Sentence examples for by the continuous mapping from inspiring English sources

Finally, by the continuous mapping theorem, we arrive at the expression in (29).

Also, by the continuous mapping theorem (see Appendix A), we infer from (10) that if (C_{n}stackrel {d}{rightarrow}C), then C satisfies the distributional identity Cstackrel{d}AC+Delta, quad C text{ and } (A,Delta ) text{ independent}.

Because x B,m converges weakly to standard normal distribution, then by the continuous mapping theorem, σ x B,m converges weakly to normal distribution with variance σ 2 [12].

(H^{2n}(Y, {mathbb {Z}}) cong H^{2n}(Gamma, {mathbb {Z}})) via the natural homomorphism of cohomology groups induced by the continuous map of Y to the classifying space (X = B Gamma ), associated to the homomorphism (pi _1(Y) cong pi _1(X) cong Gamma ).

where f : C V → S V 2 q is the continuous mapping defined by f = ( φ ( 0 ), φ ).

By the Brouwer fixed point theorem, the continuous mapping (fcircxi delta_{n}rightarrowdelta_{n}) has a fixed point (p^indelta_{n}); that is, (p^=f xi(p^))).

Define the continuous mapping (mathcal{F}:mathbb{R}^{2}rightarrow mathby{R}^{2}) by (mathcal{F}=(mathcal{F}_{1}, mathcal{F}_{2})=mathcal{P}-mathrm{id}).

Use again the complete metric space with the supremum metric and defined in (2.4) and replace the continuous mapping (2.5), using (2.12), by defined as (2.14).

Define the continuous mapping (mathcal{F}:mathbb{R}^{2}rightarrow mathby{R}^{2}) by (mathcal{F}=(mathcal{F}_{1}, mathcal{F}_{2})=mathcal{P}-mathrm{id}), where (mathcal{P}) denotes the Poincaré mapping associated to system (4.19).

If (mu(C_{N})=0) for some (N inmathbb{N}) then (C_{N}) is a compact set and by virtue of Schauder's theorem the continuous map (T C_{N} to C_{N}) has a fixed point in (C_{N} subset C).

In this case, the relationship is defined by learning continuous mapping functions between the face image and the pose space [29 31].