Sentence examples for regular values of from inspiring English sources

Consequently, the set of regular values of Φ is dense in ({mathbb {R}}^{n}).

The regular value of the shear fracture toughness is included within the additive range from 0% to 23%.

We prove that if dimcX=2 and c is a regular value of a minimal function ϕ then the nonempty level sets Σc1=Σ1∩{ϕ=c} are compact spaces foliated by holomorphic curves.

Thus, λ is not a regular value of the operator.

If (0in R^{k}) is a regular value of Φ, then for almost all (ain V), 0 is a regular value of (Phi_{a}equivPhi a, cdot)).

If (0in{mathbb {R}}^{k}) is a regular value of Φ, then for almost all (ain V), 0 is a regular value of (Phi_{a}=Phi a,cdot)).

If 0 ∈ R ( k ) is a regular value of Φ, then for almost all a ∈ V, 0 is a regular value of Φ a ≡ Φ ( a, ⋅ ).

Let (Phi R^{n+1}rightarrow R^{n}) be a (C^{1}) map and 0 a regular value of Φ.

Let be open and bounded, and, that is, is a regular value of.

Hence, we derive a contradiction from (4.14), (4.20), and the fact that 0 is a regular value of ρ.

Let the homotopy (Phi :R^{n+1}rightarrow R^{n}) be a (C^{1}) map and 0 be regular value of Φ.