Abstract: Numerical integration of a function over a unit sphere is performed using a new partition scheme. At least one octant of the sphere is partitioned into triangular convexes, and functional values are calculated at the vertexes of the triangular convexes. Typically, an octant is partitioned into N bands, respectively containing 1, 3, 5 . . . 2N'triangular convexes. Each triangular convex may be subpartitioned into smaller triangular convexes. An interpolation method may be used to calculate functional values at points within the convexes. Typically, cubic spline interpolation is used for points along the edges of the triangular convexes, and linear interpolation is used for points within the triangular convexes. The partition method is particularly useful in computer simulation of magnetic resonance spectra as it significantly reduces computational time.

Abstract: Homotopy principles are used in computer simulation of magnetic resonance spectra. Multidimensional homotopy provides an efficient method for accurately tracing energy levels, and hence transitions, in the presence of energy level anticrossings and looping transitions. The application describes the implementation of homotopy to the analysis of continuous wave electron paramagnetic resonance spectra. The method can also be applied to electron nuclear double resonance, electron spin echo envelope modulation, solid state nuclear magnetic resonance and nuclear quadrupole resonance spectra.