We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of co...We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.展开更多
In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a K...In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium. From this work, one can see that the IEO method in many eases is simpler and easier on obtaining the energy-level gap formula than the usual way.展开更多
For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （...For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.展开更多
We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through analyzing the standard Jaynes-Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric ge...We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through analyzing the standard Jaynes-Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric generators of this model, which diretly leads to the energy-level gap for Jaynes Cummings Hamiltonian.展开更多
Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75...Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.展开更多
By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can b...By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.展开更多
Based on the invariant eigen-operator method （lEO） [Phys. Left. A 321 （2004） 75] we derive the exact energy gap for some Hamiltonians, which describe some polariton systems. The result shows that in some cases the...Based on the invariant eigen-operator method （lEO） [Phys. Left. A 321 （2004） 75] we derive the exact energy gap for some Hamiltonians, which describe some polariton systems. The result shows that in some cases the IEO method, stemming from the Heisenberg approach, is more direct and convenient for deriving the energy-level gap formula than via the approach of solving the Schrodinger equation.展开更多
By using Gumming （JC） model. energy-level gap of this the pseudo invariant eigen-operator method we The pseudo-invariant eigen-operator is found in JC Hamiltonian is derived. This approach seems analyze the field-in...By using Gumming （JC） model. energy-level gap of this the pseudo invariant eigen-operator method we The pseudo-invariant eigen-operator is found in JC Hamiltonian is derived. This approach seems analyze the field-intensity-dependent Jaynes terms of the supersymmetric generators. The concise.展开更多
A system of a three-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium is proposed, and its pseudo-invariant eigen-operator （PIEO） and energy-l...A system of a three-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium is proposed, and its pseudo-invariant eigen-operator （PIEO） and energy-level gap are presented under one-order approximation.展开更多
Using the ＂pseudo-invariant eigen-operator＂ method we find the energy-gap of the Jaynes-Cummings Hamiltonian model of an atom-cavity system. This model takes the atomic centre-of-mass motion into account. The supers...Using the ＂pseudo-invariant eigen-operator＂ method we find the energy-gap of the Jaynes-Cummings Hamiltonian model of an atom-cavity system. This model takes the atomic centre-of-mass motion into account. The supersymmetric structure is involved in the Hamiltonian of an atom-cavity system. By selecting suitable supersymmettic generators and using supersymmetrie transformation the Hamiltonian is diagonalized and energy eigenvectors are obtained.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
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
We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to...We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to address challenges related to variations in 3D facial sizes during recognition.By applying the Mellin transform to computer-generated holograms and performing correlation between them,which,to the best of our knowledge,is being done for the first time,we have developed a robust recognition framework capable of managing significant scale variations without compromising recognition accuracy.Digital holograms of 3D faces are generated from a face database,and the Mellin transform is employed to enable robust recognition across scale factors ranging from 0.4 to 2.0.Within this range,the method achieves 100%recognition accuracy,as confirmed by both simulation-based and hybrid optical/digital experimental validations.Numerical calculations demonstrate that our method significantly enhances the accuracy and reliability of 3D face recognition,as evidenced by the sharp correlation peaks and higher peak-to-noise ratio(PNR)values than that of using conventional holograms without the Mellin transform.Additionally,the hybrid optical/digital joint transform correlation hardware further validates the method's effectiveness,demonstrating its capability to accurately identify and distinguish 3D faces at various scales.This work provides a promising solution for advanced biometric systems,especially for those which require 3D scale-invariant recognition.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
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
基金supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No.10475657
文摘We show that the recently proposed invariant eigen-operator （IEO） method can be successfully applied to solving energy levels for SSH Hamiltonian describing Peierls phase transition. The electronic energy band of compound lattice is also studied by IEO method.
文摘In this paper, we find the invariant eigen-operators （IEOs） and the energy-level gap of a system with a two-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium. From this work, one can see that the IEO method in many eases is simpler and easier on obtaining the energy-level gap formula than the usual way.
