In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODE...This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.展开更多
The variational principle of minimum free energy(MFEVP)has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary ...The variational principle of minimum free energy(MFEVP)has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method)to find approximate solutions to these equilibrium equations.We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.展开更多
The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Und...The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility prob- lems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.展开更多
The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent m...The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.展开更多
The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The f...The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.展开更多
Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality pr...Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.展开更多
In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The p...In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.展开更多
The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and ...The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.展开更多
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti...First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.展开更多
In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regul...In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.展开更多
Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters accordi...Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.展开更多
This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress...This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.展开更多
Satellite altimetry missions at high latitude have opened new avenues for understanding the changes occurring over the ice-covered region.By incorporating Arctic satellite remote sensing data-including sea surface tem...Satellite altimetry missions at high latitude have opened new avenues for understanding the changes occurring over the ice-covered region.By incorporating Arctic satellite remote sensing data-including sea surface temperature(SST),sea surface height anomaly(SSHA),and sea surface salinity(SSS).This study employs a variational method to reconstruct the three-dimensional thermohaline structure of the Arctic Ocean.Compared to the Regional Arctic Reanalysis(RARE),the reconstruction well captures both the horizontal and vertical temperature and salinity structures in the Arctic.It demonstrates superior skill over RARE,when compared with Argo profiles and Ice-Tethered Profiler(ITP)observations.The reconstruction is particularly effective in ice-covered regions,where it more accurately captures the transition from Pacific water to Atlantic water compared to RARE.These findings underscore the potential of applying Arctic satellite data to reconstruct vertical thermohaline structures in the Arctic,particularly in areas due to lack of the subsurface observation reanalysis data exhibit significant biases.As Arctic satellite observations continue to advance,the applications of this method are becoming increasingly promising,which is useful for monitoring the ice-covered region environment and can be applied to oceanographic research.展开更多
Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents ...Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents one of the most hazardous failure modes for such structures. In this paper, the smeared stiffness method, which incorporates the effect of component torsion, is used to obtain the equivalent stiffness coefficients for composite lattice conical shells with triangular and hexagonal patterns. A unified framework based on the variational differential quadrature (VDQ) method is established, leveraging its suitability for asymptotic expansion to determine the critical buckling loads and the b-imperfection sensitivity parameter of lattice conical shells with axially varying stiffness due to rib layout. The influence of pre-buckling deformation is taken into account to enhance the accuracy of predictions on the linear buckling loads. The feasibility of the present equivalent continuum model is verified, and the differences in buckling behaviors for composite lattice conical shells with both triangular and hexagonal unit cells are numerically evaluated through the finite element (FE) simulations and the VDQ method.展开更多
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenario...In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenarios with non-Gaussian noise and heavy-tailed outliers.The proposed design modifies the extended Kalman filter(EKF)for the global navigation satellite system(GNSS),integrating the maximum correntropy criterion(MCC)and the variational Bayesian(VB)method.This adaptive algorithm effectively reduces non-line-of-sight(NLOS)reception contamination and improves estimation accuracy,particularly in time-varying GNSS measurements.Experimental results show that the proposed method significantly outperforms conventional approaches in estimation accuracy under heavy-tailed outliers and non-Gaussian noise.By combining MCC with VB approximation for real-time noise covariance estimation using fixed-point iteration,the VBMCEKF achieves superior filtering performance in challenging GNSS conditions.The method’s adaptability and precision make it ideal for improving satellite navigation performance in stochastic environments.展开更多
Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vi...Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.展开更多
Abstract Some modified Levitin Polyak projection methods are proposed in this paper for solving monotone linear variational inequalityx∈Ω,(x′-x) T(Hx+c)≤0,\ x′∈Ω.It is pointed out that there are similar methods...Abstract Some modified Levitin Polyak projection methods are proposed in this paper for solving monotone linear variational inequalityx∈Ω,(x′-x) T(Hx+c)≤0,\ x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.展开更多
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error...In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.展开更多
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
文摘This paper compares the variational iteration method(VIM),the Adomian decomposition method(ADM)and the Picard iteration method(PIM)for solving a system of first o rder n onlinear o rdinary d ifferential e quations(ODEs).A unification of the concepts underlying these three methods is attempted by considering a very general iterative algorithm for VIM.It is found that all the three methods can be regarded as special cases of using a very general matrix of Lagrange multipliers in the iterative algorithm of VIM.The global variational iteration method is briefly reviewed,and further recast into a Local VIM,which is much more convenient and capable of predicting long term complex dynamic responses of nonlinear systems even if they are chaotic.
