This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation ...This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.展开更多
Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two...Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.展开更多
This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault dia...This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.展开更多
There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are di...There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.展开更多
In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curv...In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock mater...The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.展开更多
In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped ...In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.展开更多
As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accura...As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.展开更多
Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural informa...Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.展开更多
Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totall...Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.展开更多
With the increase of the number of agents in multi-agent systems and the rapid increase of the complexity of the overall structure of the system,the fault detection and diagnosis work has brought great challenges.Rese...With the increase of the number of agents in multi-agent systems and the rapid increase of the complexity of the overall structure of the system,the fault detection and diagnosis work has brought great challenges.Researchers have carried out considerable research work on fault detection and diagnosis of multi-agent systems,but there is no research on fault state estimation and diagnosis based on the information and state of the whole multi-agent system.Based on the global perspective of information geometry theory,this paper presents two new physical quantities of the information manifold of multi-agent systems,as Lagrangian and energy–momentum tensor,to express the state of the overall information of multi-agent systems,and to characterize the energy state and development trend of faults.In this paper,two new physical parameters are introduced into the research of multi-agent fault detection and diagnosis,and the fault state and trend of multi-agent system are evaluated from the global perspective,which provides more comprehensive theoretical support for designing more scientific and reasonable fault diagnosis and fault recovery strategies.Simulation of the application example confirms the competitive performance of the proposed method.展开更多
The robustness against noise, outliers, and corruption is a crucial issue in image feature extraction. To address this concern, this paper proposes a discriminative low-rank embedding image feature extraction algorith...The robustness against noise, outliers, and corruption is a crucial issue in image feature extraction. To address this concern, this paper proposes a discriminative low-rank embedding image feature extraction algorithm. Firstly, to enhance the discriminative power of the extracted features, a discriminative term is introduced using label information, obtaining global discriminative information and learning an optimal projection matrix for data dimensionality reduction. Secondly, manifold constraints are incorporated, unifying low-rank embedding and manifold constraints into a single framework to capture the geometric structure of local manifolds while considering both local and global information. Finally, test samples are projected into a lower-dimensional space for classification. Experimental results demonstrate that the proposed method achieves classification accuracies of 95.62%, 95.22%, 86.38%, and 86.54% on the ORL, CMUPIE, AR, and COIL20 datasets, respectively, outperforming dimensionality reduction-based image feature extraction algorithms.展开更多
For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-d...For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-dual spinor bundle on M.Now V(D)forms an almost complex structure on dual bundle.Moreover,they showed that this almost complex structure is integrable if and only if M is self-dual.In this paper,we extend the construction of V(D)to 4-dimensional pseudo-Riemannian manifolds of signature(2,2).And we give a new method to prove the curvature condition in the integrability condition of V(D).Using this new method,we study the integrability conditions and structure of V(D)when the signature of g is(2,2).展开更多
In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piece...In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.展开更多
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element ...The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.展开更多
In this paper,we derive a Hamilton-Souplet-Zhang type gradient estimate for exponentially harmonic type heat equation on Riemannian manifolds.As its application,we obtain a Liouville type theorem.
