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
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
Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifth...Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.展开更多
The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invari...The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.展开更多
In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl（n,R）. The conditions of G = Gl（n, R） -equivalence of a pair of curves are found in terms of G = Gl（n, R）-invariants...In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl（n,R）. The conditions of G = Gl（n, R） -equivalence of a pair of curves are found in terms of G = Gl（n, R）-invariants. And the independence of GL（n, R） -invariants is shown.展开更多
A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and ca...A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.展开更多
The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for t...The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results.展开更多
Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan...Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan's type is constructed for Birkhoffian systems. Finally, one_dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré's type is found.展开更多
In order to discover characteristics of various kinds of weld pool image and identify a single image, seven image features are extracted to describe the corresponding surface formation quality by the moment iavariants...In order to discover characteristics of various kinds of weld pool image and identify a single image, seven image features are extracted to describe the corresponding surface formation quality by the moment iavariants method. An image feature matrix is composed by the seven characteristics. Then the matrix is projected on a line through the Fisher criterion in order to entirely distinguish various kinds of image features. And finally, transforming a seven-dimensional problem into a one-dimensional problem has been done. Compared with the three kinds of samples included in the arc welding process and quality weld pool visual image database, the images are classified into the three kinds such as superior weld formation in the condition of optimal gas flow, poor weld formation image in the condition of insuffwient gas flow, inferior weld formation in the condition of too low gas flow. Experiments show that the Fisher classification method based on moment invariants can recognize various weld pool images effectively, and it achieves a correct recognizable rate of 100%.展开更多
The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagr...The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.展开更多
Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge sta...Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge states,but fail to describe the number and distribution of defective edge states in non-Hermitian topological systems.The state-dependent topological invariants,instead of a global topological invariant,are developed to accurately characterize the bulk-boundary correspondence of the NH systems,which is very different from their Hermitian counterparts.At the same time,we obtain the accurate phase diagram of the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with a generalized inversion symmetry from the state-dependent topological invariants.Therefore,these results will be helpful for understanding the exotic topological properties of various non-Hermitian systems.展开更多
Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.How...Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.However,no reliable examination has been embraced to decide,how much these invariants are related with a network graph or molecular graph.In this paper,it will discuss three different variants of bridge networks with good potential of prediction in the field of computer science,mathematics,chemistry,pharmacy,informatics and biology in context with physical and chemical structures and networks,because k-banhatti sombor invariants are freshly presented and have numerous prediction qualities for different variants of bridge graphs or networks.The study solved the topology of a bridge graph/networks of three different types with two invariants KBanhatti Sombor Indices and its reduced form.These deduced results can be used for the modeling of computer networks like Local area network(LAN),Metropolitan area network(MAN),and Wide area network(WAN),backbone of internet and other networks/structures of computers,power generation,bio-informatics and chemical compounds synthesis.展开更多
Quality inspection of a PCB （Printed Circuit Board） always requires us to stitch some separated images into an integral one. However, during image acquisition, some environmental influences such as vibration, noise ...Quality inspection of a PCB （Printed Circuit Board） always requires us to stitch some separated images into an integral one. However, during image acquisition, some environmental influences such as vibration, noise and illumination will cause image degradation. An efficient image mosaic method has been urgently required to obtain a high-quality PCB panorama. Hence, an image mosaic method based on Gaussian-Hermite moments is presented in this paper. The characteristic points in the neighborhood of a PCB are represented by Gaussian-Hermite moment in- variants. They are characterized by independence to translation or rotation transformations. Meanwhile, such feature representation shows better noise robustness. Experimental results show that the proposed method produces a qualified mosaic of PCB image.展开更多
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases ...It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calculated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric tensor and a vector. By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1] and in the second case there are only nine independent scale invariants which are less than that obtained in Ref.[1].展开更多
