To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical c...To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.展开更多
This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.展开更多
In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challe...In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challenges:firstly,the dynamic nature of the automatic picking process requires fruit target detection algorithms to adapt to multi-view characteristics,ensuring effective recognition of the same fruit from different perspectives.Secondly,fruits in natural environments often suffer from interference factors such as overlapping,occlusion,and illumination fluctuations,which increase the difficulty of image capture and recognition.To address these challenges,this study conducted an in-depth analysis of the key features in fruit recognition and discovered that the stem,body,and base serve as constant and core information in fruit identification,exhibiting long-term dependent semantic relationships during the recognition process.These invariant features provide a stable foundation for dynamic fruit recognition,contributing to improved recognition accuracy and robustness.Specifically,the morphology and position of the stem,body,and base are relatively fixed,and the effective extraction of these features plays a crucial role in fruit recognition.This paper proposes a novel model,TransSSA,and designs two innovative modules to effectively extract fruit image features.The Self-Attention Core Feature Extraction(SAF)module integrates YOLOV8 and Swin Transformer as backbone networks and introduces the Shuffle Attention self-attention mechanism,significantly enhancing the ability to extract core features.This module focuses on constant features such as the stem,body,and base,ensuring accurate fruit recognition in different environments.On the other hand,the Squeeze and Excitation Aggregation(SAE)module combines the network’s ability to capture channel patterns with global knowledge,further optimizing the extraction of effective features.Additionally,to improve detection accuracy,this studymodifies the regression loss function to EIOU.To validate the effectiveness of the TransSSA model,this study conducted extensive visualization analysis to support the interpretability of the SAF and SAE modules.Experimental results demonstrate that TransSSA achieves a performance of 91.3%on a tomato dataset,fully proving its innovative capabilities.Through this research,we provide amore effective solution for using fruit harvesting robots in complex environments.展开更多
We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to...We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to address challenges related to variations in 3D facial sizes during recognition.By applying the Mellin transform to computer-generated holograms and performing correlation between them,which,to the best of our knowledge,is being done for the first time,we have developed a robust recognition framework capable of managing significant scale variations without compromising recognition accuracy.Digital holograms of 3D faces are generated from a face database,and the Mellin transform is employed to enable robust recognition across scale factors ranging from 0.4 to 2.0.Within this range,the method achieves 100%recognition accuracy,as confirmed by both simulation-based and hybrid optical/digital experimental validations.Numerical calculations demonstrate that our method significantly enhances the accuracy and reliability of 3D face recognition,as evidenced by the sharp correlation peaks and higher peak-to-noise ratio(PNR)values than that of using conventional holograms without the Mellin transform.Additionally,the hybrid optical/digital joint transform correlation hardware further validates the method's effectiveness,demonstrating its capability to accurately identify and distinguish 3D faces at various scales.This work provides a promising solution for advanced biometric systems,especially for those which require 3D scale-invariant recognition.展开更多
The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux...The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.展开更多
This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in tradition...This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in traditional feedback control,to the domain of motion planning for autonomous vehicles.Thus,closed-loop system uncertainty can be preemptively addressed during vehicle motion planning.This involves selecting collision-free trajectories to minimize the volume of robust invariant tubes.Furthermore,constraints on state and control variables are translated into constraints on the RCI tubes of the closed-loop system,ensuring that motion planning produces a safe and optimal trajectory while maintaining flexibility,rather than solely optimizing for the open-loop nominal model.Additionally,to expedite the solving process,we were inspired by L2gain to parameterize the RCI tubes and developed a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets within closedloop systems.Furthermore,we applied the pseudospectral orthogonal collocation method to parameterize the optimization problem of transcribing trajectories using high-order Lagrangian polynomials.Finally,under various operating conditions,we incorporate both the kinematic and dynamic models of the vehicle and also conduct simulations and analyses of uncertainties such as heading angle measurement,chassis response,and steering hysteresis.Our proposed robust motion planning framework has been validated to effectively address nearly all bounded uncertainties while anticipating potential tracking errors in control during the planning phase.This ensures fast,closed-loop safety and robustness in vehicle motion planning.展开更多