Image clustering has received significant attention due to the growing importance of image recognition.Researchers have explored Riemannian manifold clustering,which is capable of capturing the non-linear shapes found...Image clustering has received significant attention due to the growing importance of image recognition.Researchers have explored Riemannian manifold clustering,which is capable of capturing the non-linear shapes found in real-world datasets.However,the complexity of image data poses substantial challenges for modelling and feature extraction.Traditional methods such as covariance matrices and linear subspace have shown promise in image modelling,and they are still in their early stages and suffer from certain limitations.However,these include the uncertainty of representing data using only one Riemannian manifold,limited feature extraction capacity of single kernel functions,and resulting incomplete data representation and redundancy.To overcome these limitations,the authors propose a novel approach called join multiple Riemannian manifold representation and multi-kernel non-redundancy for image clustering(MRMNR-MKC).It combines covariance matrices with linear subspace to represent data and applies multiple kernel functions to map the non-linear structural data into a reproducing kernel Hilbert space,enabling linear model analysis for image clustering.Additionally,the authors use matrix-induced regularisation to improve the clustering kernel selection process by reducing redundancy and assigning lower weights to identical kernels.Finally,the authors also conducted numerous experiments to evaluate the performance of our approach,confirming its superiority to state-of-the-art methods on three benchmark datasets.展开更多
Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and ...Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.展开更多
Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermit...Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermitian M 6 O to be a minimal submanifold of M 6.展开更多
基金National Natural Science Foundation of China(Grant No.62266045)National Science and Technology Major Project of China(No.2022YFE0138600)。
文摘This paper presents a manifold-optimized Error-State Kalman Filter(ESKF)framework for unmanned aerial vehicle(UAV)pose estimation,integrating Inertial Measurement Unit(IMU)data with GPS or LiDAR to enhance estimation accuracy and robustness.We employ a manifold-based optimization approach,leveraging exponential and logarithmic mappings to transform rotation vectors into rotation matrices.The proposed ESKF framework ensures state variables remain near the origin,effectively mitigating singularity issues and enhancing numerical stability.Additionally,due to the small magnitude of state variables,second-order terms can be neglected,simplifying Jacobian matrix computation and improving computational efficiency.Furthermore,we introduce a novel Kalman filter gain computation strategy that dynamically adapts to low-dimensional and high-dimensional observation equations,enabling efficient processing across different sensor modalities.Specifically,for resource-constrained UAV platforms,this method significantly reduces computational cost,making it highly suitable for real-time UAV applications.
基金supported by Scientific Research Project of Guangdong Provincial Department of Education(2024KQNCX152).
文摘Flow velocity uniformity of the microchannel plate is a major factor affecting the performance of microchannel devices.In order to improve the velocity distribution uniformity of the microchannel plate,we designed two new microchannel structures:V-type and A-type.The effects of various structural parameters of the manifolds on the velocity distribution are reported.The V-type and A-type microchannel plates had a more uniform velocity distribution compared to the Z-type microchannel plate.The final result showed that it is beneficial for the V-type microchannel plate to obtain a more uniform velocity distribution when the manifold structure parameters are X_(in)=-1,X_(out)=0,Y_(in)=10,Y_(out)=6,Hin=4,H_(out)=1,and R=0.5.
文摘This paper introduces a new method based on deep belief networks(DBNs)to integrate intrinsic vibration information and assess the similarity of subspaces established on the Grassmann manifold for intelligent fault diagnosis of a reciprocating compressor(RC).Initially,raw vibration signals undergo empirical mode decomposition to break them down into multiple intrinsic mode functions(IMFs).This operation can reveal inherent vibration patterns of fault and other components hidden in the original signals.Subsequently,features are refined from all the IMFs and concatenated into a high-dimensional representative vector,offering localized and comprehensive insights into RC operation.Through DBN,the fault-sensitive information is further refined from the features to enhance their performance in fault identification.Finally,similarities among subspaces on the Grassmann manifold are computed to match fault types.The efficacy of the method is validated usingfield data.Comparative analysis with traditional approaches for feature dimension reduction,feature extraction,and Euclidean distance-based fault identification underscores the effectiveness and superiority of the proposed method in RC fault diagnosis.
基金fully supported by National Natural Science Foundation of China(61871422)Natural Science Foundation of Sichuan Province(2023NSFSC1422)Central Universities of South west Minzu University(ZYN2022032)。
文摘There are all kinds of unknown and known signals in the actual electromagnetic environment,which hinders the development of practical cognitive radio applications.However,most existing signal recognition models are difficult to discover unknown signals while recognizing known ones.In this paper,a compact manifold mixup feature-based open-set recognition approach(OR-CMMF)is proposed to address the above problem.First,the proposed approach utilizes the center loss to constrain decision boundaries so that it obtains the compact latent signal feature representations and extends the low-confidence feature space.Second,the latent signal feature representations are used to construct synthetic representations as substitutes for unknown categories of signals.Then,these constructed representations can occupy the extended low-confidence space.Finally,the proposed approach applies the distillation loss to adjust the decision boundaries between the known categories signals and the constructed unknown categories substitutes so that it accurately discovers unknown signals.The OR-CMMF approach outperformed other state-of-the-art open-set recognition methods in comprehensive recognition performance and running time,as demonstrated by simulation experiments on two public datasets RML2016.10a and ORACLE.
