Advances in Adjoint Functions of Connection Number in Water Resources Complex Systems: A Systematic Review.

The adjoint function of connection number has unique advantages in solving uncertainty problems of water resource complex systems, and has become an important frontier and research hotspot in the uncertainty research of water resource complex problems. However, in the rapid evolution of the adjoint function, some problems greatly limit the application of the adjoint function in the research of water resources. Therefore, based on bibliometric analysis, development, practical application issues, and prospects of the hot directions are analyzed. It is found that the development of the connection number of water resource set pair analysis can be divided into three stages: (1) relatively sluggish development before 2005, (2) a period of rapid advancement in adjoint function research spanning from 2005 to 2017, and (3) a subsequent surge post-2018. The introduction of the adjoint function of connection number promotes the continuous development of set pair analysis of water resources. Set pair potential and partial connection number are the crucial research directions of the adjoint function. Subtractive set pair potential has rapidly developed into a relatively independent and important trajectory. The research on connection entropy is comparatively less, which needs to be further strengthened, while that on adjacent connection number is even less. The adjoint function of set pair potential can be divided into three major categories: division set pair potential, exponential set pair potential, and subtraction set pair potential. The subtraction set pair potential, which retains the original dimension and quantity variation range of the connection number, is widely used in water resources and other fields. Coupled with the partial connection number, a series of new connection number adjoint functions have been developed. The partial connection number can be mainly divided into two categories: total partial connection number, and semi-partial connection number. Among these, the calculation expression and connotation of total partial connection numbers have not yet reached a consensus, accompanied by the slow development of high-order partial connection numbers. Semi-partial connection number can describe the mutual migration movement between different components of the connection number, which develops rapidly. With the limitations and current situation described above, promoting the exploration and application of the adjoint function of connection number in the field of water resources and other fields of complex systems has become the focus of future research.

Connection number based model for coordination development evaluation of regional water resources, social economy and ecological environment complex system.

The development of social economy often requires a large consumption of water resources, and will also discharge a large amount of pollutants to the environment. Currently, the rapid development of regional water resources, social economy and ecological environment (WSE) complex system encounters significant challenges, and the coordination development of WSE complex system becomes important and necessary condition of regional sustainable development. Therefore, to scientifically evaluate the coordination development state of WSE system, based on the establishment of evaluation index system, the connection number and distance coordination model coupling approach for the coordination development evaluation of WSE complex system was proposed in this manuscript. The application results of the proposed method in Anhui Province, China indicate that, during 2011-2020, the coordination level of Anhui province is relatively high, and the coordination grade of most cities are in grade I or II. The coordination development degree of Anhui province presented a distinct improving trend with time, from most cities in grade IV or V in 2011 to most cities in grade II in 2020, from the worst 0.0580 in 2011 to the best 0.9200 in 2020. In terms of space, the coordinated development level of southern Anhui is higher than that of northern Anhui. Meanwhile, the coordination development status of the 16 cities in Anhui province can be divided into three patterns according to its historical variation characteristics, i.e., coordination development mode, ecological environment backward mode, and social and economic backward mode. Compared with the commonly used coordination evaluation method, the method of this paper can solve the problem of homogenization, and its calculation results are more reasonable and practical.

Structure Simulation and Equilibrium Evaluation Analysis of Regional Water Resources, Society, Economy and Ecological Environment Complex System.

Currently, the implementation of water resource spatial equilibrium strategy is a fundamental policy of water resource integrated management in China; it is also a considerable challenge to explore the relationship structure features of water resources, society, economy and ecological environment (WSEE) complex system. For this purpose, firstly, we applied information entropy, ordered degree and connection number coupling method to reveal the membership characteristics between different evaluation indicators and grade criterion. Secondly, the system dynamics approach was introduced to describe the relationship features among different equilibrium subsystems. Finally, the ordered degree, connection number, information entropy and system dynamics integrated model was established to conduct relationship structure simulation and evolution trend evaluation of the WSEE system. The application results in Hefei city, Anhui Province, China, demonstrated that: (1) the variation of overall equilibrium conditions of WSEE system in Hefei city, 2020-2029 was higher compared to that of 2010-2019, though the increasing rate of ordered degree and connection number entropy (ODCNE) became slower after 2019; and (2) the annual ODCNE value from 2020 to 2029 of WSEE system under dry year scenarios increased about 0.0812, which indicated that the construction of Yangtze-Huaihe Diversion (YHD) project could play significant positive role in mitigating the equilibrium situation of WSEE system in Hefei city in the future. On the whole, this study is capable of providing the guidance basis for constructing a theoretical framework of structure simulation and equilibrium evaluation analysis of WSEE complex system.

[Mineral Spectrum Change Analysis under the Conditions of Different Particle Size].

Mineral particle size is an important factor affecting mineral spectrum characteristics, so to explore the changes of the mineral spectrum curves under different particle sizes and the spectrum difference of different minerals under the same particle size are the keys of hyperspectral remote sensing information mineral identification and the theoretical basis of research on spectral differences of different particle -sizes. Six kinds of collected minerals were observed by spectrometer to get the reflectivity spectrum curve and first order differential spectral curve under different particle sizes, and the spectral characteristics of various kinds of minerals under different particle sizes were analyzed. At the same time, spectrum difference of different mineral under the same particle size was compared to explore possible wavelengths of hyperspectral remote sensing mineral identify. Results show that the spectrum curves of various minerals have a larger difference with the change of the particle size, but change law is not the same. The whole spectrum curve of hypersthene will be decreased with the increase of particle size, and the spectrum curve at a specific wavelength range of antigorite, hematite, kaolinite and chlorite will be decreased with the increase of particle size, and there is no direct correlation between the spectrum of olivine and the particle size. Under the same size, different mineral spectral reflectance change a lot in most band range and it provides the possibility for high precision identification of mineral. Antigorite, kaolinite and chlorite all have more absorption peaks of narrow width and smaller intensity than the other minerals. Spectrum curves of hematite, olivine and hypersthene are relatively smooth, and the number of the absorption and reflection peaks is relatively small. This study aims at providing basic data and theoretical support for mineral spectral library construction and mineral hyperspectral identification technology.