10 problems

Let the softmax policy gradient objective be the objective considered in the paper, and let $\texttt{RMSProp}$ and $\texttt{Adam}$ denote the corresponding optimization methods. RM…

Interface-residual conjecture. The quantity $\eta^\Gamma$ can indicate the modelling error caused by replacing the 2D model by the 0D one, and can therefore drive the choice of the…

Uniform boundedness of the $H$-orthogonal projectors with respect to the $V$-norm is assumed for a family of finite element spaces associated with sufficiently mildly graded locall…

Let $\breve{\boldsymbol{U}}_{\tilde{\mathcal{T}}}^{\delta}$ be the discrete trial space on the refined partition…

Optimal $H^{1/2}$-approximability conjecture. The convergence rate $(\operatorname{dim}V^h)^{-(p+1/2)}$ corresponds to optimal convergence in the $H^{1/2}$-norm in one dimension.

$L^{\infty}(L^{\infty})$ error-analysis conjecture. Conducting an error analysis for the $L^{\infty}(L^{\infty})$ norm may lead to a recovery of the rates seen in Chapter 4.

Square-root blow-up-time rate conjecture. It is conjectured that

Adaptive blow-up-time rate conjecture. It is conjectured that

Blow-up time error-rate conjecture. The difference between the true and numerical blow-up times satisfies

Let $B^\alpha_{p,q;m+1}(\Omega)$ be the Besov space and let $A^\alpha_{p,q;m}(\Omega)$ denote the adaptive approximation space associated with an initial triangulation $P_0$. Consi…