In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infin...In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.展开更多
In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic vi...In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic visiting to Central China Normal University.As early as in 2005,Huang Kaihong conducted an interview with Professor Nie Zhenzhao on the topic of the general introduction of ethical literary criticism.So around 11 years later,the second interview mainly covers not only the ethical literary criticism theory,but the game theory and the relationship between them as well.Professor Nie thinks whether the game theory can be applied to literature research is still under discussion.The theory of ethical literary criticism is a kind of methodology based on science and it can get the attention of literary critics at home and abroad,which is because it fits the practical needs of literary criticism,draws the literary criticism away from only emphasizing criticism genres and the research of criticism terms,and pays attention to the true nature of the literary text in literature research.After consulting Professor Nie Zhenzhao about some related questions from the perspective of game theory.Huang Kaihong gets some significant information concerning literature research and understands the latest core terms and the concrete application method of ethical literary criticism,especially the relationship between the instructing and aesthetic functions of literature.展开更多
In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value ...In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.展开更多
A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on th...A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.展开更多
By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deepl...By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .展开更多
As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct valu...As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct values in the future development of students.Influenced by traditional teaching ideas,students have many difficulties when learning this course,such as insufficient theoretical understanding,inadequate ability improvement,and not enough investment in course learning.In response to the above issues,this course focuses closely on the fundamental task of“cultivating virtue and nurturing people”,relying on modern information technology and introducing research methods of digital humanities.This course uses“7C”teaching mode under the“three-level integration”,in which“teaching”and“education”are carried out synchronously,and“teacher”and“student”are developed together,in order to greatly enhance students’learning participation and course satisfaction.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
In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those...In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems.Compared with the known results,this work establishes the variational structure in an appropriate Sobolev’s space.Then,by applying the mountain pass theorem and symmetric mountain pass theorem,the existence and multiplicity of the solutions are obtained.Finally,some examples with numerical simulation results are given to illustrate the correctness of the results obtained.展开更多
Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critica...Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.展开更多
In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z(t)+B(t)z(t)+f(t,z(t+τ),z(t),z(t-τ))=0.
In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point th...In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.展开更多
This paper outlines the main context of relevance theory,an inferential approach to pragmatics,which is based on a defi- nition of relevance and two principles of relevance:a Cognitive Principle(that human cognition i...This paper outlines the main context of relevance theory,an inferential approach to pragmatics,which is based on a defi- nition of relevance and two principles of relevance:a Cognitive Principle(that human cognition is geared to the maxi- mization of relevance),and a Communicative Principle(that utterances create expectations of optimal relevance).Defi- nition of relevance and the motivation for these principles will be explained,and criticisms of them will be presented re- spectively in this paper.展开更多
This paper contains a generalization of the well–known Palais–Smale andCerami compactness conditions. The compactness condition introduced is used to prove some generalexistence theorems for critical points. Some ap...This paper contains a generalization of the well–known Palais–Smale andCerami compactness conditions. The compactness condition introduced is used to prove some generalexistence theorems for critical points. Some applications are given to differential equations.展开更多
The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the sta...The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.展开更多
In this article, we prove the local wellposedness of Three-Dimensional incompressible magnetohydrodynamic system(MHD) with initial data in the critical spaces, without assumptions of small density variation.
This study offers a multifaceted perspective on the history and theory of North American urban development.It extends a framework that deconstructs the complex urban evolution process into the three stages of assembly...This study offers a multifaceted perspective on the history and theory of North American urban development.It extends a framework that deconstructs the complex urban evolution process into the three stages of assembly,disassembly,and reassembly.Urban development is explained through planning,architectural and critical theoretical perspectives.This study examines the inextricable links among land use regulations,public policies,transportation,urban economics,and communication technologies and underlines their impacts on shaping suburbia and downtown redevelopments.It argues that today’s revived traditional cores and medium-to-high-density mixed use developments are not mere incarnations of historic urban models.Despite responding to certain real-market demands for livable and vibrant urban environments,these quasi-traditional developments are driven by globalization forces and facilitated by cutting-edge technological advancements.Using combined evidence from theoretical investigations and interviews with experienced professionals,this research demonstrates the complexity and multidimensionality of urban development processes that require in-depth understanding of current global socioeconomic and technological transformations.展开更多
An existence theorem for the solution to the equation -△u+b(x)u=f(x,u),in R^N is given by means of variational method where b(x)→∞,as丨x丨→∞ and f(x,s)has linear growth in s at infinity and sublinear growth in s ...An existence theorem for the solution to the equation -△u+b(x)u=f(x,u),in R^N is given by means of variational method where b(x)→∞,as丨x丨→∞ and f(x,s)has linear growth in s at infinity and sublinear growth in s at zero.For a special case,some multiplicity result is proved.展开更多
In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonom...In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems (H) ü+A(t)u+∨V(t, u)=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.展开更多
In this paper, we study and discuss the existence of multiple solutions of a class of non–linear elliptic equations with Neumann boundary condition, and obtain at least seven non–trivial solutions in which two are p...In this paper, we study and discuss the existence of multiple solutions of a class of non–linear elliptic equations with Neumann boundary condition, and obtain at least seven non–trivial solutions in which two are positive, two are negative and three are sign–changing. The study of problem (1.1): is based on the variational methods and critical point theory. We form our conclusion by using the sub–sup solution method, Mountain Pass Theorem in order intervals, Leray–Schauder degree theory and the invariance of decreasing flow.展开更多
By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitab...By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions.展开更多
文摘In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.
