This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilt...This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.展开更多
A clustering algorithm and a probability statistics method were applied to different phases of a flight to analyze operation time during aircraft ground taxiing and airborne flight.And the clustering pattern,distribut...A clustering algorithm and a probability statistics method were applied to different phases of a flight to analyze operation time during aircraft ground taxiing and airborne flight.And the clustering pattern,distribution characteristics and dynamically changing rules of the two phases were identified.Further,an estimate method was established to measure operation time of flight legs,with creative steps of calculating individual segment separately and then integrating them accordingly.The method can both objectively and dynamically measure operation time,and accurately reflect real situation.It helps to better utilize airport slot resources and provides a strong support for air traffic flow management when scheduling flight plan in strategic and pre-tactic phases.展开更多
Background: Hypoxia is a primary cause of mountain sickness and a common pathological condition in patients with heart failure, shock, stroke, and chronic obstructive pulmonary disease(COPD). Thus far, little advancem...Background: Hypoxia is a primary cause of mountain sickness and a common pathological condition in patients with heart failure, shock, stroke, and chronic obstructive pulmonary disease(COPD). Thus far, little advancement in countering hypoxic damage has been achieved, and one of the main reasons is the absence of an ideal algorithm or calculation method to normalize hypoxia tolerance scores when evaluating an animal model. In this study, we improved a traditional calculation formula for assessment of hypoxia tolerance.Methods: We used a sealed bottle model in which the oxygen is gradually consumed by a mouse inside. To evaluate the hypoxia tolerance of mice, the survival time(ST) of the mouse is recorded and was used to calculate standard hypoxia tolerance time(STT) and adjusted standard hypoxia tolerance time(ASTT). Mice administered with methazolamide and saline were used as positive and negative controls, respectively.Results: Since mice were grouped according to either body weight(BW) or bottle volume, we found a strongly negative correlation between STT and BW instead of between STT and bottle volume, suggesting that different BWs could cause false positive or negative errors in the STT results. Furthermore, both false positive and negative errors could be rectified when ASTT was used as the evaluation index. Screening for anti-hypoxic medicines by using mice as the experimental subjects would provide more credible results with the improved ASTT method than with the STT method.Conclusions: ASTT could be a better index than STT for the evaluation of hypoxia tolerance abilities as it could eliminate the impact of animal BW.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11572212 and 11272227)the Innovation Program of Suzhou University of Science and Technology,China(Grant No.SKYCX16 012)
文摘This paper focuses on studying the Noether symmetry and the conserved quantity with non-standard Lagrangians, namely exponential Lagrangians and power-law Lagrangians on time scales. Firstly, for each case, the Hamilton prin- ciple based on the action with non-standard Lagrangians on time scales is established, with which the corresponding Euler-Lagrange equation is given. Secondly, according to the invariance of the Hamilton action under the infinitesimal transformation, the Noether theorem for the dynamical system with non-standard Lagrangians on time scales is established. The proof of the theorem consists of two steps. First, it is proved under the infinitesimal transformations of a special one-parameter group without transforming time. Second, utilizing the technique of time-re-parameterization, the Noether theorem in a general form is obtained. The Noether-type conserved quantities with non-standard Lagrangians in both clas- sical and discrete cases are given. Finally, an example in Friedmann-Robertson-Walker spacetime and an example about second order Duffing equation are given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China(No.U1333202)
文摘A clustering algorithm and a probability statistics method were applied to different phases of a flight to analyze operation time during aircraft ground taxiing and airborne flight.And the clustering pattern,distribution characteristics and dynamically changing rules of the two phases were identified.Further,an estimate method was established to measure operation time of flight legs,with creative steps of calculating individual segment separately and then integrating them accordingly.The method can both objectively and dynamically measure operation time,and accurately reflect real situation.It helps to better utilize airport slot resources and provides a strong support for air traffic flow management when scheduling flight plan in strategic and pre-tactic phases.
基金supported by the grants from the Natural Science Foundation of China(No.81071610 and No.81471814)Consultative Project of Transformation Medicine in Southwest Hospital of the Third Military Medical University(SWH2014ZH05)
文摘Background: Hypoxia is a primary cause of mountain sickness and a common pathological condition in patients with heart failure, shock, stroke, and chronic obstructive pulmonary disease(COPD). Thus far, little advancement in countering hypoxic damage has been achieved, and one of the main reasons is the absence of an ideal algorithm or calculation method to normalize hypoxia tolerance scores when evaluating an animal model. In this study, we improved a traditional calculation formula for assessment of hypoxia tolerance.Methods: We used a sealed bottle model in which the oxygen is gradually consumed by a mouse inside. To evaluate the hypoxia tolerance of mice, the survival time(ST) of the mouse is recorded and was used to calculate standard hypoxia tolerance time(STT) and adjusted standard hypoxia tolerance time(ASTT). Mice administered with methazolamide and saline were used as positive and negative controls, respectively.Results: Since mice were grouped according to either body weight(BW) or bottle volume, we found a strongly negative correlation between STT and BW instead of between STT and bottle volume, suggesting that different BWs could cause false positive or negative errors in the STT results. Furthermore, both false positive and negative errors could be rectified when ASTT was used as the evaluation index. Screening for anti-hypoxic medicines by using mice as the experimental subjects would provide more credible results with the improved ASTT method than with the STT method.Conclusions: ASTT could be a better index than STT for the evaluation of hypoxia tolerance abilities as it could eliminate the impact of animal BW.
