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Euler angles for the above three Cartesian frames can be defined as a set of angle describing the rotation of (xmol ymol zmol) with respect to (xlab ylab zlab), a set of angle (θ p, φ p, χ p ) describing the rotation of (x p y p z p ) with respect to (xlab ylab zlab), and a set of angle describing the rotation of (xmol ymol zmol) with respect to (x p y p z p ).
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Definition 5. A mobility path is defined as a set of consecutive coordinates and angles of travel over a time interval : (21).
The dihedral bonds of a rotamer are represented as a set of integers depending on the angle measure as explained in Fig. 2.
A representative sandwich structure, containing catalyst particles, is modeled as a set of triangular tubes ("Toblerones"), intersecting at 90° angles.
Different from the histogram of angles treating the 2D object as a set of points, F-histogram method handles the shapes as longitudinal segments.
The program "CURVATURE" [ 5] was among the first to allow the calculation of DNA curvature of an arbitrarily long DNA sequence, and provided a set of wedge angles as structural parameters estimated from experimental data.
The input for this step is the set Q of residue positions that are modeled as flexible using backrubs and rotamers, and a set of allowed primary rotation angles.
Grid points at 0.2° spacing were set as point sources and a set of rays with different take-off angles were shot to CHNAR from each grid point.
The numerical results are arranged in a set of equations as a function of parametric angle, crack depth, crack length, y- order and z- order of the monomials.
Hence, using as input only: (1) a set of residues for which backrubs will be applied and (2) a set of primary rotation angles, backrub conformations can be generated using the automated procedure described in this section.
Here, every feature is described by a set of geometric constraints such as distances between edges and angles between faces.
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