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China has been undergoing rapid economic growth since its reform and opening-up at the expense of resource depletion and environmental pollution. We estimated the monetary costs of resource depletion and environmental pollution in China over the past 14 recent years by establishing integrated mathematical models with System for Integrated Environmental and Economic Accounting (SEEA) framework. Results showed four points. Firstly, the total temporal costs of natural resource depletion and environmental pollution witnessed an inverted ‘U’ shape pattern with the turning point in 2012. The relationship between cost of mineral resource depletion, as well as water pollution cost, and per capita GDP were found to follow the Inverted-U shape environmental Kuznets curve (EKC). Secondly, the average annual share of natural resources of the total costs was more than 80%, indicating that the rapid economic growth of China is highly dependent on resource depletion. Thirdly, Although China still has the highest worldwide in its total energy consumption and CO2 emission, China's struggles with adjustment of industrial & energy consumption structure, and pollution controls have resulted in a general temporal decline of the share of resource and environmental costs to China's GDP. The green GDP of China is growing at an average rate of 14.76%. Finally, although in the process of manufactured goods for the whole world, China has reduced environmental pollution and left it at home as much as possible. Driving forces behind the progress in green GDP of China were analyzed by using Differences-in-Differences method and Spearman rank correlation analysis.

Evaluation on sustainability of coastline utilization was one of the hot topics in marine environmental science. Based on high-resolution remote sensing images, coastlines can be divided into natural coastlines and artificial coastlines. Natural coastlines are mainly converted to harbor coastline and mariculture coastline. In this study, a new comprehensive model was proposed to assess the sustainability on utilization of coastline and applied to a typical case of Beibu Gulf, China. Comprehensive economic output efficiency (EOE) of artificial coastlines was obtained by integrating the contribution weight and applying linear combination model. In addition, the P–S-R framework integrated with fuzzy mathematics model and linear combination method was constructed to evaluate the disturbance intensity of human activities on the natural coastlines (DI) by taking petrochemical plants, ports, sewage outlets and aquaculture intensity as pressure indicators, seawater quality status near the coastline as state indicators, and whether the coastline was within nature reserve boundaries as the response indicator. Rely on the EOE and DI, the cities involved in the evaluation were finally categorized into four groups: group 1 with high economic output efficiency and low ecological impacts, group 2 with high economic output efficiency and high ecological impacts, group 3 with low economic output efficiency and low ecological impacts, group 4 with low economic output efficiency and high ecological impacts. The results showed that: (1) natural coastlines retention ratios were 52.45%, 57.97% and 76.15% in Guangdong, Guangxi and Hainan Province respectively. In addition, 8.66%, 10.47% and 5.17% of the coastlines with high disturbance from human activities in Guangdong, Guangxi and Hainan Province respectively were identified; (2) only 4 of 29 cities were categorized into the group with high economic output and low ecological impacts, indicating that most of the coastal cities in Beibu Gulf of China was at a relatively low level of sustainability. The proposed indices system and the integrated analysis framework were proved to be feasible for evaluating sustainable utilization of coastlines, which can be applied to other case studies. The results of evaluation provided valuable information for decision-makers to optimize coastal land use policy targeting at the balance of development and conservation.

In this paper, we propose the generalized B divided difference, with which the (k − 1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k − 2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-spline curves are proposed using the constrained optimization methods.  2001 Elsevier Science B.V. All rights reserved.