基金supported by the National Science Foundation for Young Scientists of China(Grant No.12004082)Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme(2019),2020 Li Ka Shing Foundation Cross-Disciplinary Research(Grant No.2020LKSFG08A)+3 种基金Provincial Science Foundation of Guangdong(Grant No.2019A1515110809)Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310005)Featured Innovative Projects(Grant No.2018KTSCX282)Youth Talent Innovative Platforms(Grant No.2018KQNCX318)in Universities in Guangdong Province。
文摘The variational principle of minimum free energy(MFEVP)has been widely used in research of soft matter statics.The MFEVP can be used not only to derive equilibrium equations(including both bulk equations and boundary conditions),but also to develop direct variational methods(such as Ritz method)to find approximate solutions to these equilibrium equations.We apply these variational methods to study long-range force transmission in nonlinear elastic biopolymer gels.It is shown that the slow decay of cell-induced displacements measured experimentally for fibroblast spheroids in threedimensional fibrin gels can be well explained by variational approximations based on the three-chain model of biopolymer gels.
基金supported by the National Natural Science Foundation of China(11361070)the Natural Science Foundation of China Medical University,Taiwan
文摘The purpose of this paper is to introduce and study the split equality variational inclusion problems in the setting of Banach spaces. For solving this kind of problems, some new iterative algorithms are proposed. Under suitable conditions, some strong convergence theorems for the sequences generated by the proposed algorithm are proved. As applications, we shall utilize the results presented in the paper to study the split equality feasibility prob- lems in Banach spaces and the split equality equilibrium problem in Banach spaces. The results presented in the paper are new.
基金Project supported by the Key Science Foundation of Education Department of Sichuan Province of China (No.2003A081)Sichuan Province Leading Academic Discipline Project (No.SZD0406)
文摘The classical variational inequality problem with a Lipschitzian and strongly monotone operator on a nonempty closed convex subset in a real Hilbert space is studied. A new three-step relaxed hybrid steepest-descent method for this class of variational inequalities is introduced. Strong convergence of this method is established under suitable assumptions imposed on the algorithm parameters.
基金National Natural Science Foundations of China(No.11601143,11801160)School Level Scientific Research Project of Hunan First Normal University,China(No.XYS14N15)
文摘The author aimed to investigate the solvability for nonlinear differential equations with not instantaneous impulses.Variational approach was adopted to obtain the existence of weak solutions as critical points. The findings of this study may serve as a reference for multiplicity of impulsive problems.
基金supported by the University of KwaZulu-Natal(UKZN)Doctoral Scholarshipsupported by the National Research Foundation(NRF)South Africa(S&F-DSI/NRF Free Standing Postdoctoral Fellowship(120784)supported by the National Research Foundation(NRF)South Africa Incentive Funding for Rated Researchers(119903).
文摘Many methods have been proposed in the literature for solving the split variational inequality problem.Most of these methods either require that this problem is transformed into an equivalent variational inequality problem in a product space,or that the underlying operators are co-coercive.However,it has been discovered that such product space transformation may cause some potential difficulties during implementation and its approach may not fully exploit the attractive splitting nature of the split variational inequality problem.On the other hand,the co-coercive assumption of the underlying operators would preclude the potential applications of these methods.To avoid these setbacks,we propose two new relaxed inertial methods for solving the split variational inequality problem without any product space transformation,and for which the underlying operators are freed from the restrictive co-coercive assumption.The methods proposed,involve projections onto half-spaces only,and originate from an explicit discretization of a dynamical system,which combines both the inertial and relaxation techniques in order to achieve high convergence speed.Moreover,the sequence generated by these methods is shown to converge strongly to a minimum-norm solution of the problem in real Hilbert spaces.Furthermore,numerical implementations and comparisons are given to support our theoretical findings.
基金The author was supported by NSFC Grant 10271054MOEC grant 20020284027 and Jiangsur NSF grant BK20002075.
文摘In this paper we study the proximal point algorithm (PPA) based predictioncorrection (PC) methods for monotone variational inequalities. Each iteration of these methods consists of a prediction and a correction. The predictors are produced by inexact PPA steps. The new iterates are then updated by a correction using the PPA formula. We present two profit functions which serve two purposes: First we show that the profit functions are tight lower bounds of the improvements obtained in each iteration. Based on this conclusion we obtain the convergence inexactness restrictions for the prediction step. Second we show that the profit functions are quadratically dependent upon the step lengths, thus the optimal step lengths are obtained in the correction step. In the last part of the paper we compare the strengths of different methods based on their inexactness restrictions.
基金The NNSF (10071031) of China and National 973 Project.
文摘The finite-dimensional variational inequality problem (VIP) has been studied extensively in the literature because of its successful applications in many fields such as economics, transportation, regional science and operations research. Barker and Pang[1] have given an excellent survey of theories, methods and applications of VIPs.
文摘First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.
文摘In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y<sub>0</sub>, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.
基金supported by the Innovation Foundation of Provincial Education Department of Gansu(2024B-005)the Gansu Province National Science Foundation(22YF7GA182)the Fundamental Research Funds for the Central Universities(No.lzujbky2022-kb01)。
文摘Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.
文摘This paper presents and proves the mixed compatible finite element variationalprinciples in dynamics of viscous barotropic fluids. When the principles are proved, itis found that the compatibility conditions of stress can be naturally satisfied. The gene-rallzed variational principles with mixed hybrid incompatible finite elements are alsopresented and proved, and they can reduce the computation of incompatible elements indynamics of viscous barotropic flows.
