In order to predict the amplitude of the pattern, one needs to extend weakly nonlinear expansion to higher orders as suggested by [49] and references therein.
Expression in the cochlea starts at around E14.5 in Pillar cells, Deiter's cells and outer hair cells, and also extends weakly to nonsensory parts of the ear [29].
Compared to the existing related work, e.g., [12 14], strongly relatively non-expansive mappings are extended to weakly relatively non-expansive mappings.
By our proof we can see that Theorem 3.7 in [3] can be extended to weakly mean dominated pairwise independent random variables.
Conceivably, the writhing of live spirochetes may dislodge long, extended and weakly bound CFH molecules from the bacterial surface, whereas the much smaller serum proteins CFHR1, CFHR2, and CFHR5 are more likely to be retained.
We conclude that the results of the optimizations indicate that the ERAS model can be extended even to weakly self-associating components previously considered impossible in especially engineering thermodynamical applications, with the above modifications and refinements.
Even if electronic states are extended or localized (weakly or strongly) and the k vector conservation is thus released, the effective mass theory has still been successfully applied when effective masses are considered as parameters giving average effects in a nonregular lattice [12, 13].
Theorem 1.1 in the present paper can also be extended to a weakly coupled system of the type left { textstylebegin{array}{l} x_{i}'=f_{i} y_{i})+p_{1i} t, x, y), y_{i}'=-g_{i}(x_{i})+p_{2i} t, x, y) end{array}displaystyle right.
Next, Oprocha and Zhang [12] extended the notion of weakly mixing set and gave the concept of 'transitive set' and discussed its basic properties.
It would be interesting to extend it for weakly commuting and compatible mappings and so forth.
