The Dirac equation for a charged particle in a static electromagnetic field is written for the special case of a spherically symmetric potential. Besides the well-known Dirac-Coulomb and Dirac-oscillator potentials, we obtain a relativistic version of the S-wave Morse potential. This is accomplished by adding a simple exponential potential term to the Dirac operator, which in the nonrelativisti...

In our discussion of linear models relating rCBF to design factors and gCBF, we have not considered the computational problems of simultaneously fitting the model for thousands of voxels.32 Viewing the problem from a multivariate perspective provides efficient computation, and offers some insight into the problem. In this section we demonstrate the relationship between the simultaneous general ...

Several adaptive order statistic filters (OSF) are developed and compared for channel characterization and noise suppression in images and 3-D CT data. Emphasis has been put on the situation when a noise-free reference image is not available but instead we can have a sequence of two noisy versions of the same image (or a 3-D data slice). One of the noisy images is used as the reference in the O...

We consider the Cauchy problem for the massive Dirac equation in the non-extreme Kerr-Newman geometry outside the event horizon. We derive an integral representation for the Dirac propagator involving the solutions of the ODEs which arise in Chandrasekhar's separation of variables. It is proved that for initial data with compact support, the probability of the Dirac particle to be in any compac...

A regular equivalence on a relation induces matrix blocks that are either 0-blocks or regular-blocks, where a regular-block contains at least one positive entry in each row and column. The authors devise both a permutation test and an exact statistical test that separates these two aspects of regular equivalence, 0-blocks and regular-blocks. To test for the regular-block property, the natural t...

Pseudo-Dirac dark matter is a viable type of dark matter which originates from a new Dirac fermion whose two Weyl states get slightly split in mass by a small Majorana term. The decay of the heavier to the lighter state naturally occurs over a detectable length scale. Thus, whenever pseudo-Dirac dark matter is produced in a collider, it leaves a clear trace: a visible displaced vertex in associ...

Let g be a complex semisimple Lie algebra and let r ⊂ g be any reductive Lie subalgebra such that B|r is nonsingular where B is the Killing form of g. Let Z(r) and Z(g) be, respectively, the centers of the enveloping algebras of r and g. Using a Harish-Chandra isomorphism one has a homomorphism η : Z(g) → Z(r) which, by a well-known result of H. Cartan, yields the the relative Lie algebra cohom...

We propose a framework for supersymmetric Dirac operators to have threshold energies. We apply the obtained results to magnetic Dirac operators with positive mass in order to investigate the asymptotic behaviors at infinity of the threshold eigenfunctions. It turns out that the results of most of the existing works on the zero modes of the Weyl-Dirac operators remain to hold for the threshold e...