A surprising result that byperbolicity is almost equivalent to quasi-Anosov was given byMänéin[1].Here a concise and intuitive prcof of it is presented.
The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms.One meets difficulties when trying to extend these definitions to vector f...The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms.One meets difficulties when trying to extend these definitions to vector fields and Shantao Liao has shown that it is more relevant to consider the linear Poincare flow rather than the tangent flow in order to study the properties of the derivative.In this paper,we define the notion of singular domination,an analog of the dominated splitting for the linear Poincar´e flow which is robust under perturbations.Based on this,we give a new definition of multi-singular hyperbolicity which is equivalent to the one recently introduced by Bonatti and da Luz(2017).The novelty of our definition is that it does not involve the blow-up of the singular set and the rescaling cocycle of the linear flows.展开更多
The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces （with their Poincare metrics）. We prove that quasiconformal maps between Riemann su...The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces （with their Poincare metrics）. We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; however, we also show that arbitrary twists along simple closed geodesics do not preserve it, in general.展开更多
The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,...The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.展开更多
In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C 1 -star invariant sets of C 1 -class differential systems on a closed manifold of dimension≤ 4, without using the C 1 -connecting lemma...In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C 1 -star invariant sets of C 1 -class differential systems on a closed manifold of dimension≤ 4, without using the C 1 -connecting lemma and even the ergodic closing lemma.展开更多
In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a conse...In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.展开更多
In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic...In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.展开更多
For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic fu...Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.展开更多
Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study prov...Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates.The inverse hyperbolic shear deformation theory(IHSDT)of plates is employed to characterize the displacement field,with the incorporation of Green-Lagrange nonlinearity.The problem is modeled using the C0finite element method(FEM),and an in-house code is developed in the MATLAB environment to solve it numerically.Various helicoidal layup configurations including helicoidal recursive(HR),helicoidal exponential(HE),helicoidal semi-circular(HS),linear helicoidal(LH),and Fibonacci helicoidal(FH)with different layup sequences and quasi-isotropic configurations are studied.The model is validated,and parametric studies are conducted.These studies investigate the effects of layup configurations,side-to-thickness ratio,modulus ratios,boundary conditions,and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates.The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors.Moreover,this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.展开更多
A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separati...A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separation and power-law spectral density,the more interesting phenomena predicted in coupled Luttinger liquids of neighboring 1D conductors have been rarely observed due to the difficulty in creating such structures.Recently,we have successfully grown close-packed carbon nanotube(CNT)arrays with uniform chirality,providing an ideal material system for studying the coupled Luttinger liquids.Here,we report on the observation of tunable hyperbolic plasmons in the coupled Luttinger liquids of CNT arrays using scanning near-field optical microscopy.These hyperbolic plasmons,resulting from the conductivity anisotropy in the CNT array,exhibit strong spatial confinement,in situ tunability,and a wide spectral range.Despite their hyperbolic wavefronts,the plasmon propagation in the axial direction still adheres to the Luttinger-liquid theory.Our work not only demonstrates a fascinating phenomenon in coupled Luttinger liquids for fundamental physics exploration,but also provides a highly confined and in situ tunable hyperbolic plasmon in close-packed CNT arrays for future nanophotonic devices and circuits.展开更多
We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyper...We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.展开更多
Dear Editor,This letter focuses on the distributed cooperative regulation problem for a class of networked re-entrant manufacturing systems(RMSs).The networked system is structured with a three-tier architecture:the p...Dear Editor,This letter focuses on the distributed cooperative regulation problem for a class of networked re-entrant manufacturing systems(RMSs).The networked system is structured with a three-tier architecture:the production line,the manufacturing layer and the workshop layer.The dynamics of re-entrant production lines are governed by hyperbolic partial differential equations(PDEs)based on the law of mass conservation.展开更多
