双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Ku...双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.展开更多
This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground commu...This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground communication.The array consists of ten broadside-radiating,ultrawide-beamwidth elements that are cascaded by a central-symmetry series-fed network with tapered currents following Dolph-Chebyshev distribution to provide low SLL.First,an innovative design of end-fire Huygens source antenna that is compatible with metal ground is presented.A low-profile,half-mode Microstrip Patch Antenna(MPA)is utilized to serve as the magnetic dipole and a monopole is utilized to serves as the electric dipole,constructing the compact,end-fire,grounded Huygens source antenna.Then,two opposite-oriented end-fire Huygens source antennas are seamlessly integrated into a single antenna element in the form of monopole-loaded MPA to accomplish the ultrawide,broadside-radiating beam.Particular consideration has been applied into the design of series-fed network as well as antenna element to compensate the adverse coupling effects between elements on the radiation performance.Experiment indicates an ultrawide Half-Power Beamwidth(HPBW)of 161°and a low SLL of-25 dB with a high gain of 12 d Bi under a single-layer configuration.The concurrent ultrawide beamwidth and low SLL make it particularly attractive for applications of UAV air-to-ground communication.展开更多
利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较...利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较了两种边界条件施加方法下两种重心插值法的数值算法。数值算例表明了重心插值配点法的高精度性。The two-dimensional steady convection-diffusion equation is solved by barycentric interpolation method. Firstly, the two barycentric interpolation collocation methods are introduced, and the differential matrices are given. Secondly, the two-dimensional steady convection-diffusion equation and initial boundary conditions are dispersed, and the boundary conditions are treated by substitution and addition. Numerical calculations are carried out by using the second type of Chebyshev node and the equidistant node. Numerical examples demonstrate that this barycentric interpolation collocation method has high accuracy.展开更多
Next-generation 6G networks seek to provide ultra-reliable and low-latency communications,necessitating network designs that are intelligent and adaptable.Network slicing has developed as an effective option for resou...Next-generation 6G networks seek to provide ultra-reliable and low-latency communications,necessitating network designs that are intelligent and adaptable.Network slicing has developed as an effective option for resource separation and service-level differentiation inside virtualized infrastructures.Nonetheless,sustaining elevated Quality of Service(QoS)in dynamic,resource-limited systems poses significant hurdles.This study introduces an innovative packet-based proactive end-to-end(ETE)resource management system that facilitates network slicing with improved resilience and proactivity.To get around the drawbacks of conventional reactive systems,we develop a cost-efficient slice provisioning architecture that takes into account limits on radio,processing,and transmission resources.The optimization issue is non-convex,NP-hard,and requires online resolution in a dynamic setting.We offer a hybrid solution that integrates an advanced Deep Reinforcement Learning(DRL)methodology with an Improved Manta-Ray Foraging Optimization(ImpMRFO)algorithm.The ImpMRFO utilizes Chebyshev chaotic mapping for the formation of a varied starting population and incorporates Lévy flight-based stochastic movement to avert premature convergence,hence facilitating improved exploration-exploitation trade-offs.The DRL model perpetually acquires optimum provisioning strategies via agent-environment interactions,whereas the ImpMRFO enhances policy performance for effective slice provisioning.The solution,developed in Python,is evaluated across several 6G slicing scenarios that include varied QoS profiles and traffic requirements.The DRL model perpetually acquires optimum provisioning methods via agent-environment interactions,while the ImpMRFO enhances policy performance for effective slice provisioning.The solution,developed in Python,is evaluated across several 6G slicing scenarios that include varied QoS profiles and traffic requirements.Experimental findings reveal that the proactive ETE system outperforms DRL models and non-resilient provisioning techniques.Our technique increases PSSRr,decreases average latency,and optimizes resource use.These results demonstrate that the hybrid architecture for robust,real-time,and scalable slice management in future 6G networks is feasible.展开更多
