We present a detailed experimental investigation of the easy-hard-easy phase transition for randomly generated instances of satisfiability problems. Problems in the hard part of the phase transition have been extensively used for benchmarking satisfiability algorithms. This study demonstrates that problem classes and regions of the phase transition previously thought to be easy can sometimes be...

and Introduction: A synthesis of a diverse suite of observations of H2O-related landforms that are possible Mars analogs from terrestrial polar regions (Devon Island in the Arctic; the Dry Va lleys of Antarctica) put into question any requirement for extended episode(s) of warm and wet climate in Mars’s past. Geologically transient episodes of localized H2O cycling, forced by exogenic impacts, ...

We consider the heat flux through a domain with subregions in which the thermal capacity approaches zero. In these subregions the parabolic heat equation degenerates to an elliptic one. We show the well-posedness of such parabolic-elliptic differential equations for general non-negative L∞-capacities and study the continuity of the solutions with respect to the capacity, thus giving a rigorous ...

There are some new developments on Plancherel formula and growth of matrix coefficients for unitary representations of nilpotent Lie groups. These have several consequences for the geometry of weakly symmetric spaces and analysis on parabolic subgroups of real semisimple Lie groups, and to (infinite dimensional) locally nilpotent Lie groups. Many of these consequences are still under developmen...

The aim of this paper is to construct the parabolic version of the Donaldson–Uhlenbeck compactification for the moduli space of parabolic stable bundles on an algenraic surface with parabolic structures along a divisor with normal crossing singularities. We prove the non–emptiness of the moduli space of parabolic stable bundles of rank 2 and also prove the existence of components with smooth po...

Representation of functionals of non-Markov processes is studied for bounded and unbounded domains. These functionals are represented via solutions of backward parabolic Ito equations. This results is based on an analog of the second fundamental inequality and the related existence theorem are obtained for backward parabolic Ito equations. AMS 1991 subject classification: Primary 60J55, 60J60, ...

Rigidity and Stability for Isometry Groups in Hyperbolic 4-Space by Youngju Kim Advisor: Professor Ara Basmajian It is known that a geometrically finite Kleinian group is quasiconformally stable. We prove that this quasiconformal stability cannot be generalized in 4-dimensional hyperbolic space. This is due to the presence of screw parabolic isometries in dimension 4. These isometries are topol...

A Gauss–Galerkin finite-difference method is proposed for the numerical solution of a class of linear, singular parabolic partial differential equations in two space dimensions. The method generalizes a Gauss– Galerkin method previously used for treating similar singular parabolic partial differential equations in one space dimension. Two test problems are studied and the numerical results are ...