Sentence examples for exists a smooth from inspiring English sources

Property A.2 If there exists a smooth subset ℰ of R q such that 1.

Thus there exists a smooth effect of traffic states for (mathrm{CDI}^{r}).

Suppose there exists a smooth function (eta :X rightarrow {mathbb R}) and a (q -positive, a.e.

In such a case, [19, 29, 30] has proven that there exists a smooth heat kernel : (2.13).

Under the same hypothesis as Theorem 3 in [2], there exists a smooth bifurcation branch from ((d_{j}, (0,0))).

Hence, there exists a smooth map: (h: R^{2}rightarrow R) guaranteed by the implicit function theorem such that (widetilde{Y}=h(Y)) locally holds.

As easily shown (cf. [113]), since, for any of these two actions of ({mathbb {Z}}/3), the nodes are not fixed, then there exists a smoothing for both actions of ({mathbb {Z}}/3) on the curve D. This shows that the strata (N_a) and (N_{a+3}) have D in their closure.

There exist a smooth complex projective surface X and (a,b,c in H^1 XX, {mathbb {Z}}/l)) such that ( a cup b = b cup c = 0,) but (langle {a,b,c}rangle ne 0).

(i) There exist a smooth complex projective surface X and (a,b,c in H^1 XX, {mathbb {Z}}/l)) such that ( a cup b = b cup c = 0,) but (langle {a,b,c}rangle ne 0).   (ii) Let (X rightarrow {mathbb {P}}^6) be an embedding and let Y be the blow up of ({mathbb {P}}^6) along X.

About (4): Since u ≥ ψ, then T k (u) ≥ T k and there exist a smooth function v j ≥ T k such that v j → T k (u) for the modular convergence in W 0 1, x L M ( Q ). ( 4 ) = n ∫ Q T n ( ( u n - ψ ) - ) ( T k ( u n ) - T k ( v j ) μ ) ρ m ( u n ) d x d t ≤ ε ( n, j, μ ).

In particular, if X is a real 2-uniformly smooth Banach space, then there exists a best smooth constant (K>0) such that Vert x+yVert ^{2}leq Vert xVert ^{2}+2 langle y,jx rangle+2Vert KyVert ^{2} for all (x,yin X). ([20]).