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Abstract: This paper investigates the stability of periodic delay systems with non-smooth coefficients using a multi-interval Chebyshev collocation approach (MIC). In this approach, each piecewise continuous interval is expanded in a Chebyshev basis of the first order. The boundaries of these intervals are placed at the points of discontinuity to recover the fast convergence properties of spectral methods. Stability is examined for a set of case studies that contain the complexities of periodic coefficients, delays and discontinuities. The new approach is also compared to the conventional Chebyshev collocation method. [Copyright &y& Elsevier]

Abstract: In the last decade, two scientific tools have been extensively used worldwide to measure the human impact on nature: ecological footprint (EF) and emergy analysis (EA). Papers trying to combine the strong points of EF and EA, and obtain more accurate results have appeared in scientific literature, in which Zhao’s et al. (2005) approach is an important one. Unfortunately, some weak points of the original methods still remain on the new approaches proposed. The aim of this present work is to discuss some weak points found in Zhao’s approach, trying to overcome them through a new approach called emergetic ecological footprint (EEF). The main difference between Zhao’s approach and EEF is that the last one accounted for the internal storage of capital natural in the biocapacity calculation. Besides that, soil loss and water for human consume were considered as additional categories in the footprint calculation. After discussing it through comparisons with other approaches, EEF was used to assess Peru as a case study, resulting in a biocapacity of 51.76ghacapita−1 and a footprint of 12.23ghacapita−1, with 2004 data; that resulted in an ecological surplus of 39.53ghacapita−1. The load capacity factor obtained was 4.23, meaning that Peru can support a population 4.23 times bigger considering the life style of 2004. The main limitations of the EEF are: (i) it is impossible to make comparisons between the biocapacity and footprint for each category; (ii) a need for a handbook with emergy intensity factors with good quality. On the other hand, the main positive points are: (i) its easiness of application in global and national scales; (ii) its final indicators account for all the previous energy (or emergy) used to make something; (iii) internal natural capital storage was accounted for in the biocapacity calculation, which can be a valid step towards the evaluation and assess of services provided by nature. [Copyright &y& Elsevier]

Abstract: Due to the increasingly serious ecological degradation of river systems, the river health research has attracted more and more attention of the researchers and decision-makers. This paper aims to integrate the fuzzy assessment method with analytic hierarchy process to establish the integrative fuzzy hierarchical assessment model, thus combing qualitative analysis and quantitative assessment and overcoming the disadvantages of subjectivity of the previous evaluation methods. The results show that the proposed assessment method is able to reveal how the river system is disturbed by human activities. Finally, the integrative fuzzy hierarchical method is validated and applied to the case study of Yong River in Ningbo City, China. [Copyright &y& Elsevier]

Abstract: Ecological treatment engineering has been widely accepted as an artificially designed work to deal with the deteriorating ecological environment with low energy and resource consumption. To measure the energy and resource consumption and environmental support contained in the constructed wetland as a kind of ecological treatment engineering, emergy as embodied solar energy based assessment is performed and relative emergy-based indices including emergy yield ratio (EYR), emergy load ratio (ELR), emergy sustainability index (ESI), net economic benefit index (Np), and renewable percentage index (Pr), are also modified to evaluate the local sustainability of the constructed wetland in this paper. A case study on Longdao River constructed wetland compared with those of some earlier conventional treatment systems indicate that more local renewable resources and less ecological cost are involved, thus promoting the economic benefit due to less energy and resource consumption and simultaneously lowering the environmental stress of the treatment system on the local areas. [Copyright &y& Elsevier]