Since the solution lacks regularity, uniform refinement leads to the suboptimal rate O (N − 4 / 7 ), whereas adaptive refinement leads to the optimal rate O (N − 7 / 2 ).
This may account in part for the association between lack of regularity and clinical symptomatology in bipolar disorder.
We construct solutions that do not vanish, so as to avoid any issue related to the lack of regularity of the nonlinearity at u="0.
Due to the lack of regularity of u in time, we also use the Steklov average of u instead of u itself.
The only way to overcome the lack of regularity for { q ε } is to consider divergence-free test functions, i.e. div h ε = 0. (1.18).
The main character of the equation is its degeneracy on the boundary, since the weak solutions generally lack the regularity to define the trace on the boundary.
As it turns out, we have not been able to let ε → 0. up to now due to the lack of regularity in the time variable.
A third of the Characteristics consists of "miscellaneous reflections" in which Shaftesbury, in the voice of an anonymous commentator, boasts of the "random" presentation and lack of "regularity and order" in his writing (C 336, 339).
The emphasis on hierarchical representations of functions on intervals helps to address issues of both high-order approximation and efficient application of integral operators, and the lack of regularity of multiwavelets does not preclude their use in representing differential operators.
The theory of random graphs is widely used to model and analyze most complex networks for studying their behavior and for capturing the uncertainty and the lack of regularity.
A lack of regularity or routine, insufficient or excessive food intake, perceived health outcomes, and limited food variety were cited in different proportions to justify this perception, as shown in Table 1.
