Investigations into the BFKL Mechanism with a Running QCD Coupling

We present approximations of varying degree of sophistication to the integral equations for the (gluon) structure functions of a hadron (``the partonic flux factor'') in a model valid in the Leading Log Approximation with a running coupling constant. The results are all of the BFKL-type, i.e. a power in the Bjorken variable x_B^{-\lambda} with the parameter \lambda determined from the size \alpha_0 of the ``effective'' running coupling \bar{\alpha}\equiv 3\alpha_s/\pi= \alpha_0/\log(k_{\perp}^2) and varying depending upon the treatment of the transverse momentum pole. We also consider the implications for the transverse momentum (k_{\perp}) fluctuations along the emission chains and we obtain an exponential falloff in the relevant \kappa\equiv \log(k_{\perp}^2)-variable, i.e. an inverse power (k_{\perp}^2)^{-(2+\lambda)} with the same parameter \lambda. This is different from the BFKL-result for a fixed coupling, where the distributions are Gaussian in the \kappa-variable with a width as in a Brownian motion determined by ``the length'' of the emission chains, i.e. \log(1/x_B). The results are verified by a realistic Monte Carlo simulation and we provide a simple physics motivation for the change.Comment: 24 pages, 10 supplementary files, submitted to Physical Review

A note on matrix inversion

AbstractWe generalize a recent result of Thompson on inverses of block matrices over principal ideal domains to isomorphisms of direct sums of modules over an arbitrary ring

Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection

In this work we continue the description of soliton-like solutions of some slowly varying, subcritical gKdV equations. In this opportunity we describe, almost completely, the allowed behaviors: either the soliton is refracted, or it is reflected by the potential, depending on its initial energy. This last result describes a new type of soliton-like solution for gKdV equations, also present in the NLS case. Moreover, we prove that the solution is not pure at infinity, unlike the standard gKdV soliton.Comment: 51 pages, submitte

Financing North Dakota's Agriculture

Agricultural Finance,

The Role of International Law and Practice in Addressing International Tax Issues in the Global Era

The article discusses the role of international law and practice in deciphering complex international tax policy and administration issues as of July 2011. An August 2009 deal between the U.S. and Switzerland, known as the U.S.-Swiss Agreement, is also mentioned. The international law of jurisdiction is examined as it relates to the issue of double taxation

The Role of International Law and Practice in Addressing International Tax Issues in the Global Era

The article discusses the role of international law and practice in deciphering complex international tax policy and administration issues as of July 2011. An August 2009 deal between the U.S. and Switzerland, known as the U.S.-Swiss Agreement, is also mentioned. The international law of jurisdiction is examined as it relates to the issue of double taxation