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...

{\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...

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...

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...

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...

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

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...

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...

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...

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

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

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

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...

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...

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

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...

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

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

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

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

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

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:...

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...

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

any one-parameter unitary group of symmetries of the physical system. Time would be replaced by a suitable coordinate parameterizing the unitary group (for...

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

form of the mean ergodic theorem, let Ut be a strongly continuous one-parameter group of unitary operators on H. Then the operator 1 T ∫ 0 T U t d t {\displaystyle...