This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the F...This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.展开更多
We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional invest...We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional investigation study. Anthropometric parameters, whole body reaction time and one leg with eye closed balance were measured. Whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in 70’s than those in 60’s in both sexes. Two hundred twenty seven men (31.1%) and 533 women (40.1%) were having no medications. In men, whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in subjects with medications than those in subjects without in 60’s. However, significant differences of whole body reaction time and one leg with eye closed balance between subjects with and without medications in men with 70’s and women with 60’s and 70’s were not noted. This standard mean value may provide a useful reference database for evaluating whole body reaction time and one leg with eye closed balance in Japanese elderly subjects.展开更多
For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based o...For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.展开更多
The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmla...The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmlations. The power-law scaling of the translocation time T with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be T - N^a with the exponent a varying from a = 0.71 for relatively short chains to a = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α= 1.27 for the transloeation of double-strand DNA. The distribution of translocation time D（τ） is close to a Gaussian function for duration time τ 〈 τp and follows a falling exponential function for duration time T 〉 wp. For closed knotted polymers, the scaling exponent a is 1.27 for small field force （F = 5） and 1.38 for large field force （F = 10）. The distribution of translocation time D（τ） remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.展开更多
The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cro...The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.展开更多
基金supported by the Mathematical Tianyuan Foundation (No. 10826078)the National Natural Science Foundation of China (No. 60874006)
文摘This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.
文摘We evaluated whole body reaction time and one leg with eye closed balance in elderly Japanese. A total of 2059 elderly Japanese (730 men and 1329 women), aged 60 - 79 years, were enrolled in the cross-sectional investigation study. Anthropometric parameters, whole body reaction time and one leg with eye closed balance were measured. Whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in 70’s than those in 60’s in both sexes. Two hundred twenty seven men (31.1%) and 533 women (40.1%) were having no medications. In men, whole body reaction time was significantly higher and one leg with eye closed balance was significantly lower in subjects with medications than those in subjects without in 60’s. However, significant differences of whole body reaction time and one leg with eye closed balance between subjects with and without medications in men with 70’s and women with 60’s and 70’s were not noted. This standard mean value may provide a useful reference database for evaluating whole body reaction time and one leg with eye closed balance in Japanese elderly subjects.
文摘For maneuvering target, the optimal trajectory shaping guidance law which can simultaneously achieve the designed specifications on miss distance and final impact angle was deduced using optimal control theory based on the time-to-go weighted function. Based on the same cost function, the closed-form solutions of the guidance law were derived when the initial displacement of missile, final impact angle, heading error and target maneuver was introduced into the lag-free guidance system. To validate the closed-form solutions, the simulation of the lag-free system was done and the simulation results exactly matched the closed-form solutions and only when the exponent is greater than zero, the final acceleration approaches to zero.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 20574052, 20774066, 20974081 and 20934004)the Program for New Century Excellent Talents in University,China (Grant No. NCET-05-0538)the Natural Science Foundation of Zhejiang Province, China (Grant No. Y4090098)
文摘The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics sinmlations. The power-law scaling of the translocation time T with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be T - N^a with the exponent a varying from a = 0.71 for relatively short chains to a = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α= 1.27 for the transloeation of double-strand DNA. The distribution of translocation time D（τ） is close to a Gaussian function for duration time τ 〈 τp and follows a falling exponential function for duration time T 〉 wp. For closed knotted polymers, the scaling exponent a is 1.27 for small field force （F = 5） and 1.38 for large field force （F = 10）. The distribution of translocation time D（τ） remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.
基金supported by the National Natural Science Foundation of China(Grant No.11374133)the Taishan Scholars Project of Shandong Province,China(Grant No.ts2015110055)
文摘The photodetachment dynamics of H^- ion in a harmonic potential plus an oscillating electric field is studied using the time-dependent closed orbit theory. An analytical formula for calculating the photodetachment cross section of this system is put forward. It is found that the photodetachment cross section of this system is nearly unaffected for the weak oscillating electric field strength, but oscillates complicatedly when the oscillating electric field strength turns strong. In addition, the frequency of the harmonic potential and the oscillating electric field （the frequency of the harmonic potential and the frequency of the oscillating electric field are the same in the paper, unless otherwise stated.） can also affect the photodetachment dynamics of this system. With the increase of the frequency in the harmonic potential and the oscillating electric field, the number of the closed orbits for the detached electrons increased, which makes the oscillatory structure in the photodetachment cross section much more complex. Our study presents an intuitive understanding of the photodetachment dynamics driven by a harmonic potential plus an oscillating electric field from a space and time dependent viewpoint. This study is very useful in guiding the future experimental research for the photodetachment dynamics in the electric field both changing with space and time.
