The nonclassical symmetries of a class of nonlinear partial differential equations obtained by the compatibility method is investigated. We show the nonclassicaJ symmetries obtained in [J. Math. Anal. Appl. 289 （2004...The nonclassical symmetries of a class of nonlinear partial differential equations obtained by the compatibility method is investigated. We show the nonclassicaJ symmetries obtained in [J. Math. Anal. Appl. 289 （2004） 55, J. Math. Anal. Appl. 311 （2005） 479] are not all the nonclassical symmetries. Based on a new assume on the form of invariant surface condition, all the nonclassical symmetries for a class of nonlinear partial differential equations can be obtained through the compatibility method. The nonlinear Klein-Gordon equation and the Cahn-Hilliard equations all serve as examples showing the compatibility method leads quickly and easily to the determining equations for their all nonclassical symmetries for two equations.展开更多
In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equa...In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equations (PDEs). This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution. so, it reduces significantly the difficulties of the problem and raise computing efficiency. The whole procedure of the algorithm is carried out automatically by using any computer algebra system. In general, this algorithm can yields many more important symmetries for PDEs.展开更多
The time-dependent Jones Wilkins-Lee equation products for aluminized explosives. To obtain the of state （JWL-EOS） is applied to describe detonation state time-dependent JWL-EOS parameters, cylinder tests and underw...The time-dependent Jones Wilkins-Lee equation products for aluminized explosives. To obtain the of state （JWL-EOS） is applied to describe detonation state time-dependent JWL-EOS parameters, cylinder tests and underwater explosion experiments are performed. According to the result of the wall radial velocity in cylinder tests and the shock wave pressures in underwater explosion experiments, the time-dependent JWL-EOS parameters are determined by iterating these variables in AUTODYN hydroeode simulations until the experimental values are reproduced. In addition, to verify the reliability of the derived JWL-EOS parameters, the aluminized explosive experiment is conducted in concrete. The shock wave pressures in the affected concrete bodies are measured by using manganin pressure sensors, and the rod velocity is obtained by using a high-speed camera. Simultaneously, the shock wave pressure and the rod velocity are calculated by using the derived time-dependent JWL equation of state. The calculated results are in good agreement with the experimental data.展开更多
Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve ...Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.展开更多
The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, th...The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.展开更多
This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the c...This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.展开更多
A high-efficiency mode of high-low seedbed cultivation(HLSC)has been listed as the main agricultural technology to increase land utilization ratio and grain yield in Shandong Province,China.However,limited information...A high-efficiency mode of high-low seedbed cultivation(HLSC)has been listed as the main agricultural technology to increase land utilization ratio and grain yield in Shandong Province,China.However,limited information is available on the optimized water and nitrogen management for yield formation,especially the grain-filling process,under HLSC mode.A three-year field experiment with four nitrogen rates and three irrigation rates of HLSC was conducted to reveal the response of grain-filling parameters,grain weight percentage of spike weight(GPS),spike moisture content(SMC),and winter wheat yield to water and nitrogen rates.The four nitrogen rates were N1(360 kg ha^(-1) pure N),N2(300 kg ha^(-1) pure N),N3(240 kg ha^(-1) pure N),and N4(180 kg ha^(-1) pure N),respectively,and the three irrigation quotas were W1(120 mm),W2(90 mm),and W3(60 mm),respectively.Results showed that the determinate growth function generally performed well in simulating the temporal dynamics of grain weight(0.989<R^(2)<0.999,where R2 is the determination coefficient).The occurrence time of maximum filling rate(T_(max))and active grain-filling period(AGP)increased with the increase in the water or nitrogen rate,whereas the average grain-filling rate(G_(mean))had a decreasing trend.The final 1,000-grain weight(FTGW)increased and then decreased with the increase in the nitrogen rates and increased with the increase in the irrigation rates.The GPS and SMC had a highly significant quadratic polynomial relationship with grain weight and days after anthesis.Nitrogen,irrigation,and year significantly affected the T_(max),AGP,G_(mean),and FTGW.Particularly,the AGP and FTGW were insignificantly different between high seedbed(HLSC-H)and low seedbed(HLSC-L)across the water and nitrogen levels.Moreover,the moderate water and nitrogen supply was more beneficial for grain yield,as well as for spike number and grain number per hectare.The principal component analysis indicated that combining 240-300 kg N ha^(-1) and 90^(-1)20 mm irrigation quota could improve grain-filling efficiency and yield for the HLSC-cultivated winter wheat.展开更多
