Regressive formulae to calculate the quantity of plant leaf area for 13 species of ornamental plants were set up based on investigation data of 30 species on 3 major public squares (Dongfeng square, Shengli square and...Regressive formulae to calculate the quantity of plant leaf area for 13 species of ornamental plants were set up based on investigation data of 30 species on 3 major public squares (Dongfeng square, Shengli square and Guandu square) in Kun-ming City, China, which were applied to calculate quantities of plant leaf area of these 13 species. The quantities of plant leaf area for the other 17 ornamental plant species on these squares were directly measured, and the total quantity of plant leaf area of each studied square was obtained individually. The results showed that the quantity of plant leaf area on Shengli square with ornamental plants structure composed of arbor tree species, shrub tree species and turf grass was highest among the three squares. It is believed that the design model of multi-storied vertical structure and proper tending of plant community could not only increase the quantity of plant leaf area, but also play an important role in generating ecological and landscaping benefits. Some corresponding suggestions were put forward on the basis of comprehensive analyses on the plant leaf area quantity of the three representative squares in Kunming urban area.展开更多
Proposed a new method to disclose the complicated non-linearity structure of the water-resource system, introducing chaos theory into the hydrology and water resources field, and combined with the chaos theory and art...Proposed a new method to disclose the complicated non-linearity structure of the water-resource system, introducing chaos theory into the hydrology and water resources field, and combined with the chaos theory and artificial neural networks. Training data construction and networks structure were determined by the phase space reconstruction, and establishing nonlinear relationship of phase points with neural networks, the forecasting model of the resource quantity of the surface water was brought forward. The keystone of the way and the detailed arithmetic of the network training were given. The example shows that the model has highly forecasting precision.展开更多
The research performed statistical analysis on 186 data concerning the amount of discharged industrial wastewater, the amount of oxygen demand of industrial wastewater, the amount of ammonia and nitrogen discharged fr...The research performed statistical analysis on 186 data concerning the amount of discharged industrial wastewater, the amount of oxygen demand of industrial wastewater, the amount of ammonia and nitrogen discharged from industries, the amount of urban discharged domestic sewage, the amount of daily life chemical oxygen demand, and the amount of domestic ammonia and nitrogen to explore source of pollutants from wastewater and guarantee urban water quality.Factor analysis was then performed with SPSS according to discharge quantity of pollutants. The results should that the major pollutants are from domestic sewage it is expected scientific suggestions be proposed on water quality in our country.展开更多
[Objective] The study was to determine the optimal quantity of fertilizer required for Yongbao 2 during heading. [Method] According to a randomized block design with three replicates, four fertilizer treatments and on...[Objective] The study was to determine the optimal quantity of fertilizer required for Yongbao 2 during heading. [Method] According to a randomized block design with three replicates, four fertilizer treatments and one blank control were set in field trials. Each plot had a net area of 66.7 m2, Finally, the mustard yield and economic benefit per plot among the treatments were compared. [Result] There was no significant difference in yield among the four fertilizer treatments. The agronomic traits and yield of Yongbao 2 were improved when the quantity of fertilizer was gradually increased. The treatment with 750 kg/hm2 compound fertilizer during mus- tard heading had the highest yield. However, the treatment with 450 kg/hm2 of compound fertilizer during mustard heading had the highest economic benefit. By considering both yield and benefit, 450 kg/hm2 was the optimal quantity of fertilizer required for Yongbao 2 during heading. [Conclusion] The results will provide references for future application and extension of Yongbao 2.展开更多
[Objective] The aim was to research the appropriate seeding quantities of double-season machine-transplanted rice in middle and low-yielding district of southern Jiangxi Province. [Method] The research set five differ...[Objective] The aim was to research the appropriate seeding quantities of double-season machine-transplanted rice in middle and low-yielding district of southern Jiangxi Province. [Method] The research set five different seeding quantities treatments, and compared with conventional seedling treatment, and the appropriate seeding quantities of double season machine-transplanted rice in middle and lowyielding district of southern Jiangxi Province was discussed. [Result] The yields were highest when the seeding quantity was 70 g per tray of early rice by mechanical transplanting and 60 g per tray of late rice. The yield of early rice by mechanical transplanting showed significantly positive correlation with the number of productive ear and the number of seed per ear, and late rice yield showed significant correlation with the number of productive ear by mechanical transplanting. It is key for improving high yields by guaranteeing the number of productive ear. [Conclusion] The issue of proper sowing quantity should be taken into consideration for double-cropping rice in the region, which is crucial for high yields.展开更多
Objective] The alm was to provide scientific references for determination of optimal N and P quantities of malze. [Method] The research conducted a test in field to expIore the effects of N and P fertiIizers on malze ...Objective] The alm was to provide scientific references for determination of optimal N and P quantities of malze. [Method] The research conducted a test in field to expIore the effects of N and P fertiIizers on malze yield. [Result] Both of N and P fertiIizers have significant effects on malze yield. When malze yield reached the highest, the quantities of N fertiIizers and P fertiIizers were 530.56 and 105.44 kg/hm2, respectiveIy. [Conclusion] Malze yield keeps growing upon N or P fertiIizers to certaln extent, and excessive quantities of N and P fertiIizer wouId reduce malze yield.展开更多
