They need consistency, regularity, and discipline.
Mom points out, with regularity, that they need jobs with benefits.
Fundamental questions such as existence, regularity, and the asymptotic behavior of solutions are frequent topics of study and, since such problems are intrinsically non-autonomous, they need to be considered in a non-autonomous setting.
For that we need some regularity on the Lévy measure.
For classical solutions of PPDEs, we need further regularity of the processes.
In this paper, we no longer require the compact property in (1), the uniform boundedness in (2), and the inequality constraint on the range condition of the controller, but instead we need the regularity and a variation of solutions of the given equations.
To prove the next theorem, we need a regularity condition for v such that for 1 ≤ p < ∞, we assume that for a measurable set E ⊂ Q and for σ(E) ≤ θσ(Q) with 0 ≤ θ ≤ 1, we get v ( E ) ≤ 1 - ( 1 - θ ) p v ( Q ).
However, they are of limited utility as one needs sufficient regularity with respect to stochastic variables in order to employ tools such as sparse grids to keep the computational cost feasible.
And the spike variational needs more regularity for the coefficients and the solutions to the state equations, especially in the stochastic case.
Critics of direct-to-consumer (DTC) drug advertising contended that commercials such as those for Vioxx prompted patients to ask their doctors for expensive prescription medications that they did not need, and that, with considerable regularity, doctors complied.
