orthogonal projection n. The two-dimensional graphic representation of an object formed by the perpendicular intersections of lines drawn from points on the object to a plane of projection. Also calledorthographic projection. American Heritage® Dictionary of the English Language, Fifth Edition. Copyrig...
Finds the orthogonal projection of a point onto a lineAaron Olsen
Assume that gr is sufficiently regular that its asymptotical expansion may be calculated by the APE condition. Let E00 denote E∂∂r,∂∂r and E⊥ denote the projection of E orthogonal to ∂∂r. A straightforward calculation shows that (2)E00=−12trgrgr″+12rtrgrgr′+14|gr′...
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The first number indicates the total angular momentum, so that l = 1 is a dipole, l = 2 a quadrupole, and so forth. The second is the absolute value of the projection of angular momentum to the z-axis, while p denotes the magnetic or electric character of the multipole (p...
In the VASP, the pre-factors for the cubic parts are almost negligible leading to an efficient scaling with respect to system size. This is possible by evaluating the non local contributions to the potentials in real space and by keeping the number of orthogonalisations small. For systems...
In the perovskite/infinite-layer system, the orientation of empty oxygen planes effectively defines the local c-axis (orthogonal to the rare-earth planes). Without the imposition of additional symmetry by oxygen occupancy, however, the cation lattice directions are essentially equivalent within the ...
The formula for the orthogonal projection is shown to be simple and easy to integrate into the traditional neural model. This projection concept was first developed by Wolfe et al. (1993), but here we show that the projection can be computed in a much simpler way, and that the addition ...
This angular-spectral sensitive front end combines a metal–insulator–metal (MIM) Fabry–Perot color filter and diffractive optics to produce the measurement of orthogonal light-field information from two distinct colors within a single photodetector. The result is the ability to add independent color...
If we restrict f to be in [L.sup.2](0, 1), then [Q.sub.n]f is exactly the orthogonal projection of [L.sup.2](0,1) onto [[DELTA].sub.n] [subset] [L.sup.2](0,1) under the [L.sup.2]- norm [[parallel]f[parallel].sup.2] = [square root of ([[integral].sup.1....