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Flocculation control study based on fractal theory

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Journal of Zhejiang University-Science B(Biomedicine & Biotechnology) 2005年第10期6卷 1038-1044页

作者：常颖刘前军张金松 Guangzhou Water Supply Co. Guangzhou 510160 China Zhejiang Urban and Rural Planning Design Institute Hangzhou 310007 China Shenzhen Water (Group) Co. Limited Shenzhen 518031 China

A study on flocculation control based on fractal theory was carried out. Optimization test of chemical coagulant dosage confirmed that the fractal dimension could reflect the flocculation degree and settling characteristics of aggregates and the good correlation with the turbidity of settled effluent. So that the fractal dimension can be used as the major parameter for floc-culation system control and achieve self-acting adjustment of chemical coagulant dosage. The fractal dimension flocculation control system was used for further study carried out on the effects of various flocculation parameters, among which are the dependency relationship among aggregates fractal dimension, chemical coagulant dosage, and turbidity of settled effluent under the conditions of variable water quality and quantity. And basic experimental data were obtained for establishing the chemical coagulant dosage control model mainly based on aggregates fractal dimension.

关键词： Aggregates, Flocculation control, Fractal dimension, Image analysis, Turbidity

On nulls of perturbed Fredholm operators and degenerate homoclinic bifurcations

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Science China Mathematics 2004年第4期47卷 617-627页

作者： ZHANG WeinianDepartment of Mathematics, Sichuan University, Chengdu 610064, China 1. Department of Mathematics Sichuan University 610064 Chengdu China

It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which has an exactly κ-dimensional null. Actually, our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.

关键词： Fredholm operator, perturbation, dimension, decomposition, degenerate homoclinic bifurcation.

The multifractal spectrum of some Moran measures

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Science China Mathematics 2005年第8期48卷 1097-1112页

作者： WU Min School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

The multifractal formalism is shown to hold for a class of Moran measures supported on the Moran fractals associated with the sequences of which the frequency of the letter exists.

关键词： multifractal spectrum, Moran fractal, Hausdorff dimension, Packing dimension.

Fractal Determination of Coastal Types Based on GIS——A Case Study of China

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Marine Science Bulletin 2002年第2期4卷 61-67页

作者：朱晓华吴秀芹王建 College of Environmental Science Beij University Beijing 100871 College of Geographical Science Nanjing Normal University Nanjing 210097

The probability of fractal determination of coastal types based on GIS is preliminarily discussed with China as an example. Finally, some significant conclusions are drawn: (1) The fractal dimension of coastline of the bedrock coast is larger than that of the plain coast on the same scale map; (2) As far as the bedrock coast is concerned, the larger fractal dimension of coastline of the bedrock coast on the same scale map indicates that the bedrock coast is probably not typical; (3) As far as the plain coast is concerned, the smaller fractal dimension of coastline of the plain coast on the same scale map indicates that it is probably the silt plain coast; (4) The different substantial compositions affect the fractal ,dimensions of coastlines of different coastal types. In generalthe coast which lies in the north of the Hangzhou Bay consists of sand mainly, its surface is flat, and it is connected with the coastal plain, its landform is broad shoal, its total change is comparatively homogenous in the tidal dynamic process, and thus, the relatively smaller fractal dimension of coastline results from this. For the bedrock coast, there is more bedrock, the coastline is comparatively smooth and straight, being affected by the faults and ocean dynamic process, which result in the larger fractal dimension.

关键词： GIS, Fractal, Fractal dimension, Determination of coastal type, China