A new human action recognition approach was presented based on chaotic invariants and relevance vector machines(RVM).The trajectories of reference joints estimated by skeleton graph matching were adopted for represent...A new human action recognition approach was presented based on chaotic invariants and relevance vector machines(RVM).The trajectories of reference joints estimated by skeleton graph matching were adopted for representing the nonlinear dynamical system of human action.The C-C method was used for estimating delay time and embedding dimension of a phase space which was reconstructed by each trajectory.Then,some chaotic invariants representing action can be captured in the reconstructed phase space.Finally,RVM was used to recognize action.Experiments were performed on the KTH,Weizmann and Ballet human action datasets to test and evaluate the proposed method.The experiment results show that the average recognition accuracy is over91.2%,which validates its effectiveness.展开更多
Axis orbit is an important characteristic to be used in the condition monitoring and diagnosis system of rotating machine.The wavelet moment has the invariant to the translation,scaling and rotation.A method,which use...Axis orbit is an important characteristic to be used in the condition monitoring and diagnosis system of rotating machine.The wavelet moment has the invariant to the translation,scaling and rotation.A method,which uses a neural network based on Radial Basis Function(RBF)and wavelet moment invariants to identify the orbit of shaft centerline of rotating machine is discussed in this paper.The principle and its application procedure of the method are introduced in detail.It gives simulation results of automatic identification for three typical axis orbits.It is proved that the method is effective and practicable.展开更多
Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First,Noether theorem of a system is presented.Secondly,the criterion of perturbation to Noether symmetry...Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First,Noether theorem of a system is presented.Secondly,the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants,Noether adiabatic invariants of the system are obtained.Finally,An example is given to support these results.展开更多
Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engine...Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.展开更多
This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial sh...This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.展开更多
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.
基金funded by the Deanship of Scientific Research(DSR),King Abdul-Aziz University,Jeddah,Saudi Arabia under Grant No.(RG−11–611–43).
文摘Due to a tremendous increase in mobile traffic,mobile operators have started to restructure their networks to offload their traffic.Newresearch directions will lead to fundamental changes in the design of future Fifthgeneration(5G)cellular networks.For the formal reason,the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory.Any number that can be uniquely calculated by a graph is known as a graph invariant.During the last two decades,innumerable numerical graph invariants have been portrayed and used for correlation analysis.In any case,no efficient assessment has been embraced to choose,how much these invariants are connected with a network graph.This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks.Since K-banhatti sombor invariants(KBSO)and Contrharmonic-quadratic invariants(CQIs)are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks.As the hexagonal networks are used in mobile base stations in layered,forms called honeycomb.The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms.The deduced outcomes can be utilized for the modeling of mobile cellular networks,multiprocessors interconnections,microchips,chemical compound synthesis and memory interconnection networks.The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network(MBSN)for the high load of traffic and minimal traffic also.
基金Supported by National Natural Science Foundation of China(10801045)Supported by the Foundation of Henan Educational Committee(2007110002)Supported by the Foundation of Henan Technology Commit tee(082300410020)
文摘The theory of moving frames developed by Peter J Olver and M Fels has impor-tant applications to geometry, classical invariant theory. We will use this theory to classify joint invariants and joint differential invariants of some transformation groups.
文摘In this paper, the generator set of R 〈 x1,x2 〉G is obtained in according to the group G = Gl（n,R）. The conditions of G = Gl（n, R） -equivalence of a pair of curves are found in terms of G = Gl（n, R）-invariants. And the independence of GL（n, R） -invariants is shown.
文摘A new feature based on higher order statistics is proposed for classification of MPSKsignals, which is invariant with respect to translation (shift), scale and rotation transforms of MPSK signal constellations, and can suppress additive color or white Gaussian noise. Application of the new feature to classification of MPSK signals, at medium signal-to-noise ratio with specified sample size, results in high probability of correct identification. Finally, computer simulations and comparisons with existing algorithms are given.
基金The project supported by the National Natural Science Foundation(19972010)the Doctoral Program Foundation of Institution of Higher Education of Chinathe Natural Science Foundation of Henan Province
文摘The perturbation of symmetries of the free Birkhoff system under small excitation is discussed. The concept of high-order adiabatic invariant is presented, and the form of adiabatic invariants and the conditions for their existence are given. Then these results are generalized to the constrained Birkhoff system. One example is presented to illustrate these results.