[Objective] The study was to test the optimum quantity of nitrogen fertilizer of Yongxian 975. [Method] According to randomized block arrangement with three replications, there were 5 nitrogen fertilizer treatments an...[Objective] The study was to test the optimum quantity of nitrogen fertilizer of Yongxian 975. [Method] According to randomized block arrangement with three replications, there were 5 nitrogen fertilizer treatments and 1 blank control, the net area of each plot was 13.4 m2. [Result] There was no significant difference between different nitrogen fertilizer treatments. The spike, grain and weight were more coor- dinated and the yield-increasing potential was great when the quantity of pure nitro- gen was 210.0 kg/hm2. The real harvest yield was the highest and the profit was the best, but the utilization rate of fertilizer was poor, plant diseases, insect pests, lodging risk and the ecological burden were increased when the quantity of pure nitrogen was 270.0 kg/hm2. While the quantity of pure nitrogen was 150.0 kg/hm2, the fertilizer utilization rate was the highest, the yield and the economic benefit were high. [Coaclusie,] With comprehensively considering the high and stable yield and the efficiency, the best quantity of nitrogen fertilizer on Yongxian 975 was controlled at about 150.0 kg/hm2. The quantity of pure nitrogen could be increased to 180.0 kg/hm2 when the field fertility was moderate or low. In order to explore its high-yield potential, the quantity of nitrogen fertilizer could be increased to 210.0 kg/hm2 in the high-yield tackling field.展开更多
Two estimaton methods are used to calculate the theoretical reservoir potential of China's oceanic thermal energy. One is based on the measured temperature difference between the surface water and the deep water, ...Two estimaton methods are used to calculate the theoretical reservoir potential of China's oceanic thermal energy. One is based on the measured temperature difference between the surface water and the deep water, the other on the net radiation energy income from solar insolation either measured or deduced. The results from these two methods are compared and examined. Then, the maximum amount of the exploitable thermal energy is calculated based on the assumption of a Carnot cycle efficiency. In the process of estimation, such factors as water depth, seasonal water temperature variation and geographic location have been taken into account.The theoretical reservoir capacity and the exploitable quantity of the thermal energy of China's four seas are thus estimated separately.展开更多
There are 9.56 million accountants in China, who are working in different size firms and nonprofit organizations. The objective of this article is to examine the quantitative relationship between the firm size and the...There are 9.56 million accountants in China, who are working in different size firms and nonprofit organizations. The objective of this article is to examine the quantitative relationship between the firm size and the quantity of accountants working for the firm. In this paper, the employees, sales revenues, and total assets in a firm are employed to measure firm size. The authors collect and analyze the data of 436 listed firms from the Chinese Shenzhen Stock Exchange. The result of this study indicates there is a positive relationship between the firm size and the quantity of accountants employed by the firm. The study also establishes the multiple regression equation, which can be used to predict the quantity of accountants of listed firms. And it provides a way to predict the quantity of accountants of legal organizations.展开更多
Because of the various elements that come into play in natural soil formation, the impact of varied proportions of mineral composition and fines amount on Atterberg limits and compaction characteristics of soils is no...Because of the various elements that come into play in natural soil formation, the impact of varied proportions of mineral composition and fines amount on Atterberg limits and compaction characteristics of soils is not well known. Three distinct soil samples were used in this investigation. The findings indicated the effect of varied mineral composition proportions and fines amount on the liquid limit, plastic limit, and plasticity index as assessed by the Casagrande test and hand-rolling method. The fluctuation of maximum dry density and optimal moisture content with these three soils has also been studied. Furthermore, correlations were established to indicate the compaction parameters and the amount of minerals and particles in the soil. The data show that the mineral content of the soil has a direct impact on the Atterberg limits and compaction characteristics. Soils containing larger percentages of expansive minerals, such as montmorillonite, have more flexibility and volume change capability. Mineral composition influences compaction parameters such as maximum dry density, ideal water content, axial strain, and axial stress. Soils with a larger proportion of fines, such as Soil 2 and Soil 3, have stronger flexibility and lower compaction qualities, with higher ideal water content and lower maximum dry density. Soil 1 has moderate flexibility and intermediate compaction qualities due to its low fines percentage. The effect of different mineral compositions and fines on the Atterberg limits and compaction characteristics of soils can be used to predict the behavior of compacted soils encountered in engineering practices, reducing the time and effort required to assess soil suitability for engineering use.展开更多
Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tz...Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.展开更多
This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The defini...This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.展开更多
We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-elec...We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.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
This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions o...This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.展开更多
This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, ...This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.展开更多
This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equati...This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.展开更多
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
Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating...Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.展开更多
Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which kee...Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.展开更多
基金This research was sponsored by Educational Department of Yunnan Province (No. 03Z583B).
