9 (right), we see that the L∞ error dominates over the L2 one, meaning that the local effects due to the microstructure still have a big impact on the whole solution. Rather than including a large number of POD modes, it is therefore preferable to retain just few of them, and then ...
$$ \Delta ^{4} x(n-2)=f\bigl(n, x(n)\bigr),\quad n\in [1, N] , $$ (1.1) with Dirichlet boundary conditions $$ x(-1)=x(0)=0=x(N+1)=x(N+2) $$ (1.2) or periodic boundary conditions $$ \Delta ^{i} x(-1)=\Delta ^{i} x(N-1),\quad i=0, 1, ...
The --simplify-by-decoration option allows you to view only the big picture of the topology of the history, by omitting commits that are not referenced by tags. Commits are marked as !TREESAME (in other words, kept after history simplification rules described above) if (1) they are ...
a few researchers adopted the tie braking method [40] for a decision tree. The tie-breaking method increases the performance of model. However, the memory overflow problem remains in the big data environment [41]. Random sampling [42]
On all small stencils and the big stencil we use standard reconstruc- tion, obtaining vi(+0)1/2 = 1 3 v炉i + 5 6 v炉i+1 鈭 1 6 v炉i+2 vi(+1)1/2 = 鈭 1 6 v炉i鈭 1 + 5 6 v炉i + 1 3 v炉i+1 vi(+2)1/2 = 1 3 v炉i鈭 2 鈭 7 6 v炉i鈭 1 + 11...
In this section, we consider properties of the difference operatorA. We first give the following notations which will be used in the proofs. Let $$ C_{\omega }:=\bigl\{ x\in C(\mathbb{R},\mathbb{R}): x(t+\omega )=x(t), t \in \mathbb{R}\bigr\} $$ ...
CommitLimitingBesides specifying a range of commits that should be listed using the special notations explained in the description, additional commit limiting may be applied. Using more options generally further limits the output (e.g. --since=<date1> limits to commits newer than <date1>, and ...
Big difference. => 巨大差距。 Third-rate cover up. => 三流掩盖。 whoever did it probably wasn't expecting an investigation. => 谁做的可能不会期待调查。 whoever wrote meperidine also wrote acetaminophen. => 谁写了哌替啶也写对乙酰氨基酚。
\begin{aligned} B_{q}(x,s):={}& \int_{0}^{1}t^{(x-1)}(1-qt)^{(s-1)}\,d_{q}t \\ ={}&(1-q) \sum_{n=0}^{\infty}q^{n} \bigl(1-q^{n+1}\bigr)^{(\alpha -1)} \bigl(q^{n} \bigr)^{(x-1)}=\frac{\Gamma_{q}(x)\Gamma_{q}(s)}{\Gamma _{...
{N,k}}\left( n_1,\dots ,n_k \right) \Big \}+\frac{\lambda N\left( N-k \right) }{\left( N-1 \right) }\widehat{F_{N,k}}\left( n_1,\dots ,n_k \right) \sum _{i\le k}\left( \widehat{g_N}\left( n_i \right) -1 \right) , \end{aligned} \end{aligned}$...