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...
( t , x )-depending coefficients and complex-valued lower-order terms. we assume the initial data to be gevrey regular with an exponential decay at infinity, that is, the data belong to some gelfand–shilov space of type \({\mathscr {s}}\) . under suitable assumptions on the decay...
Finds the orthogonal projection of a point onto a lineAaron Olsen
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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′...
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...
Alternatively, we demonstrate that they can be obtained using the conservation of the projection of the total angular momentum on the quantization axis. We discuss how the harmonic spectra of atomic targets depend on the type of the ground state or, for molecular targets, on the pertinent ...
We denote by J and the closures in and the Sobolev space respectively of the set of all smooth solenoidal vectors with compact supports in , where . Let be the orthogonal projection . We introduce the Stokes operator with domain , where is the Laplace operator. It is easy to verify that ...
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...
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....