Twisted quantum affine superalgebra U-q[sl(2/2)((2))], U-q[osp(2/2)] invariant R-matrices and a new integrable electronic model

We describe the twisted affine superalgebra sl(2\2)((2)) and its quantized version U-q[sl(2\2)((2))]. We investigate the tensor product representation of the four-dimensional grade star representation for the fixed-point sub superalgebra U-q[osp(2\2)]. We work out the tensor product decomposition explicitly and find that the decomposition is not completely reducible. Associated with this four-dimensional grade star representation we derive two U-q[osp(2\2)] invariant R-matrices: one of them corresponds to U-q [sl(2\2)(2)] and the other to U-q [osp(2\2)((1))]. Using the R-matrix for U-q[sl(2\2)((2))], we construct a new U-q[osp(2\2)] invariant strongly correlated electronic model, which is integrable in one dimension. Interestingly this model reduces in the q = 1 limit, to the one proposed by Essler et al which has a larger sl(2\2) symmetry.

A cost-benefit analysis of hedgerow intercropping in the Philippine uplands using the SCUAF model

Soil erosion in the Philippine uplands is severe. Hedgerow intercropping is widely advocated as an effective means of controlling soil erosion from annual cropping systems in the uplands. However, few farmers adopt hedgerow intercropping even in areas where it has been vigorously promoted. This may be because farmers find hedgerow intercropping to be uneconomic compared to traditional methods of farming. This paper reports a cost-benefit analysis comparing the economic returns from traditional maize farming with those from hedgerow intercropping in an upland community with no past adoption of hedgerows. A simple erosion/productivity model, Soil Changes Under Agroforestry (SCUAF), is used to predict maize yields over 25 years. Economic data were collected through key informant surveys with experienced maize farmers in an upland community. Traditional methods of open-field farming of maize are economically attractive to farmers in the Philippine uplands. In the short term, establishment costs are a major disincentive to the adoption of hedgerow intercropping. In the long term, higher economic returns from hedgerow intercropping compared to open-field farming are realised, but these lie beyond farmers' limited planning horizons.

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

On the validity of the dispersion model of hepatic drug elimination when intravascular transit time densities are long-tailed

The dispersion model with mixed boundary conditions uses a single parameter, the dispersion number, to describe the hepatic elimination of xenobiotics and endogenous substances. An implicit a priori assumption of the model is that the transit time density of intravascular indicators is approximated by an inverse Gaussian distribution. This approximation is limited in that the model poorly describes the tail part of the hepatic outflow curves of vascular indicators. A sum of two inverse Gaussian functions is proposed as ail alternative, more flexible empirical model for transit time densities of vascular references. This model suggests that a more accurate description of the tail portion of vascular reference curves yields an elimination rate constant (or intrinsic clearance) which is 40% less than predicted by the dispersion model with mixed boundary conditions. The results emphasize the need to accurately describe outflow curves in using them as a basis for determining pharmacokinetic parameters using hepatic elimination models. (C) 1997 Society for Mathematical Biology.

Interconnected-tubes model of hepatic elimination

The distributed-tubes model of hepatic elimination is extended to include intermixing between sinusoids, resulting in the formulation of a new, interconnected-tubes model. The new model is analysed for the simple case of two interconnected tubes, where an exact solution is obtained. For the case of many strongly-interconnected tubes, it is shown that a zeroth-order approximation leads to the convection-dispersion model. As a consequence the dispersion number is expressed, for the first time, in terms of its main physiological determinants: heterogeneity of flow and density of interconnections between sinusoids. The analysis of multiple indicator dilution data from a perfused liver preparation using the simplest version of the model yields the estimate 10.3 for the average number of interconnections. The problem of boundary conditions for the dispersion model is considered from the viewpoint that the dispersion-convection equation is a zeroth-order approximation to the equations for the interconnected-tubes model. (C) 1997 Academic Press Limited.

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil pore-solid structure is formalized. Soil pore-solid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set ''pore,'' termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Two-dimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other pore-solid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one-and two-dimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.

Proton transport model in the ionosphere .1. Multistream approach of the transport equations

The suprathermal particles, electrons and protons, coming from the magnetosphere and precipitating into the high-latitude atmosphere are an energy source of the Earth's ionosphere. They interact with ambient thermal gas through inelastic and elastic collisions. The physical quantities perturbed by these precipitations, such as the heating rate, the electron production rate, or the emission intensities, can be provided in solving the kinetic stationary Boltzmann equation. This equation yields particle fluxes as a function of altitude, energy, and pitch angle. While this equation has been solved through different ways for the electron transport and fully tested, the proton transport is more complicated. Because of charge-changing reactions, the latter is a set of two-coupled transport equations that must be solved: one for protons and the other for H atoms. We present here a new approach that solves the multistream proton/hydrogen transport equations encompassing the collision angular redistributions and the magnetic mirroring effect. In order to validate our model we discuss the energy conservation and we compare with another model under the same inputs and with rocket observations. The influence of the angular redistributions is discussed in a forthcoming paper.

An isolated perfused human placental lobule model for multiple indicator dilution studies

We describe a method for multiple indicator dilution studies in the isolated perfused human placental lobule developed to investigate the relationships between changes in pressure and flow and solute clearance. A peripheral lobule of a human placenta is perfused with a tissue culture-based medium and the perfusate oxygen tension, arterial and venous pressures, pH and perfusion temperature continuously monitored by a computerized system. Flow rates are readily changed. Bolus injections of vascular, extracellular and water space markers, and study compounds can be made into either maternal or fetal circulations, and precisely timed outflow fractions can be collected with computer-controlled fraction collectors, allowing simultaneous determination of concentration-time profiles of each marker. (C) 1997 Elsevier Science Inc.

Cell cycle model to describe animal cell size variation and lag between cell number and biomass dynamics

The use of cell numbers rather than mass to quantify the size of the biotic phase in animal cell cultures causes several problems. First, the cell size varies with growth conditions, thus yields expressed in terms of cell numbers cannot be used in the normal mass balance sense. Second, experience from microbial systems shows that cell number dynamics lag behind biomass dynamics. This work demonstrates that this lag phenomenon also occurs in animal cell culture. Both the lag phenomenon and the variation in cell size are explained using a simple model of the cell cycle. The basis for the model is that onset of DNA synthesis requires accumulation of G1 cyclins to a prescribed level. This requirement is translated into a requirement for a cell to reach a critical size before commencement of DNA synthesis. A slower gl-owing cell will spend more time in G1 before reaching the critical mass. In contrast, the period between onset of DNA synthesis and mitosis, tau(B), is fixed. The two parameters in the model, the critical size and tau(B), were determined from eight steady-state measurements of mean cell size in a continuous hybridoma culture. Using these parameters, it was possible to predict with reasonable accuracy the transient behavior in a separate shift-up culture, i.e., a culture where cells were transferred from a lean environment to a rich environment. The implications for analyzing experimental data for animal cell culture are discussed. (C) 1997 John Wiley & Sons, Inc.

Characterizing QALYs under a general rank dependent utility model

This paper provides a characterization of QALYs, the most important outcome measure in medical decision making, in the context of a general rank dependent utility model. We show that both for chronic and for nonchronic health states the characterization of QALYs depends on intuitive conditions. This facilitates the assessment of the validity of QALYs in rank dependent non-expected utility theories and a comparison with other utility based measures of health.