Sentence examples for following commutation from inspiring English sources

The non-commutative output processes y have the following commutation relations bigl[y(t),y(s)^{T}bigr]=2DT_{w}D^{T}s, quadtextit{for all } tgeq s.

This determines the following commutation relations for the noise components bigl[dw(t),dw^{T}(t bigr]=2T_{w},dt, (3) with (T_{w}=frac{1}{2}(F_{w}-F_{w}^{T})).5.5

Pullbacks to the composite mappings of Equation 14 satisfy the following commutation rule: Then, just operation by to Equations 10 and 13 will give the boundary values for the fields κ*C τ and κ*i T C: (15) (15).

A and B satisfy the following commutation property: A bigl( B ( x,y ),B ( y,x ) bigr) =B bigl( A ( x,y ),A ( y,x ) bigr) for all (x,yinOmega); A and B have at least one common lower (resp. upper) coupled fixed point (( u_{0},v_{0} ) ) with (u_{0}leq v_{0}) (resp. (u_{0}geq v_{0})); A is (( alpha^{times},alpha ) )-condensing; B is a (1- ( alpha^{times},alpha ) )-contraction.

(2.4) The Askey-Wilson algebra (AW(3)) involves a nonzero scalar q and three parameters (omega_{1}), (omega_{2}), and (omega_{3}), it was introduced by Zhedanov [15] as an associative algebra generated by X, Y, and Z subject to the following commutation relations: begin{aligned} &YX -q XY = mu_{3}Z + omega_{3},qquad ZY -qYZ = mu_{2}X + omega_{2}, & XZ -qZXY = mu_{1}Y + omega_{1}.

He spoke with VICE in the days following the commutation news about what it means to him, to her, for those she's inspired, and what's next.

For mapping of light propagation in a PC to a tight binding model, we introduce photon creation and annihilation operators a l † Open image in new window and a l α Open image in new window for the site (l a0,α a0) with the following bosonic particle commutation relations: [ a l α, a l α ′ † ] = δ l, l ′ α, α ′ †, [ a l †, a l α ′ † ] = 0, [ a l α, a l ′ α ′ ] = 0. Open image in new window (9).

Analogously, one may obtain, by a direct but cumbersome commutation, the following estimates.

The Poisson brackets are represented here as square brackets (not curly braces), both for consistency with the references and because they will be interpreted as quantum mechanical commutation relations in the next section and as Lie brackets in a following section.

The commutation relations for the processes dy is determined by the matrix (T_{y}) given by the following bigl[dy(t),dy^{T}(t bigr]=2T_{y},dt, with (T_{y}=frac{1}{2} (F_{y}-F_{y}^{T})).

We use the following Hamiltonian to describe DNA molecules, which is modeled as a harmonic oscillator and described by the position and momentum operators q and p, which have a commutation relation [q, p] = i ħ [21], and then H D = ∑ i = 1 n p i 2 2 m i + 1 2 m i ω i 2 q i 2, (2).