基金The National Key R&D Program of China under contract No.2022YFE0106400the China Scholarship Council under contract No.202206710071+2 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province under contract No.KYCX23_0657the Special Founds for Creative Research under contract No.2022C61540the Opening Project of the Key Laboratory of Marine Environmental Information Technology under contract No.521037412.
文摘Satellite altimetry missions at high latitude have opened new avenues for understanding the changes occurring over the ice-covered region.By incorporating Arctic satellite remote sensing data-including sea surface temperature(SST),sea surface height anomaly(SSHA),and sea surface salinity(SSS).This study employs a variational method to reconstruct the three-dimensional thermohaline structure of the Arctic Ocean.Compared to the Regional Arctic Reanalysis(RARE),the reconstruction well captures both the horizontal and vertical temperature and salinity structures in the Arctic.It demonstrates superior skill over RARE,when compared with Argo profiles and Ice-Tethered Profiler(ITP)observations.The reconstruction is particularly effective in ice-covered regions,where it more accurately captures the transition from Pacific water to Atlantic water compared to RARE.These findings underscore the potential of applying Arctic satellite data to reconstruct vertical thermohaline structures in the Arctic,particularly in areas due to lack of the subsurface observation reanalysis data exhibit significant biases.As Arctic satellite observations continue to advance,the applications of this method are becoming increasingly promising,which is useful for monitoring the ice-covered region environment and can be applied to oceanographic research.
基金Project supported by the Shanghai Aerospace Science and Technology Innovation Foundation(No.SAST2021048)。
文摘Anisogrid composite lattice conical shells, which exhibit varying stiffness along their cone generators, are widely used as interstage structures in aerospace applications. Buckling under axial compression represents one of the most hazardous failure modes for such structures. In this paper, the smeared stiffness method, which incorporates the effect of component torsion, is used to obtain the equivalent stiffness coefficients for composite lattice conical shells with triangular and hexagonal patterns. A unified framework based on the variational differential quadrature (VDQ) method is established, leveraging its suitability for asymptotic expansion to determine the critical buckling loads and the b-imperfection sensitivity parameter of lattice conical shells with axially varying stiffness due to rib layout. The influence of pre-buckling deformation is taken into account to enhance the accuracy of predictions on the linear buckling loads. The feasibility of the present equivalent continuum model is verified, and the differences in buckling behaviors for composite lattice conical shells with both triangular and hexagonal unit cells are numerically evaluated through the finite element (FE) simulations and the VDQ method.
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金supported by the National Science and Technology Council,Taiwan under grants NSTC 111-2221-E-019-047 and NSTC 112-2221-E-019-030.
文摘In this paper,an advanced satellite navigation filter design,referred to as the Variational Bayesian Maximum Correntropy Extended Kalman Filter(VBMCEKF),is introduced to enhance robustness and adaptability in scenarios with non-Gaussian noise and heavy-tailed outliers.The proposed design modifies the extended Kalman filter(EKF)for the global navigation satellite system(GNSS),integrating the maximum correntropy criterion(MCC)and the variational Bayesian(VB)method.This adaptive algorithm effectively reduces non-line-of-sight(NLOS)reception contamination and improves estimation accuracy,particularly in time-varying GNSS measurements.Experimental results show that the proposed method significantly outperforms conventional approaches in estimation accuracy under heavy-tailed outliers and non-Gaussian noise.By combining MCC with VB approximation for real-time noise covariance estimation using fixed-point iteration,the VBMCEKF achieves superior filtering performance in challenging GNSS conditions.The method’s adaptability and precision make it ideal for improving satellite navigation performance in stochastic environments.
基金funded by the National Natural Science Foundation of China(No.41962016)the Natural Science Foundation of NingXia(Nos.2023AAC02023,2023A1218,and 2021AAC02006).
文摘Soil improvement is one of the most important issues in geotechnical engineering practice.The wide application of traditional improvement techniques(cement/chemical materials)are limited due to damage ecological en-vironment and intensify carbon emissions.However,the use of microbially induced calcium carbonate pre-cipitation(MICP)to obtain bio-cement is a novel technique with the potential to induce soil stability,providing a low-carbon,environment-friendly,and sustainable integrated solution for some geotechnical engineering pro-blems in the environment.This paper presents a comprehensive review of the latest progress in soil improvement based on the MICP strategy.It systematically summarizes and overviews the mineralization mechanism,influ-encing factors,improved methods,engineering characteristics,and current field application status of the MICP.Additionally,it also explores the limitations and correspondingly proposes prospective applications via the MICP approach for soil improvement.This review indicates that the utilization of different environmental calcium-based wastes in MICP and combination of materials and MICP are conducive to meeting engineering and market demand.Furthermore,we recommend and encourage global collaborative study and practice with a view to commercializing MICP technique in the future.The current review purports to provide insights for engineers and interdisciplinary researchers,and guidance for future engineering applications.
文摘Abstract Some modified Levitin Polyak projection methods are proposed in this paper for solving monotone linear variational inequalityx∈Ω,(x′-x) T(Hx+c)≤0,\ x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.
文摘In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation.
