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
In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contrac...In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.展开更多
This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twost...This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.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
In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was...Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.展开更多
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
In this paper,the oscillation of solutions of hyperbolic partial functional differential equations is studied,and oscillatory criteria of solutions with three kinds of boundary conditions are obtained.
In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the followin...In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the following evolution equation δ^2F /δt^2 （u, t） = k（u, t）N（u, t）-▽ρ（u, t）, ∨（u, t） ∈ S^1 × [0, T ） with the initial data F （u, 0） = F0（u） and δF/δt （u, 0） = f（u）N0, where k is the mean curvature and N is the unit inner normal vector of the plane curve F （u, t）, f（u） and N0 are the initial velocity and the unit inner normal vector of the initial convex closed curve F0, respectively, and ▽ρ is given by ▽ρ Δ=（δ^2F /δsδt ,δF/δt） T , in which T stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F , it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere equation. Based on this, we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at a finite time interval [0, Tmax） and when t goes to Tmax, either the solution convergesto a point or shocks and other propagating discontinuities are generated. Furthermore, we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support functions and the curvature of the curve. In the end, we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time R^1,1.展开更多
Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze th...Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze the electrical resistivity development. The peak point （Ph） on the hyperbolic curve could be easily read. The time （th） to reach the point Ph had strong relations with the setting time. th was delayed with the increment of the dosage of superplasticizer. The time th was used to plot the relationship between the initial setting time and final setting time. The hyperbolic equation was established to predict the ultimate resistivity. The retardation effect of the superplasticizer was confirmed in the same W/C ratio by setting time and isothermal heat evolution.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary ...In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.展开更多
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.
基金supported by the NSFC(12271122)the Fundamental Research Funds for the Central Universities.Han’s research was supported by the Fundamental Research Funds for the Central Universities(3072023GIP2401).
文摘In this paper,we consider the initial boundary value problem for the 2-D hyperbolic viscous Cahn-Hilliard equation.Firstly,we prove the existence and uniqueness of the local solution by the Galerkin method and contraction mapping principle.Then,using the potential well theory,we study the global well-posedness of the solution with initial data at different levels of initial energy,i.e.,subcritical initial energy,critical initial energy and arbitrary positive initial energy.For subcritical initial energy,we prove the global existence,asymptotic behavior and finite time blowup of the solution.Moreover,we extend these results to the critical initial energy using the scaling technique.For arbitrary positive initial energy,including the sup-critical initial energy,we obtain the sufficient conditions for finite time blow-up of the solution.As a further study for estimating the blowup time,we give a unified expression of the lower bound of blowup time for all three initial energy levels and estimate the upper bound of blowup time for subcritical and critical initial energy.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2503).
文摘This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity,thermal radiation,and coupled heat andmass transfer effects.Amodified twostage Exponential Time Integrator is introduced for temporal discretization,providing second-order accuracy in time.A compact finite difference method is employed for spatial discretization,yielding sixth-order accuracy at most grid points.The proposed framework ensures numerical stability and convergence when solving stiff,nonlinear parabolic systems arising in fluid flow and heat transfer problems.The novelty of the work lies in combining exponential integrator schemes with compact high-order spatial discretization,enabling accurate and efficient simulations of tangent hyperbolic fluids under complex boundary conditions,such as oscillatory plates and varying thermal conductivity.This approach addresses limitations of classical Euler,Runge–Kutta,and spectral methods by significantly reducing numerical errors(up to 45%)and computational cost.Comprehensive parametric studies demonstrate how viscous dissipation,chemical reactions,the Weissenberg number,and the Hartmann number influence flow behaviour,heat transfer,and mass transfer.Notably,heat transfer rates increase by 18.6%with stronger viscous dissipation,while mass transfer rates rise by 21.3%with more intense chemical reactions.The real-world relevance of the study is underscored by its direct applications in polymer processing,heat exchanger design,radiative thermal management in aerospace,and biofluid transport in biomedical systems.The proposed scheme thus provides a robust numerical framework that not only advances the mathematical modelling of non-Newtonian fluid flows but also offers practical insights for engineering systems involving tangent hyperbolic fluids.
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.
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
文摘Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘In this paper,the oscillation of solutions of hyperbolic partial functional differential equations is studied,and oscillatory criteria of solutions with three kinds of boundary conditions are obtained.
基金Kong and Wang was supported in part by the NSF of China (10671124)the NCET of China (NCET-05-0390)the work of Liu was supported in part by the NSF of China
文摘In this paper we investigate the one-dimensional hyperbolic mean curvatureflow for closed plane curves. More precisely, we consider a family of closed curves F ： S1 × [0, T ） → R^2 which satisfies the following evolution equation δ^2F /δt^2 （u, t） = k（u, t）N（u, t）-▽ρ（u, t）, ∨（u, t） ∈ S^1 × [0, T ） with the initial data F （u, 0） = F0（u） and δF/δt （u, 0） = f（u）N0, where k is the mean curvature and N is the unit inner normal vector of the plane curve F （u, t）, f（u） and N0 are the initial velocity and the unit inner normal vector of the initial convex closed curve F0, respectively, and ▽ρ is given by ▽ρ Δ=（δ^2F /δsδt ,δF/δt） T , in which T stands for the unit tangent vector. The above problem is an initial value problem for a system of partial differential equations for F , it can be completely reduced to an initial value problem for a single partial differential equation for its support function. The latter equation is a hyperbolic Monge-Ampere equation. Based on this, we show that there exists a class of initial velocities such that the solution of the above initial value problem exists only at a finite time interval [0, Tmax） and when t goes to Tmax, either the solution convergesto a point or shocks and other propagating discontinuities are generated. Furthermore, we also consider the hyperbolic mean curvature flow with the dissipative terms and obtain the similar equations about the support functions and the curvature of the curve. In the end, we discuss the close relationship between the hyperbolic mean curvature flow and the equations for the evolving relativistic string in the Minkowski space-time R^1,1.
基金the National Natural Science Foundation of China(No.50778078)
文摘Electrical measurement was employed to investigate the early hydration characteristics of cement pastes with different dosages of superplasticizer in the same W/C ratio. The hyperbolic method was applied to analyze the electrical resistivity development. The peak point （Ph） on the hyperbolic curve could be easily read. The time （th） to reach the point Ph had strong relations with the setting time. th was delayed with the increment of the dosage of superplasticizer. The time th was used to plot the relationship between the initial setting time and final setting time. The hyperbolic equation was established to predict the ultimate resistivity. The retardation effect of the superplasticizer was confirmed in the same W/C ratio by setting time and isothermal heat evolution.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
基金Projects supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program (973) of China (No.G2002CB312101)
文摘In this paper, two new kinds of B-basis functions called algebraic hyperbolic （AH） Bézier basis and AH B-Spline basis are presented in the space Гk=span{ l,t ……f^k-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bézier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms： AH B-Spline surface and AH T-Spline surface.