In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distribu...In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.展开更多
The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattic...The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.展开更多
Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face...Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.展开更多
We constructed a new set of diabatic poten-tial energy surfaces(PESs)for the two low-est states involved in Li+Li_(2)reaction by us-ing the fundamental-invariant neural net-work method.The Li_(3)system exhibits a coni...We constructed a new set of diabatic poten-tial energy surfaces(PESs)for the two low-est states involved in Li+Li_(2)reaction by us-ing the fundamental-invariant neural net-work method.The Li_(3)system exhibits a coni-cal intersection(CI)at the geometric D_(3)h symmetries with the energy of the CI point significantly lower than the ground-state en-ab initio ergy of the diatomic molecule.The diabaitc PESs accurately reproduce adiabatic en-ergies,derivative coupling,and energy gradient information,thereby providing a high-fideli-ty description of the CI between the two lowest electronic states.Quantum dynamical calcu-lations have revealed significant non-adiabatic effects in the Li+Li_(2)reaction.展开更多
This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We c...This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.展开更多
Hypernuclei,nuclei containing one or more hyperons,serve as unique laboratories for probing the non-perturbative quantum chromodynamics(QCD).Recent progress in hypernuclear physics,driven by advanced experimental tech...Hypernuclei,nuclei containing one or more hyperons,serve as unique laboratories for probing the non-perturbative quantum chromodynamics(QCD).Recent progress in hypernuclear physics,driven by advanced experimental techniques and theoretical innovations,is briefly reviewed with a focus on key findings and unresolved challenges,such as the precise determination of the hypertriton binding energy,investigations of charge symmetry breaking in mirror hypernuclei,and the search for exotic systems,including the neutral nnΛstate.Experimental breakthroughs,including invariant-mass analyses and femtoscopy studies in heavy-ion collisions,as well as high-resolutionγ-spectroscopy,have enabled precise studies of light hypernuclei and offered critical insights into the hyperon–nucleon interaction.Theoretical progress,including ab initio calculations based on chiral effective field theory and lattice QCD,has further enhanced our understanding of hyperon–nucleon and hyperon–hyperon interactions.展开更多
A new two-state diabatic potential energy matrix(DPEM)for H3 has been constructed,based on the fun-damental invariant neural network(FI-NN)diabatization method pro-posed in our previous work[Phys.Chem.Chem.Phys.21,150...A new two-state diabatic potential energy matrix(DPEM)for H3 has been constructed,based on the fun-damental invariant neural network(FI-NN)diabatization method pro-posed in our previous work[Phys.Chem.Chem.Phys.21,15040(2019)].In that initial effort,a two-state DPEM was constructed only with a 10 eV energy threshold.The current work aims to expand the en-ergy range and improve the accura-cy of DPEM.This is achieved by the utilization of full configuration inter-action(FCI)with aug-cc-pVnZ ba-sis sets and complete basis set(CBS)extrapolation.The original dataset is augmented with additional points with higher adiabatic energies,which give rise to a total of 10985 data points.The DPEM constructed in this work now enables accurate representation of adiabatic energies up to 18 eV.Quantum dynamic calculations based on this DPEM are nearly identical to those obtained from benchmark surfaces,which makes it the most accurate DPEM for the H3 system to date,therefore facilitating detailed exploration of reaction mechanisms at higher collision energies.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
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
The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mappin...The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.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
To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relati...To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.展开更多
The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation b...The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.展开更多
基金Supported by Shanxi Province Natural Science Research(202203021212249)Special/Youth Foundation of Taiyuan University of Technology(2022QN101)+3 种基金National Natural Science Foundation of China(12301556)Research Project Supported by Shanxi Scholarship Council of China(2021-029)International Cooperation Base and Platform Project of Shanxi Province(202104041101019)Basic Research Plan of Shanxi Province(202203021211129)。
文摘To enhance the computational efficiency of spatio-temporally discretized phase-field models,we present a high-speed solver specifically designed for the Poisson equations,a component frequently used in the numerical computation of such models.This efficient solver employs algorithms based on discrete cosine transformations(DCT)or discrete sine transformations(DST)and is not restricted by any spatio-temporal schemes.Our proposed methodology is appropriate for a variety of phase-field models and is especially efficient when combined with flow field systems.Meanwhile,this study has conducted an extensive numerical comparison and found that employing DCT and DST techniques not only yields results comparable to those obtained via the Multigrid(MG)method,a conventional approach used in the resolution of the Poisson equations,but also enhances computational efficiency by over 90%.
