187 research outputs found
The dimension of splines of arbitrary degree on a tetrahedral partition
We consider the linear space of piecewise polynomials in three variables which are globally smooth, i.e., trivariate splines. The splines are defined on a uniform tetrahedral partition , which is a natural generalization of the four-directional mesh. By using Bernstein-B{\´e}zier techniques, we establish formulae for the dimension of the splines of arbitrary degree
Random Dirac operators with time-reversal symmetry
Quasi-one-dimensional stochastic Dirac operators with an odd number of
channels, time reversal symmetry but otherwise efficiently coupled randomness
are shown to have one conducting channel and absolutely continuous spectrum of
multiplicity two. This follows by adapting the criteria of Guivarch-Raugi and
Goldsheid-Margulis to the analysis of random products of matrices in the group
SO, and then a version of Kotani theory for these operators. Absence of
singular spectrum can be shown by adapting an argument of Jaksic-Last if the
potential contains random Dirac peaks with absolutely continuous distribution.Comment: parts of introduction made more precise, corrections as follow-up on
referee report
Mathematics and Algorithms in Tomography
This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis
- …