Let X be a C1 vector field on a compact boundaryless Riemannian manifold M（dim M≥2）,and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = Es Eu with Es uniformly contracting and E...Let X be a C1 vector field on a compact boundaryless Riemannian manifold M（dim M≥2）,and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = Es Eu with Es uniformly contracting and Eu uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.展开更多
The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple char...The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.展开更多
The authors study the fluid dynamic behavior of the stochastic Galerkin(SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty.While the SG system at the kinetic level is hyperbolic,...The authors study the fluid dynamic behavior of the stochastic Galerkin(SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty.While the SG system at the kinetic level is hyperbolic, its fluid dynamic limit, as the Knudsen number goes to zero and the underlying kinetic equation approaches to the uncertain isentropic Euler equations, is not necessarily hyperbolic, as will be shown in the case study fashion for various orders of the SG approximations.展开更多
In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbo...In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.展开更多
In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-det...In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.展开更多
Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exp...Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exploring homogeneous regions of temperature volatility and analyzing the driving factors.To investigate the regionalization of temperature volatility in China's mainland,a network constructed by the cosine similarity of temperature volatility series from China's mainland was embedded in hyperbolic space.Subsequently,we partitioned the network on the hyperbolic map using the critical gap method and then found eight regions in all.Ultimately,a network of communities was constructed while the interaction among communities was quantified.This yields a perspective of temperature volatility regionalization that can accurately reflect factors including altitude,climate type,and the geographic location of mountains.Further analysis demonstrates that the regionalization in the hyperbolic map is distinct from provinces and has a realistic basis:communities in southwest China show strong correlations due to the temperature sensitivity to altitude,and communities in northern China show a convergence in the area of Dingxi,Gansu,mainly owing to the strong temperature sensitivity to climate types.As a consequence,node distributions and community divisions in the hyperbolic map can offer new insights into the regionalization of temperature volatility in China's mainland.The results demonstrate the potential of hyperbolic embedding of complex networks in forecasting future node associations in real-world data.展开更多
Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent prob...Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.展开更多
文摘A surprising result that byperbolicity is almost equivalent to quasi-Anosov was given byMänéin[1].Here a concise and intuitive prcof of it is presented.
基金The first author was supported by the European Research Council(Grant No.692925)The third author was supported by National Natural Science Foundation of China(Grant Nos.11671288,11822109 and 11790274)The fourth author was supported by the starting grant from Beihang University and the European Research Council(Grant No.692925).
文摘The properties of uniform hyperbolicity and dominated splitting have been introduced to study the stability of the dynamics of diffeomorphisms.One meets difficulties when trying to extend these definitions to vector fields and Shantao Liao has shown that it is more relevant to consider the linear Poincare flow rather than the tangent flow in order to study the properties of the derivative.In this paper,we define the notion of singular domination,an analog of the dominated splitting for the linear Poincar´e flow which is robust under perturbations.Based on this,we give a new definition of multi-singular hyperbolicity which is equivalent to the one recently introduced by Bonatti and da Luz(2017).The novelty of our definition is that it does not involve the blow-up of the singular set and the rescaling cocycle of the linear flows.
文摘The main aim of this paper is to study whether the Gromov hyperbolicity is preserved under some transformations on Riemann surfaces （with their Poincare metrics）. We prove that quasiconformal maps between Riemann surfaces preserve hyperbolicity; however, we also show that arbitrary twists along simple closed geodesics do not preserve it, in general.
基金supported by National Natural Science Foundation of China (Grant No.11131004)
文摘The linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three body problem depends on the mass parameter β = 27（m1m2 ＋ m2m3 ＋ m3m1）/（m1 ＋ m2 ＋ m3）2∈ [0,9] and the eccentricity e ∈ [0,1）.In this paper we use Maslov-type index to study the stability of these solutions and prove that the elliptic Lagrangian solutions is hyperbolic for β ＆gt; 8 with any eccentricity.
基金supported by National Natural Science Foundation of China (Grant No. 10671088)National Basic Research Program of China (973 Project) (Grant No. 2006CB805903)
文摘In this paper, we simply prove, in the framework of Liao, the hyperbolicity of C 1 -star invariant sets of C 1 -class differential systems on a closed manifold of dimension≤ 4, without using the C 1 -connecting lemma and even the ergodic closing lemma.
