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
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
Time scale is a new and powerful tool for dealing with complex dynamics problems. The main result of this study is the exact invariants and adiabatic invariants of the generalized Birkhoffian system and the constraine...Time scale is a new and powerful tool for dealing with complex dynamics problems. The main result of this study is the exact invariants and adiabatic invariants of the generalized Birkhoffian system and the constrained Birkhoffian system on time scales. Firstly, we establish the differential equations of motion for the above two systems and give the corresponding Noether symmetries and exact invariants. Then, the perturbation to the Noether symmetries and the adiabatic invariants for the systems mentioned above under the action of slight disturbance are investigated, respectively. Finally, two examples are provided to show the practicality of the findings.展开更多
The presentation and modeling of turbulence anisotropy are crucial for studying large-scale turbulence structures and constructing turbulence models.However,accurately capturing anisotropic Reynolds stresses often rel...The presentation and modeling of turbulence anisotropy are crucial for studying large-scale turbulence structures and constructing turbulence models.However,accurately capturing anisotropic Reynolds stresses often relies on expensive direct numerical simulations(DNS).Recently,a hot topic in data-driven turbulence modeling is how to acquire accurate Reynolds stresses by the Reynolds-averaged Navier-Stokes(RANS)simulation and a limited amount of data from DNS.Many existing studies use mean flow characteristics as the input features of machine learning models to predict high-fidelity Reynolds stresses,but these approaches still lack robust generalization capabilities.In this paper,a deep neural network(DNN)is employed to build a model,mapping from tensor invariants of RANS mean flow features to the anisotropy invariants of high-fidelity Reynolds stresses.From the aspects of tensor analysis and input-output feature design,we try to enhance the generalization of the model while preserving invariance.A functional framework of Reynolds stress anisotropy invariants is derived theoretically.Complete irreducible invariants are then constructed from a tensor group,serving as alternative input features for DNN.Additionally,we propose a feature selection method based on the Fourier transform of periodic flows.The results demonstrate that the data-driven model achieves a high level of accuracy in predicting turbulence anisotropy of flows over periodic hills and converging-diverging channels.Moreover,the well-trained model exhibits strong generalization capabilities concerning various shapes and higher Reynolds numbers.This approach can also provide valuable insights for feature selection and data generation for data-driven turbulence models.展开更多
A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have...A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.展开更多
We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the...We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.展开更多
Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generator...Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.展开更多
Synthetic aperture radar(SAR)is a high-resolution two-dimensional imaging radar.However,during the imaging process,SAR is susceptible to intentional and unintentional interference,with radio frequency inter⁃ference(RF...Synthetic aperture radar(SAR)is a high-resolution two-dimensional imaging radar.However,during the imaging process,SAR is susceptible to intentional and unintentional interference,with radio frequency inter⁃ference(RFI)being the most common type,leading to a severe degradation in image quality.To address the above problem,numerous algorithms have been proposed.Although inpainting networks have achieved excellent results,their generalization is unclear.Whether they still work effectively in cross-sensor experiments needs fur⁃ther verification.Through the time-frequency analysis to interference signals,this work finds that interference holds domain invariant features between different sensors.Therefore,this work reconstructs the loss function and extracts the domain invariant features to improve its generalization.Ultimately,this work proposes a SAR RFI suppression method based on domain invariant features,and embeds the RFI suppression into SAR imaging pro⁃cess.Compared to traditional notch filtering methods,the proposed approach not only removes interference but also effectively preserves strong scattering targets.Compared to PISNet,our method can extract domain invariant features and hold better generalization ability,and even in the cross-sensor experiments,our method can still achieve excellent results.In cross-sensor experiments,training data and testing data come from different radar platforms with different parameters,so cross-sensor experiments can provide evidence for the generalization.展开更多
This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtaine...This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.展开更多
Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale late...Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale lateral resolution).However,the conventional excitation source of rapidly diverging Gaussian beam imposes limitations on the depth of focus(DOF)in OR-PAM,which in turn affects the depth-resolving ability and detection sensitivity.Here,we proposed a flexible DOF,depth-invariant resolution photoacoustic microscopy(FDIR-PAM)with nondiffraction of Airy beams.The spatial light modulator was incorporated into the optical pathway of the excitation source with matched switching phase patterns,achieving the flexibly adjustable modulation parameters of the Airy beam.We conducted experiments on phantoms and intravital tissue to validate the effectiveness of the proposed approach for high sensitivity and highresolution characterization of variable topology of tissue,offering a promising DOF of 926μm with an invariant lateral resolution of 3.2μm,which is more than 17-fold larger compared to the Gaussian beam.In addition,FDIR-PAM successfully revealed clear individual zebrafish larvae and the pigment pattern of adult zebrafishes,as well as fine morphology of cerebral vasculature in a large depth range with high resolution,which has reached an evident resolving capability improvement of 62%mean value compared with the Gaussian beam.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
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
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.
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 by the National Natural Science Foundation of China (12172241, 12272248, 11972241, 12002228)Qing Lan Project of Colleges and Universities in Jiangsu Province。
文摘Time scale is a new and powerful tool for dealing with complex dynamics problems. The main result of this study is the exact invariants and adiabatic invariants of the generalized Birkhoffian system and the constrained Birkhoffian system on time scales. Firstly, we establish the differential equations of motion for the above two systems and give the corresponding Noether symmetries and exact invariants. Then, the perturbation to the Noether symmetries and the adiabatic invariants for the systems mentioned above under the action of slight disturbance are investigated, respectively. Finally, two examples are provided to show the practicality of the findings.
