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We present a dispersive representation of the partial-wave amplitude based on unitarity and analyticity. In this representation, the right-hand-cut contribution responsible for final-state-interaction effects is taken into account via an Omnés formalism with elastic phase shifts as inputs, while the left-hand-cut contribution is estimated by invoking chiral perturbation theory. Numerical fits are performed to pin down the involved subtraction constants. Good fit quality can be achieved with only one free parameter, and the experimental data regarding the multipole amplitude in the energy region below the are well described. Furthermore, we extend the partial-wave amplitude to the second Riemann sheet to extract the couplings of the . The modulus of the residue of the multipole amplitude (S ) is , and the partial width of at the pole is approximately , which is almost the same as that of the resonance, indicating that strongly couples to the system.

Purpose – The purpose of this paper is to optimize manure allocation through nutrient budgeting strategy to meet crop nutrient requirements under maximizing economic returns and environmental constraints, and then to evaluate the economic and environmental effects of different nutrient budgeting strategies in animal excreta treatment. Design/methodology/approach – In this study, a holistic integrated “ecological-economic” model is developed. It incorporates the systems of animal-crop production and waste treatment is developed for a pilot pig farm in China in order to simulate the economic and environmental effects of several nutrient budgeting strategies in excreta treatment for resource use. Findings – The results reveal nutrient management deficiencies cause some serious environmental problems. The operations including biogas and composting are economically and environmentally efficient methods for manure management through nutrient budgeting strategy in an intensive animal farming with limited access to cropland. The nutrient budgeting strategy of constrained phosphorus, however, creates better environmental effects and brings more income from the waste treatment than the strategy of constrained nitrogen. The current standard of manure application in cropland which emphasizes on crop requirements for nitrogen should be reconsidered. Originality/value – The paper is an original work and its methodology makes a meaningful contribution to understanding the relations between different nutrient budgeting strategies and their economic and environmental effects.

Extensive dynamical calculations are conducted in the study of channel low energy scatterings, based on various phenomenological model inputs of left cuts at the tree level. The subtleties of the singular behavior of the partial wave amplitude, at the origin of the complex plane, are analysed in detail. Furthermore, it is found that the dispersion representation for the phase shift, , must be modified in the case of scatterings. An additional contribution from the dispersion integral exists, which approximately cancels the contribution of the two virtual poles located near the end points of the segment cut, induced by channel nucleon exchanges. With limited reliance on the details of the dynamical inputs, the subthreshold resonance survives.

We give a pedagogical analysis on K-matrix models describing the πN scattering amplitude, in S11 channel at low energies. We show how the correct use of analyticity in the s-channel and crossing symmetry in t- and u-channels leads to a much improved analytic behavior in the negative s region, in agreement with the prediction from chiral perturbation amplitudes in its validity region. The analysis leads again to the conclusion that a genuine N*(890) resonance exists.

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BackgroundChina currently faces severe environmental pollution caused by burning agricultural straw; thus, resource utilization of these straws has become an urgent policy and practical objective for the Chinese government.MethodsThis study develops a bio-economic model, namely, “straw resource utilization for fungi in China (SRUFIC),” on the basis of a field survey of an edible fungi plant in Zhejiang, China, to investigate an integrated economic and environmental performance of straw reuse in fungi production. Five scenarios, which cover changes in the production scale, wage level, and price fluctuations of the main product and inputs, are simulated.ResultsResults reveal that (1) the pilot plant potentially provides enhanced economic benefits and disposes added agricultural residues by adjusting its production strategy; (2) the economic performance is most sensitive to fungi price fluctuations, whereas the environmental performance is more sensitive to production scale and price of fungi than other factors; (3) expanding the production scale can be the most efficient means of improving the performance of a plant economically and environmentally.DiscussionOverall, agricultural straw reuse in the edible fungi industry can not only reduce the environmental risk derived from burning abandoned straws but also introduce economic benefits. Thus, the straw reuse in the fungi industry should be practiced in China, and specific economic incentive policies, such as price support or subsidies, must be implemented to promote the utilization of agricultural straws in the fungi industry.