Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a ...Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.展开更多
A statistical analysis of monthly mean and daily maximum rainfall data at New Delhi during the mon-soon (June-September) period 1940-1980 is presented. It has been observed that a good correlation exists between the m...A statistical analysis of monthly mean and daily maximum rainfall data at New Delhi during the mon-soon (June-September) period 1940-1980 is presented. It has been observed that a good correlation exists between the monthly and daily maximum rainfall. A linear regression analysis of the data is found to be sig nificant for all the four months. Some key statistical parameters like the mean values of Coefficient of Vari ability (CV), Relative Variability (RV) and Percentage Interannual Variability (PIV) have been studied and found to be at variance. However, their corresponding ratios between mean daily maximum and mean monthly rainfall are significantly lower.展开更多
Purpose:The purpose of this study was to compare the coordination between the trunk and the pelvis during a sustained asymmetric repetitive lifting task between a group with a history of low back pain(LBP;HBP) and a g...Purpose:The purpose of this study was to compare the coordination between the trunk and the pelvis during a sustained asymmetric repetitive lifting task between a group with a history of low back pain(LBP;HBP) and a group with no history of LBP(NBP).Methods:Volunteers lifted a 11-kg box from ankle height in front to a shelf 45° off-center at waist height,and lowered it to the start position at12 cycles/min for 10 min.Lifting side was alternated during the trial.Continuous relative phase was used to calculate coordination between the pelvis and trunk rotation at the beginning(Min 1),middle(Min 5),and end of the bout(Min 9).Results:While there were no main effects for group,a significant interaction between time and group indicated that,in the frontal plane,the NBP group coordination was more anti-phase toward the end of the bout,with no such differences for the HBP group.Analysis of sagittal-axial(bend and twist) coordination revealed the HBP group coordination was more in-phase at the end of the bout over the entire cycle and for the lifting phase alone,with no such differences for the NBP group.Conclusion:Differences between groups demonstrate residual consequences of LBP in an occupational scenario,even though the HBP group was pain-free for >6 months prior to data collection.More in-phase coordination in the HBP group may represent a coordination pattern analogous to'guarded gait' which has been observed in other studies,and may lend insight as to why these individuals are at increased risk for re-injury.展开更多
The radiative Euler equations is a typical model describing the motion of astrophysical flows.For its mathematical studies,it is now well-understood that the radiation effect can indeed induce some dissipative mechani...The radiative Euler equations is a typical model describing the motion of astrophysical flows.For its mathematical studies,it is now well-understood that the radiation effect can indeed induce some dissipative mechanism,which can guarantee the global regularity of smooth solutions to the radiative Euler equations for small initial data.Thus a problem of interest is to see to what extent does the viscosity and/or thermal conductivity influence the global regularity of smooth solutions to the one-dimensional radiative Euler equations for large initial data.For results in this direction,it is shown in[30]that,for a class of state equations,even if a special class of thermal conductivity is further added to the radiative Euler equations,its smooth solutions will still blow up in finite time for large initial data.The main purpose of this paper focuses on the case when both viscosity and thermal conductivity are considered.We first show that,for the state equations and the heat conductivity considered in[30],if the viscosity is further taken into account,the corresponding radiative Navier-Stokes equations does admit a unique global smooth solution for any large initial data provided that the viscosity is a smooth function of the density satisfying certain growth conditions as the density tends to zero and infinity.Moreover,we also show that similar result still holds for the case when the thermodynamics variables satisfy the state equations for ideal polytropic gases,the heat conductivity takes the form studied in[30],and the viscosity is assumed to satisfy the same conditions imposed in the first result.展开更多
文摘Lie symmetry and the generalized Hojman conserved quantity of Nielsen equations for a variable mass holonomic system of relative motion are studied. The determining equation of Lie symmetry of Nielsen equations for a variable mass holonomic system of relative motion under the infinitesimal transformations of groups is given. The expression of generalized Hojman conserved quantity deduced directly from Lie symmetry for a variable mass holonomic system of relative motion is obtained. An example is given to illustrate the application of the results.
文摘A statistical analysis of monthly mean and daily maximum rainfall data at New Delhi during the mon-soon (June-September) period 1940-1980 is presented. It has been observed that a good correlation exists between the monthly and daily maximum rainfall. A linear regression analysis of the data is found to be sig nificant for all the four months. Some key statistical parameters like the mean values of Coefficient of Vari ability (CV), Relative Variability (RV) and Percentage Interannual Variability (PIV) have been studied and found to be at variance. However, their corresponding ratios between mean daily maximum and mean monthly rainfall are significantly lower.
文摘Purpose:The purpose of this study was to compare the coordination between the trunk and the pelvis during a sustained asymmetric repetitive lifting task between a group with a history of low back pain(LBP;HBP) and a group with no history of LBP(NBP).Methods:Volunteers lifted a 11-kg box from ankle height in front to a shelf 45° off-center at waist height,and lowered it to the start position at12 cycles/min for 10 min.Lifting side was alternated during the trial.Continuous relative phase was used to calculate coordination between the pelvis and trunk rotation at the beginning(Min 1),middle(Min 5),and end of the bout(Min 9).Results:While there were no main effects for group,a significant interaction between time and group indicated that,in the frontal plane,the NBP group coordination was more anti-phase toward the end of the bout,with no such differences for the HBP group.Analysis of sagittal-axial(bend and twist) coordination revealed the HBP group coordination was more in-phase at the end of the bout over the entire cycle and for the lifting phase alone,with no such differences for the NBP group.Conclusion:Differences between groups demonstrate residual consequences of LBP in an occupational scenario,even though the HBP group was pain-free for >6 months prior to data collection.More in-phase coordination in the HBP group may represent a coordination pattern analogous to'guarded gait' which has been observed in other studies,and may lend insight as to why these individuals are at increased risk for re-injury.
基金supported by the NSFC(12001495)supported by the NSFC(12221001,12371225)the Science and Technology Department of Hubei Province(2020DFH002)。
文摘The radiative Euler equations is a typical model describing the motion of astrophysical flows.For its mathematical studies,it is now well-understood that the radiation effect can indeed induce some dissipative mechanism,which can guarantee the global regularity of smooth solutions to the radiative Euler equations for small initial data.Thus a problem of interest is to see to what extent does the viscosity and/or thermal conductivity influence the global regularity of smooth solutions to the one-dimensional radiative Euler equations for large initial data.For results in this direction,it is shown in[30]that,for a class of state equations,even if a special class of thermal conductivity is further added to the radiative Euler equations,its smooth solutions will still blow up in finite time for large initial data.The main purpose of this paper focuses on the case when both viscosity and thermal conductivity are considered.We first show that,for the state equations and the heat conductivity considered in[30],if the viscosity is further taken into account,the corresponding radiative Navier-Stokes equations does admit a unique global smooth solution for any large initial data provided that the viscosity is a smooth function of the density satisfying certain growth conditions as the density tends to zero and infinity.Moreover,we also show that similar result still holds for the case when the thermodynamics variables satisfy the state equations for ideal polytropic gases,the heat conductivity takes the form studied in[30],and the viscosity is assumed to satisfy the same conditions imposed in the first result.