文摘This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
基金supported in part by the Basic Research Project of Science and Technology Department of Jilin Province,China(Grant No.202002044JC).
文摘In the field of automated fruit harvesting,precise and efficient fruit target recognition and localization play a pivotal role in enhancing the efficiency of harvesting robots.However,this domain faces two core challenges:firstly,the dynamic nature of the automatic picking process requires fruit target detection algorithms to adapt to multi-view characteristics,ensuring effective recognition of the same fruit from different perspectives.Secondly,fruits in natural environments often suffer from interference factors such as overlapping,occlusion,and illumination fluctuations,which increase the difficulty of image capture and recognition.To address these challenges,this study conducted an in-depth analysis of the key features in fruit recognition and discovered that the stem,body,and base serve as constant and core information in fruit identification,exhibiting long-term dependent semantic relationships during the recognition process.These invariant features provide a stable foundation for dynamic fruit recognition,contributing to improved recognition accuracy and robustness.Specifically,the morphology and position of the stem,body,and base are relatively fixed,and the effective extraction of these features plays a crucial role in fruit recognition.This paper proposes a novel model,TransSSA,and designs two innovative modules to effectively extract fruit image features.The Self-Attention Core Feature Extraction(SAF)module integrates YOLOV8 and Swin Transformer as backbone networks and introduces the Shuffle Attention self-attention mechanism,significantly enhancing the ability to extract core features.This module focuses on constant features such as the stem,body,and base,ensuring accurate fruit recognition in different environments.On the other hand,the Squeeze and Excitation Aggregation(SAE)module combines the network’s ability to capture channel patterns with global knowledge,further optimizing the extraction of effective features.Additionally,to improve detection accuracy,this studymodifies the regression loss function to EIOU.To validate the effectiveness of the TransSSA model,this study conducted extensive visualization analysis to support the interpretability of the SAF and SAE modules.Experimental results demonstrate that TransSSA achieves a performance of 91.3%on a tomato dataset,fully proving its innovative capabilities.Through this research,we provide amore effective solution for using fruit harvesting robots in complex environments.
基金financial supports from the National Natural Science Foundation of China(Grant No.6227511362405124).
文摘We present a novel method for scale-invariant 3D face recognition by integrating computer-generated holography with the Mellin transform.This approach leverages the scale-invariance property of the Mellin transform to address challenges related to variations in 3D facial sizes during recognition.By applying the Mellin transform to computer-generated holograms and performing correlation between them,which,to the best of our knowledge,is being done for the first time,we have developed a robust recognition framework capable of managing significant scale variations without compromising recognition accuracy.Digital holograms of 3D faces are generated from a face database,and the Mellin transform is employed to enable robust recognition across scale factors ranging from 0.4 to 2.0.Within this range,the method achieves 100%recognition accuracy,as confirmed by both simulation-based and hybrid optical/digital experimental validations.Numerical calculations demonstrate that our method significantly enhances the accuracy and reliability of 3D face recognition,as evidenced by the sharp correlation peaks and higher peak-to-noise ratio(PNR)values than that of using conventional holograms without the Mellin transform.Additionally,the hybrid optical/digital joint transform correlation hardware further validates the method's effectiveness,demonstrating its capability to accurately identify and distinguish 3D faces at various scales.This work provides a promising solution for advanced biometric systems,especially for those which require 3D scale-invariant recognition.
基金supported by the Agencia Estatal de Investigación grant PID2019-104658GB-I00the H2020 European Research Council grant MSCA-RISE-2017-777911+2 种基金AGAUR(Generalitat de Catalunya)grant 2021SGR00113the Reial Acadèmia de Ciències i Arts de Barcelonasupported by FCT/Portugal through CAMGSD,IST-ID,projects UIDB/04459/2020 and UIDP/04459/2020.
文摘The differential system ẋ=ax−yz,ẏ=−by+xz,ż=−cz+x^(2),where a,b and c are positive real parameters,has been studied numerically due to the big variety of strange attractors that it can exhibit.This system has a Darboux invariant when c=2b.Using this invariant and the Poincarécompactification technique we describe analytically its global dynamics.
