is, by definition, the

orthogonal projection of [x.sup.2] in the direction of [x.sup.1] (or of [[??].sup.1]).

Next, we consider the

orthogonal projection [mathematical expression not reproducible] is defined by

By (30), Lemma 5, condition (i), and the linearity

orthogonal projection of [P.sub.C], we have

On the other hand, for closed-loop systems subject to the input and output measurement noises, [23] developed a new closed-loop subspace identification algorithm (SOPIM) by adopting the EIV model structure of SIMPCA and proposed an

orthogonal projection approach to avoid identifying the parity space of the feedback controller.

Or equivalently, M is a reducing subspace for S if and only if S[P.sub.M] = [P.sub.M]S and [S.sup.*][P.sub.M] = [P.sub.M][S.sup.*], where [P.sub.M] is the

orthogonal projection from H onto M.

If v and w are two vector fields defined in a neighborhood of S, then the covariant derivative [[nabla].sup.S.sub.v]w is equal, at x [member of] S, to the

orthogonal projection of [D.sub.v]w, projected orthogonally to the tangent space [T.sub.x]S (cf.

In a radial plane, radially on the inside of the radially innermost point of the at least one layer of carcass reinforcement and axially on the outside of the geometric center of the bead wire, the radius of curvature at a point on the exterior surface of the bead is greater than the radius of curvature at the point of

orthogonal projection of the point of the exterior surface of the bead onto the at least one layer of carcass reinforcement.

Electronic auction: auction in electronic form for the right to conclude a civil law contract for the performance of works on the overhaul of the

orthogonal projection of the building of the headquarters of the kgb mod no.

In this study, an automated method is proposed to align high-throughput metabolite profiles using the

orthogonal projection technique, which is a powerful chemometric strategy [14].

An element [x.sup.r] [member of] X is a reflection point with respect to H of the element x [member of] X if and only if [h.sub.x] := (x + [x.sup.r])/2 is an

orthogonal projection of the point x onto H, that is, if and only if

Then calculate the

orthogonal projection of the measurement vector y on this support set.

Denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the vector bundle so induced and, correspondingly, denote by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] the

orthogonal projection. Define the linear Poincare flow as [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].