The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear function...The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.展开更多
The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen s...The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil＇s mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin＇s analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin＇s analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.展开更多
Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area...Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area: Thiessen Polygon (TP) Method;Reciprocal Distance Squared (RDS) Method;Kriging Method (KM) and Multiquadric Equations (ME) Method. The comparison was done indirectly, using GORE and BALANCE index to assess the convergence results from each method by increasing the rain gauges density in a region, through six scenarios. The Coremas/Mae D’água Watershed employed as study area, with an area of 8385 km2, is situated on Brazilian semi-arid. The results showed the TP, as RDS and ME techniques to be employed successfully to obtain the average rainfall over an area, highlighting the MEM. On the other hand, KM, using two variograms models, had an unstable behavior, pointing the prior study of data and variogram’s choice as a need to practical applying.展开更多
In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary co...In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.展开更多
为提高浮动车数据中异常数据检测能力及不同载客状态下的模型检测分析能力,提出基于S-DTA-IIForest(Summation&Difference Third Order Average&Improvement-Isolation Forest)的浮动车数据异常检测算法。构建由相邻两项求和(S...为提高浮动车数据中异常数据检测能力及不同载客状态下的模型检测分析能力,提出基于S-DTA-IIForest(Summation&Difference Third Order Average&Improvement-Isolation Forest)的浮动车数据异常检测算法。构建由相邻两项求和(S)、三阶求和平均差分(DTA)的二维度空间SDTA特征向量;提出差额累计更新和动态区分辨识的改进孤立森林IIForest算法,通过设置停止阈值参数,避免当出现新样本异常值分数大于停止阈值时,仅更新样本不更新孤立森林模型的问题,设计每个二叉树区分辨识度参数,区分辨识度位于停止区间时停止二叉树生长,提高算法收敛性能,以ROC(Receiver Operating Characteristic)曲线下面积AUC(Area Under ROC Cure)、F1-score为指标对模型精度进行对比分析,并以重庆市中心城区学府大道开展实例验证。结果表明:本文S-DTA-IIForest组合算法AUC、F1-score分别为86.63%、0.89,AUC较传统孤立森林IForest(Isolation Forest)提高32.4%,运行效率提高1.29%,具有收敛速度更快、精度更高的优势,载客条件下模型AUC、F1-score较未载客分别提高7.7%、10.8%,组合算法对载客数据有更高的检测精度,且未载客状态数据异常率较载客状态增加71.4%,未载客数据异常率更高。展开更多
基金supported by the National Natural Science Foundation of China(11471043,11671271)the Beijing Natural Science Foundation(1172004)
文摘The purpose of this article is to investigate (s, t)-weak tractability of multivariate linear problems in the average case set ting. The considered algorithms use finitely many evaluations of arbitrary linear functionals. Generally, we obtained matching necessary and sufficient conditions for (s,t)-weak tractability in terms of the corresponding non-increasing sequence of eigenvalues. Specifically, we discussed (s, t)-weak tractability of linear tensor product problems and obtained necessary and sufficient conditions in terms of the corresponding one-dimensional problem. As an example of applications, we discussed also (s,t)-weak tractability of a multivariate approximation problem.
基金supported by the National Natural Science Foundation of China (No. 50578120)the National High Technology Research and Development Program of China (863 Program) (No. 2006AA11Z118)
文摘The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil＇s mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin＇s analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin＇s analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.
文摘Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area: Thiessen Polygon (TP) Method;Reciprocal Distance Squared (RDS) Method;Kriging Method (KM) and Multiquadric Equations (ME) Method. The comparison was done indirectly, using GORE and BALANCE index to assess the convergence results from each method by increasing the rain gauges density in a region, through six scenarios. The Coremas/Mae D’água Watershed employed as study area, with an area of 8385 km2, is situated on Brazilian semi-arid. The results showed the TP, as RDS and ME techniques to be employed successfully to obtain the average rainfall over an area, highlighting the MEM. On the other hand, KM, using two variograms models, had an unstable behavior, pointing the prior study of data and variogram’s choice as a need to practical applying.
文摘In this article, we report the derivation of high accuracy finite difference method based on arithmetic average discretization for the solution of Un=F(x,u,u′)+∫K(x,s)ds , 0 x s < 1 subject to natural boundary conditions on a non-uniform mesh. The proposed variable mesh approximation is directly applicable to the integro-differential equation with singular coefficients. We need not require any special discretization to obtain the solution near the singular point. The convergence analysis of a difference scheme for the diffusion convection equation is briefly discussed. The presented variable mesh strategy is applicable when the internal grid points of the solution space are both even and odd in number as compared to the method discussed by authors in their previous work in which the internal grid points are strictly odd in number. The advantage of using this new variable mesh strategy is highlighted computationally.
文摘为提高浮动车数据中异常数据检测能力及不同载客状态下的模型检测分析能力,提出基于S-DTA-IIForest(Summation&Difference Third Order Average&Improvement-Isolation Forest)的浮动车数据异常检测算法。构建由相邻两项求和(S)、三阶求和平均差分(DTA)的二维度空间SDTA特征向量;提出差额累计更新和动态区分辨识的改进孤立森林IIForest算法,通过设置停止阈值参数,避免当出现新样本异常值分数大于停止阈值时,仅更新样本不更新孤立森林模型的问题,设计每个二叉树区分辨识度参数,区分辨识度位于停止区间时停止二叉树生长,提高算法收敛性能,以ROC(Receiver Operating Characteristic)曲线下面积AUC(Area Under ROC Cure)、F1-score为指标对模型精度进行对比分析,并以重庆市中心城区学府大道开展实例验证。结果表明:本文S-DTA-IIForest组合算法AUC、F1-score分别为86.63%、0.89,AUC较传统孤立森林IForest(Isolation Forest)提高32.4%,运行效率提高1.29%,具有收敛速度更快、精度更高的优势,载客条件下模型AUC、F1-score较未载客分别提高7.7%、10.8%,组合算法对载客数据有更高的检测精度,且未载客状态数据异常率较载客状态增加71.4%,未载客数据异常率更高。
