In mathematics, a one-parameter group or one-parameter subgroup usually means a continuous group homomorphism φ : R → G {\displaystyle \varphi :\mathbb...

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...

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...

a scale parameter is a special kind of numerical parameter of a parametric family of probability distributions. The larger the scale parameter, the more...

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...

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...

{\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...

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...

The Immirzi parameter (also known as the Barbero–Immirzi parameter) is a numerical coefficient appearing in loop quantum gravity (LQG), a nonperturbative...

gravitational parameter μ of a celestial body is the product of the gravitational constant G and the mass M of that body. For two bodies, the parameter may be...

Principles and parameters is a framework within generative linguistics in which the syntax of a natural language is described in accordance with general...

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...

Specifically, let X be a vector field on M. Then X generates a one-parameter group of local diffeomorphisms FlXt, the flow along X. The differential...

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...

parameter rapidity, which specifies a change in frame of reference. This rapidity parameter corresponds to the real variable in a one-parameter group...

principal tool, and one of his greatest achievements, was the discovery that continuous transformation groups (now called, after him, Lie groups) could be better...

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...

relationship between thermal radiation and spacetimes that admit a one-parameter group of isometries possessing a bifurcate Killing horizon, which consists...

correct absolute structure. One of the more powerful and simple approaches is using the Flack parameter, because this single parameter clearly indicates the...

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...

reciprocal of its fractional part, and so on. Circle group Equidistributed sequence One-parameter group Pisot–Vijayaraghavan number Poussin proof Significand...

property that velocity does not have. Thus the rapidity parameter forms a one-parameter group, a foundation for physical models. The Bunney identity represents...

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...

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...

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:...

value, Sterimol parameters consist of three sub-parameters: one length parameter (L), and two width parameters (B1, B5). The three parameters add together...

literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined in one of the following equivalent...

transformation groups: the Galilean group, the Lorentz group, the Poincaré group and the conformal group of spacetime. The one-parameter groups are the first...

mathematical analysis, a C0-semigroup, also known as a strongly continuous one-parameter semigroup, is a generalization of the exponential function. Just as...

field XH, which exponentiates to a one-parameter group of Hamiltonian diffeomorphisms. It follows that the group of symplectomorphisms is always very...