Sentence examples for using the commutation from inspiring English sources

Moreover, related families of TPMs are also deducted using the commutation of factors in any products of spatial translations and rotations around an axis.

Now, suppose the symmetry maps (H_{j}) to (H_{k}), meaning (H_{k} = U_{g} H_{j} U_{g}^{dagger}), then using the commutation properties stated above, begin{aligned}& operatorname{tr}frac{ partial e^{-beta H} }{partiallambda_{k}} =- betaoperatorname{tr}e^{-beta H} U_{g} H_{j}U_{g}^{dagger} = operatorname{tr} frac{ partial e^{-beta H} }{partiallambda _{j}}.

Using the commutation relations between E i j and U i j, one can convince oneself that the infinitesimal generator of a gauge transformation at site m is given by (4) G m = E i m + E k m − E m j − E m ℓ.

The eigen values of the total angular momentum operator can be obtained by using the commutation relations of the components of the angular momentum with each other and by using the raising the lowering operators that is made by the combination and subtraction of the components of the angular momentum.

This proof uses the commutation method and shares structure with the proofs in [2, 5].

Also, for the last equality, we have used the commutation relations for the processes dw given in (3).

A 22.9 kV class hybrid fault current limiter (FCL) developed by Korea Electric Power Corporation and LS Industrial Systems in 2006 operates using the line commutation mechanism and begins to limit the fault current after the first half-cycle.

Using the identities above, the commutation relations of the ℓ k Q operators, and some trigonometric identities, we obtain [ i h a 1, i h b Z ] = [ i h a 1, i h b X ] = [ i h a 1, i h b Y ] = 0, (48a).

It is an important development direction of using the HVDC Flexible in the overhead line transmission systems to solve the commutation failures caused by the system faults at the same time of saving the construction costs.

Spikes or vibration effect and eddy currents due to the commutation of strong diffusion gradient pulses, were corrected using the Quality Check pipeline of the Connectomist toolbox used in this study (Duclap et al., 2012).

Using the interaction picture is advantageous because the equations of motion as well as, under certain conditions, the commutation relations are the same for interacting fields as for free fields.