基金Supported by National Natural Science Foundation of China(Grant No.11201023)Specialized Research Fund for the Doctoral Program of Higher Education
文摘In this paper, we prove that every star flow on the closed surface has finitely many chain recurrent classes. Furthermore, it is singular hyperbolic if every non-trivial singular chain component is a graph. As a consequence, every star flow on the 2-sphere or the projective plane is singular hyperbolic.
文摘In this paper,we establish a stability estimate for the isoperimetric inequality of horospherically convex domains in hyperbolic plane.This estimate involves a relationship between the Hausdorff distance to a geodesic ball and the deficit in the isoperimetric inequality,where the coefficient of the deficit is a universal constant.
基金supported by the National Natural Science Foundation of China(12371217)the Fundamental Research Funds for the Central Universities(2232022D-27).
文摘For multidimensional first order semilinear hyperbolic systems of diagonal form without self-interaction,we show the global nonlinear stability of traveling wave solutions.
基金financially supported by the National Natural Science Foundation of China (8225041038)the Sichuan Science and Technology Program (23NSFSC2916)the Fundamental Research Funds for the Central Universities, Southwest Minzu University (ZYN2024077)
文摘Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.
文摘Bio-inspired helicoidal composite laminates,inspired by the intricate helical structures found in nature,present a promising frontier for enhancing the mechanical properties of structural designs.Hence,this study provides a comprehensive investigation into the nonlinear free vibration and nonlinear bending behavior of bio-inspired composite plates.The inverse hyperbolic shear deformation theory(IHSDT)of plates is employed to characterize the displacement field,with the incorporation of Green-Lagrange nonlinearity.The problem is modeled using the C0finite element method(FEM),and an in-house code is developed in the MATLAB environment to solve it numerically.Various helicoidal layup configurations including helicoidal recursive(HR),helicoidal exponential(HE),helicoidal semi-circular(HS),linear helicoidal(LH),and Fibonacci helicoidal(FH)with different layup sequences and quasi-isotropic configurations are studied.The model is validated,and parametric studies are conducted.These studies investigate the effects of layup configurations,side-to-thickness ratio,modulus ratios,boundary conditions,and loading conditions at different load amplitudes on the nonlinear vibration and nonlinear bending behaviors of bio-inspired composite plates.The results show that the laminate sequence exerts a substantial impact on both nonlinear natural frequencies and nonlinear bending behaviors.Moreover,this influence varies across different side-to-thickness ratios and boundary conditions of the bio-inspired composite plate.
基金supported by the National Key R&D Program of China(Grant No.2021YFA1202902)the National Natural Science Foundation of China(Grant Nos.12374292 and 12074244)B.L.acknowledges support from the Development Scholarship for Outstanding Ph.D.of Shanghai Jiao Tong University.J.K.acknowledges support from the National Research Foundation of Korea(NRF)grant funded by the Korean government(MSIT)(Grant No.NRF-RS-2024-00454528).
文摘A Luttinger liquid is a theoretical model describing interacting electrons in one-dimensional(1D)conductors.While individual 1D conductors have shown interesting Luttinger-liquid behaviors such as spin-charge separation and power-law spectral density,the more interesting phenomena predicted in coupled Luttinger liquids of neighboring 1D conductors have been rarely observed due to the difficulty in creating such structures.Recently,we have successfully grown close-packed carbon nanotube(CNT)arrays with uniform chirality,providing an ideal material system for studying the coupled Luttinger liquids.Here,we report on the observation of tunable hyperbolic plasmons in the coupled Luttinger liquids of CNT arrays using scanning near-field optical microscopy.These hyperbolic plasmons,resulting from the conductivity anisotropy in the CNT array,exhibit strong spatial confinement,in situ tunability,and a wide spectral range.Despite their hyperbolic wavefronts,the plasmon propagation in the axial direction still adheres to the Luttinger-liquid theory.Our work not only demonstrates a fascinating phenomenon in coupled Luttinger liquids for fundamental physics exploration,but also provides a highly confined and in situ tunable hyperbolic plasmon in close-packed CNT arrays for future nanophotonic devices and circuits.
