In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challe...In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challenges:firstly,the dynamic nature of the automatic picking process requires fruit target detection algorithms to adapt to multi-view characteristics,ensuring effective recognition of the same fruit from different perspectives.Secondly,fruits in natural environments often suffer from interference factors such as overlapping,occlusion,and illumination fluctuations,which increase the difficulty of image capture and recognition.To address these challenges,this study conducted an in-depth analysis of the key features in fruit recognition and discovered that the stem,body,and base serve as constant and core information in fruit identification,exhibiting long-term dependent semantic relationships during the recognition process.These invariant features provide a stable foundation for dynamic fruit recognition,contributing to improved recognition accuracy and robustness.Specifically,the morphology and position of the stem,body,and base are relatively fixed,and the effective extraction of these features plays a crucial role in fruit recognition.This paper proposes a novel model,TransSSA,and designs two innovative modules to effectively extract fruit image features.The Self-Attention Core Feature Extraction(SAF)module integrates YOLOV8 and Swin Transformer as backbone networks and introduces the Shuffle Attention self-attention mechanism,significantly enhancing the ability to extract core features.This module focuses on constant features such as the stem,body,and base,ensuring accurate fruit recognition in different environments.On the other hand,the Squeeze and Excitation Aggregation(SAE)module combines the network’s ability to capture channel patterns with global knowledge,further optimizing the extraction of effective features.Additionally,to improve detection accuracy,this studymodifies the regression loss function to EIOU.To validate the effectiveness of the TransSSA model,this study conducted extensive visualization analysis to support the interpretability of the SAF and SAE modules.Experimental results demonstrate that TransSSA achieves a performance of 91.3%on a tomato dataset,fully proving its innovative capabilities.Through this research,we provide amore effective solution for using fruit harvesting robots in complex environments.展开更多
The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux...The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.展开更多
This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in tradition...This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in traditional feedback control,to the domain of motion planning for autonomous vehicles.Thus,closed-loop system uncertainty can be preemptively addressed during vehicle motion planning.This involves selecting collision-free trajectories to minimize the volume of robust invariant tubes.Furthermore,constraints on state and control variables are translated into constraints on the RCI tubes of the closed-loop system,ensuring that motion planning produces a safe and optimal trajectory while maintaining flexibility,rather than solely optimizing for the open-loop nominal model.Additionally,to expedite the solving process,we were inspired by L2gain to parameterize the RCI tubes and developed a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets within closedloop systems.Furthermore,we applied the pseudospectral orthogonal collocation method to parameterize the optimization problem of transcribing trajectories using high-order Lagrangian polynomials.Finally,under various operating conditions,we incorporate both the kinematic and dynamic models of the vehicle and also conduct simulations and analyses of uncertainties such as heading angle measurement,chassis response,and steering hysteresis.Our proposed robust motion planning framework has been validated to effectively address nearly all bounded uncertainties while anticipating potential tracking errors in control during the planning phase.This ensures fast,closed-loop safety and robustness in vehicle motion planning.展开更多
Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equatio...Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.展开更多
Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradien...Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradient invariants in existing research is seldom a concern.The gravity gradient tensor has three invariants,named as I_(1),I_(2)and I_(3).I_(1) is a Laplace operator outside the Earth and a Poison operator inside the Earth.The focus of this study is to discuss the performance of the other two invariants of gravity gradients in matching navigation based on the Iterative Closest Contour Point(ICCP)algorithm and compare the matching results with that of the gravity gradient Tzz.The results show that they have almost the same performance when there is no noise,and the background data noises have a large impact on the matching results.There are differences in the anti-interference ability of observation noises for the different components.Under the same random noises in the observations,I2performs a little better than the other two components in terms of position error standard deviation.According to the investigations,since attitude errors can not be avoided and influence the positioning based on Tzz,we recommend adopting invariants of gravity gradients,especially I2,for matching navigation in actual cases.展开更多