X-ray pulsars offer stable, periodic X-ray pulse sequences that can be used in spacecraft positioning systems. A method using X-ray pulsars to determine the initial orbit of a satellite is presented in this paper. Thi...X-ray pulsars offer stable, periodic X-ray pulse sequences that can be used in spacecraft positioning systems. A method using X-ray pulsars to determine the initial orbit of a satellite is presented in this paper. This method suggests only one detector to be equipped on the satellite and assumes that the detector observes three pulsars in turn. To improve the performance, the use of incremental phase in one observation duration is proposed, and the incremental phase is combined with the time difference of arrival(TDOA). Then, a weighted least squares(WLS) algorithm is formulated to calculate the initial orbit. Numerical simulations are performed to assess the proposed orbit determination method.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10735030Shanghai Leading Academic Discipline Project under Grant No.B412,NSFC No.90718041+1 种基金Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)K.C.Wong Magna Fund in Ningbo University
文摘The nonclassical symmetries of a class of nonlinear partial differential equations obtained by the compatibility method is investigated. We show the nonclassicaJ symmetries obtained in [J. Math. Anal. Appl. 289 （2004） 55, J. Math. Anal. Appl. 311 （2005） 479] are not all the nonclassical symmetries. Based on a new assume on the form of invariant surface condition, all the nonclassical symmetries for a class of nonlinear partial differential equations can be obtained through the compatibility method. The nonlinear Klein-Gordon equation and the Cahn-Hilliard equations all serve as examples showing the compatibility method leads quickly and easily to the determining equations for their all nonclassical symmetries for two equations.
文摘In this article, based on the Taylor expansions of generating functions and stepwise refinement procedure, authors suggest a algorithm for finding the Lie and high (generalized) symmetries of partial differential equations (PDEs). This algorithm transforms the problem having to solve over-determining PDEs commonly encountered and difficulty part in standard methods into one solving to algebraic equations to which one easy obtain solution. so, it reduces significantly the difficulties of the problem and raise computing efficiency. The whole procedure of the algorithm is carried out automatically by using any computer algebra system. In general, this algorithm can yields many more important symmetries for PDEs.
基金Supported by the National Natural Science Foundation of China under Grant No 11172042
文摘The time-dependent Jones Wilkins-Lee equation products for aluminized explosives. To obtain the of state （JWL-EOS） is applied to describe detonation state time-dependent JWL-EOS parameters, cylinder tests and underwater explosion experiments are performed. According to the result of the wall radial velocity in cylinder tests and the shock wave pressures in underwater explosion experiments, the time-dependent JWL-EOS parameters are determined by iterating these variables in AUTODYN hydroeode simulations until the experimental values are reproduced. In addition, to verify the reliability of the derived JWL-EOS parameters, the aluminized explosive experiment is conducted in concrete. The shock wave pressures in the affected concrete bodies are measured by using manganin pressure sensors, and the rod velocity is obtained by using a high-speed camera. Simultaneously, the shock wave pressure and the rod velocity are calculated by using the derived time-dependent JWL equation of state. The calculated results are in good agreement with the experimental data.
基金National Natural Science Foundation of China(No.61862048)。
文摘Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.
文摘The invariance of the differential equations under the infinitesimal transformations was used to study the Lie symmetries and conserved quantities of arbitrary order nonholonomic systems. The determining equations, the restriction equations, the structure equation and the form of the conserved quantities were obtained.
