Ads
related to: loose wave bundles with frontal plane linesebay.com has been visited by 1M+ users in the past month
Search results
Results from the WOW.Com Content Network
From the basic one-dimensional plane-wave solutions, a general form of a wave packet can be expressed as (,) = (()). where the amplitude A(k), containing the coefficients of the wave superposition, follows from taking the inverse Fourier transform of a "sufficiently nice" initial wave u(x, t) evaluated at t = 0: = (,) . and / comes from Fourier ...
There is a rank 2 vector bundle over the 3-dimensional complex projective space associated to V, that assigns to each line L of V the 2-dimensional vector space L ⊥ /L. Then a plane of V corresponds to a jumping line of this vector bundle if and only if it is isotropic for the skew-symmetric form.
Suppose that is a space and that is a line bundle on .A global section of is a function : such that if : is the natural projection, then =.In a small neighborhood in in which is trivial, the total space of the line bundle is the product of and the underlying field , and the section restricts to a function .
The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile () is a sinusoidal function. That is, (,) = (() +) The parameter , which may be a scalar or a vector, is called the amplitude of the wave; the scalar coefficient is its "spatial frequency"; and the scalar is its "phase shift".
The projective bundle P(E) of a vector bundle E is characterized by the universal property that says: [2] Given a morphism f: T → X, to factorize f through the projection map p: P(E) → X is to specify a line subbundle of f * E. For example, taking f to be p, one gets the line subbundle O(-1) of p * E, called the tautological line bundle on ...
The light from this type of wave is referred to as collimated light. The plane wavefront is a good model for a surface-section of a very large spherical wavefront; for instance, sunlight strikes the earth with a spherical wavefront that has a radius of about 150 million kilometers (1 AU). For many purposes, such a wavefront can be considered ...
Ads
related to: loose wave bundles with frontal plane linesebay.com has been visited by 1M+ users in the past month