Graphical functions in parametric space

Graphical functions are positive functions on the punctured complex plane $\mathbb{C}\setminus\{0,1\}$ which arise in quantum field theory. We generalize a parametric integral representation for graphical functions due to Lam, Lebrun and Nakanishi, which implies the real analyticity of graphical functions. Moreover we prove a formula that relates graphical functions of planar dual graphs.Comment: v2: extended introduction, minor changes in notation and correction of misprint

Competitiveness of Broiler Producers in North America Under Alternative Free Trade Scenarios

International Relations/Trade,

MARKETS FOR NORTHERN PLAINS AQUACULTURE--CASE STUDY OF TILAPIA

The purpose of this study is to identify and investigate alternative fresh and frozen fillet markets for tilapia within the region. The competition for this market is primarily an imported product from Asia and Central America. Total imports plus domestic production has increased from 16.95 million pounds in 1992 to 70.74 million pounds in 1997. Thirty-seven of the 79 respondents handled tilapia in their business. Thirty of these businesses handled and preferred fresh fillets while ten handled frozen tilapia. The tilapia businesses were clear in their preferences: 5 to 7 ounce fillets, quick delivery response time, constant supply, taste and size, and suppliers oriented toward customer service. Twenty-six of the 37 respondents were open to new suppliers. The responding businesses which did not handle tilapia gave their reasons: lack of demand due to customer unfamiliarity, name recognition and taste of tilapia. The need for an established market, i.e., consumer demand, was the major factor. The domestically produced tilapia did not test well in any of the three sensory perception taste tests. The results of these tests indicate both a quality issue and a variation in quality from test to test. These issues need to be solved prior to initiating a marketing effort for fresh and frozen fillets.tilapia, North American Fish Farmers Cooperative, North Central Region, sensory evaluation, production, prices, size, imports, Marketing, Production Economics,

Solute transport in a porous medium: a mass-conserving solution for the convection-dispersion equation in a finite domain

This dissertation considers the proper mathematical description for the physical problem of a miscible solute undergoing longitudinal convective-dispersive transport with constant production, first-order decay, and equilibrium sorption in a porous medium. Initial and input concentrations may be any continuously differentiable functions and the mathematical system is articulated for a finite domain. This domain yields a mass balance which requires Robin (i.e., third-type) boundaries, which describe a continuous flux but a discontinuous resident-concentration. The discontinuity in the resident concentration at the outflow boundary yields an underdetermined system when the exit concentration is not experimentally measured. This is resolved by defining the unknown effluent concentration from a semi-infinite problem which satisfies a Dirichlet (i.e., first-type) condition at the origin. The solution is represented in a uniformly convergent series of real variables. The representation can be sequenced to describe any configuration of discrete reactors or approach reservoirs. Individual reacting segments are allowed to have differing lengths and transport parameters up to the complexity of the governing equation. Such discrete segments may be constructed from finitely small slices to approximate a continuous variation in any of the modeled parameters, such as velocity or diffusion. The physical phenomenon that can be described include layered hydrogeologic strata, as well as two- or three- dimensional transport when hydrodynamic properties exhibit a spatial proportionality. The large volume of antecedent literature on finite solutions for convective-dispersive transport equations grew out of the historical precedents set by Danckwerts (1953) and Wehner and Wilhelm (1956) whom made simplifying assumptions of continuous boundary concentrations. This dissertation includes the demonstration that continuous-concentration hypotheses, whether rendered as Dirichlet or homogeneous Neumann (i.e., second-type) conditions, satisfy external mass conservation yet fail to provide solutions that are internally consistent with the governing equation