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Computing statistical quantities of interest of the solution of PDE on random domains is an important and challenging task in engineering.
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Hadamard Finite Part integrals (shortly FP integrals), regarded as pth derivative of Cauchy principal value integrals, are of interest in the solution of hypersingular BIE, which model many different kind of Physical and Engineering problems (see [1] and the references therein, [2], [3, 4]).
The single images are derived from the cross spectral densities of all combinations of MEG sensors averaged over the time frequency range of interest, and the solution of the forward problem for each location on a grid specified by input voxel space.
A computational implementation of our technique shows that the method preserves in practice the mathematical features of interest of the exact solutions considered.
Understanding the flow behavior of wormlike micelle solutions in porous media is important due to the growing interest of these solutions in enhanced oil recovery.
As is well known there has been a great deal of interest in the solution of fractional differential equations in the analytic and numerical sense [4 9].
In the case of Spitzer and the investment banks' conflict-of-interest issue, the solution could simply focus on better disclosures concerning which reports written by the analysts involve companies that are the bank's clients.
The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain.
This step provides us with a result of independent interest: the trapping of the solution in self-similar variables near the set of stationary solutions, valid also for non-characteristic points.
The main idea of this extension is to design a new "quantity of interest" based on the solution of the direct problem and the given multiple goals.
There has been a great deal of interest in the solutions of fractional evolution equations in infinite dimensional space.
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