The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems o...The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.展开更多
This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequal...This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.展开更多
This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality techniq...This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.展开更多
The multiple time scale climate changes are studied and calculated with statistical analysis and wavelet transformation on the basis of daily series of observed data over the period 1901-2007 in Macao.The result shows...The multiple time scale climate changes are studied and calculated with statistical analysis and wavelet transformation on the basis of daily series of observed data over the period 1901-2007 in Macao.The result shows that statistically significant oscillations with 2 to 5 years of period generally exist in the series of climate variables(e.g.annual mean surface air temperature and precipitation as well as evaporation etc.),but with obvious locality in time domain.The variation of annual mean surface air temperature has a quasi 60-year period.The phases of the 60-year variation approximately and consistently match that of Atlantic Multidecadal Oscillation(AMO).The oscillations of seasonal mean surface air temperature in summer and winter have the periods of quasi 30-year and quasi 60-year,respectively.These two periods of oscillations have statistically significant correlation with Pacific decadal oscillation(PDO) and AMO,individually.The multidecadal variations of the precipitation of the annually first flood period and annual evaporation are dominated by periods of quasi 30-year and quasi 50-year,respectively.展开更多
： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati tech...： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.展开更多
本文提出一种基于多尺度时空优化的空气质量预测方法(multi-scale spatial-temporal network for air quality prediction,MSSTN-AQP),结合空气质量系统中存在的长短期时间依赖关系和动态空间依赖性,提高长期空气质量预测的准确性。首先...本文提出一种基于多尺度时空优化的空气质量预测方法(multi-scale spatial-temporal network for air quality prediction,MSSTN-AQP),结合空气质量系统中存在的长短期时间依赖关系和动态空间依赖性,提高长期空气质量预测的准确性。首先,通过构建多尺度时空特征提取模块,从多源异构数据中提取时空特征。其次,构建动态空间特征提取模块。通过将图卷积网络与注意力机制进行有效结合,捕捉空气质量网络中的全局空间特征,用于对多种空间依赖关系的联合建模。最后,构建时间特征提取模块,对Transformer模型进行改进与优化。自适应时间Transformer模块主要用于模拟跨多个时间步长的双向时间依赖关系。此外,将上述时空特征提取模块进行有效集成化,构建端到端的空气质量预测模型。为了验证模型的有效性,在两个真实数据集中进行实验验证。实验结果表明,MSSTN-AQP在预测精度上更具优势,尤其是在长期的空气质量预测任务中优势更加明显。展开更多
The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the proble...The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the problem. This is achieved by means of the Laplace transformation. We specify the particular concepts of the q-Laplace transform. The convolution for these transforms is considered in some detail.展开更多
为能够及时地获取纺纱过程中纱线质量变化信息,为优化纱线工艺参数服务,提出一种实时检测纱线条干均匀度的测量方法。为提高测量效率,首先使用最小外接矩形对实时采集的连续纱线图像进行感兴趣区域(region of interest,ROI)获取,对获取...为能够及时地获取纺纱过程中纱线质量变化信息,为优化纱线工艺参数服务,提出一种实时检测纱线条干均匀度的测量方法。为提高测量效率,首先使用最小外接矩形对实时采集的连续纱线图像进行感兴趣区域(region of interest,ROI)获取,对获取纱线图像根据纱线方向进行自动裁剪。其次基于最大类间方差法(OTSU)阈值分割及形态学运算获得的纱线条干二值图像。最后利用尺度不变特征转换(scale-invariant feature transform,SIFT)算法检测特征点对重合部分数据去除,保证纱线数据的完整及连续性,提出加入纱线倾斜角计算纱线直径方法。基于此方法计算对3种线密度的紧密纺纯棉纱的纱线直径并对纱线条干及纱疵进行检测。实验测量直径平均误差为2.38%,变异系数(coefficient of variation,CV)值与Uster Classimat5条干测试仪测试结果基本一致,表明此方法可满足纱线运动速度为5~30 m/min的纱线条干均匀度实时检测。展开更多
基金supported by the National Natural Science Foundation of China(Grants 11972241 and 11572212)
文摘The theory of time scales,which unifies continuous and discrete analysis,provides a powerful mathematical tool for the study of complex dynamic systems.It enables us to understand more clearly the essential problems of continuous systems and discrete systems as well as other complex systems.In this paper,the theory of generalized canonical transformation for second-order Birkhoffian systems on time scales is proposed and studied,which extends the canonical transformation theory of Hamilton canonical equations.First,the condition of generalized canonical transformation for the second-order Birkhoffian system on time scales is established.Second,based on this condition,six basic forms of generalized canonical transformation for the second-order Birkhoffian system on time scales are given.Also,the relationships between new variables and old variables for each of these cases are derived.In the end,an example is given to show the application of the results.
