Sentence examples for by the singular solution from inspiring English sources
We show that the limiting behavior is dominated by the singular solution ΔG−Gq="0 in Ω\{P}, G="0 on ∂Ω.
Therefore, the criterion for oscillatory solutions is not satisfied by the singular solution for any odd value of (n>3) and this includes the marginal case with (n=5).
It is worth noting that the solution of the problem of order zero is contained in the singular surface S filled by the singular solutions for ((mathcal {P}_{S})), defined by (23).
This is achieved by combining the SBM with the singularity subtraction techniques where the solution is decomposed into the singular solution and the regular solution.
The singular solution is related to the general solution by its being what is called the envelope of that family of curves representing the general solution.
But he made it clear that in his view physician-assisted death was not the singular solution it was in 1991, when he made history by publishing an account about his role in a patient's death.
If the singular solution is an envelope, it can be found from the general solution by solving the maximum (or minimum) problem of finding the value of the parameter c for which y has a maximum (or minimum) value for a fixed x, and then substituting this value for c back into the general solution.
For the problem under consideration, apart from the singular solution, the solutions of equations (36) and (40) are finally given by (43).
The singular solutions at corners and the fundamental solution are essential in both theory and computation.
The singular solutions for linear elastostatics at corners are essential in both theory and computation.
