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Lorentzian Algebra
Lorentzian may refer to * Cauchy distribution, also known as the Lorentz distribution, Lorentzian function, or Cauchy–Lorentz distribution * Lorentz transformation * Lorentzian manifold See also *Lorentz (other) Lorentz is a surname and a given name. Lorentz may also refer to: Things named for Hendrik Lorentz * Lorentz factor, Doppler effect *The Lorentz-Lorenz law, the law regarding the refractive index of a substance discovered independently by Hendri ... * Lorenz (other), spelled without the 't' {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cauchy Distribution
The Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f(x; x_0,\gamma) is the distribution of the -intercept of a ray issuing from (x_0,\gamma) with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero. The Cauchy distribution is often used in statistics as the canonical example of a "pathological" distribution since both its expected value and its variance are undefined (but see below). The Cauchy distribution does not have finite moments of order greater than or equal to one; only fractional absolute moments exist., Chapter 16. The Cauchy distribution has no moment generating function. In mathematics, it is closely related to the P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Transformation
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the origins coinciding at 0, where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \left ( \sqrt\right )^ is the Lorentz factor. When speed is much smaller than , the Lorentz factor is negligibly different from 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentzian Manifold
In differential geometry, a pseudo-Riemannian manifold, also called a semi-Riemannian manifold, is a differentiable manifold with a metric tensor that is everywhere nondegenerate. This is a generalization of a Riemannian manifold in which the requirement of positive-definiteness is relaxed. Every tangent space of a pseudo-Riemannian manifold is a pseudo-Euclidean vector space. A special case used in general relativity is a four-dimensional Lorentzian manifold for modeling spacetime, where tangent vectors can be classified as timelike, null, and spacelike. Introduction Manifolds In differential geometry, a differentiable manifold is a space which is locally similar to a Euclidean space. In an ''n''-dimensional Euclidean space any point can be specified by ''n'' real numbers. These are called the coordinates of the point. An ''n''-dimensional differentiable manifold is a generalisation of ''n''-dimensional Euclidean space. In a manifold it may only be possible to defi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz (other)
Lorentz is a surname and a given name. Lorentz may also refer to: Things named for Hendrik Lorentz * Lorentz factor, Doppler effect *The Lorentz-Lorenz law, the law regarding the refractive index of a substance discovered independently by Hendrik Lorentz and Ludvig Lorenz * * Lorentz force, the force exerted on a charged particle in an electromagnetic field * Lorentz transformation, the formula that provides the mathematical backbone for Einstein's theory of special relativity * The Lorentz group, the group containing all Lorentz transformations * Lorentz-Cauchy distribution, a distribution used in fitting peaks in a spectrum * Lorentz surface, a two-dimensional oriented smooth manifold with a conformal equivalence class of Lorentzian metrics. It is the analogue of a Riemann surface in indefinite signature * Lorentz curve (other), various meanings * Lorentz scalar, a scalar which is invariant under a Lorentz transformation * Lorentz Institute, Instituut-Lorentz in Dut ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