In order to obtain a large number of correct matches with high accuracy,this article proposes a robust wide baseline point matching method,which is based on Scott s proximity matrix and uses the scale invariant featur...In order to obtain a large number of correct matches with high accuracy,this article proposes a robust wide baseline point matching method,which is based on Scott s proximity matrix and uses the scale invariant feature transform (SIFT). First,the distance between SIFT features is included in the equations of the proximity matrix to measure the similarity between two feature points; then the normalized cross correlation (NCC) used in Scott s method,which has been modified with adaptive scale and orientation,...展开更多
This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.展开更多
Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presen...Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.展开更多
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a La...Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.展开更多
The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the ...The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.展开更多
The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undistur...The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undisturbed system with unilateral constraints is given. Based on the concept of high-order adiabatic invariant of mechanical systems, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the system with unilateral holonomic constraints is obtained, which can be called Hojman adiabatic invariant. In the end of the paper, an example is given to illustrate the application of the results.展开更多
For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of re...For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.展开更多
Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the no...Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the nonholonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the forms of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetr...The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.展开更多
Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholo...Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variab...By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.展开更多
In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and suffici...In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.展开更多
This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the co...This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.展开更多
The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a...The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.展开更多
The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetri...The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.展开更多
基金supported in part by the Basic Research Project of Science and Technology Department of Jilin Province,China(Grant No.202002044JC).
文摘In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challenges:firstly,the dynamic nature of the automatic picking process requires fruit target detection algorithms to adapt to multi-view characteristics,ensuring effective recognition of the same fruit from different perspectives.Secondly,fruits in natural environments often suffer from interference factors such as overlapping,occlusion,and illumination fluctuations,which increase the difficulty of image capture and recognition.To address these challenges,this study conducted an in-depth analysis of the key features in fruit recognition and discovered that the stem,body,and base serve as constant and core information in fruit identification,exhibiting long-term dependent semantic relationships during the recognition process.These invariant features provide a stable foundation for dynamic fruit recognition,contributing to improved recognition accuracy and robustness.Specifically,the morphology and position of the stem,body,and base are relatively fixed,and the effective extraction of these features plays a crucial role in fruit recognition.This paper proposes a novel model,TransSSA,and designs two innovative modules to effectively extract fruit image features.The Self-Attention Core Feature Extraction(SAF)module integrates YOLOV8 and Swin Transformer as backbone networks and introduces the Shuffle Attention self-attention mechanism,significantly enhancing the ability to extract core features.This module focuses on constant features such as the stem,body,and base,ensuring accurate fruit recognition in different environments.On the other hand,the Squeeze and Excitation Aggregation(SAE)module combines the network’s ability to capture channel patterns with global knowledge,further optimizing the extraction of effective features.Additionally,to improve detection accuracy,this studymodifies the regression loss function to EIOU.To validate the effectiveness of the TransSSA model,this study conducted extensive visualization analysis to support the interpretability of the SAF and SAE modules.Experimental results demonstrate that TransSSA achieves a performance of 91.3%on a tomato dataset,fully proving its innovative capabilities.Through this research,we provide amore effective solution for using fruit harvesting robots in complex environments.
基金supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00the H2020 European Research Council grant MSCA-RISE-2017-777911+2 种基金AGAUR(Generalitat de Catalunya)grant 2021SGR00113the Reial Acadèmia de Ciències i Arts de Barcelonasupported by FCT/Portugal through CAMGSD,IST-ID,projects UIDB/04459/2020 and UIDP/04459/2020.
文摘The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.
