In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is disc...In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.展开更多
In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determ...In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.展开更多
目的探讨Poincare散点图在分析糖尿病(DM)、慢性心力衰竭(HF)及糖尿病合并慢性心力衰竭(DM+HF)患者心率变异(HRV)中的使用价值。方法分别分析100例DM患者,100例HF患者,100例DM+HF患者和100例正常人24 h HRV的Poincare散点图及其定量指标...目的探讨Poincare散点图在分析糖尿病(DM)、慢性心力衰竭(HF)及糖尿病合并慢性心力衰竭(DM+HF)患者心率变异(HRV)中的使用价值。方法分别分析100例DM患者,100例HF患者,100例DM+HF患者和100例正常人24 h HRV的Poincare散点图及其定量指标,矢量长度指数(VLI)和矢量角度指数(VAI),并与部分时域指标(SDNN,SDSD)进行相关分析。结果正常人散点图均呈慧星型;DM组、HF组呈鱼雷型及短棒型;DM+HF组短棒型,3组患者24 h、清醒、睡眠时的SDNN、SDSD、VLI、VAI与正常组比较均显著降低,且昼夜变化节律消失。与DM组、HF组比较,DM+HF组SDNN、SDSD、VLI、VAI明显降低。相关分析显示VLI与SDNN和VAI与SDSD分别呈正相关。结论DM合并HF时自主神经受损严重。Poincare散点图能直观地反映DM、HF、DM+HF患者心脏自主神经功能状况,结合其量化指标可定量分析其HRV。展开更多
Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced ...Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced the method and algorithm how to get them, and tested them with clinical and animal experiment data. The result showed that these four parameters have certain idiosyncrasy with different heart diseases, and the animal experiment result also showed that these parameters were changed remarkably after coronary artery ligation compared with before, which indicated these parameters might be useful for clinical diagnosis. Because the algorithm we used was based only on the shape of the graph, one can apply this algorithm on any other type of graphs like Poincare dispersed dot plot.展开更多
In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebe...In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincare inequalities for vector fields satisfying Hormander＇s condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p（x）-subLaplacian. Our results are only stated and proved for vector fields satisfying Hormander＇s condition, but they also hold for Grushin vector fields as well with obvious modifications.展开更多
Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P（ ）（Ω）, where p（.） ： Ω → [1, ∞[ is a variable exponent. This inequality is...Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P（ ）（Ω）, where p（.） ： Ω → [1, ∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space ;D（Ω） in the space {v ∈ Wl,P（ ）（Ω）; tr v = 0 on δΩ}. Two applications are also discussed.展开更多
文摘In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.
文摘In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced.
文摘目的探讨Poincare散点图在分析糖尿病(DM)、慢性心力衰竭(HF)及糖尿病合并慢性心力衰竭(DM+HF)患者心率变异(HRV)中的使用价值。方法分别分析100例DM患者,100例HF患者,100例DM+HF患者和100例正常人24 h HRV的Poincare散点图及其定量指标,矢量长度指数(VLI)和矢量角度指数(VAI),并与部分时域指标(SDNN,SDSD)进行相关分析。结果正常人散点图均呈慧星型;DM组、HF组呈鱼雷型及短棒型;DM+HF组短棒型,3组患者24 h、清醒、睡眠时的SDNN、SDSD、VLI、VAI与正常组比较均显著降低,且昼夜变化节律消失。与DM组、HF组比较,DM+HF组SDNN、SDSD、VLI、VAI明显降低。相关分析显示VLI与SDNN和VAI与SDSD分别呈正相关。结论DM合并HF时自主神经受损严重。Poincare散点图能直观地反映DM、HF、DM+HF患者心脏自主神经功能状况,结合其量化指标可定量分析其HRV。
基金Supported by the National Natural Science Foundation of China(71403069)the 51th of the Postdoctoral Science Foundation of China(AUGA4130916512)Introduction of Hainan Medical University Scientific Research Grants Project
基金This project is supported by the National Natural Science Foundation of China(No.3 9970 2 0 5)
文摘Poincare dispersed dot plot was an important method in studying heart nonlinear state and rate variability(HRV). Based on the shape of Poincare dispersed dot plot, we proposed four quantitative parameters, introduced the method and algorithm how to get them, and tested them with clinical and animal experiment data. The result showed that these four parameters have certain idiosyncrasy with different heart diseases, and the animal experiment result also showed that these parameters were changed remarkably after coronary artery ligation compared with before, which indicated these parameters might be useful for clinical diagnosis. Because the algorithm we used was based only on the shape of the graph, one can apply this algorithm on any other type of graphs like Poincare dispersed dot plot.
基金supported by NSFC(Grant No.11371056)supported by a US NSF grant
文摘In this paper, we will establish Poincare inequalities in variable exponent non-isotropic Sobolev spaces. The crucial part is that we prove the boundedness of the fractional integral operator on variable exponent Lebesgue spaces on spaces of homogeneous type. We obtain the first order Poincare inequalities for vector fields satisfying Hormander＇s condition in variable non-isotropic Sobolev spaces. We also set up the higher order Poincare inequalities with variable exponents on stratified Lie groups. Moreover, we get the Sobolev inequalities in variable exponent Sobolev spaces on whole stratified Lie groups. These inequalities are important and basic tools in studying nonlinear subelliptic PDEs with variable exponents such as the p（x）-subLaplacian. Our results are only stated and proved for vector fields satisfying Hormander＇s condition, but they also hold for Grushin vector fields as well with obvious modifications.
文摘Let Ω be a domain in RN. It is shown that a generalized Poincaré inequality holds in cones contained in the Sobolev space Wl,P（ ）（Ω）, where p（.） ： Ω → [1, ∞[ is a variable exponent. This inequality is itself a corollary to a more general result about equivalent norms over such cones. The approach in this paper avoids the difficulty arising from the possible lack of density of the space ;D（Ω） in the space {v ∈ Wl,P（ ）（Ω）; tr v = 0 on δΩ}. Two applications are also discussed.
