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Finding the symmetric rank-1 approximation to a given symmetric tensor is an important problem due to its wide applications and its close relationship to the Z-eigenpair of a tensor. In this paper, we propose a method based on the proximal alternating linearized minimization to directly solve the optimization problem. Global convergence of our algorithm is established. Numerical experiments show that our algorithm is very competitive in speed, accuracy and robustness compared to other state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Frequent and intense mining activity is the main cause of rice field conversion into dry land in the coal mining subsidence area in mountain region of southwest China. Study on causes, mechanisms and reclamation of rice field damage plays an important role in ensuring sustainable agriculture and food security in the study area. In order to understand the impact of coal mining subsidence on soil physical characteristic and develop reasonable land reclamation strategy, field test and laboratory analysis of controlled trials were conducted in mountain region of southwest China, and the soil bulk density, water content, porosity, mechanical composition, seepage discharge, seepage velocity and permeability coefficient were analyzed. The soil physical characteristic changes of rice field before and after damage were analyzed by drying method using cutting ring, hydrometer and the soil permeability test. The causes and mechanisms of water shortage of destroyed rice field were also explored. The results showed that: 1) In 0-40 cm soil layer, dry land soil bulk density increased compared with the control rice fields, while water content and porosity (excepted for dry land 1 and 2 in 0-20 cm soil layers) decreased obviously. Vertical soil profile structure and succession laws didn't change in 0-60 cm soil layer except the similar trend of soil water content losses in different soil layers; 2) Clay content of destroyed rice field was closely associated with parent material. Variation of clay content (<0.005 mm) in 0-40 cm soil layer were presented as follows: dry land 3 (shale efflorescence) > dry land 1 (limestone and shale efflorescence) > dry land 2 (limestone, sandstone and shale efflorescence). The eluviation and illuviation effect became weaker in 20-40 cm soil depth after the conversion from destroyed rice field to dry land. Meanwhile, it was strong for hydroponic paddy soil of a long history, huge leakage and mean clay (<0.005 mm) mass fraction of rice field soil after damage increased cumulatively from top to bottom, while the hydroponic rice field of short history and weak leakage showed an opposite trend; 3) Soil profile configuration and parent material in experimental sites were the main reason of the decreasing trend of seepage discharge and seepage velocity, and the initial fluctuations and post-stabilization with accumulated time. Mining subsidence didn't have a serious impact on water permeability in soil vadose zone; 4) Coal mining subsidence didn't affect the soil physical characteristics of typical rice field in research area, the mechanism for water loss in destroyed rice field may be related to changing hydrogeological factors between soil layer and basement strata. Moreover, taking land use pattern, parent materials and permeability of reclaimed soil into consideration, the destroyed rice fields with permeability coefficient were less than 3 m/d, areas with a long time of hydroponic history, and being located on the weathered shale and limestone zone were recommended to give preference to reclamation in the research area. [ABSTRACT FROM AUTHOR]