This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge group<i>SU</i>(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/<i>r</i> ², as<i>r</i> tends to infinity.

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We consider for <i>j</i>=, a spherically symmetric, static system of (2<i>j</i>+1) Dirac particles, each having total angular momentum <i>j</i>. The Dirac particles interact via a classical gravitational and electromagnetic field.

We explore the tunneling behavior of a quantum particle on a finite graph in the presence of an asymptotically large potential with two or three potential wells. The behavior of the particle is primarily governed by the local spectral symmetry of the graph around the wells. In the case of two wells the behavior is stable in the sense that it can be predicted from a sufficiently large neighborhood of the wells. However in the case of three wells we are able to exhibit examples where the tunneling behavior can be changed significantly by perturbing the graph arbitrarily far from the wells.

We consider a class of two-dimensional Schrdinger operator with a singular interaction of the type and a fixed strength supported by an infinite family of concentric, equidistantly spaced circles, and discuss what happens below the essential spectrum when the system is amended by an AharonovBohm flux in the center. It is shown that if , there is a critical value such that the discrete spectrum has an accumulation point when , while for the number of eigenvalues is at most finite, in particular, the discrete spectrum is empty for any fixed and small enough.