phylogenetic X-trees T and T ′ into smaller subtrees.
Zuo et al. [ 21] have shown that low-frequency amplitudes in the slow-4 band were higher than those in the slow-5 in the basal ganglia, thalamus, precuneus, and so on by decomposing into four distinct frequency bands (slow-5 (0.01–0.027 Hz), slow-4 (0.027–0.073 Hz), slow-3 (0.073–0.198 Hz), and slow-2 (0.198–0.25 Hz)).
Accordingly, the IPDC problem is solved by decomposing it into four hierarchical stages: (i) preanalysis, (ii) design analysis, (iii) controller design analysis, and (iv) final selection and verification.
In this study, this problem will be formulated as a mathematical programming (optimizattion with constraints) and solved by decomposing it into four hierarchiacal stages: (i) target selection, (ii) HEN design analysis, (iii) controllability analysis, and (iv) optimal selection and verification.
The solution of the mp-MIQP problems is approached by decomposing it into two subproblems, which converge based upon an iterative methodology.
We analyse the relaxation process by decomposing it into three consecutive steps: (i) atom X relaxes along the line Q X, (ii) atom X rotates around the M1 M3 axis, and (iii) atom M2 relaxes along the line Q M2.
We optimize the train operational plan in a special network layout, an urban rail corridor with one terminal yard, by decomposing it into two sub-problems, i.e., the train departure profile optimization and the rolling stock circulation optimization.
When considering the eikonal equation with point-source conditions, we further utilize a factorization approach to resolve the source singularities of the eikonal by decomposing it into two parts, either multiplicatively or additively.
The analytical equations for channel potential and characteristic length have been derived by decomposing TMQG into two 2D perpendicular cross-sections (triple metal double gate, TMDG) and the effective characteristic length of TMQG is found using equivalent number of gates (ENG) method.
Therefore, we can solve (19) by decomposing it into two layers.