This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we co...This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we construct the multivariate barycentric Lagrange interpolation approximation function and process the integral terms by using the Gauss-Legendre quadrature formula.We provide a detailed error analysis of the discrete format on the second kind of Chebyshev nodes.The efficacy of the proposed method is substantiated by some numerical experiments.The results of these experiments demonstrate that our method can obtain high-precision numerical solutions for fractional partial differential equations.Additionally,the method's capability to achieve high precision with a reduced number of nodes is confirmed.展开更多
在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动...在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动扩散反应问题、奇异摄动对流扩散反应问题这两个算例的研究,表明基于Chebyshev点的B样条配置法与等距节点下的B样条配置法相比,前者具有高精度和高效率的优势。In solving the singular perturbation two-point boundary value problems, this paper constructs a Chebyshev B-spline collocation method. This method uses cubic B-spline functions as basis functions and utilizes the Chebyshev point as the configuration point to solve the equation directly. The specific steps in the implementation of the method and several details that need to be noted are discussed in the paper. Through the study of two arithmetic cases, namely, the singular regent diffusion response problem and the singular regent convection diffusion response problem, it is shown that the Chebyshev B-spline collocation method has the advantages of high accuracy and high efficiency as compared with the B-spline configuration method under equidistant nodes.展开更多
文摘双曲偏微分方程是重要的偏微分方程之一。提出求解电报方程的Chebyshev谱法,采用Chebyshev-Gauss-Lobatto配点,利用Chebyshev多项式构造导数矩阵,将电报方程近似为常微分方程,证明了电报方程的离散Chebyshev谱法的误差估计,采用Runge-Kutta进行求解。将该法得到的数值结果与精确解进行比较,验证了方法的有效性,数据结果的误差与其他方法相比有较高的精确度。Hyperbolic partial differential equation is one of the important partial differential equations. The Chebyshev spectral method is proposed to solve the telegraph equation. Chebyshev-gauss-lobatto is used to assign points, the derivative matrix is constructed by Chebyshev polynomial, and the telegraph equation is approximated as an ordinary differential equation. The error estimation of the discrete Chebyshev spectral method for the telegraph equation was proved. Runge-Kutta was used to solve the problem. The numerical results obtained by the method are compared with the exact solution, and the effectiveness of the method is verified. The error of the data results is more accurate than that of other methods.
基金supported by the National Natural Science Foundation of China(No.62371080 and 62031006)the National Science Foundation of Chongqing,China(No.CSTB2022NSCQ-MSX0597)the Venture&Innovation Support Program for Chongqing Overseas Returnees,China(No.cx2022063)。
文摘This paper presents a design method to implement an antenna array characterized by ultra-wide beam coverage,low profile,and low Sidelobe Level(SLL)for the application of Unmanned Aerial Vehicle(UAV)air-to-ground communication.The array consists of ten broadside-radiating,ultrawide-beamwidth elements that are cascaded by a central-symmetry series-fed network with tapered currents following Dolph-Chebyshev distribution to provide low SLL.First,an innovative design of end-fire Huygens source antenna that is compatible with metal ground is presented.A low-profile,half-mode Microstrip Patch Antenna(MPA)is utilized to serve as the magnetic dipole and a monopole is utilized to serves as the electric dipole,constructing the compact,end-fire,grounded Huygens source antenna.Then,two opposite-oriented end-fire Huygens source antennas are seamlessly integrated into a single antenna element in the form of monopole-loaded MPA to accomplish the ultrawide,broadside-radiating beam.Particular consideration has been applied into the design of series-fed network as well as antenna element to compensate the adverse coupling effects between elements on the radiation performance.Experiment indicates an ultrawide Half-Power Beamwidth(HPBW)of 161°and a low SLL of-25 dB with a high gain of 12 d Bi under a single-layer configuration.The concurrent ultrawide beamwidth and low SLL make it particularly attractive for applications of UAV air-to-ground communication.
文摘利用重心插值配点法求解二维定常对流扩散方程。首先介绍了两种重心插值配点法,并给出微分矩阵。其次,离散二维定常对流扩散方程以及初边值条件,利用置换法和附加法处理边界条件。采用第二类Chebyshev节点和等距节点进行数值计算,比较了两种边界条件施加方法下两种重心插值法的数值算法。数值算例表明了重心插值配点法的高精度性。The two-dimensional steady convection-diffusion equation is solved by barycentric interpolation method. Firstly, the two barycentric interpolation collocation methods are introduced, and the differential matrices are given. Secondly, the two-dimensional steady convection-diffusion equation and initial boundary conditions are dispersed, and the boundary conditions are treated by substitution and addition. Numerical calculations are carried out by using the second type of Chebyshev node and the equidistant node. Numerical examples demonstrate that this barycentric interpolation collocation method has high accuracy.