基金Supported by National Natural Science Foundation of China(Grant Nos.52025121,52394263)National Key R&D Plan of China(Grant No.2023YFD2000301)+2 种基金Foundation of State Key Laboratory of Automobile Safety and Energy Saving of China(Grant No.KFZ2201)the Jiangsu Provincial Scientific Research Center of Applied Mathematics under(Grant No.BK20233002)Special Fund of Jiangsu Province for the Transformation of Scientific and Technological Achievements under(Grant No.BA2021023)。
文摘This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in traditional feedback control,to the domain of motion planning for autonomous vehicles.Thus,closed-loop system uncertainty can be preemptively addressed during vehicle motion planning.This involves selecting collision-free trajectories to minimize the volume of robust invariant tubes.Furthermore,constraints on state and control variables are translated into constraints on the RCI tubes of the closed-loop system,ensuring that motion planning produces a safe and optimal trajectory while maintaining flexibility,rather than solely optimizing for the open-loop nominal model.Additionally,to expedite the solving process,we were inspired by L2gain to parameterize the RCI tubes and developed a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets within closedloop systems.Furthermore,we applied the pseudospectral orthogonal collocation method to parameterize the optimization problem of transcribing trajectories using high-order Lagrangian polynomials.Finally,under various operating conditions,we incorporate both the kinematic and dynamic models of the vehicle and also conduct simulations and analyses of uncertainties such as heading angle measurement,chassis response,and steering hysteresis.Our proposed robust motion planning framework has been validated to effectively address nearly all bounded uncertainties while anticipating potential tracking errors in control during the planning phase.This ensures fast,closed-loop safety and robustness in vehicle motion planning.
文摘Lie symmetry analysis is applied to a(3+1)-dimensional combined potential Kadomtsev-Petviashvili equation with B-type Kadomtsev-Petviashvili equation(pKP-BKP equation)and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions and constants for the(3+1)-dimensional pKP-BKP equation,including the lump solution,the periodic-lump solution,the two-kink solution,the breather solution and the lump-two-kink solution,have been studied analytically and graphically.
基金funded by the Key Laboratory of Smart Earth(No.KF2023YB01-12)the National Natural Science Foundation of China(No.42074017)+1 种基金the Key Laboratory Fund Project for Simulation of Complex Electronic Systems(614201004022210)the Chinese Academy of Sciences Youth Innovation Promotion Association(2022126)。
文摘Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradient invariants in existing research is seldom a concern.The gravity gradient tensor has three invariants,named as I_(1),I_(2)and I_(3).I_(1) is a Laplace operator outside the Earth and a Poison operator inside the Earth.The focus of this study is to discuss the performance of the other two invariants of gravity gradients in matching navigation based on the Iterative Closest Contour Point(ICCP)algorithm and compare the matching results with that of the gravity gradient Tzz.The results show that they have almost the same performance when there is no noise,and the background data noises have a large impact on the matching results.There are differences in the anti-interference ability of observation noises for the different components.Under the same random noises in the observations,I2performs a little better than the other two components in terms of position error standard deviation.According to the investigations,since attitude errors can not be avoided and influence the positioning based on Tzz,we recommend adopting invariants of gravity gradients,especially I2,for matching navigation in actual cases.
基金National High-tech Research and Development Program (2007AA01Z314)National Natural Science Foundation of China (60873085)
文摘In order to obtain a large number of correct matches with high accuracy,this article proposes a robust wide baseline point matching method,which is based on Scott s proximity matrix and uses the scale invariant feature transform (SIFT). First,the distance between SIFT features is included in the equations of the proximity matrix to measure the similarity between two feature points; then the normalized cross correlation (NCC) used in Scott s method,which has been modified with adaptive scale and orientation,...
文摘This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
基金Project supported by the National Natural Science Foundation of China （Grant No 10372053） and the Natural Science Foundation of Henan Province, China （Grant No 0311010900）.
文摘Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10472040 and 10372053）, the Natural Science Foundation of Hunan Province, China （Grant No 03JJY3005）, the Natural Science Foundation of Henan Province, China （Grant No 0311010900）, the 0utstanding Young Talents Training Fund of Liaoning Province, China （Grant No 3040005） and the Foundation of Young Key Member of the teachers in Institutions of Higher Learning of Henan Province of China.
