In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism φ : R → G {\displaystyle \varphi :\mathbb...
7 KB (1,003 words) - 23:13, 6 May 2024
mathematics, Stone's theorem on one-parameter unitary groups is a basic theorem of functional analysis that establishes a one-to-one correspondence between self-adjoint...
10 KB (1,607 words) - 16:33, 14 April 2024
action of T. In Lie theory, a one-dimensional subspace of a Lie algebra is mapped to a one-parameter group under the Lie group–Lie algebra correspondence...
3 KB (377 words) - 09:59, 13 February 2024
Continuous symmetry (category Group actions (mathematics))
{\displaystyle h\in H} . The simplest motions follow a one-parameter subgroup of a Lie group, such as the Euclidean group of three-dimensional space. For example translation...
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recognize the one-parameter matrix group of rotations exp(iλJz) about the z-axis. Differentiating with respect to the group parameter λ and setting it...
65 KB (9,740 words) - 16:15, 2 February 2024
the one-parameter group of transformations generated by A. Thus, for example, if A is a skew-Hermitian matrix, then U(t) = exp(tA) is a one-parameter group...
6 KB (866 words) - 01:13, 3 July 2024
maps on the circle. This gives the circle group the structure of a one-parameter group, an instance of a Lie group. In fact, up to isomorphism, it is the...
13 KB (2,025 words) - 17:26, 20 May 2024
a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more...
7 KB (997 words) - 05:20, 18 July 2022
Symmetry of second derivatives (redirect from Clairaut's Parameter)
That is, Di in a sense generates the one-parameter group of translations parallel to the xi-axis. These groups commute with each other, and therefore...
34 KB (5,331 words) - 16:20, 9 July 2024
The Immirzi parameter (also known as the Barbero–Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative...
12 KB (1,524 words) - 18:52, 24 July 2022
words, a parameter word is a string over a given alphabet having some number of wildcard characters. The set of strings matching a given parameter word is...
12 KB (1,743 words) - 15:46, 27 April 2022
gravitational parameter μ of a celestial body is the product of the gravitational constant G and the total mass M of the bodies. For two bodies, the parameter may...
15 KB (1,465 words) - 16:55, 29 January 2024
Principles and parameters is a framework within generative linguistics in which the syntax of a natural language is described in accordance with general...
15 KB (2,088 words) - 01:52, 8 November 2023
Hansen solubility parameters were developed by Charles M. Hansen in his Ph.D thesis in 1967 as a way of predicting if one material will dissolve in another...
9 KB (1,290 words) - 00:21, 1 August 2024
Sophus Lie (category Group theorists)
principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called, after him, Lie groups) could be better...
17 KB (1,673 words) - 22:09, 27 July 2024
reciprocal of its fractional part, and so on. Circle group Equidistributed sequence One-parameter group Pisot–Vijayaraghavan number Poussin proof Significand...
4 KB (534 words) - 03:34, 17 May 2024
and densely defined. Definition (one-parameter group). Let A {\displaystyle A} be a C*-algebra. A one-parameter group on A {\displaystyle A} is a family...
10 KB (1,826 words) - 19:57, 24 November 2023
parameter rapidity which specifies a change in frame of reference. This rapidity parameter corresponds to the real variable in a one-parameter group of...
19 KB (2,804 words) - 22:37, 12 July 2024
By integrating a vector field we get (at least a small part of) a one-parameter group of diffeomorphisms on the sphere; and all of the mappings in it are...
14 KB (1,803 words) - 03:23, 10 August 2024
relationship between thermal radiation and spacetimes that admit a one-parameter group of isometries possessing a bifurcate Killing horizon, which consists...
6 KB (865 words) - 03:33, 26 December 2023
value, Sterimol parameters consist of three sub-parameters: one length parameter (L), and two width parameters (B1, B5). The three parameters add together...
20 KB (2,055 words) - 22:58, 2 December 2023
property that velocity does not have. Thus the rapidity parameter forms a one-parameter group, a foundation for physical models. The Bunney identity represents...
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correct absolute structure. One of the more powerful and simple approaches is using the Flack parameter, because this single parameter clearly indicates the...
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quantum mechanical system, its time evolution is described by a one-parameter group of automorphisms {αt}t of Q. This can be narrowed to unitary transformations:...
20 KB (2,831 words) - 21:20, 28 May 2024
discovered that the coupling parameter g(μ) at the energy scale μ is effectively given by the (one-dimensional translation) group equation g ( μ ) = G − 1...
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Symplectomorphism (redirect from Symplectomorphism group)
field XH, which exponentiates to a one-parameter group of Hamiltonian diffeomorphisms. It follows that the group of symplectomorphisms is always very...
9 KB (1,104 words) - 17:24, 15 August 2024
literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent...
6 KB (1,011 words) - 10:23, 14 August 2023
any one-parameter unitary group of symmetries of the physical system. Time would be replaced by a suitable coordinate parameterizing the unitary group (for...
58 KB (8,100 words) - 00:53, 6 August 2024
the case of a homogeneous system, the mappings Gt = Ft,0 form a one-parameter group of transformations of X, that is G t + s = G t G s . {\displaystyle...
8 KB (1,014 words) - 09:11, 19 July 2024
Lie theory (category Lie groups)
transformation groups: the Galilean group, the Lorentz group, the Poincaré group and the conformal group of spacetime. The one-parameter groups are the first...
10 KB (1,257 words) - 23:09, 27 July 2024