We present a generalized equations-of-motion method that efficiently calculates energy spectra and matrix elements for algebraic models. The method is applied to a five-dimensional quartic oscillator that exhibits a quantum phase transition between vibrational and rotational phases. For certain parameters, 10 x 10 matrices give better results than obtained by diagonalizing 1000 x 1000 matrices.

The present work concerns the algebra of semi-magic square matrices. These can be decomposed into matrices of specific rotational symmetry types, where the square of a matrix of pure type always has a particular type. We examine the converse problem of categorising the square roots of such matrices, observing that roots of either type occur, but only one type is generated by the functional calc...

It is often useful to compute a lot of matrix exponentials in computer graphics (CG). The exponential of a matrix is used for the smooth deformation of 2D or 3D meshed CG objects. Hence, we need to compute a large number of the exponentials of 3 × 3 rotational matrices and 3 × 3 real symmetric matrices. For rotational matrices, Rodrigues’ formula is known to compute their exponentials. We inves...

While steady empirical progress has been made in understanding the structure and composition of hot planet atmospheres, direct measurements velocity signatures, including winds, rotation, jets, have lagged behind. Quantifying atmospheric dynamics planets is critical to a complete their atmospheres such may even illuminate other planetary properties, as magnetic field strengths. In this manuscri...

Three and four parameter representations of 3x3 orthogonal matrices are extended to the general case of proper NxN orthogonal matrices. These developments generalize the classical Rodrigues parameter, the Euler parameters, and the recently introduced modified Rodrigues parameters to higher dimensions. The developments presented generalize and extend the classical result known as the Cayley tran...

In general, the diffusion and mobility matrices of a particle depend on the choice of the reference center which is used to describe the rotational and translational motion. The requirement that the rotational-translational mobility matrix μ is symmetric defines uniquely the so-called center of mobility. In Ref. [1], this center was used to analyze the Brownian motion of a particle with arbitra...

As a core component of Substitution-Permutation Networks, diffusion layer is mainly introduced by matrices from maximum distance separable (MDS) codes. Surprisingly, up to now, most constructions of MDS matrices require to perform an equivalent or even exhaustive search. Especially, not many MDS proposals are known that obtain an excellent hardware efficiency and simultaneously guarantee a rema...

To quantitatively evaluate dosimetric effects of rotational offsets in stereotactic body radiation therapy (SBRT) for lung cancer. Overall, 11 lung SBRT patients (8 female and 3 male; mean age: 75.0 years) with medially located tumors were included. Treatment plans with simulated rotational offsets of 1°, 3°, and 5° in roll, yaw, and pitch were generated and compared with the original plans. Bo...