基金国家自然科学基金，国家自然科学基金，国家自然科学基金，Science Research Foundation of Liaoning Educational Committee of China
文摘Based on modern differential geometry, the symplectic structure of a Birkhoffian system which is an extension of conservative and nonconservative systems is analyzed. An integral invariant of Poincaré_Cartan's type is constructed for Birkhoffian systems. Finally, one_dimensional damped vibration is taken as an illustrative example and an integral invariant of Poincaré's type is found.
基金Fund projects： National Natural Science Foundation of China（ No 51075214）funding.
文摘In order to discover characteristics of various kinds of weld pool image and identify a single image, seven image features are extracted to describe the corresponding surface formation quality by the moment iavariants method. An image feature matrix is composed by the seven characteristics. Then the matrix is projected on a line through the Fisher criterion in order to entirely distinguish various kinds of image features. And finally, transforming a seven-dimensional problem into a one-dimensional problem has been done. Compared with the three kinds of samples included in the arc welding process and quality weld pool visual image database, the images are classified into the three kinds such as superior weld formation in the condition of optimal gas flow, poor weld formation image in the condition of insuffwient gas flow, inferior weld formation in the condition of too low gas flow. Experiments show that the Fisher classification method based on moment invariants can recognize various weld pool images effectively, and it achieves a correct recognizable rate of 100%.
基金National Natural Science Foundations of China(Nos.11572212,11272227)Innovation Program for Postgraduate of Suzhou University of Science and Technology,China(No.SKCX15_062)
文摘The perturbation to Noether symmetry and adiabatic invariants for dynamical systems with nonstandard Lagrangians are studied.Based on two kinds of nonstandard Lagrangians(i.e.exponential Lagrangians and power-law Lagrangians),the exact invariants of Noether type are given.Based on the definition of highorder adiabatic invariants,the relationship between the perturbation of Noether symmetry and the adiabatic invariants of the system under a small disturbance is studied,and then the corresponding theorems of adiabatic invariants are established.Finally,two examples are given to illustrate the methods and results appear in this paper.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11674026 and 11974053)。
文摘Breakdown of bulk-boundary correspondence in non-Hermitian(NH)topological systems with generalized inversion symmetries is a controversial issue.The non-Bloch topological invariants determine the existence of edge states,but fail to describe the number and distribution of defective edge states in non-Hermitian topological systems.The state-dependent topological invariants,instead of a global topological invariant,are developed to accurately characterize the bulk-boundary correspondence of the NH systems,which is very different from their Hermitian counterparts.At the same time,we obtain the accurate phase diagram of the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with a generalized inversion symmetry from the state-dependent topological invariants.Therefore,these results will be helpful for understanding the exotic topological properties of various non-Hermitian systems.
基金This project was funded by the Deanship of Scientific Research(DSR),King Abdul-Aziz University,Jeddah,Saudi Arabia under Grant No.(RG-11-611-43).
文摘Any number that can be uniquely determined by a graph is called a graph invariant.During the last twenty years’countless mathematical graph invariants have been characterized and utilized for correlation analysis.However,no reliable examination has been embraced to decide,how much these invariants are related with a network graph or molecular graph.In this paper,it will discuss three different variants of bridge networks with good potential of prediction in the field of computer science,mathematics,chemistry,pharmacy,informatics and biology in context with physical and chemical structures and networks,because k-banhatti sombor invariants are freshly presented and have numerous prediction qualities for different variants of bridge graphs or networks.The study solved the topology of a bridge graph/networks of three different types with two invariants KBanhatti Sombor Indices and its reduced form.These deduced results can be used for the modeling of computer networks like Local area network(LAN),Metropolitan area network(MAN),and Wide area network(WAN),backbone of internet and other networks/structures of computers,power generation,bio-informatics and chemical compounds synthesis.
