A D5 elliptic fibration is a fibration whose generic fiber is modeled by the complete intersection of two quadric surfaces in P3. They provide simple examples of elliptic fibrations admitting a rich spectrum of singular fibers (not all on the list of Kodaira) without introducing singularities in the total space of the fibration and therefore avoiding a discussion of their resolutions. We study systematically the fiber geometry of such fibrations using Segre symbols and compute several topological invariants.

We prove that in the nonextreme KerrNewman black hole geometry, the Dirac equation has no normalizable, timeperiodic solutions. A key tool is Chandrasekhar's separation of the Dirac equation in this geometry. A similar nonexistence theorem is established in a more general class of stationary, axisymmetric metrics in which the Dirac equation is known to be separable. These results indicate that, in contrast to the classical situation of massive particle orbits, a quantum mechanical Dirac particle must either disappear into the black hole or escape to infinity. 2000 John Wiley & Sons, Inc.

There is an unmet medical need to identify neuroimaging biomarkers that allow us to accurately diagnose and monitor Alzheimer's disease (AD) at its very early stages and to assess the response to AD-modifying therapies. To a certain extent, volumetric and functional magnetic resonance imaging (fMRI) studies can detect changes in structure, cerebral blood flow, and blood oxygenation that distinguish AD and mild cognitive impairment (MCI) subjects from healthy control (HC) subjects. However, it has been challenging to use fully automated MRI analytic methods to identify potential AD neuroimaging biomarkers. We have thus proposed a method based on independent component analysis (ICA) for studying potential AD-related MR image features that can be coupled with the use of support vector machine (SVM) for classifying scans into categories of AD, MCI, and HC subjects. The MRI data were selected from

The coupled Einstein-Dirac equations for a static, spherically symmetric system of two fermions in a singlet spinor state are derived. Using numerical methods, we construct an infinite number of solitonlike solutions of these equations. The stability of the solutions is analyzed. For weak coupling (ie, small rest mass of the fermions), all the solutions are linearly stable (with respect to spherically symmetric perturbations), whereas for stronger coupling, both stable and unstable solutions exist. For the physical interpretation, we discuss how the energy of the fermions and the (ADM) mass behave as functions of the rest mass of the fermions. Although gravitation is not renormalizable, our solutions of the Einstein-Dirac equations are regular and well behaved even for strong coupling.

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a ReissnerNordstrm black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.