RURAL ECONOMIC DEVELOPMENT: NEW OPPORTUNITIES AND CHALLENGES FOR COMMERCIAL BANKERS

The report discusses commercial banks' role in supporting economic development in rural America. It details demographic and economic trends in rural America. It discusses a number of economic development programs available to commercial bankers and to private sector/public sector partnerships. Finally, the report proposes a set of new tools for commercial bankers to further strengthen their participation in rural community economic development. Note: Figures are not included in the machine readable copy--contact the authors for more information.demographic trends, economic trends, rural America, role of commercial banks, economic development programs, new tools for bankers, Community/Rural/Urban Development, Financial Economics,

Dependence on the spin structure of the eta and rokhlin invariants

We study the dependence of the eta invariant $\eta_D$ on the spin structure, where $D$ is a twisted Dirac operator on a (4k+3)-dimensional spin manifold. The difference between the eta invariants for two spin structures related by a cohomolgy class which is the reduction of a H^1(M,\Za)-class is shown to be a half integer. As an application of the technique of proof the generalized Rokhlin invariant is shown to be equal modulo 8 for two spin structures related in this way.Comment: 10 page

Large volume behavior of Yang-Mills propagators

We summarize results on finite-volume effects in the propagators of Landau gauge Yang-Mills theory using Dyson-Schwinger equations on a 4-dimensional torus. We demonstrate explicitly how the solutions for the gluon and the ghost propagator tend towards their respective infinite volume forms in the corresponding limit. We discuss the relation of our solutions with results from lattice Monte-Carlo simulations.Comment: 7 pages, 2 figures, Presented by CF at the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Vertex functions and infrared fixed point in Landau gauge SU(N) Yang-Mills theory

The infrared behaviour of vertex functions in an SU(N) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three- and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.Comment: 14 pages, 8 figures, v2: typos corrected, version to be published in PL

An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Temperature Dependence of Gluon and Ghost Propagators in Landau-Gauge Yang-Mills Theory below the Phase Transition

The Dyson-Schwinger equations of Landau-gauge Yang-Mills theory for the gluon and ghost propagators are investigated. Numerical results are obtained within a truncation scheme which has proven to be successful at vanishing temperature. For temperatures up to 250 MeV we find only minor quantitative changes in the infrared behaviour of the gluon and ghost propagators. The effective action calculated from these propagators is temperature-independent within the numerical uncertainty.Comment: 9 pages, 14 figures, submitted to EPJ C, typos corrected, reference and 2 minor clarifications added, in v3: one paragraph extended, some references added, version to appear in EPJ

Solving the Ghost-Gluon System of Yang-Mills Theory on GPUs

We solve the ghost-gluon system of Yang-Mills theory using Graphics Processing Units (GPUs). Working in Landau gauge, we use the Dyson-Schwinger formalism for the mathematical description as this approach is well-suited to directly benefit from the computing power of the GPUs. With the help of a Chebyshev expansion for the dressing functions and a subsequent appliance of a Newton-Raphson method, the non-linear system of coupled integral equations is linearized. The resulting Newton matrix is generated in parallel using OpenMPI and CUDA(TM). Our results show, that it is possible to cut down the run time by two orders of magnitude as compared to a sequential version of the code. This makes the proposed techniques well-suited for Dyson-Schwinger calculations on more complicated systems where the Yang-Mills sector of QCD serves as a starting point. In addition, the computation of Schwinger functions using GPU devices is studied.Comment: 19 pages, 7 figures, additional figure added, dependence on block-size is investigated in more detail, version accepted by CP