Replicating the chaotic characteristics inherent in nonlinear dynamical systems via machine learning(ML)is a key challenge in this rapidly advancing interdisciplinary field.In this work,we explore the potential of var...Replicating the chaotic characteristics inherent in nonlinear dynamical systems via machine learning(ML)is a key challenge in this rapidly advancing interdisciplinary field.In this work,we explore the potential of variational quantum circuits(VQC)for learning the stochastic properties of classical nonlinear dynamical systems.Specifically,we focus on the one-and two-dimensional logistic maps,which,while simple,remain under-explored in the context of learning dynamical characteristics.Our findings reveal that,even for such simple dynamical systems,accurately replicating longterm characteristics is hindered by a pronounced sensitivity to overfitting.While increasing the parameter complexity of the ML model typically enhances short-term prediction accuracy,it also leads to a degradation in the model’s ability to replicate long-term characteristics,primarily due to the detrimental effects of overfitting on generalization power.By comparing the VQC with two widely recognized classical ML techniques,which are long short-term memory(LSTM)networks for timeseries processing and reservoir computing,we demonstrate that VQC outperforms these methods in terms of replicating long-term characteristics.Our results suggest that for the ML of dynamics,it is demanded to develop more compact and efficient models(such as VQC)rather than more complicated and large-scale ones.展开更多
In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of th...In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.展开更多
Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of...Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of informing the optimization of disclosure processes and meeting the communication needs of affected families.Methods In accordance with the Joanna Briggs Institute(JBI)methodology for mixed methods systematic reviews,the convergent segregated approach was used in this review.Articles were retrieved from 11 databases,including PubMed,Web of Science,CINAHL,CENTRAL,Embase,Ovid/Medline,PsycINFO,PsycArticles,Scopus,ERIC,and China National Knowledge Infrastructure(CNKI).The quality of the selected articles was assessed using the Mixed Method Appraisal Tool(MMAT).The review protocol was registered on PROSPERO(CRD42024542746).Results A total of 21 studies from 10 countries were included.Their methodological quality was generally medium to high,with MMAT scores ranging from 60%to 100%.The synthesis yielded three core themes:1)the spectrum of professional and societal attitudes toward disclosure;2)the dynamic practices of navigating disclosure amid uncertainty,including timing and environment,stakeholders,and content of disclosure;and 3)factors influencing disclosure,including children’s,parental,healthcare professionals’,and socio-cultural factors.Conclusions This review synthesized the perspectives and experiences of healthcare professionals regarding disclosure in childhood cancer,highlighting the complexity and multidimensional nature of this process in clinical practice.Future research should further investigate the experiences and needs of children and their parents,explore cultural variations in disclosure practices,develop context-appropriate assessment tools,and construct multidimensional intervention strategies to enhance the humanistic care and professional effectiveness of the disclosure process.展开更多
The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to...The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to analyze the methods of its English-to-Chinese subtitle translation by considering social,cultural,and historic backgrounds between China and America.After data collection and case analysis,the study found that:(1)Five major translation methods are adopted in the subtitle translation of The Good Wife.They are free translation,variation,literal translation,addition,and omission.Among them,free translation is the most frequently used,while omission is used least.(2)The subtitle translation of films and TV series is limited by time and space restrictions,social-cultural differences,and other factors.When translating,translators should try to use humorous words,euphemism,intonation,and other ways,and combine different methods such as literal translation,free translation,variation,addition,omission,and other methods to seek equivalence both in the meaning and function of subtitles under the guidance of Functional Equivalence Theory.展开更多