文摘Regressive formulae to calculate the quantity of plant leaf area for 13 species of ornamental plants were set up based on investigation data of 30 species on 3 major public squares (Dongfeng square, Shengli square and Guandu square) in Kun-ming City, China, which were applied to calculate quantities of plant leaf area of these 13 species. The quantities of plant leaf area for the other 17 ornamental plant species on these squares were directly measured, and the total quantity of plant leaf area of each studied square was obtained individually. The results showed that the quantity of plant leaf area on Shengli square with ornamental plants structure composed of arbor tree species, shrub tree species and turf grass was highest among the three squares. It is believed that the design model of multi-storied vertical structure and proper tending of plant community could not only increase the quantity of plant leaf area, but also play an important role in generating ecological and landscaping benefits. Some corresponding suggestions were put forward on the basis of comprehensive analyses on the plant leaf area quantity of the three representative squares in Kunming urban area.
基金Supported by 863 Program of China(2002AA2Z4291) Henan Innovation Project for University Prominent Research Talents(2005KYCX015)Henan Project for University Prominent Talents
文摘Proposed a new method to disclose the complicated non-linearity structure of the water-resource system, introducing chaos theory into the hydrology and water resources field, and combined with the chaos theory and artificial neural networks. Training data construction and networks structure were determined by the phase space reconstruction, and establishing nonlinear relationship of phase points with neural networks, the forecasting model of the resource quantity of the surface water was brought forward. The keystone of the way and the detailed arithmetic of the network training were given. The example shows that the model has highly forecasting precision.
文摘The research performed statistical analysis on 186 data concerning the amount of discharged industrial wastewater, the amount of oxygen demand of industrial wastewater, the amount of ammonia and nitrogen discharged from industries, the amount of urban discharged domestic sewage, the amount of daily life chemical oxygen demand, and the amount of domestic ammonia and nitrogen to explore source of pollutants from wastewater and guarantee urban water quality.Factor analysis was then performed with SPSS according to discharge quantity of pollutants. The results should that the major pollutants are from domestic sewage it is expected scientific suggestions be proposed on water quality in our country.
文摘[Objective] The study was to determine the optimal quantity of fertilizer required for Yongbao 2 during heading. [Method] According to a randomized block design with three replicates, four fertilizer treatments and one blank control were set in field trials. Each plot had a net area of 66.7 m2, Finally, the mustard yield and economic benefit per plot among the treatments were compared. [Result] There was no significant difference in yield among the four fertilizer treatments. The agronomic traits and yield of Yongbao 2 were improved when the quantity of fertilizer was gradually increased. The treatment with 750 kg/hm2 compound fertilizer during mus- tard heading had the highest yield. However, the treatment with 450 kg/hm2 of compound fertilizer during mustard heading had the highest economic benefit. By considering both yield and benefit, 450 kg/hm2 was the optimal quantity of fertilizer required for Yongbao 2 during heading. [Conclusion] The results will provide references for future application and extension of Yongbao 2.