基金Supported by National Natural Science Foundation of China(Grant Nos.52025121,52394263)National Key R&D Plan of China(Grant No.2023YFD2000301)+2 种基金Foundation of State Key Laboratory of Automobile Safety and Energy Saving of China(Grant No.KFZ2201)the Jiangsu Provincial Scientific Research Center of Applied Mathematics under(Grant No.BK20233002)Special Fund of Jiangsu Province for the Transformation of Scientific and Technological Achievements under(Grant No.BA2021023)。
文摘This paper tackles uncertainties between planning and actual models.It extends the concept of RCI(robust control invariant)tubes,originally a parameterized representation of closed-loop control robustness in traditional feedback control,to the domain of motion planning for autonomous vehicles.Thus,closed-loop system uncertainty can be preemptively addressed during vehicle motion planning.This involves selecting collision-free trajectories to minimize the volume of robust invariant tubes.Furthermore,constraints on state and control variables are translated into constraints on the RCI tubes of the closed-loop system,ensuring that motion planning produces a safe and optimal trajectory while maintaining flexibility,rather than solely optimizing for the open-loop nominal model.Additionally,to expedite the solving process,we were inspired by L2gain to parameterize the RCI tubes and developed a parameterized explicit iterative expression for propagating ellipsoidal uncertainty sets within closedloop systems.Furthermore,we applied the pseudospectral orthogonal collocation method to parameterize the optimization problem of transcribing trajectories using high-order Lagrangian polynomials.Finally,under various operating conditions,we incorporate both the kinematic and dynamic models of the vehicle and also conduct simulations and analyses of uncertainties such as heading angle measurement,chassis response,and steering hysteresis.Our proposed robust motion planning framework has been validated to effectively address nearly all bounded uncertainties while anticipating potential tracking errors in control during the planning phase.This ensures fast,closed-loop safety and robustness in vehicle motion planning.
基金Supported by the National Key Research and Development Program of China(2022YFA1005501)the Natural Science Foundation of Jiangsu Province(BK20241433).
文摘In this paper,we study scalar curvature rigidity of non-smooth metrics on smooth manifolds with non-positive Yamabe invariant.We prove that if the scalar curvature is not less than the Yamabe invariant in the distributional sense,then the manifold must be isometric to an Einstein manifold.This result extends Theorem 1.4 in Jiang,Sheng and Zhang[27],from a special case where the manifolds have zero Yamabe invariant to general cases where the manifolds have non-positive Yamabe invariant.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074101 and 11604081)sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040)。
文摘The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.
基金supported in part by the Natural Sciences and Engineering Research Council of Canada(NSERC)supported by the National Natural Science Foundation of China under Grant 62303403Zhejiang Provincial Natural Science Foundation of China under Grants LR25F030004 and LQ24F030022。
文摘Switched systems play an imperative role in modeling many real industrial systems with abrupt changes.Due to possible exposure to unreliable and complex physical environments,switching dynamics may simultaneously face multiple faults,including the unexpected controller disconnect,the temporary mismatch between subsystems and desired corresponding controllers,and the intermittent disordering of mode transitions.These commonly arising faults may result in severe and detrimental impacts on the reliability and convergence of the closed-loop solution,thereby bringing significant yet challenging issues to be tackled.This paper provides the first attempt to investigate the stabilization problem for a class of constrained switched linear systems with multiple faults under mode-dependent dwell time(MDT).From a set-theory perspective,we demonstrate a critical necessary and sufficient stability condition for switched systems without uncertainties.Moreover,the non-conservative stability criterion is further extended to the perturbed switched systems with rigorous proof.A switching communication network example verifies the validity of the theoretical result and demonstrates their advantages.
基金supported by the National Natural Science Foundation of China(Nos.22103084 and 22233003 to Jiayu Huang,and No.22288201 to Dong H.Zhang)the Innovation Program for Quantum Science and Technology(No.2021ZD0303305)to Dong H.Zhangthe Dalian Innovation Support Program(No.2021RD05)to Dong H.Zhang.
文摘We constructed a new set of diabatic poten-tial energy surfaces(PESs)for the two low-est states involved in Li+Li_(2)reaction by us-ing the fundamental-invariant neural net-work method.The Li_(3)system exhibits a coni-cal intersection(CI)at the geometric D_(3)h symmetries with the energy of the CI point significantly lower than the ground-state en-ab initio ergy of the diatomic molecule.The diabaitc PESs accurately reproduce adiabatic en-ergies,derivative coupling,and energy gradient information,thereby providing a high-fideli-ty description of the CI between the two lowest electronic states.Quantum dynamical calcu-lations have revealed significant non-adiabatic effects in the Li+Li_(2)reaction.