基金supported by Guangzhou Science and Technology Program(202102021174)Guangdong Basic and Applied Basic Research Foundation(2023A1515012121).The second author was supported by the Natural Science Foundation of Jiangsu Province(BK20230900)+1 种基金the Fundamental Research Funds for the Central Universities(30924010838)Both authors are partially supported by NSF in China(12141104).
文摘In this paper,we study the basic p-harmonic forms on the complete foliated Riemannian manifolds.By using the method in[1],we show that if the basic mean curvature form is bounded and co-closed,and the transversal curvature operator is nonnegative and positive at least one point,then we obtain a vanishing theorem for L^(p)-integrably p-harmonic r-forms.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the National Natural Science Foundation of China(Grant Nos.42172312 and 52211540395)support from the Institut Universitaire de France(IUF).
文摘The modeling of crack growth in three-dimensional(3D)space poses significant challenges in rock mechanics due to the complex numerical computation involved in simulating crack propagation and interaction in rock materials.In this study,we present a novel approach that introduces a 3D numerical manifold method(3D-NMM)with a geometric kernel to enhance computational efficiency.Specifically,the maximum tensile stress criterion is adopted as a crack growth criterion to achieve strong discontinuous crack growth,and a local crack tracking algorithm and an angle correction technique are incorporated to address minor limitations of the algorithm in a 3D model.The implementation of the program is carried out in Python,using object-oriented programming in two independent modules:a calculation module and a crack module.Furthermore,we propose feasible improvements to enhance the performance of the algorithm.Finally,we demonstrate the feasibility and effectiveness of the enhanced algorithm in the 3D-NMM using four numerical examples.This study establishes the potential of the 3DNMM,combined with the local tracking algorithm,for accurately modeling 3D crack propagation in brittle rock materials.
文摘In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.
基金supported by the National Natural Science Foundation of China(Grant No.42277165)the Fundamental Research Funds for the Central Universities,China University of Geosciences(Wuhan)(Grant No.CUGCJ1821)the National Overseas Study Fund(Grant No.202106410040).
文摘As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.
基金the National Natural Science Foundation of China(Grant Nos.41941017 and U1702241).
文摘Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.
文摘Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.
基金supported by the National Natural Science Foundation of China (No. 62020106003)the Natural Science Foundation of Jiangsu Province of China (No. BK20222012)the Natural Science Foundation Integration Project,China (No. U22B6001)
文摘With the increase of the number of agents in multi-agent systems and the rapid increase of the complexity of the overall structure of the system,the fault detection and diagnosis work has brought great challenges.Researchers have carried out considerable research work on fault detection and diagnosis of multi-agent systems,but there is no research on fault state estimation and diagnosis based on the information and state of the whole multi-agent system.Based on the global perspective of information geometry theory,this paper presents two new physical quantities of the information manifold of multi-agent systems,as Lagrangian and energy–momentum tensor,to express the state of the overall information of multi-agent systems,and to characterize the energy state and development trend of faults.In this paper,two new physical parameters are introduced into the research of multi-agent fault detection and diagnosis,and the fault state and trend of multi-agent system are evaluated from the global perspective,which provides more comprehensive theoretical support for designing more scientific and reasonable fault diagnosis and fault recovery strategies.Simulation of the application example confirms the competitive performance of the proposed method.