基金supported by the National Natural Science Foundation of China (Grant No.10874174)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20070358009)
文摘For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056
文摘We extend the concept of invariant eigen-operator to pseudo-invariant eigen-operator case through analyzing the standard Jaynes-Cummings model. We find the pseudo-invariant eigen-operator in terms of supersymmetric generators of this model, which diretly leads to the energy-level gap for Jaynes Cummings Hamiltonian.
基金supported by the National Natural Science Foundation of China (Grant No. 10574060)the Natural Science Foundation of Shandong Province of China (Grant No. Y2008A23)the Shandong Province Higher Educational Science and Technology Program (Grant No. J09LA07)
文摘Noticing that the equation with double-Poisson bracket, where On is normal coordinate, Hc is classical Hamiltonian, is the classical correspondence of the invariant eigen-operator equation （2004 Phys. Left. A. 321 75）, we can find normal coordinates in harmonic crystal by virtue of the invaxiant eigen-operator method.
基金National Natural Science Foundation of China under grant No.10775097the President Foundation of the Chinese Academy of Sciences
文摘By virtue of the invariant eigen-operator method we search for the invariant eigen-operators for someHamiltonians describing nonlinear processes in particle physics.In this way the energy-gap of the Hamiltonians can benaturally obtained.The characteristic polynomial theory has been fully employed in our derivation.
基金The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the President Foundation of the Chinese Academy of Sciences.
文摘Based on the invariant eigen-operator method （lEO） [Phys. Left. A 321 （2004） 75] we derive the exact energy gap for some Hamiltonians, which describe some polariton systems. The result shows that in some cases the IEO method, stemming from the Heisenberg approach, is more direct and convenient for deriving the energy-level gap formula than via the approach of solving the Schrodinger equation.
基金Supported by Foundation of President of Chinese Academy of Science
文摘By using Gumming （JC） model. energy-level gap of this the pseudo invariant eigen-operator method we The pseudo-invariant eigen-operator is found in JC Hamiltonian is derived. This approach seems analyze the field-intensity-dependent Jaynes terms of the supersymmetric generators. The concise.
文摘A system of a three-level atom interacting with single mode cavity field through multi-photon transition in the presence of a Kerr-like medium is proposed, and its pseudo-invariant eigen-operator （PIEO） and energy-level gap are presented under one-order approximation.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and the research fund provided by Graduate School of University of Science and Technology of China
文摘Using the ＂pseudo-invariant eigen-operator＂ method we find the energy-gap of the Jaynes-Cummings Hamiltonian model of an atom-cavity system. This model takes the atomic centre-of-mass motion into account. The supersymmetric structure is involved in the Hamiltonian of an atom-cavity system. By selecting suitable supersymmettic generators and using supersymmetrie transformation the Hamiltonian is diagonalized and energy eigenvectors are obtained.
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financial supports from the National Natural Science Foundation of China(Grant No.6227511362405124).
文摘We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to address challenges related to variations in 3D facial sizes during recognition.By applying the Mellin transform to computer-generated holograms and performing correlation between them,which,to the best of our knowledge,is being done for the first time,we have developed a robust recognition framework capable of managing significant scale variations without compromising recognition accuracy.Digital holograms of 3D faces are generated from a face database,and the Mellin transform is employed to enable robust recognition across scale factors ranging from 0.4 to 2.0.Within this range,the method achieves 100%recognition accuracy,as confirmed by both simulation-based and hybrid optical/digital experimental validations.Numerical calculations demonstrate that our method significantly enhances the accuracy and reliability of 3D face recognition,as evidenced by the sharp correlation peaks and higher peak-to-noise ratio(PNR)values than that of using conventional holograms without the Mellin transform.Additionally,the hybrid optical/digital joint transform correlation hardware further validates the method's effectiveness,demonstrating its capability to accurately identify and distinguish 3D faces at various scales.This work provides a promising solution for advanced biometric systems,especially for those which require 3D scale-invariant recognition.
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.