基金supported by the National Key R&D Program of China(2023YFA1009200)the NSFC(11925102)the Liaoning Revitalization Talents Program(XLYC2202042)。
文摘This paper is devoted to proving the polynomial mixing for a weakly damped stochastic nonlinear Schröodinger equation with additive noise on a 1D bounded domain.The noise is white in time and smooth in space.We consider both focusing and defocusing nonlinearities,with exponents of the nonlinearityσ∈[0,2)andσ∈[0,∞),and prove the polynomial mixing which implies the uniqueness of the invariant measure by using a coupling method.In the focusing case,our result generalizes the earlier results in[12],whereσ=1.
基金supported by the the National Key R&D Program of China(Grant Nos.2022YFA1604900 and 2023YFA1606703)the National Natural Science Foundation of China(Grant Nos.12025501,12435007,12405133,and 12347180)+1 种基金China Postdoctoral Science Foundation(Grant No.2023M740189)the Postdoctoral Fellowship Program of CPSF(Grant No.GZC20233381).
文摘Hypernuclei,nuclei containing one or more hyperons,serve as unique laboratories for probing the non-perturbative quantum chromodynamics(QCD).Recent progress in hypernuclear physics,driven by advanced experimental techniques and theoretical innovations,is briefly reviewed with a focus on key findings and unresolved challenges,such as the precise determination of the hypertriton binding energy,investigations of charge symmetry breaking in mirror hypernuclei,and the search for exotic systems,including the neutral nnΛstate.Experimental breakthroughs,including invariant-mass analyses and femtoscopy studies in heavy-ion collisions,as well as high-resolutionγ-spectroscopy,have enabled precise studies of light hypernuclei and offered critical insights into the hyperon–nucleon interaction.Theoretical progress,including ab initio calculations based on chiral effective field theory and lattice QCD,has further enhanced our understanding of hyperon–nucleon and hyperon–hyperon interactions.
基金supported by the National Natural Science Foundation of China(No.22288201)the Inno-vation Program for Quantum Science and Technology(No.2021ZD0303305)the Dalian Innovation Sup-port Program(No.2021RD05).
文摘A new two-state diabatic potential energy matrix(DPEM)for H3 has been constructed,based on the fun-damental invariant neural network(FI-NN)diabatization method pro-posed in our previous work[Phys.Chem.Chem.Phys.21,15040(2019)].In that initial effort,a two-state DPEM was constructed only with a 10 eV energy threshold.The current work aims to expand the en-ergy range and improve the accura-cy of DPEM.This is achieved by the utilization of full configuration inter-action(FCI)with aug-cc-pVnZ ba-sis sets and complete basis set(CBS)extrapolation.The original dataset is augmented with additional points with higher adiabatic energies,which give rise to a total of 10985 data points.The DPEM constructed in this work now enables accurate representation of adiabatic energies up to 18 eV.Quantum dynamic calculations based on this DPEM are nearly identical to those obtained from benchmark surfaces,which makes it the most accurate DPEM for the H3 system to date,therefore facilitating detailed exploration of reaction mechanisms at higher collision energies.
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supported by the National High Technology Research and Development Program of China(863 Program)(No.2013AA063901 and No.2006AA06A201)
文摘The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.
基金National High-tech Research and Development Program (2007AA01Z314)National Natural Science Foundation of China (60873085)
文摘In order to obtain a large number of correct matches with high accuracy,this article proposes a robust wide baseline point matching method,which is based on Scott s proximity matrix and uses the scale invariant feature transform (SIFT). First,the distance between SIFT features is included in the equations of the proximity matrix to measure the similarity between two feature points; then the normalized cross correlation (NCC) used in Scott s method,which has been modified with adaptive scale and orientation,...
文摘To study a form invariance of Lagrange system, the form invariance of Lagrange equations under the infinitesimal transformations was used. The definition and criterion for the form invariance are given. The relation between the form invariance and the Noether symmetry was established.
文摘The form invariance of Birkhoffian systems is a kind of invariance of the Birkhoffian equations under the infinitesimal transformations. The definition and criteria of the form invariance are given, and the relation between the form invariance and the Noether symmetry is studied.