基金supported by a grant from DGI(BFM 2003-04870)Spainsupported by a grant from DGI(BFM 2000-0022)Spain
文摘We study the hyperbolicity in the Gromov sense of Riemann surfaces. We deduce the hyperbolicity of a surface from the hyperbolicity of its ＂building block components＂. We also prove the equivalence between the hyperbolicity of a Riemann surface and the hyperbolicity of some graph associated with it. These results clarify how the decomposition of a Riemann surface into Y-pieces and funnels affects the hyperbolicity of the surface. The results simplify the topology of the surface and allow us to obtain global results from local information.
文摘Dear Editor,This letter focuses on the distributed cooperative regulation problem for a class of networked re-entrant manufacturing systems(RMSs).The networked system is structured with a three-tier architecture:the production line,the manufacturing layer and the workshop layer.The dynamics of re-entrant production lines are governed by hyperbolic partial differential equations(PDEs)based on the law of mass conservation.
基金supported by the State Key Development Program for Basic Research of China(973 Project)(Grant No.2011CB808002)National Natural Science Foundation of China(Grant Nos.11025101 and 11231001)
文摘Let X be a C1 vector field on a compact boundaryless Riemannian manifold M（dim M≥2）,and A a compact invariant set of X.Suppose that A has a hyperbolic splitting,i.e.,T∧M = Es Eu with Es uniformly contracting and Eu uniformly expanding.We prove that if,in addition,A is chain transitive,then the hyperbolic splitting is continuous,i.e.,A is a hyperbolic set.In general,when A is not necessarily chain transitive,the chain recurrent part is a hyperbolic set.Furthermore,we show that if the whole manifold M admits a hyperbolic splitting,then X has no singularity,and the flow is Anosov.
基金Supported by Ministerio de Ciencia e Innovaci'on of Spain(Grant No.MTM 2009-07800)the last author also by a grant from CONACY of TM'exico(Grant No.CONACYT-UAG I0110/62/10)
文摘The study of hyperbolic graphs is an interesting topic since the hyperbolicity of a geodesic metric space is equivalent to the hyperbolicity of a graph related to it.The main result in this paper is a very simple characterization of the hyperbolicity of a large class of periodic planar graphs.
基金supported by NSF Grants DMS-1522184,DMS-1819012,DMS-1107291:RNMS KI-Netthe National Natural Science Foundation of China(Nos.31571071,11871297)
文摘The authors study the fluid dynamic behavior of the stochastic Galerkin(SG for short) approximation to the kinetic Fokker-Planck equation with random uncertainty.While the SG system at the kinetic level is hyperbolic, its fluid dynamic limit, as the Knudsen number goes to zero and the underlying kinetic equation approaches to the uncertain isentropic Euler equations, is not necessarily hyperbolic, as will be shown in the case study fashion for various orders of the SG approximations.
基金supported by the National Natural Science Foundation of China(21972131)。
文摘In this study,we systematically investigated the effect of proton concentration on the kinetics of the oxygen reduction reaction(ORR)on Pt(111)in acidic solutions.Experimental results demonstrate a rectangular hyperbolic relationship,i.e.,the ORR current excluding the effect of other variables increases with proton concentration and then tends to a constant value.We consider that this is caused by the limitation of ORR kinetics by the trace oxygen concentration in the solution,which determines the upper limit of ORR kinetics.A model of effective concentration is further proposed for rectangular hyperbolic relationships:when the reactant concentration is high enough to reach a critical saturation concentration,the effective reactant concentration will become a constant value.This could be due to the limited concentration of a certain reactant for reactions involving more than one reactant or the limited number of active sites available on the catalyst.Our study provides new insights into the kinetics of electrocatalytic reactions,and it is important for the proper evaluation of catalyst activity and the study of structureperformance relationships.
