Therefore, researchers have investigated extending the solution-processed layers [4 6].
Finally, extending the solution uniquely to the closed interval [ 0, 1 ], we reach the result.
This approach takes into account the a priori structural constraints of the synthesis problem, analytically extending the solution to the subdomain of synthesis as well as finding the tolerances for small perturbations of the objective functional.
Extending the solution beyond wave breaking imposes significant challenge as can be illustrated in the case of multipeakons given by u ( t, x ) = ∑ i = 1 n p i ( t ) e − | x − q i ( t ) |, (5.1).
By extending the solution of a given ordinary differential equation (ODE) into the complex domain, one has the possibility, instead of asking for a global solution for an ODE, to look for solutions locally and obtain a more global result by analytic continuation.
The remaining part from the right hand side can be written in the form | x N + 1 | p R N + 1 ( 1 + Φ ( Δ z N + 1 z N + 1 ) ), where Δ z N + 1 is evaluated by extending the solution z from the interval [ 0, N − 1 ] to [ 0, N ].
To extend the solutions globally we build on an idea due to Colliander, Holmer and Tzirakis.
This article extends the solutions to the prediction problem for factorizable real random signals to the class of improper complex-valued random signals.
Now we need estimates which allow us to extend the solutions to the whole interval ([0, T]) and pass to limit as (mrightarrowinfty) and (epsilonrightarrow0). Hence, uniform estimates with respect to m and ϵ are needed.
Broman (2005) extended the solutions to the two- and three-locus haplotype probabilities for the two, four, or eight-way RIL by sibling mating.
