Sentence examples for be the projection operator from inspiring English sources

Let be the projection operator and be the homotopy operator.

Let (P_{Omega}(cdot)) be the projection operator onto Ω under the Euclidean norm.

Let,,, be a smooth differential form in a bounded, convex domain, be the projection operator and be the homotopy operator.

Let,,, be a solution of the nonhomogeneous -harmonic equation (1.2) in a bounded domain, let be the projection operator and let be the homotopy operator.

Let (varphi(t) = t^{p} ), (p geq1), (u in L^{p}(Omega, wedge^{l})) be a solution of the non-homogeneous A-harmonic equation, T be the homotopy operator, and H be the projection operator.

Let,,, be a solution of the nonhomogeneous -harmonic equation in a bounded, convex domain, be the projection operator and be the homotopy operator, where the measure and are defined by, and for some and with for any.

where is the projection operator from to.

Assume that is the projection operator and is the homotopy operator.

Denote by y the observation: (5 where H is the projection operator, and z° is the observation error.

If (f_{1}(cdot)=|cdot|_{1}), then we can deduce that ((I+partial f_{1}^)^{-1} v =operatorname{proj}(v)), where proj is the projection operator.

To be more precise, let Q K r = I − h − 1 P K r, where P K r is the projection operator, h − 1 is the inverse of the nonlinear operator h and I is the identity operator.