基金National Natural Science Foundation of China,Grant/Award Number:61602157Henan scientific and technological project,Grant/Award Number:242102210020Basal Research Fund,Grant/Award Number:NSFRF240618。
文摘In the metric-based meta-learning detection model,the distribution of training samples in the metric space has great influence on the detection performance,and this influence is usually ignored by traditional meta-detectors.In addition,the design of metric space might be interfered with by the background noise of training samples.To tackle these issues,we propose a metric space optimisation method based on hyperbolic geometry attention and class-agnostic activation maps.First,the geometric properties of hyperbolic spaces to establish a structured metric space are used.A variety of feature samples of different classes are embedded into the hyperbolic space with extremely low distortion.This metric space is more suitable for representing tree-like structures between categories for image scene analysis.Meanwhile,a novel similarity measure function based on Poincarédistance is proposed to evaluate the distance of various types of objects in the feature space.In addition,the class-agnostic activation maps(CCAMs)are employed to re-calibrate the weight of foreground feature information and suppress background information.Finally,the decoder processes the high-level feature information as the decoding of the query object and detects objects by predicting their locations and corresponding task encodings.Experimental evaluation is conducted on Pascal VOC and MS COCO datasets.The experiment results show that the effectiveness of the authors’method surpasses the performance baseline of the excellent few-shot detection models.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12275179,12005079,and 41975100),the Shanghai Natural Science Foundation of China(Grant No.21ZR1443900),Natural Science Foundation of Jiangsu Province(Grant No.BK20220511),the funding for Scientific Research Startup of Jiangsu University(Grant No.4111710001),and the Joint Research Project for Meteorological Capacity Improvement(Grant No.22NLTSZ004).
文摘Abrupt temperature volatility has detrimental effects on daily activities,macroeconomic growth,and human health.Predicting abrupt temperature volatility and thus diminishing its negative impacts can be achieved by exploring homogeneous regions of temperature volatility and analyzing the driving factors.To investigate the regionalization of temperature volatility in China's mainland,a network constructed by the cosine similarity of temperature volatility series from China's mainland was embedded in hyperbolic space.Subsequently,we partitioned the network on the hyperbolic map using the critical gap method and then found eight regions in all.Ultimately,a network of communities was constructed while the interaction among communities was quantified.This yields a perspective of temperature volatility regionalization that can accurately reflect factors including altitude,climate type,and the geographic location of mountains.Further analysis demonstrates that the regionalization in the hyperbolic map is distinct from provinces and has a realistic basis:communities in southwest China show strong correlations due to the temperature sensitivity to altitude,and communities in northern China show a convergence in the area of Dingxi,Gansu,mainly owing to the strong temperature sensitivity to climate types.As a consequence,node distributions and community divisions in the hyperbolic map can offer new insights into the regionalization of temperature volatility in China's mainland.The results demonstrate the potential of hyperbolic embedding of complex networks in forecasting future node associations in real-world data.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.52204258 and 52106099)the Postdoctoral Research Foundation of China (Grant No.2023M743779)+2 种基金the Fundamental Research Funds for the Central Universities (Grant No.2022QN1017)the Key Research Development Projects in Xinjiang Uygur Autonomous Region (Grant No.2022B03003-3)the Shandong Provincial Natural Science Foundation (Grant No.ZR2020LLZ004)。
文摘Anisotropic hyperbolic phonon polaritons(PhPs)in natural biaxial hyperbolic materialα-MoO_(3) has opened up new avenues for mid-infrared nanophotonics,while active tunability ofα-MoO_(3) PhPs is still an urgent problem necessarily to be solved.In this study,we present a theoretical demonstration of actively tuningα-MoO_(3) PhPs using phase change material VO_(2) and graphene.It is observed thatα-MoO_(3) PhPs are greatly dependent on the propagation plane angle of PhPs.The insulator-to-metal phase transition of VO_(2) has a significant effect on the hybridization PhPs of theα-MoO_(3)/VO_(2) structure and allows to obtain actively tunableα-MoO_(3) PhPs,which is especially obvious when the propagation plane angle of PhPs is 900.Moreover,when graphene surface plasmon sources are placed at the top or bottom ofα-MoO_(3) inα-MoO_(3)/VO_(2)structure,tunable coupled hyperbolic plasmon-phonon polaritons inside its Reststrahlen bands(RB s)and surface plasmonphonon polaritons outside its RBs can be achieved.In addition,the above-mentionedα-MoO_(3)-based structures also lead to actively tunable anisotropic spontaneous emission(SE)enhancement.This study may be beneficial for realization of active tunability of both PhPs and SE ofα-MoO_(3),and facilitate a deeper understanding of the mechanisms of anisotropic light-matter interaction inα-MoO_(3) using functional materials.
