Sentence examples for and considering the function from inspiring English sources

Given and considering the function : defined by (4.15).

(i) Let α j ∈ ℝ (j = 1,..., n) and consider the function.

Now, assume that (Ggamma_{1} nleqslant Ggamma_{2}) and consider the function hat{alpha}(x)=maxbigl{ Ggamma_{1}(x),Ggamma_{2}(x) bigr}.

For the moment, we fix x 0,…,x N−1 and consider the function u t,x):=v N−1 t,x 0,…,x N−1,x).

Let z 0 ∈ E 0 be fixed and consider the function h : E − × E + → R defined by h ( z −, z + ) = I ( z 0 + z − + z + ).

Let (H=C=mathbb{R}= -infty,infty)) and consider tH=C=mathbb{R}= -infty defined by (F(x)=arctan(x)-frac{pi }{2}),infty C).

The subspace W is spanned by eigenfunctions corresponding to the eigenvalues λ k, k ≥ 2. Let v ∈ V be fixed and consider the function h : W → R defined by h ( w ) = I ( v + w, s ).

Indeed, if (12) is satisfied, then according to Lemma 3 the solution v ( x ) of Dirichlet problem (10) with g 1 ( x ) = Γ 2 m [ g ] ( x ) exists and v ( 0 ) = 0. Therefore, we may apply the operator Γ 0 − 1 to v ( x ) and consider the function u ( x ) = C + Γ 0 − 1 [ v ] ( x ).

Now, we let h > 0 and f ∈ L ∞, ∞ r ( G ) be arbitrary, and consider the function f h ( x ) : = f ( x / h ), x ∈ G. Evidently, f h ∈ L ∞, ∞ r ( G ) and by substituting f h into (22) we derive inequality (18).

Recall Example 3.1 and consider the function hat{F}(t)=1big/ biggl[cos biggl(frac{ln vert sqrt{2}tvert }{ln (1/P_{1})} pi biggr)+cos biggl( frac{ln vert sqrt{3}tvert }{ln (1/P_{2})}pi biggr) biggr], where (P_{1}neq P_{2}), (P_{1},P_{2}>1) and (tin mathbb{T}^= mathbb{R}backslash {0}).

Let us make a mesh partition on the area (Sigma_{0}) and consider the function (U x, tau)) at the discrete set of points begin{aligned}& x_{i} = M^ + (i - 1)h,quad i = 1, 2, ldots, m,m + 1; h = frac{M^ - M^{m};& tau_{j} = (j - 1 p,quad j = 1, 2, ldots, n,n + 1 p = frac{tilde{T}}{n}.