Ranking is represented by a dominance hierarchy or pecking order that may be linear, meaning that each individual clearly expresses its personal rank from alpha (most dominant) to omega (least dominant, submissive, or deferent) under all conditions (Fig. 1.3). • Ranking may be decisive or ...
·\(\omega_1^\mathfrak{Ch}\)(Omega one of chess) ·\(\omega_1^{\text{CK}}\) (Church-Kleene ordinal)·\(\omega_\alpha^\text{CK}\) (admissible ordinal)·recursively inaccessible ordinal·recursively Mahlo ordinal·reflecting ordinal·stable ordinal·\(\lambda,\gamma,\zeta,\Sigma\) (...
·\(\omega_1^\mathfrak{Ch}\)(Omega one of chess) ·\(\omega_1^{\text{CK}}\) (Church-Kleene ordinal)·\(\omega_\alpha^\text{CK}\) (admissible ordinal)·recursively inaccessible ordinal·recursively Mahlo ordinal·reflecting ordinal·stable ordinal·\(\lambda,\gamma,\zeta,\Sigma\) (...
Fig. 1: Hierarchy of lattice vibrations in La2Zr2O7. The vibrational modes are assigned as normal phonons or diffuson-like phonons according toaCriterion I, whether their mean free path (l) is above or below the vibrational wavelength (λ);cCriterion II, whether theirlis above or below the...
The\alpha _n(t)are the choice ofQwe left open previously. Referring again to [2], the\alpha _ncontrol the weight of each individual flow (induced each byI_{n+1}) in the overall Eq. (2.3). Thus by choosing the coefficients\alpha _n(t)appropriately we will be able to recover NLS ...
Herein, the infection rate and recovery rate are \(\alpha \) and \(\beta \), respectively. Then, the spread procedure is continued until there are no individuals with infected state in the network. The final cumulative count of infected individuals is considered as the real spread ability ...
$$\begin{array}{l}{\tilde{q}}_{n}=-\,\tfrac{({\alpha }_{2}[n]-{\gamma }_{1}[n])\,({\alpha }_{2}[n]-{\gamma }_{2}[n])\,({\lambda }_{2}^{2}-{\lambda }_{1}^{2})}{{\lambda }_{2}({\beta }_{2}[n]-1)\,({\alpha }_{1}[n]-{\gamma }_{1}[...