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We modify the force equations of a weakly magnetized disk to include a diffusive term. This term is meant to approximate the effects of nonlinear turbulence in the disk. The Velikhov-Chandrasekhar instability appears as a local instability centered on a corotation radius. Imposing the natural boundary condition that the instability vanishes far from this radius eliminates the instability in the absence of noise or dissipation. The diffusive term restores it. We combine our equations to give a sixth order equation in the radial velocity. We examine this equation for meanful singularities using a local Taylor expansion. Real singularities in the complex frequency plane can imply the existence of branch lines, which will permit the existence of localized solutions corresponding to physically interesting instabilities. Having determined the singularities we plot their behavior as a function of the diffusion coeficient. Finally, we solve the original equation using the natural boundary conditions and discuss the application of our solutions to real, localized disk instabilities.
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