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X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering, when there is no change in the energy of the waves. The resulting map of the directions of the X-rays far from the sample is called a diffraction pattern.
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.
X-ray optics is the branch of optics dealing with X-rays, rather than visible light.It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray diffraction, X-ray crystallography, X-ray fluorescence, small-angle X-ray scattering, X-ray microscopy, X-ray phase-contrast imaging, and X-ray astronomy.
where the dot represents differentiation with respect to . Because timelike geodesics are maximal, one may apply the Euler–Lagrange equation directly, and thus obtain a set of equations equivalent to the geodesic equations. This method has the advantage of bypassing a tedious calculation of Christoffel symbols.
D-notation leaves implicit the variable with respect to which differentiation is being done. However, this variable can also be made explicit by putting its name as a subscript: if f is a function of a variable x, this is done by writing [6] for the first derivative, for the second derivative,
X-ray absorption (left) and differential phase-contrast (right) image of an in-ear headphone obtained with a grating interferometer at 60kVp. Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images.
In the theory of Lorentzian manifolds, Fermi–Walker differentiation is a generalization of covariant differentiation.In general relativity, Fermi–Walker derivatives of the spacelike vector fields in a frame field, taken with respect to the timelike unit vector field in the frame field, are used to define non-inertial and non-rotating frames, by stipulating that the Fermi–Walker ...
X-ray standing waves, another X-ray variant where the intensity decay into a sample from diffraction is used to analyze chemistry. [ 4 ] Grazing-incidence small-angle scattering (GISAS) a hybrid approach using small scattering (diffraction) angles with X-rays or neutrons.