Fast methods to numerically integrate the Reynolds equation for gas fluid films

The alternating direction implicit (ADI) method is adopted, modified, and applied to the Reynolds equation for thin, gas fluid films. An efficient code is developed to predict both the steady-state and dynamic performance of an aerodynamic journal bearing. An alternative approach is shown for hybrid journal gas bearings by using Liebmann's iterative solution (LIS) for elliptic partial differential equations. The results are compared with known design criteria from experimental data. The developed methods show good accuracy and very short computer running time in comparison with methods based on an inverting of a matrix. The computer codes need a small amount of memory and can be run on either personal computers or on mainframe systems

Quantum Field Theory and the Volume Conjecture

The volume conjecture states that for a hyperbolic knot K in the three-sphere S^3 the asymptotic growth of the colored Jones polynomial of K is governed by the hyperbolic volume of the knot complement S^3\K. The conjecture relates two topological invariants, one combinatorial and one geometric, in a very nonobvious, nontrivial manner. The goal of the present lectures is to review the original statement of the volume conjecture and its recent extensions and generalizations, and to show how, in the most general context, the conjecture can be understood in terms of topological quantum field theory. In particular, we consider: a) generalization of the volume conjecture to families of incomplete hyperbolic metrics; b) generalization that involves not only the leading (volume) term, but the entire asymptotic expansion in 1/N; c) generalization to quantum group invariants for groups of higher rank; and d) generalization to arbitrary links in arbitrary three-manifolds.Comment: 32 pages, 6 figures; acknowledgements update

Economic and Financial Crime Management in the Context of International Financial Crisis - Opinions

Economic and financial crime in its complexity, included practically all spheres of economy. One can notice, more frequently, an intersection of violent crime with economic and financial crime. Practice shows, more strongly, that the authorities face, with great difficulty, this veritable explosion acts of crime. Starting from the fact that the phenomenon of economic and financial crime occurs on a background of a radical social change during the international financial crisis, the perspective does not provide grounds for optimism. There are forms of economic and financial crime which developed by their own laws. In this context national and European bodies charged with preventing and combating financial and economic crime must adopt effective management to meet the new challenges posed by organized crime groups specialized in the commission of economic crimes with transnational character