We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth tr...We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.展开更多
This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ...This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.展开更多
Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channe...Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channel in a fixed time slot per frame,while the other intra-frame channels are usually recovered by interpolation.However,these approaches suffer from a serious interpolation loss,especially for mobile millimeter-wave communications.To solve this challenging problem,we propose a tensor neural ordinary differential equation(TN-ODE)based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels.Specifically,inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning,we first utilize the neural ODE model to predict future continuous-time channels.To improve the channel prediction accuracy and reduce computational complexity,we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform.Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes.展开更多
The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic...The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.展开更多
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions ...An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.展开更多
In this paper,we get a necessary and sufficient condition such that a class of differential inequalities hold.Using this necessary and sufficient condition,we prove that a class of first order nonhomogeneous ordinary ...In this paper,we get a necessary and sufficient condition such that a class of differential inequalities hold.Using this necessary and sufficient condition,we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability.And then,we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions.展开更多
Cosmetic safety assessment has distinct characteristics of interdisciplinary and extensive intersection,intensive technical knowledge,and high professional requirements.China is confronted with problems such as a lack...Cosmetic safety assessment has distinct characteristics of interdisciplinary and extensive intersection,intensive technical knowledge,and high professional requirements.China is confronted with problems such as a lack of professional safety assessment personnel and review personnel for cosmetic safety assessment.The compliance of safety assessment reports has become one of the important factors affecting the process of cosmetic filing and listing.This article contains the comprehensive analysis on the requirements of relevant regulations and technical documents for cosmetic safety assessment,as well as the judgment principles,and specific requirements of safety assessment reports.The key issues in current cosmetic safety assessment and the safety assessment requirements for typical products also are being focused on,so as to help standardize and unify the review standards of cosmetic safety assessment report,and provide reference for cosmetic filers.展开更多
基金Supported by Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Au-tonomous Region(XJEDU2021Y048)Doctoral Initiation Fund of Xinjiang Institute of Engineering(2020xgy012302).
基金Natural Science Foundation of Xinjiang Uygur Autonomous Region(2021D01B35)Natural Science Foundation of colleges and universities in Xinjiang Uygur Autonomous Region(XJEDU2021Y048)。
基金partially supported by the NSFC(11971179,12371205)partially supported by the National Key R&D Program of China(2021YFA1002900)+1 种基金the Guangdong Province Basic and Applied Basic Research Fund(2021A1515010235)the Guangzhou City Basic and Applied Basic Research Fund(2024A04J6336)。
文摘We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian diffusion.We prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis methods.Moreover,we show the existence and regularity of an original solution via a compactness analysis.Finally,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.
基金supported by the National Natural Science Foundation of China(12301251,12271232)the Natural Science Foundation of Shandong Province,China(ZR2021QA038)the Scientific Research Foundation of Linyi University,China(LYDX2020BS014)。
文摘This paper is concerned with the following attraction-repulsion chemotaxis system with p-Laplacian diffusion and logistic source:■The system here is under a homogenous Neumann boundary condition in a bounded domainΩ ■ R^(n)(n≥2),with χ,ξ,α,β,γ,δ,k_(1),k_(2)> 0,p> 2.In addition,the function f is smooth and satisfies that f(s)≤κ-μs~l for all s≥0,with κ ∈ R,μ> 0,l> 1.It is shown that(ⅰ)if l> max{2k_(1),(2k_(1)n)/(2+n)+1/(p-1)},then system possesses a global bounded weak solution and(ⅱ)if k_(2)> max{2k_(1)-1,(2k_(1)n)/(2+n)+(2-p)/(p-1)} with l> 2,then system possesses a global bounded weak solution.
基金supported in part by the National Key Research and Development Program of China(Grant No.2020YFB1805005)in part by the National Natural Science Foundation of China(Grant No.62031019)in part by the European Commission through the H2020-MSCA-ITN META WIRELESS Research Project under Grant 956256。
文摘Channel prediction is critical to address the channel aging issue in mobile scenarios.Existing channel prediction techniques are mainly designed for discrete channel prediction,which can only predict the future channel in a fixed time slot per frame,while the other intra-frame channels are usually recovered by interpolation.However,these approaches suffer from a serious interpolation loss,especially for mobile millimeter-wave communications.To solve this challenging problem,we propose a tensor neural ordinary differential equation(TN-ODE)based continuous-time channel prediction scheme to realize the direct prediction of intra-frame channels.Specifically,inspired by the recently developed continuous mapping model named neural ODE in the field of machine learning,we first utilize the neural ODE model to predict future continuous-time channels.To improve the channel prediction accuracy and reduce computational complexity,we then propose the TN-ODE scheme to learn the structural characteristics of the high-dimensional channel by low-dimensional learnable transform.Simulation results show that the proposed scheme is able to achieve higher intra-frame channel prediction accuracy than existing schemes.
基金supported by the National Key R&D Program of China(2020YFA0710500).
文摘The peridynamics(PD),as a promising nonlocal continuum mechanics theory,shines in solving discontinuous problems.Up to now,various numerical methods,such as the peridynamic mesh-free particlemethod(PD-MPM),peridynamic finite element method(PD-FEM),and peridynamic boundary element method(PD-BEM),have been proposed.PD-BEM,in particular,outperforms other methods by eliminating spurious boundary softening,efficiently handling infinite problems,and ensuring high computational accuracy.However,the existing PD-BEM is constructed exclusively for bond-based peridynamics(BBPD)with fixed Poisson’s ratio,limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems.In this paper,we address these limitations by introducing the boundary element method(BEM)for ordinary state-based peridynamics(OSPD-BEM).Additionally,we present a crack propagationmodel embeddedwithin the framework ofOSPD-BEM to simulate crack propagations.To validate the effectiveness of OSPD-BEM,we conduct four numerical examples:deformation under uniaxial loading,crack initiation in a double-notched specimen,wedge-splitting test,and threepoint bending test.The results demonstrate the accuracy and efficiency of OSPD-BEM,highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson’s ratios.Moreover,OSPDBEMsignificantly reduces computational time and exhibits greater consistencywith experimental results compared to PD-MPM.
文摘An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.
基金Supported by Natural Science Research Projects of Liaoning Province Education Department(Grant No.LJ212410146024).
文摘In this paper,we get a necessary and sufficient condition such that a class of differential inequalities hold.Using this necessary and sufficient condition,we prove that a class of first order nonhomogeneous ordinary differential equations have the Hyers-Ulam stability.And then,we prove that some first order nonhomogeneous ordinary differential equations and some second order nonhomogeneous ordinary differential equations do not have the Hyers-Ulam instability under some suitable conditions.
文摘Cosmetic safety assessment has distinct characteristics of interdisciplinary and extensive intersection,intensive technical knowledge,and high professional requirements.China is confronted with problems such as a lack of professional safety assessment personnel and review personnel for cosmetic safety assessment.The compliance of safety assessment reports has become one of the important factors affecting the process of cosmetic filing and listing.This article contains the comprehensive analysis on the requirements of relevant regulations and technical documents for cosmetic safety assessment,as well as the judgment principles,and specific requirements of safety assessment reports.The key issues in current cosmetic safety assessment and the safety assessment requirements for typical products also are being focused on,so as to help standardize and unify the review standards of cosmetic safety assessment report,and provide reference for cosmetic filers.
