An optimal order error estimate in the fractional energy norm was proved under the assumption that the true solution to the fractional diffusion equation has the desired regularity.
However, when following this approach, it is more difficult to obtain the desired regularity of the value function.
On the basis of the iteration lemma we get the boundedness of the functional, which leads to the desired regularity in points while the excess quantity is small.
It turns out that to get the desired regularity one has to modify in a non trivial way the theory developed by Alt and Caffarelli in [5].
Lusin was so much in despair that, in a paper of 1925, he came to the "totally unexpected" conclusion that "one does not know and one will never know" whether the projective sets have the desired regularity properties (quoted in Kanamori [1993], 250).
The results indicated that, the stretched electrospun binary-PAN nanofibers possessed the most desired thermo-chemical properties, macromolecular regularity, crystal and macromolecule orientations, and dimensional stability; and thus they are suitable for the development of high-performance carbon nanofibers.
In order to determine what hard disk diameter would yield simulated distributions with nearest neighbor regularity indices of the desired value, a series of simulations were conducted with a range of hard disk diameter and the resultant regularity indices were calculated (data not shown).
Early computer programmers embraced iterate to refer to the repetitive processes that were their bread and butter, looping through a sequence of instructions with mechanical regularity to achieve a desired result.
But a mechanical regularity is not to be desired here, even in the rhythm-focused action of the first movement, and in any case Schiff had more than enough sparkle and toughness for the work.
Some of the non-religious ardently desire the warmth of human solidarity and the regularity of fixed ritual.
Herein, we developed a facile dip-coating process to fabricate desired patterns of silica nanoparticles with neat edge and high regularity.