This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learnin...This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learning anxiety and the moderating role of trust.Participants were Chinese university students(N=310,62%female,mean age=18.9,SD=0.8),of whom 15 completed interviews to both add to and to clarify the evidence from the surveys.Structural equation modeling results revealed that AI use had significant indirect effects on well-being through increased motivation and reduced language learning anxiety.Trust in AI significantly moderated both paths,amplifying the motivational benefits and anxiety reduction associated with AI use.Thematic analysis supported these results,identifying three experiential themes:(1)motivational empowerment through personalization,(2)anxiety regulation through safe practice and feedback,and(3)trust as the emotional bridge between AI and well-being.The study extends AI psychology applications by empirically linking technology engagement with affective outcomes and underscores the need for human-centered and trust-enhancing design in AI-supported education.From these findings,we conclude that adaptive,transparent,and autonomy-supportive AI systems promote self-determined motivation,emotional safety,and overall psychological health among EFL learners.展开更多
Geological prospecting and the identification of adverse geological features are essential in tunnel construction,providing critical information to ensure safety and guide engineering decisions.As tunnel projects exte...Geological prospecting and the identification of adverse geological features are essential in tunnel construction,providing critical information to ensure safety and guide engineering decisions.As tunnel projects extend into deeper and more mountainous terrains,engineers face increasingly complex geological conditions,including high water pressure,intense geo-stress,elevated geothermal gradients,and active fault zones.These conditions pose substantial risks such as high-pressure water inrush,largescale collapses,and tunnel boring machine(TBM)blockages.Addressing these challenges requires advanced detection technologies capable of long-distance,high-precision,and intelligent assessments of adverse geology.This paper presents a comprehensive review of recent advancements in tunnel geological ahead prospecting methods.It summarizes the fundamental principles,technical maturity,key challenges,development trends,and real-world applications of various detection techniques.Airborne and semi-airborne geophysical methods enable large-scale reconnaissance for initial surveys in complex terrain.Tunnel-and borehole-based approaches offer high-resolution detection during excavation,including seismic ahead prospecting(SAP),TBM rock-breaking source seismic methods,fulltime-domain tunnel induced polarization(TIP),borehole electrical resistivity,and ground penetrating radar(GPR).To address scenarios involving multiple,coexisting adverse geologies,intelligent inversion and geological identification methods have been developed based on multi-source data fusion and artificial intelligence(AI)techniques.Overall,these advances significantly improve detection range,resolution,and geological characterization capabilities.The methods demonstrate strong adaptability to complex environments and provide reliable subsurface information,supporting safer and more efficient tunnel construction.展开更多
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
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
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
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
基金Project supported in part by Beijing Natural Science Foundation(Grant No.1232025)Peng Huanwu Visiting Pro-fessor Program,and Academy for Multidisciplinary Studies,Capital Normal University.
文摘Replicating the chaotic characteristics inherent in nonlinear dynamical systems via machine learning(ML)is a key challenge in this rapidly advancing interdisciplinary field.In this work,we explore the potential of variational quantum circuits(VQC)for learning the stochastic properties of classical nonlinear dynamical systems.Specifically,we focus on the one-and two-dimensional logistic maps,which,while simple,remain under-explored in the context of learning dynamical characteristics.Our findings reveal that,even for such simple dynamical systems,accurately replicating longterm characteristics is hindered by a pronounced sensitivity to overfitting.While increasing the parameter complexity of the ML model typically enhances short-term prediction accuracy,it also leads to a degradation in the model’s ability to replicate long-term characteristics,primarily due to the detrimental effects of overfitting on generalization power.By comparing the VQC with two widely recognized classical ML techniques,which are long short-term memory(LSTM)networks for timeseries processing and reservoir computing,we demonstrate that VQC outperforms these methods in terms of replicating long-term characteristics.Our results suggest that for the ML of dynamics,it is demanded to develop more compact and efficient models(such as VQC)rather than more complicated and large-scale ones.
基金supported by the NSFC(12461012)and the NSF of Chongqing(CSTB2024NSCQ-MSX1246).
文摘In this manuscript,we consider a non-autonomous dynamical system.Using the Carathéodory structure,we define a BS dimension on an arbitrary subset and obtain a Bowen’s equation that illustrates the relation of the BS dimension to the Pesin-Pitskel topological pressure given by Nazarian[24].Moreover,we establish a variational principle and an inverse variational principle for the BS dimension of non-autonomous dynamical systems.Finally,we also get an analogue of Billingsley’s theorem for the BS dimension of non-autonomous dynamical systems.
基金supported by the Fuxing Nursing Research Foundation of Fudan University[FNF202352].