基金supported by the National Natural Science Foundation of China (Grant Nos 10572021 and 10772025)the Doctoral Program Foundation of Institution of Higher Education of China (Grant No 20040007022)
文摘This paper studies conformal invariance and conserved quantities of Hamilton system. The definition and the determining equation of conformal invariance for Hamilton system are provided. The relationship between the conformal invariance and the Lie symmetry are discussed, and the necessary and sufficient condition that the conformal invariance would be the Lie symmetry of the system under the infinitesimal one-parameter transformation group is deduced. It gives the conserved quantities of the system and an example for illustration.
基金supported by the National Key Research and Development Program of China(2023YFD1900802)the China Agriculture Research System of MOF and MARA(CARS-03-19)+2 种基金the National Natural Science Foundation of China(51879267)the Central Public-interest Scientific Institution Basal Research Fund,China(IFI2023-13)the Agricultural Science and Technology Innovation Program(ASTIP),Chinese Academy of Agricultural Sciences。
文摘A high-efficiency mode of high-low seedbed cultivation(HLSC)has been listed as the main agricultural technology to increase land utilization ratio and grain yield in Shandong Province,China.However,limited information is available on the optimized water and nitrogen management for yield formation,especially the grain-filling process,under HLSC mode.A three-year field experiment with four nitrogen rates and three irrigation rates of HLSC was conducted to reveal the response of grain-filling parameters,grain weight percentage of spike weight(GPS),spike moisture content(SMC),and winter wheat yield to water and nitrogen rates.The four nitrogen rates were N1(360 kg ha^(-1) pure N),N2(300 kg ha^(-1) pure N),N3(240 kg ha^(-1) pure N),and N4(180 kg ha^(-1) pure N),respectively,and the three irrigation quotas were W1(120 mm),W2(90 mm),and W3(60 mm),respectively.Results showed that the determinate growth function generally performed well in simulating the temporal dynamics of grain weight(0.989<R^(2)<0.999,where R2 is the determination coefficient).The occurrence time of maximum filling rate(T_(max))and active grain-filling period(AGP)increased with the increase in the water or nitrogen rate,whereas the average grain-filling rate(G_(mean))had a decreasing trend.The final 1,000-grain weight(FTGW)increased and then decreased with the increase in the nitrogen rates and increased with the increase in the irrigation rates.The GPS and SMC had a highly significant quadratic polynomial relationship with grain weight and days after anthesis.Nitrogen,irrigation,and year significantly affected the T_(max),AGP,G_(mean),and FTGW.Particularly,the AGP and FTGW were insignificantly different between high seedbed(HLSC-H)and low seedbed(HLSC-L)across the water and nitrogen levels.Moreover,the moderate water and nitrogen supply was more beneficial for grain yield,as well as for spike number and grain number per hectare.The principal component analysis indicated that combining 240-300 kg N ha^(-1) and 90^(-1)20 mm irrigation quota could improve grain-filling efficiency and yield for the HLSC-cultivated winter wheat.
基金supported by the National Natural Science Foundation of China(No.61401340)the Natural Science Basic Research Plan in Shaanxi Province of China(No.2016JM6035)+1 种基金the Fundamental Research Funds for the Central Universities,China(No.JB161303)and the Areospace T.T.&C.Innovation Program(No.201515A)
文摘X-ray pulsars offer stable, periodic X-ray pulse sequences that can be used in spacecraft positioning systems. A method using X-ray pulsars to determine the initial orbit of a satellite is presented in this paper. This method suggests only one detector to be equipped on the satellite and assumes that the detector observes three pulsars in turn. To improve the performance, the use of incremental phase in one observation duration is proposed, and the incremental phase is combined with the time difference of arrival(TDOA). Then, a weighted least squares(WLS) algorithm is formulated to calculate the initial orbit. Numerical simulations are performed to assess the proposed orbit determination method.