基金supported by the National Natural Science Foundation of China(Grant No.92152301).
文摘The presentation and modeling of turbulence anisotropy are crucial for studying large-scale turbulence structures and constructing turbulence models.However,accurately capturing anisotropic Reynolds stresses often relies on expensive direct numerical simulations(DNS).Recently,a hot topic in data-driven turbulence modeling is how to acquire accurate Reynolds stresses by the Reynolds-averaged Navier-Stokes(RANS)simulation and a limited amount of data from DNS.Many existing studies use mean flow characteristics as the input features of machine learning models to predict high-fidelity Reynolds stresses,but these approaches still lack robust generalization capabilities.In this paper,a deep neural network(DNN)is employed to build a model,mapping from tensor invariants of RANS mean flow features to the anisotropy invariants of high-fidelity Reynolds stresses.From the aspects of tensor analysis and input-output feature design,we try to enhance the generalization of the model while preserving invariance.A functional framework of Reynolds stress anisotropy invariants is derived theoretically.Complete irreducible invariants are then constructed from a tensor group,serving as alternative input features for DNN.Additionally,we propose a feature selection method based on the Fourier transform of periodic flows.The results demonstrate that the data-driven model achieves a high level of accuracy in predicting turbulence anisotropy of flows over periodic hills and converging-diverging channels.Moreover,the well-trained model exhibits strong generalization capabilities concerning various shapes and higher Reynolds numbers.This approach can also provide valuable insights for feature selection and data generation for data-driven turbulence models.
文摘A special class of cubic polynomials possessing decay of geometry property is studied.This class of cubic bimodal maps has generalized Fibonacci combinatorics.For maps with bounded combinatorics,we show that they have an absolutely continuous invariant probability measure.
基金supported by the Natural Science Foundation of Beijing(Grant No.Z180007)the National Natural Science Foundation of China(Grant Nos.1157200511874003,and 51672018)。
文摘We propose a method to construct Hopf insulators based on the study of topological defects from the geometric perspective of Hopf invariant I.Firstly,we prove two types of topological defects naturally inhering in the inner differential structure of the Hopf mapping.One type is the four-dimensional point defects.
文摘Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.
基金Supported by the National Natural Science Foundation of China(62001489)。
文摘Synthetic aperture radar(SAR)is a high-resolution two-dimensional imaging radar.However,during the imaging process,SAR is susceptible to intentional and unintentional interference,with radio frequency inter⁃ference(RFI)being the most common type,leading to a severe degradation in image quality.To address the above problem,numerous algorithms have been proposed.Although inpainting networks have achieved excellent results,their generalization is unclear.Whether they still work effectively in cross-sensor experiments needs fur⁃ther verification.Through the time-frequency analysis to interference signals,this work finds that interference holds domain invariant features between different sensors.Therefore,this work reconstructs the loss function and extracts the domain invariant features to improve its generalization.Ultimately,this work proposes a SAR RFI suppression method based on domain invariant features,and embeds the RFI suppression into SAR imaging pro⁃cess.Compared to traditional notch filtering methods,the proposed approach not only removes interference but also effectively preserves strong scattering targets.Compared to PISNet,our method can extract domain invariant features and hold better generalization ability,and even in the cross-sensor experiments,our method can still achieve excellent results.In cross-sensor experiments,training data and testing data come from different radar platforms with different parameters,so cross-sensor experiments can provide evidence for the generalization.
文摘This paper studied the invariance of the Cauchy mean with respect to the arithmetic mean when the denominator functions satisfy certain conditions. The partial derivatives of Cauchy’s mean on the diagonal are obtained by using the method of Wronskian determinant in the process of solving. Then the invariant equation is solved by using the obtained partial derivatives. Finally, the solutions of invariant equations when the denominator functions satisfy the same simple harmonic oscillator equation or the denominator functions are power functions that have been obtained.
基金supported by the National Natural Science Foundation of China(Grant Nos.62105255 and 62275210)the Xidian University Specially Funded Project for Interdisciplinary Exploration(Grant No.TZJH2024043)+1 种基金the Key Research and Development Program of Shaanxi Province(Grant No.2023-YBSF-293)the National Young Talent Program and Shaanxi Young Top-notch Talent Program,and the Fundamental Research Funds for CentralUniversities(Grant No.ZYTS23187).
文摘Optical-resolution photoacoustic microscopy(OR-PAM)has rapidly developed and is capable of characterizing optical absorption properties of biological tissue with high contrast and high resolution(micrometer-scale lateral resolution).However,the conventional excitation source of rapidly diverging Gaussian beam imposes limitations on the depth of focus(DOF)in OR-PAM,which in turn affects the depth-resolving ability and detection sensitivity.Here,we proposed a flexible DOF,depth-invariant resolution photoacoustic microscopy(FDIR-PAM)with nondiffraction of Airy beams.The spatial light modulator was incorporated into the optical pathway of the excitation source with matched switching phase patterns,achieving the flexibly adjustable modulation parameters of the Airy beam.We conducted experiments on phantoms and intravital tissue to validate the effectiveness of the proposed approach for high sensitivity and highresolution characterization of variable topology of tissue,offering a promising DOF of 926μm with an invariant lateral resolution of 3.2μm,which is more than 17-fold larger compared to the Gaussian beam.In addition,FDIR-PAM successfully revealed clear individual zebrafish larvae and the pigment pattern of adult zebrafishes,as well as fine morphology of cerebral vasculature in a large depth range with high resolution,which has reached an evident resolving capability improvement of 62%mean value compared with the Gaussian beam.
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,...
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.