基金Supported by the National Natural Science Foundation of China(61502389)the Foundation Research Funds for Central University(3102015ZY047)
文摘Quality inspection of a PCB （Printed Circuit Board） always requires us to stitch some separated images into an integral one. However, during image acquisition, some environmental influences such as vibration, noise and illumination will cause image degradation. An efficient image mosaic method has been urgently required to obtain a high-quality PCB panorama. Hence, an image mosaic method based on Gaussian-Hermite moments is presented in this paper. The characteristic points in the neighborhood of a PCB are represented by Gaussian-Hermite moment in- variants. They are characterized by independence to translation or rotation transformations. Meanwhile, such feature representation shows better noise robustness. Experimental results show that the proposed method produces a qualified mosaic of PCB image.
文摘It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calculated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric tensor and a vector. By using the eigentensor notation it is proved that in the first case there are only six independent scale invariants rather than seven as reported in Ref.[1] and in the second case there are only nine independent scale invariants which are less than that obtained in Ref.[1].
基金Project(50808025) supported by the National Natural Science Foundation of ChinaProject(20090162110057) supported by the Doctoral Fund of Ministry of Education,China
文摘A new human action recognition approach was presented based on chaotic invariants and relevance vector machines(RVM).The trajectories of reference joints estimated by skeleton graph matching were adopted for representing the nonlinear dynamical system of human action.The C-C method was used for estimating delay time and embedding dimension of a phase space which was reconstructed by each trajectory.Then,some chaotic invariants representing action can be captured in the reconstructed phase space.Finally,RVM was used to recognize action.Experiments were performed on the KTH,Weizmann and Ballet human action datasets to test and evaluate the proposed method.The experiment results show that the average recognition accuracy is over91.2%,which validates its effectiveness.
基金Supported by the Programming of the National Ministry of Education(20002175)
文摘Axis orbit is an important characteristic to be used in the condition monitoring and diagnosis system of rotating machine.The wavelet moment has the invariant to the translation,scaling and rotation.A method,which uses a neural network based on Radial Basis Function(RBF)and wavelet moment invariants to identify the orbit of shaft centerline of rotating machine is discussed in this paper.The principle and its application procedure of the method are introduced in detail.It gives simulation results of automatic identification for three typical axis orbits.It is proved that the method is effective and practicable.
基金Supported by the Research Plan of Higher Education Institutions of Xinjiang Autonomous Region(No XJEDU2010S31)the Foundation for Prior Development Subject of Theory Physics of Xinjiang Normal University.
文摘Perturbation to Noether symmetry of discrete mechanico-electrical systems on an uniform lattice is investigated.First,Noether theorem of a system is presented.Secondly,the criterion of perturbation to Noether symmetry of the system is given.Based on the definition of adiabatic invariants,Noether adiabatic invariants of the system are obtained.Finally,An example is given to support these results.
文摘Recently, orthogonal moments have become efficient tools for two-dimensional and three-dimensional（2D and 3D） image not only in pattern recognition, image vision, but also in image processing and applications engineering. Yet, there is still a major difficulty in 3D rotation invariants. In this paper, we propose new sets of invariants for 2D and 3D rotation, scaling and translation based on orthogonal radial Hahn moments. We also present theoretical mathematics to derive them. Thus, this paper introduces in the first case new 2D radial Hahn moments based on polar representation of an object by one-dimensional orthogonal discrete Hahn polynomials, and a circular function. In the second case, we present new 3D radial Hahn moments using a spherical representation of volumetric image by one-dimensional orthogonal discrete Hahn polynomials and a spherical function. Further 2D and 3D invariants are derived from the proposed 2D and 3D radial Hahn moments respectively, which appear as the third case. In order to test the proposed approach, we have resolved three issues： the image reconstruction, the invariance of rotation, scaling and translation, and the pattern recognition. The result of experiments show that the Hahn moments have done better than the Krawtchouk moments, with and without noise. Simultaneously, the mentioned reconstruction converges quickly to the original image using 2D and 3D radial Hahn moments, and the test images are clearly recognized from a set of images that are available in COIL-20 database for 2D image, and Princeton shape benchmark（PSB） database for 3D image.
文摘This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments： a 3D substituted radial shifted Legendre moments （3DSRSLMs） and a 3D weighted radial one （3DWRSLMs）. Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments （3DSRSLMs/3DWRSLMs） are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues： rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark （PSB） database for 3D image.