基金National Key Technology R&D Program of the Ministry of Science and Technology(2011BAD16B04,(2012BAD04B11)~~
文摘[Objective] The aim was to research the appropriate seeding quantities of double-season machine-transplanted rice in middle and low-yielding district of southern Jiangxi Province. [Method] The research set five different seeding quantities treatments, and compared with conventional seedling treatment, and the appropriate seeding quantities of double season machine-transplanted rice in middle and lowyielding district of southern Jiangxi Province was discussed. [Result] The yields were highest when the seeding quantity was 70 g per tray of early rice by mechanical transplanting and 60 g per tray of late rice. The yield of early rice by mechanical transplanting showed significantly positive correlation with the number of productive ear and the number of seed per ear, and late rice yield showed significant correlation with the number of productive ear by mechanical transplanting. It is key for improving high yields by guaranteeing the number of productive ear. [Conclusion] The issue of proper sowing quantity should be taken into consideration for double-cropping rice in the region, which is crucial for high yields.
基金Supported by Yantai Science and Technology Development Program(2007155)~~
文摘Objective] The alm was to provide scientific references for determination of optimal N and P quantities of malze. [Method] The research conducted a test in field to expIore the effects of N and P fertiIizers on malze yield. [Result] Both of N and P fertiIizers have significant effects on malze yield. When malze yield reached the highest, the quantities of N fertiIizers and P fertiIizers were 530.56 and 105.44 kg/hm2, respectiveIy. [Conclusion] Malze yield keeps growing upon N or P fertiIizers to certaln extent, and excessive quantities of N and P fertiIizer wouId reduce malze yield.
文摘[Objective] The study was to test the optimum quantity of nitrogen fertilizer of Yongxian 975. [Method] According to randomized block arrangement with three replications, there were 5 nitrogen fertilizer treatments and 1 blank control, the net area of each plot was 13.4 m2. [Result] There was no significant difference between different nitrogen fertilizer treatments. The spike, grain and weight were more coor- dinated and the yield-increasing potential was great when the quantity of pure nitro- gen was 210.0 kg/hm2. The real harvest yield was the highest and the profit was the best, but the utilization rate of fertilizer was poor, plant diseases, insect pests, lodging risk and the ecological burden were increased when the quantity of pure nitrogen was 270.0 kg/hm2. While the quantity of pure nitrogen was 150.0 kg/hm2, the fertilizer utilization rate was the highest, the yield and the economic benefit were high. [Coaclusie,] With comprehensively considering the high and stable yield and the efficiency, the best quantity of nitrogen fertilizer on Yongxian 975 was controlled at about 150.0 kg/hm2. The quantity of pure nitrogen could be increased to 180.0 kg/hm2 when the field fertility was moderate or low. In order to explore its high-yield potential, the quantity of nitrogen fertilizer could be increased to 210.0 kg/hm2 in the high-yield tackling field.
文摘Two estimaton methods are used to calculate the theoretical reservoir potential of China's oceanic thermal energy. One is based on the measured temperature difference between the surface water and the deep water, the other on the net radiation energy income from solar insolation either measured or deduced. The results from these two methods are compared and examined. Then, the maximum amount of the exploitable thermal energy is calculated based on the assumption of a Carnot cycle efficiency. In the process of estimation, such factors as water depth, seasonal water temperature variation and geographic location have been taken into account.The theoretical reservoir capacity and the exploitable quantity of the thermal energy of China's four seas are thus estimated separately.
文摘There are 9.56 million accountants in China, who are working in different size firms and nonprofit organizations. The objective of this article is to examine the quantitative relationship between the firm size and the quantity of accountants working for the firm. In this paper, the employees, sales revenues, and total assets in a firm are employed to measure firm size. The authors collect and analyze the data of 436 listed firms from the Chinese Shenzhen Stock Exchange. The result of this study indicates there is a positive relationship between the firm size and the quantity of accountants employed by the firm. The study also establishes the multiple regression equation, which can be used to predict the quantity of accountants of listed firms. And it provides a way to predict the quantity of accountants of legal organizations.
