Multiplication orthogonal

The most convenient way to plot a projection of an w-dimensional system in an m-dimensional linear projective subspace is to use multiple orthogonal projection, in which the directions of projection rays are parallel to the normal vectors (qi, q>,. .., qn-m) defining the projective subspace. Under this projection, a point is first projected in the direction of qi, then of q/, and so on. A convenient set of canonical coordinates describing the projective subspace is given by... 

A special case of orthogonal projection in homogeneous space is the frequently used Janecke projection, where one reference component is neglected and the composition of the remaining species are renormalized. As a special case of multiple orthogonal projection, we define multiple Janecke projection, where the dimensionality is reduced directly to m. If components (m + 1) to (C - 1) are taken to be the reference components, the elements of the projection ray vectors (gi, qi, qc-m-1 are... 

Equation (9) describes a linear stoichiometric variety of dimension R. A reactive projection is defined as a multiple orthogonal projection from a C-dimensional space to a (C - R - 1)-dimensional subspace, where the directions of the R projection rays follow the directions of (qi, q>,. .., q ) defined in Eq. (10). Such projection causes the stoichiometric variety to disappear, leaving a reaction-invariant projection. The set of canonical coordinates defining the projective subspace can be found by substituting Eq. (10) into Eqs. (2)—(4) [7]. 

Hardy LW, Peet NP. The multiple orthogonal tools approach to define molecular causation in the validation of druggable targets. Drug Discov Today 2004 9(3) 117-126. 

Beal DM, Jones LH (2012) Molecular scaffolds using multiple orthogonal conjugations applications in chemical biology and drug discovery. Angew Chem Int Ed 51 (26) 6320-6326. doi 10.1002/ anie.201200002... 

Shelbourne M, Brown T Jr, El-Sagheer AH, Brown T (2012) Fast and efficient DNA crosslinking and multiple orthogonal labelling by copper-free click chemistry. Chem Commun 48(91) 1184-11186. doi 10.1039/c2cc35084j... 

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