The treatment engineering of landslide hazard is a complicated systemengineering. The selecting treatment scheme is influenced by many factors such as technology,economics, environment, and risk. The decision-making o...The treatment engineering of landslide hazard is a complicated systemengineering. The selecting treatment scheme is influenced by many factors such as technology,economics, environment, and risk. The decision-making of treatment schemes of landslide hazard is aproblem of comprehensive judgment with multi-hierarchy and multi-objective. The traditional analysishierarchy process needs identity test. The traditional analysis hierarchy process is improved bymeans of optimal transfer matrix here. An improved hierarchy decision-making model for the treatmentof landslide hazard is set up. The judgment matrix obtained by the method can naturally meet therequirement of identity, so the identity test is not necessary. At last, the method is applied tothe treatment decision-making of the dangerous rock mass at the Slate Mountain, and its applicationis discussed in detail.展开更多
An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT...An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.展开更多
As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme ...As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.展开更多
文摘The treatment engineering of landslide hazard is a complicated systemengineering. The selecting treatment scheme is influenced by many factors such as technology,economics, environment, and risk. The decision-making of treatment schemes of landslide hazard is aproblem of comprehensive judgment with multi-hierarchy and multi-objective. The traditional analysishierarchy process needs identity test. The traditional analysis hierarchy process is improved bymeans of optimal transfer matrix here. An improved hierarchy decision-making model for the treatmentof landslide hazard is set up. The judgment matrix obtained by the method can naturally meet therequirement of identity, so the identity test is not necessary. At last, the method is applied tothe treatment decision-making of the dangerous rock mass at the Slate Mountain, and its applicationis discussed in detail.
文摘An accelerated singular value thresholding (SVT) algorithm was introduced for matrix completion in a recent paper [1], which applies an adaptive line search scheme and improves the convergence rate from O(1/N) for SVT to O(1/N2), where N is the number of iterations. In this paper, we show that it is the same as the Nemirovski’s approach, and then modify it to obtain an accelerate Nemirovski’s technique and prove the convergence. Our preliminary computational results are very favorable.
基金supported by the National Natural Science Foundation of China (No. 12071432)Zhejiang Provincial Natural Science Foundation (No. LZ24A010007)。
文摘As a torqued version of the lattice potential Korteweg–de Vries equation, the H1^(a) is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.
