Sentence examples for rotation operator from inspiring English sources

For a rotation R in the three-dimensional rotational group SO(3), let Λ R be the rotation operator, such that (Λ Rg )(x) := g[ R-1 x)]. R-1 x

Indeed, taking with the usual inner product and norm and taking, let be a rotation operator defined by (2.15).

Also, as it can be seen from Equation 9 that this rotation operator is not supposed to cause a lag in the latter coefficient.

In time-frequency plane, Fourier transform can be interpreted as a counterclockwise rotation operator from the time axis to the frequency axis.

Later Almeida analyzed the relationship between the FrFT and the Wigner-Ville Distribution (WVD) and interpreted it as a rotation operator in the time-frequency plane [15].

Referring to Eq. (147), the rotation operator (hat {sigma }_{phi_{0}}) for (mathrm{WRSE}_{k}) is treated as fixed across all pulses.

In our case, we set N = M = 4, and W is a simple rotation-scaling operator in the (Ir,R,G,B) hypercolor space.

From Table 4, it is also evident that at moderate noise level rotation invariant operators ( LBP 8, 1 ri and LBP 8, 1 riu 2 ) cannot exhibit higher accuracy as rotation invariance disregards many alternative patterns which would contribute for achieving discrimination between the fault types.

Clifford analysis is centered around the concept of monogenic functions, i.e. null solutions of a first order vector valued rotation invariant differential operator called the Dirac operator which factorizes the Laplace operator (see [3, 4]).

The theory is centred around the concept of monogenic functions, i.e. null solutions of a first-order vector-valued rotation invariant differential operator, called Dirac operator, which factorises the Laplacian; monogenic functions may thus also be seen as a generalisation of holomorphic functions in the complex plane.

QEAs are characterized by Q-bit representation, variation operators such as rotation gates, measurement operators, and population structures.