文摘Next-generation 6G networks seek to provide ultra-reliable and low-latency communications,necessitating network designs that are intelligent and adaptable.Network slicing has developed as an effective option for resource separation and service-level differentiation inside virtualized infrastructures.Nonetheless,sustaining elevated Quality of Service(QoS)in dynamic,resource-limited systems poses significant hurdles.This study introduces an innovative packet-based proactive end-to-end(ETE)resource management system that facilitates network slicing with improved resilience and proactivity.To get around the drawbacks of conventional reactive systems,we develop a cost-efficient slice provisioning architecture that takes into account limits on radio,processing,and transmission resources.The optimization issue is non-convex,NP-hard,and requires online resolution in a dynamic setting.We offer a hybrid solution that integrates an advanced Deep Reinforcement Learning(DRL)methodology with an Improved Manta-Ray Foraging Optimization(ImpMRFO)algorithm.The ImpMRFO utilizes Chebyshev chaotic mapping for the formation of a varied starting population and incorporates Lévy flight-based stochastic movement to avert premature convergence,hence facilitating improved exploration-exploitation trade-offs.The DRL model perpetually acquires optimum provisioning strategies via agent-environment interactions,whereas the ImpMRFO enhances policy performance for effective slice provisioning.The solution,developed in Python,is evaluated across several 6G slicing scenarios that include varied QoS profiles and traffic requirements.The DRL model perpetually acquires optimum provisioning methods via agent-environment interactions,while the ImpMRFO enhances policy performance for effective slice provisioning.The solution,developed in Python,is evaluated across several 6G slicing scenarios that include varied QoS profiles and traffic requirements.Experimental findings reveal that the proactive ETE system outperforms DRL models and non-resilient provisioning techniques.Our technique increases PSSRr,decreases average latency,and optimizes resource use.These results demonstrate that the hybrid architecture for robust,real-time,and scalable slice management in future 6G networks is feasible.
基金Supported by the Scientific Research Foundation for Talents Introduced of Guizhou University of Finance and Economics(Grant No.2023YJ16)the Institute of Complexity Science,Henan University of Technology(Grant No.CSKFJJ-2025-33)the International Science and Technology Cooperation Project of Henan Province(Grant No.252102520007).
文摘This paper focuses on applying the barycentric Lagrange interpolation collocation method(BLICM)for solving 2D time-fractional diffusion-wave equation(TFDWE).In order to obtain the discrete format of the equation,we construct the multivariate barycentric Lagrange interpolation approximation function and process the integral terms by using the Gauss-Legendre quadrature formula.We provide a detailed error analysis of the discrete format on the second kind of Chebyshev nodes.The efficacy of the proposed method is substantiated by some numerical experiments.The results of these experiments demonstrate that our method can obtain high-precision numerical solutions for fractional partial differential equations.Additionally,the method's capability to achieve high precision with a reduced number of nodes is confirmed.
文摘在求解奇异摄动两点边值问题时,本文构造了基于Chebyshev点的B样条配置法。该方法采用三次B样条函数作为基函数,利用Chebyshev点作为配置点直接对方程进行求解。文中探讨了该方法在实施时的具体步骤及需要注意的若干细节。通过奇异摄动扩散反应问题、奇异摄动对流扩散反应问题这两个算例的研究,表明基于Chebyshev点的B样条配置法与等距节点下的B样条配置法相比,前者具有高精度和高效率的优势。In solving the singular perturbation two-point boundary value problems, this paper constructs a Chebyshev B-spline collocation method. This method uses cubic B-spline functions as basis functions and utilizes the Chebyshev point as the configuration point to solve the equation directly. The specific steps in the implementation of the method and several details that need to be noted are discussed in the paper. Through the study of two arithmetic cases, namely, the singular regent diffusion response problem and the singular regent convection diffusion response problem, it is shown that the Chebyshev B-spline collocation method has the advantages of high accuracy and high efficiency as compared with the B-spline configuration method under equidistant nodes.