文摘Objectives This review aimed to systematically synthesize the available research on the disclosure of diagnosis and related issues in childhood cancer from the perspectives of healthcare professionals,with the goal of informing the optimization of disclosure processes and meeting the communication needs of affected families.Methods In accordance with the Joanna Briggs Institute(JBI)methodology for mixed methods systematic reviews,the convergent segregated approach was used in this review.Articles were retrieved from 11 databases,including PubMed,Web of Science,CINAHL,CENTRAL,Embase,Ovid/Medline,PsycINFO,PsycArticles,Scopus,ERIC,and China National Knowledge Infrastructure(CNKI).The quality of the selected articles was assessed using the Mixed Method Appraisal Tool(MMAT).The review protocol was registered on PROSPERO(CRD42024542746).Results A total of 21 studies from 10 countries were included.Their methodological quality was generally medium to high,with MMAT scores ranging from 60%to 100%.The synthesis yielded three core themes:1)the spectrum of professional and societal attitudes toward disclosure;2)the dynamic practices of navigating disclosure amid uncertainty,including timing and environment,stakeholders,and content of disclosure;and 3)factors influencing disclosure,including children’s,parental,healthcare professionals’,and socio-cultural factors.Conclusions This review synthesized the perspectives and experiences of healthcare professionals regarding disclosure in childhood cancer,highlighting the complexity and multidimensional nature of this process in clinical practice.Future research should further investigate the experiences and needs of children and their parents,explore cultural variations in disclosure practices,develop context-appropriate assessment tools,and construct multidimensional intervention strategies to enhance the humanistic care and professional effectiveness of the disclosure process.
文摘The Good Wife is an American TV series that focuses on women’s independence,politics,and law.The drama has been remade in China,Japan,and South Korea.This research aims to use Nida’s Functional Equivalence Theory to analyze the methods of its English-to-Chinese subtitle translation by considering social,cultural,and historic backgrounds between China and America.After data collection and case analysis,the study found that:(1)Five major translation methods are adopted in the subtitle translation of The Good Wife.They are free translation,variation,literal translation,addition,and omission.Among them,free translation is the most frequently used,while omission is used least.(2)The subtitle translation of films and TV series is limited by time and space restrictions,social-cultural differences,and other factors.When translating,translators should try to use humorous words,euphemism,intonation,and other ways,and combine different methods such as literal translation,free translation,variation,addition,omission,and other methods to seek equivalence both in the meaning and function of subtitles under the guidance of Functional Equivalence Theory.
文摘This mixed-methods study investigated how AI-enhanced English as a Foreign Language(EFL)learning environments influence students’psychological well-being through the mediating roles of motivation and language learning anxiety and the moderating role of trust.Participants were Chinese university students(N=310,62%female,mean age=18.9,SD=0.8),of whom 15 completed interviews to both add to and to clarify the evidence from the surveys.Structural equation modeling results revealed that AI use had significant indirect effects on well-being through increased motivation and reduced language learning anxiety.Trust in AI significantly moderated both paths,amplifying the motivational benefits and anxiety reduction associated with AI use.Thematic analysis supported these results,identifying three experiential themes:(1)motivational empowerment through personalization,(2)anxiety regulation through safe practice and feedback,and(3)trust as the emotional bridge between AI and well-being.The study extends AI psychology applications by empirically linking technology engagement with affective outcomes and underscores the need for human-centered and trust-enhancing design in AI-supported education.From these findings,we conclude that adaptive,transparent,and autonomy-supportive AI systems promote self-determined motivation,emotional safety,and overall psychological health among EFL learners.
基金supported by the National Natural Science Foundation of China(Grant Nos.52021005,52325904,and 51991391)。
文摘Geological prospecting and the identification of adverse geological features are essential in tunnel construction,providing critical information to ensure safety and guide engineering decisions.As tunnel projects extend into deeper and more mountainous terrains,engineers face increasingly complex geological conditions,including high water pressure,intense geo-stress,elevated geothermal gradients,and active fault zones.These conditions pose substantial risks such as high-pressure water inrush,largescale collapses,and tunnel boring machine(TBM)blockages.Addressing these challenges requires advanced detection technologies capable of long-distance,high-precision,and intelligent assessments of adverse geology.This paper presents a comprehensive review of recent advancements in tunnel geological ahead prospecting methods.It summarizes the fundamental principles,technical maturity,key challenges,development trends,and real-world applications of various detection techniques.Airborne and semi-airborne geophysical methods enable large-scale reconnaissance for initial surveys in complex terrain.Tunnel-and borehole-based approaches offer high-resolution detection during excavation,including seismic ahead prospecting(SAP),TBM rock-breaking source seismic methods,fulltime-domain tunnel induced polarization(TIP),borehole electrical resistivity,and ground penetrating radar(GPR).To address scenarios involving multiple,coexisting adverse geologies,intelligent inversion and geological identification methods have been developed based on multi-source data fusion and artificial intelligence(AI)techniques.Overall,these advances significantly improve detection range,resolution,and geological characterization capabilities.The methods demonstrate strong adaptability to complex environments and provide reliable subsurface information,supporting safer and more efficient tunnel construction.
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.
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.
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.
