Sentence examples for in the 3rd dimension from inspiring English sources

Here the matrices Q are the scattering matrices defined as Q g g ′ s s ′ = M g g ′ s s ′ exp i s K g s ⋅ d r + s ′ K g ′ s ′ ⋅ d l where s and s′ are + or – signs, g and g′ index the 2D reciprocal lattice vectors, d r and d l are right and left translation vectors, the matrix M is given in equation (11), and a 3 is the primitive unit vector representing the periodicity in the 3rd dimension.

This way, one obtains equations relating fields at adjacent layers which must also satisfy the Bloch theorem because the system is periodic in the 3rd dimension as well.

The purpose of this study was to assess four different self-ligating bracket designs to determine which has the most accurate slot dimensions in the 0.022" dimension.

Fluid-phase discrimination is achieved here in the T2 dimension; the brine relaxation time is reduced by addition of paramagnetic manganese.

Due to the heteroatom restrictions imposed in the FL criteria, the depth of the FL subsets in the PC3 dimension spanning polarity was rather limited.

The carrier frequencies were set at the water peak in the 1H dimension and at 210 ppm in the 15N dimension.

The spectra were linear-predicted to twice the number of experimental points in the 15N dimension.

Linear prediction in the t1 dimension was used before the Fourier transformation.

Gaussian and exponential weighting functions were applied in the F2 dimension, while the indirectly detected dimensions were Gaussian weighted only.

Residues 69 98 behaved differently: they were clustered between 8 and 8.5 ppm in the 1H dimension, suggesting they were poorly ordered in solution (Fig. 1D).

In the 13C dimension, with a spectral width of 21300 Hz, 96 hypercomplex increments were collected and linear predicted to a total of 384 points.