基金supported by the National Natural Science Foundation of China (No.61961037)the Gansu Provincial Department of Education 2021 Industry Support Program (No.2021CYZC-30)。
文摘The robustness against noise, outliers, and corruption is a crucial issue in image feature extraction. To address this concern, this paper proposes a discriminative low-rank embedding image feature extraction algorithm. Firstly, to enhance the discriminative power of the extracted features, a discriminative term is introduced using label information, obtaining global discriminative information and learning an optimal projection matrix for data dimensionality reduction. Secondly, manifold constraints are incorporated, unifying low-rank embedding and manifold constraints into a single framework to capture the geometric structure of local manifolds while considering both local and global information. Finally, test samples are projected into a lower-dimensional space for classification. Experimental results demonstrate that the proposed method achieves classification accuracies of 95.62%, 95.22%, 86.38%, and 86.54% on the ORL, CMUPIE, AR, and COIL20 datasets, respectively, outperforming dimensionality reduction-based image feature extraction algorithms.
基金Supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(No.YSBR-001)。
文摘For a 4-dimensional Riemannian manifold(M,g),Atiyah et al.in[Proc.Roy.Soc.London Ser.A,1978,362(1711):425-461]used the kernel of twistor operator D to construct a distribution V(D)on the dual bundle of the anti-self-dual spinor bundle on M.Now V(D)forms an almost complex structure on dual bundle.Moreover,they showed that this almost complex structure is integrable if and only if M is self-dual.In this paper,we extend the construction of V(D)to 4-dimensional pseudo-Riemannian manifolds of signature(2,2).And we give a new method to prove the curvature condition in the integrability condition of V(D).Using this new method,we study the integrability conditions and structure of V(D)when the signature of g is(2,2).
基金supported in part by the NSFC(11801496,11926352)the Fok Ying-Tung Education Foundation(China)the Hubei Key Laboratory of Applied Mathematics(Hubei University).
文摘In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.
基金Project supported by the National Natural Science Foundation of China (Nos. 12102043, 12072375U2241240)the Natural Science Foundation of Hunan Province of China (Nos. 2023JJ40698 and 2021JJ40710)。
文摘The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.
基金Supported by the National Natural Science Foundation of China(Grant No.11661043)the Foundation of Education Department of Jiangxi Province(Grant No.GJJ2200320)。
文摘In this paper,we derive a Hamilton-Souplet-Zhang type gradient estimate for exponentially harmonic type heat equation on Riemannian manifolds.As its application,we obtain a Liouville type theorem.
基金National Natural Science Foundation of China(62273290,62072391,and 61572419).
文摘Image clustering has received significant attention due to the growing importance of image recognition.Researchers have explored Riemannian manifold clustering,which is capable of capturing the non-linear shapes found in real-world datasets.However,the complexity of image data poses substantial challenges for modelling and feature extraction.Traditional methods such as covariance matrices and linear subspace have shown promise in image modelling,and they are still in their early stages and suffer from certain limitations.However,these include the uncertainty of representing data using only one Riemannian manifold,limited feature extraction capacity of single kernel functions,and resulting incomplete data representation and redundancy.To overcome these limitations,the authors propose a novel approach called join multiple Riemannian manifold representation and multi-kernel non-redundancy for image clustering(MRMNR-MKC).It combines covariance matrices with linear subspace to represent data and applies multiple kernel functions to map the non-linear structural data into a reproducing kernel Hilbert space,enabling linear model analysis for image clustering.Additionally,the authors use matrix-induced regularisation to improve the clustering kernel selection process by reducing redundancy and assigning lower weights to identical kernels.Finally,the authors also conducted numerous experiments to evaluate the performance of our approach,confirming its superiority to state-of-the-art methods on three benchmark datasets.
文摘Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.
文摘Proves that cosymplectic hypersurfaces of six dimensional Hermitian submanifolds of the octave algebra are ruled manifolds and establishes a necessary and sufficient condition for a cosymplectic hypersurface of Hermitian M 6 O to be a minimal submanifold of M 6.
