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Radon transform. Maps f on the (x, y)-domain to Rf on the (α, s)-domain.. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.
In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object, f ( x , y ) {\displaystyle f(x,y)} .
The KP equation was first written in 1970 by Soviet physicists Boris B. Kadomtsev (1928–1998) and Vladimir I. Petviashvili (1936–1993); it came as a natural generalization of the KdV equation (derived by Korteweg and De Vries in 1895). Whereas in the KdV equation waves are strictly one-dimensional, in the KP equation this restriction is ...
The way in which a Fourier transform changes x-t data into x-ω (ω is angular frequency) data shows why phase velocity dominates surface wave inversion theory. Phase velocity is the velocity of each wave with a given frequency. The modified wavefield transform is executed by doing a Fourier transform first before a slant stack.
A three dimensional form of the pressure spectrum may be combined with the Young–Laplace equation to show that: [8] G ( k ) ∝ k − 19 / 3 . {\displaystyle G(k)\propto k^{-19/3}.} Experimental observation of this k −19/3 law has been obtained by optical measurements of the surface of turbulent free liquid jets.
In X-ray computed tomography the lines on which the parameter is integrated are straight lines: the tomographic reconstruction of the parameter distribution is based on the inversion of the Radon transform. Although from a theoretical point of view many linear inverse problems are well understood, problems involving the Radon transform and its ...
Tumlirz-Tammann-Tait equation of state based on fits to experimental data on pure water. A related equation of state that can be used to model liquids is the Tumlirz equation (sometimes called the Tammann equation and originally proposed by Tumlirz in 1909 and Tammann in 1911 for pure water). [4] [10] This relation has the form
The Tetens equation is an equation to calculate the saturation vapour pressure of water over liquid and ice. It is named after its creator, O. Tetens who was an early German meteorologist. It is named after its creator, O. Tetens who was an early German meteorologist.