文摘Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
基金Project supported by the Heilongjiang Natural Science Foundation of China （Grant No 9507）.
文摘The exact invariants and the adiabatic invariants of Raitzin＇s canonical equations of motion for a nonlinear nonholonomic mechanical system are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher-order adiabatic invariant of a mechanical system under the action of a small perturbation, the forms of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.
基金The project supported by the Natural Science Foundation of High Education of Jiangsu Province under Grant No. 04KJA130135
文摘The perturbation of symmetries and adiabatic invariants for mechanical systems with unilateral holonomic constraints are studied. The exact invariant in the form of Hojman led by special Lie symmetries for an undisturbed system with unilateral constraints is given. Based on the concept of high-order adiabatic invariant of mechanical systems, the perturbation of Lie symmetries for the system under the action of small disturbance is investigated, and a new adiabatic invariant for the system with unilateral holonomic constraints is obtained, which can be called Hojman adiabatic invariant. In the end of the paper, an example is given to illustrate the application of the results.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10372053 and 10472040, the Natural Science Foundation of Hunan Province under Grant No. 03JJY3005, the Scientific Research Foundation of Eduction Department of Hunan Province under Grant No. 02C033 and the 0utstanding Young Talents Training Fund of Liaoning Province under Grant No. 309005
文摘For a relativistic Birkhoffian system, the Lie symmetrical perturbation and adiabatic invariants of generalized Bojman type are studied under general infinitesimal transformations. On the basis of the invariance of relativistic Birkhotfian equations under general infinitesimal transformations,Lie symmetrical transformations of the system are constructed, which only depend on the Birkhoffian variables. The exact invariants in the form of generalized Hojman conserved quantities led by the Lie symmetries of relativistic Birkhoffian system without perturbations are given. Based on the definition of higher-order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for relativistic Birkhoffian system with the action of small disturbance is investigated, and a new type of adiabatic invariants of the system is obtained. In the end of the paper, an example is given to illustrate the application of the results.
文摘Based on the theory of Lie symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic system in terms of quasi-coordinates are studied. The perturbation to symmetries for the nonholonomic system in terms of quasi-coordinates under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the forms of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘The perturbation to Lie symmetry and adiabatic invariants are studied.Based on the concept of higher-order adiabatic invariants of mechanical systems with action of a small perturbation,the perturbation to Lie symmetryis studied,and Hojman adiabatic invariants of Hamilton system are obtained.An example is given to illustrate theapplication of the results.
文摘Based on the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic dynamical system of relative motion are studied. The perturbation to symmetries for the nonholonomic dynamical system of relative motion under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘By the theory of symmetries and conserved quantities, the exact invariants and adiabatic invariants of nonholonomic variable mass systems are studied. The perturbation problem of symmetries for the nonholonomic variable mass systems under small excitation is discussed. The concept of high order adiabatic invariant is presented, and the form of exact invariants and adiabatic invariants as well as the conditions for their existence are given. Then the corresponding inverse problem is studied.
文摘In this paper the projective semi symmetric connection D is studied, which is projectively equivalent to the Levi_Civita connection . An intrinsic projective invariant is found out and a necessary and sufficient condition is given. Furthermore, another condition is obtained when the convariant derivative of the projective invariant is kept.
文摘This paper presents a new method for finding the natural frequency set of a linear time invariant network. In the paper deriving and proving of a common equation are described. It is for the first time that in the common equation the natural frequencies of an n th order network are correlated with the n port parameters. The equation is simple and dual in form and clear in its physical meaning. The procedure of finding the solution is simplified and standardized, and it will not cause the loss of roots. The common equation would find wide use and be systematized.
文摘The invariant determinants ha Banach algebras are discussed and a necessary and sufficient condition for those integral traced unital Barach algebra(A,τ) admitting a G-invari- ant determinant is obtained,where G is a group of trace preserving automorphisms of A.
文摘The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.
