Sentence examples for at different occurrence from inspiring English sources
Throughout this paper C > 0 denotes a generic constant independent of mesh parameters and may be different at different occurrence.
Then the following error estimates hold: Vert P_{h}boldsymbol{u}-boldsymbol{u} Vert _{s}le Ch^{2-s} Vert boldsymbol{u} Vert _{2},quad s=0,1, forallboldsymbol{u}in bigl[H^{2}(Omega bigr]^{2}, where C used hereinafter represents a general positive constant which is possibly different at different occurrence and does not rely on h and k.
On the other hand, the letters C, C ′ denote generic constants independent of the finite element division size and not necessarily the same at different occurrences.
We denote by δ a sufficiently small positive number and by ε an arbitrarily small positive number, not necessarily the same at different occurrences.
(2.16) Noting that (Vert uVert _{0}le cVert nabla uVert _{0}) in (H_{0}^{1}(Omega)) (where c is a positive constant independent of h and k, possibly different at different occurrences).
If (fin H_{0}^{s}(mathbf {B}^{d} cap H^{r}(mathbf {B}^{d})) with (rgeq s), then, for (Ngeq s), begin{aligned} &biglvert f-S_{N}^{-s}fbigrvert _{H^{k}(mathbf {B}^{d})} leq C N^{-r+k} Vert fVert _{H^{r}(mathbf {B}^{d})}, end{aligned} where C used next is a positive constant which is possibly different at different occurrences, being independent of the degree N of polynomials.