文摘In 2014,Huang Kaihong,a professor at School of Foreign Languages and Cultures,Southwest University of Science and Technology,interviewed the Doctoral advisor Professor Nie Zhenzhao during the period of his academic visiting to Central China Normal University.As early as in 2005,Huang Kaihong conducted an interview with Professor Nie Zhenzhao on the topic of the general introduction of ethical literary criticism.So around 11 years later,the second interview mainly covers not only the ethical literary criticism theory,but the game theory and the relationship between them as well.Professor Nie thinks whether the game theory can be applied to literature research is still under discussion.The theory of ethical literary criticism is a kind of methodology based on science and it can get the attention of literary critics at home and abroad,which is because it fits the practical needs of literary criticism,draws the literary criticism away from only emphasizing criticism genres and the research of criticism terms,and pays attention to the true nature of the literary text in literature research.After consulting Professor Nie Zhenzhao about some related questions from the perspective of game theory.Huang Kaihong gets some significant information concerning literature research and understands the latest core terms and the concrete application method of ethical literary criticism,especially the relationship between the instructing and aesthetic functions of literature.
基金Supported by NSFC(11326127,11101335)NWNULKQN-11-23the Fundamental Research Funds for the Gansu Universities
文摘In this paper, we consider the existence of three nontrivial solutions for a discrete non-linear multiparameter periodic problem involving the p-Laplacian. By using the similar method for the Dirichlet boundary value problems in [C. Bonanno and P. Candito, Appl. Anal., 88(4) (2009), pp. 605-616], we construct two new strong maximum principles and obtain that the boundary value problem has three positive solutions for λ and μ in some suitable intervals. The approaches we use are the critical point theory.
基金Supported by the National Natural Science Foundation of China under Grant No 11275061the National Magnetic Confinement Fusion Science Program under Grant No 2014GB108002
文摘A self-organized criticality model of a thermal sandpile is formulated for the first time to simulate the dynamic process with interaction between avalanche events on the fast time scale and diffusive transports on the slow time scale. The main characteristics of the model are that both particle and energy avalanches of sand grains are considered simultaneously. Properties of intermittent transport and improved confinement are analyzed in detail. The results imply that the intermittent phenomenon such as blobs in the low confinement mode as well as edge localized modes in the high confinement mode observed in tokamak experiments are not only determined by the edge plasma physics, but also affected by the core plasma dynamics.
文摘By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed .
基金supported by Henan Province Teaching Reform and Practice Project(Project Fund No.135)—Research on the Reform of Literary Theory Courses for English Majors in Universities.
文摘As a core compulsory course for English majors majoring in teacher education,Literary Theory and Criticism plays an important role in enhancing text understanding,cultivating critical thinking,and shaping correct values in the future development of students.Influenced by traditional teaching ideas,students have many difficulties when learning this course,such as insufficient theoretical understanding,inadequate ability improvement,and not enough investment in course learning.In response to the above issues,this course focuses closely on the fundamental task of“cultivating virtue and nurturing people”,relying on modern information technology and introducing research methods of digital humanities.This course uses“7C”teaching mode under the“three-level integration”,in which“teaching”and“education”are carried out synchronously,and“teacher”and“student”are developed together,in order to greatly enhance students’learning participation and course satisfaction.
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.
基金Project supported by the National Natural Science Foundation of China(No.11571207)the Natural Science Foundation of Shandong Province of China(Nos.ZR2021MA064 and ZR2020MA017)the Taishan Scholar Project of Shandong Province of China。
文摘In this work,the solvability of a class of second-order Hamiltonian systems on time scales is generalized to non-local boundary conditions.The measurements obtained by non-local conditions are more accurate than those given by local conditions in some problems.Compared with the known results,this work establishes the variational structure in an appropriate Sobolev’s space.Then,by applying the mountain pass theorem and symmetric mountain pass theorem,the existence and multiplicity of the solutions are obtained.Finally,some examples with numerical simulation results are given to illustrate the correctness of the results obtained.
基金supported by National Natural Science Foundation of China(Grant Nos.11822102 and 11421101)supported by Beijing Academy of Artificial Intelligence(BAAI)supported by the project funded by China Postdoctoral Science Foundation(Grant No.BX201700009)。
文摘Existing critical point theories including metric and topological critical point theories are difficult to be applied directly to some concrete problems in particular polyhedral settings,because the notions of critical sets could be either very vague or too large.To overcome these difficulties,we develop the critical point theory for nonsmooth but Lipschitzian functions defined on convex polyhedrons.This yields natural extensions of classical results in the critical point theory,such as the Liusternik-Schnirelmann multiplicity theorem.More importantly,eigenvectors for some eigenvalue problems involving graph 1-Laplacian coincide with critical points of the corresponding functions on polytopes,which indicates that the critical point theory proposed in the present paper can be applied to study the nonlinear spectral graph theory.