基金Supported by the NNSF of China(11071222)Supported by the NSF of Hunan Province(12JJ6006)Supported by Scientific Research Fund of Education Department of Guangxi Zhuang Autonomous Region(2013YB223)
文摘This paper is concerned with the oscillatory behavior of a class of third-order noonlinear variable delay neutral functional dynamic equations on time scale. By using the generalized Riccati transformation and inequality technique, we establish some new oscilla- tion criteria for the equations. Our results extend and improve some known results, but also unify the oscillation of third-order nonlinear variable delay functional differential equations and functional difference equations with a nonlinear neutral term. Some examples are given to illustrate the importance of our results.
文摘This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.
文摘The multiple time scale climate changes are studied and calculated with statistical analysis and wavelet transformation on the basis of daily series of observed data over the period 1901-2007 in Macao.The result shows that statistically significant oscillations with 2 to 5 years of period generally exist in the series of climate variables(e.g.annual mean surface air temperature and precipitation as well as evaporation etc.),but with obvious locality in time domain.The variation of annual mean surface air temperature has a quasi 60-year period.The phases of the 60-year variation approximately and consistently match that of Atlantic Multidecadal Oscillation(AMO).The oscillations of seasonal mean surface air temperature in summer and winter have the periods of quasi 30-year and quasi 60-year,respectively.These two periods of oscillations have statistically significant correlation with Pacific decadal oscillation(PDO) and AMO,individually.The multidecadal variations of the precipitation of the annually first flood period and annual evaporation are dominated by periods of quasi 30-year and quasi 50-year,respectively.
基金Supported by the Scientific Research Fund of Hunan Provincial Education Department(09A082)
文摘： The oscillation for a class of second order nonlinear variable delay dynamic equation on time scales with nonlinear neutral term and damping term was discussed in this article. By using the generalized Riccati technique, integral averaging technique and the time scales theory, some new sufficient conditions for oscillation of the equation are proposed. These results generalize and extend many knownresults for second order dynamic equations. Some examples are given to illustrate the main results of this article.
文摘本文提出一种基于多尺度时空优化的空气质量预测方法(multi-scale spatial-temporal network for air quality prediction,MSSTN-AQP),结合空气质量系统中存在的长短期时间依赖关系和动态空间依赖性,提高长期空气质量预测的准确性。首先,通过构建多尺度时空特征提取模块,从多源异构数据中提取时空特征。其次,构建动态空间特征提取模块。通过将图卷积网络与注意力机制进行有效结合,捕捉空气质量网络中的全局空间特征,用于对多种空间依赖关系的联合建模。最后,构建时间特征提取模块,对Transformer模型进行改进与优化。自适应时间Transformer模块主要用于模拟跨多个时间步长的双向时间依赖关系。此外,将上述时空特征提取模块进行有效集成化,构建端到端的空气质量预测模型。为了验证模型的有效性,在两个真实数据集中进行实验验证。实验结果表明,MSSTN-AQP在预测精度上更具优势,尤其是在长期的空气质量预测任务中优势更加明显。
文摘The Fourier transformations are used mainly with respect to the space variables. In certain circumstances, however, for reasons of expedience or necessity, it is desirable to eliminate time as a variable in the problem. This is achieved by means of the Laplace transformation. We specify the particular concepts of the q-Laplace transform. The convolution for these transforms is considered in some detail.
文摘为能够及时地获取纺纱过程中纱线质量变化信息,为优化纱线工艺参数服务,提出一种实时检测纱线条干均匀度的测量方法。为提高测量效率,首先使用最小外接矩形对实时采集的连续纱线图像进行感兴趣区域(region of interest,ROI)获取,对获取纱线图像根据纱线方向进行自动裁剪。其次基于最大类间方差法(OTSU)阈值分割及形态学运算获得的纱线条干二值图像。最后利用尺度不变特征转换(scale-invariant feature transform,SIFT)算法检测特征点对重合部分数据去除,保证纱线数据的完整及连续性,提出加入纱线倾斜角计算纱线直径方法。基于此方法计算对3种线密度的紧密纺纯棉纱的纱线直径并对纱线条干及纱疵进行检测。实验测量直径平均误差为2.38%,变异系数(coefficient of variation,CV)值与Uster Classimat5条干测试仪测试结果基本一致,表明此方法可满足纱线运动速度为5~30 m/min的纱线条干均匀度实时检测。