文摘Because of the various elements that come into play in natural soil formation, the impact of varied proportions of mineral composition and fines amount on Atterberg limits and compaction characteristics of soils is not well known. Three distinct soil samples were used in this investigation. The findings indicated the effect of varied mineral composition proportions and fines amount on the liquid limit, plastic limit, and plasticity index as assessed by the Casagrande test and hand-rolling method. The fluctuation of maximum dry density and optimal moisture content with these three soils has also been studied. Furthermore, correlations were established to indicate the compaction parameters and the amount of minerals and particles in the soil. The data show that the mineral content of the soil has a direct impact on the Atterberg limits and compaction characteristics. Soils containing larger percentages of expansive minerals, such as montmorillonite, have more flexibility and volume change capability. Mineral composition influences compaction parameters such as maximum dry density, ideal water content, axial strain, and axial stress. Soils with a larger proportion of fines, such as Soil 2 and Soil 3, have stronger flexibility and lower compaction qualities, with higher ideal water content and lower maximum dry density. Soil 1 has moderate flexibility and intermediate compaction qualities due to its low fines percentage. The effect of different mineral compositions and fines on the Atterberg limits and compaction characteristics of soils can be used to predict the behavior of compacted soils encountered in engineering practices, reducing the time and effort required to assess soil suitability for engineering use.
基金National Natural Science Foundation of China under Grant No.10672143
文摘Symmetry of Tzénoff equations for unilateral holonomic system under the infinitesimal transformationsof groups is investigated.Its definitions and discriminant equations of Mei symmetry and Lie symmetry of Tzénoffequations are given.Sufficient and necessary condition of Lie symmetry deduced by the Mei symmetry is also given.Hojman conserved quantity of Tzénoff equations for the system above through special Lie symmetry and Lie symmetryin the condition of special Mei symmetry respectively is obtained.
基金supported by the National Natural Science Foundation of China (Grant No 10572021)
文摘This paper studies the Mei symmetry and Mei conserved quantity for nonholonomic systems of unilateral Chetaev type in Nielsen style. The differential equations of motion of the system above are established. The definition and the criteria of Mei symmetry, loosely Mei symmetry, strictly Mei symmetry for the system are given in this paper. The existence condition and the expression of Mei conserved quantity are deduced directly by using Mei symmetry. An example is given to illustrate the application of the results.
基金supported by the National Natural Science Foundation of China (Grant No.11072218)
文摘We obtain a new type of conserved quantity of Mei symmetry for the motion of mechanico--electrical coupling dynamical systems under the infinitesimal transformations. A criterion of Mei symmetry for the mechanico-electrical coupling dynamical systems is given. Simultaneously, the condition of existence of the new conserved quantity of Mei symmetry for mechanico-electrical coupling dynamical systems is obtained. Finally, an example is given to illustrate the application of the results.
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.
文摘This paper studies a new type of conserved quantity which is directly induced by Lie symmetry of the Lagrange system. Firstly, the criterion of Lie symmetry for the Lagrange system is given. Secondly, the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an example is given to illustrate the application of the result.
文摘This paper studies a new type of conserved quantity which is directly induced by Mei symmetry of the Lagrange system. Firstly, the definition and criterion of Mei symmetry for the Lagrange system are given. Secondly, a coordination function is introduced, and the conditions of existence of the new conserved quantity as well as its forms are proposed. Lastly, an illustrated example is given. The result indicates that the coordination function can be selected properly according to the demand for finding the gauge function, and thereby the gauge function can be found more easily. Furthermore, since the choice of the coordination function has multiformity, many more conserved quantities of Mei symmetry for the Lagrange system can be obtained.
基金Project supported by the National Natural Science Foundation of China （Grant No 10272021） and the Doctoral Program Foundation of Institution of Higher Education of China （Grant No 20040007022）.
文摘This paper focuses on studying the Lie symmetry and a conserved quantity of a system of first-order differential equations. The determining equations of the Lie symmetry for a system of first-order differential equations, from which a kind of conserved quantity is deduced, are presented. And their general conclusion is applied to a Hamilton system, a Birkhoff system and a generalized Hamilton system. Two examples are given to illustrate the application of the results.
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.
基金the National Natural Science Foundation of China (10472060)Research Grants Council of the Hong Kong Special Administrative Region (9041145)+1 种基金Shanghai Municipal Education Commission Scientific Research Project (07ZZ07)Shanghai Leading Academic Discipline Project (Y0103)
文摘Nonlinear three-dimensional vibration of axially moving strings is investigated in the view of energetics. The governing equation is derived from the Eulerian equation of motion of a continuum for axially accelerating strings. The time-rate of the total mechanical energy associated with the vibration is calculated for the string with its ends moving in a prescribed way. For a string moving in a constant axial speed and constrained by two fixed ends, a conserved quantity is proved to remain unchanged during three-dimensional vibration, while the string energy is not conserved. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration. Numerical simulations are performed for a rubber string and a steel string. The results demonstrate the variation of the total mechanical energy and the invariance of the conserved quantity.
文摘Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.