基金supported by National Natural Science Foundation of China(51275094)by High-Level Personnel Project of Guangdong Province(2014011)by China Postdoctoral Science Foundation(20110490893)
文摘In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z(t)+B(t)z(t)+f(t,z(t+τ),z(t),z(t-τ))=0.
基金Supported by the Natural Science Foundation of Anhui Province(1408085MA02, 1208085 MA13, 1308085MA01, 1308085QA15) Supported by the Key Foundation of Anhui Education Bureau (KJ2012A019, KJ2013A028)+2 种基金 Supported by the National Natural Science Foundation of China(11271371, 11301 004) Supported by the Research Fund for the Doctoral Program of Higher Education(20113401110001) Supported by 211 Project of Anhui University(02303129, 02303303-33030011, 02303902-39020011, KYXL2012004 XJYJXKC04, yfcl00012)
文摘In this article, we investigate the existence of periodic solutions for a class of nonautonomous second-order differential systems with p(t)-Laplacian. Some multiplicity results are obtained by using critical point theory, which extend some known results.
文摘This paper outlines the main context of relevance theory,an inferential approach to pragmatics,which is based on a defi- nition of relevance and two principles of relevance:a Cognitive Principle(that human cognition is geared to the maxi- mization of relevance),and a Communicative Principle(that utterances create expectations of optimal relevance).Defi- nition of relevance and the motivation for these principles will be explained,and criticisms of them will be presented re- spectively in this paper.
文摘This paper contains a generalization of the well–known Palais–Smale andCerami compactness conditions. The compactness condition introduced is used to prove some generalexistence theorems for critical points. Some applications are given to differential equations.
文摘The description using an analytic equation of state of thermodynamic properties near the critical points of fluids and their mixtures remains a challenging problem in the area of chemical engineering. Based on the statistical associating fluid theory across the critical point (SAFT-CP), an analytic equation of state is established in this work for non-polar mixtures. With two binary parameters, this equation of state can be used to calculate not only vapor-liquid equilibria but also critical properties of binary non-polar alkane mixtures with acceptable deviations.
基金Supported by the National Natural Science Foundation of China 11331005,11201371,SRDPC20136101110015supported by the Natural Science Foundation of shaanxi province 2012JQ1020
文摘In this article, we prove the local wellposedness of Three-Dimensional incompressible magnetohydrodynamic system(MHD) with initial data in the critical spaces, without assumptions of small density variation.
文摘This study offers a multifaceted perspective on the history and theory of North American urban development.It extends a framework that deconstructs the complex urban evolution process into the three stages of assembly,disassembly,and reassembly.Urban development is explained through planning,architectural and critical theoretical perspectives.This study examines the inextricable links among land use regulations,public policies,transportation,urban economics,and communication technologies and underlines their impacts on shaping suburbia and downtown redevelopments.It argues that today’s revived traditional cores and medium-to-high-density mixed use developments are not mere incarnations of historic urban models.Despite responding to certain real-market demands for livable and vibrant urban environments,these quasi-traditional developments are driven by globalization forces and facilitated by cutting-edge technological advancements.Using combined evidence from theoretical investigations and interviews with experienced professionals,this research demonstrates the complexity and multidimensionality of urban development processes that require in-depth understanding of current global socioeconomic and technological transformations.
基金This research is supported by N.N.S.F.C.and Z.N.S.F.
文摘An existence theorem for the solution to the equation -△u+b(x)u=f(x,u),in R^N is given by means of variational method where b(x)→∞,as丨x丨→∞ and f(x,s)has linear growth in s at infinity and sublinear growth in s at zero.For a special case,some multiplicity result is proved.
基金Supported by NSFC(10471075)NSFSP(Y2003A01)NSFQN(xj0503)
文摘In this paper, we develop the local linking theorem given by Li and Willein by replacing the Palais-Smale condition with a Cerami one, and apply it to the study of the existence of periodic solutions of the nonautonomous second order Hamiltonian systems (H) ü+A(t)u+∨V(t, u)=0, u∈R^N, t∈R. We handle the case of superquadratic nonlinearities which differ from those used previously. Our results extend the theorems given by Li and Willem.
文摘In this paper, we study and discuss the existence of multiple solutions of a class of non–linear elliptic equations with Neumann boundary condition, and obtain at least seven non–trivial solutions in which two are positive, two are negative and three are sign–changing. The study of problem (1.1): is based on the variational methods and critical point theory. We form our conclusion by using the sub–sup solution method, Mountain Pass Theorem in order intervals, Leray–Schauder degree theory and the invariance of decreasing flow.
基金supported by the National Natural Science Foundation of China(11161049)
文摘By establishing the corresponding variational framework, and using critical point theory, we give the existence of multiple solutions to a fractional difference boundary value problem with parameter. Under some suitable assumptions we obtain some results which ensure the existence of well precise interval of parameter for which the problem admits multiple solutions.