Sentence examples for define the projection from inspiring English sources

We first define the projection operators in ({mathcal {H}}^{p}_{1}).

For any finite set (A subsetmathbb{N}), define the projection operator (P_{A}x=sum_{i in A}e_{i}^(x e_{i}).

For x ∈ R n, ξ ∈ F ( x ), we first define the projection residue r ( x, ξ ) = x − P X ( x − ξ ).

end{aligned} (6)(b) We define the projection operator as follows: begin{aligned} P_nbar{u} x,t)=sum _{i=1}^n B_ibar{phi }_i x,t).

This chapter discusses the way to draw layout rules, which define the projection methods used to describe artifacts and the way 3D views are represented on a 2D paper.

More specifically, we can define the projection of a particular data rate reduction ΔR on these two dimensions as follows P g ( Δ R ) = the price of greening, P f ( Δ R ) = the fairness of greening, (15).

Next we define the projections P : X → X, Q : Y → Y by. and the isomorphism J : Im Q → Im P as J y = y.

Next, define the projections (P Xrightarrow X) by Px= int_{0}^{1}x(s),ds, and (Q Yrightarrow Y) by Qy= int_{0}^{1}y(s),ds.

Quantity ΔΧ (Fig. 5) represents the distance of the projection of the center of the curvature at the end of the curve from the middle of the linear segment, which defines the projection of the whole curve.

In order to calculate a pure flexion angle in one plane (sagittal plane) and eliminate the abduction component of the movement, we defined the projection of the arm vector onto the true sagittal and frontal planes.

The closest point projection defines the projection vector p to be the shortest vector to the surface, i.e. (17) min p p, subject to d (x + p ) = 0 which is transformed into an equivalent problem using the Lagrangian (18) L (p, λ ) = p 2 + λ · d (x + p ) → min p max λ The objective function is quadratic, but the distance may be highly nonlinear, the surface may be non-convex and non-smooth.