If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t...If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.展开更多
A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are p...A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.展开更多
The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvab...The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.展开更多
The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStra...The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.展开更多
This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k ...This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].展开更多
In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A（t） satisfy Acquistapace-Terreni conditions, and with s...In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A（t） satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.展开更多
Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively...Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.展开更多
This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equatio...This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of （1＋1）-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p（x） and q（t） in our solutions, the annihilation phenomena of the fiat-basin soliton, arch-basin soliton, and fiat-top soliton are discussed.展开更多
In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.
In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKN...In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.展开更多
In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and fini...In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and finite nonsolvabie CIT-groups.展开更多
In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A clas...In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.展开更多
A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a ...A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways.展开更多
The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure.
This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integra...This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.展开更多
We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k...We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.展开更多
基金the National Natural Science Foundation of China(No.10674024)
文摘If A： D（A） X→X is a densely defined and closed linear operator, which generates a linear semigroup S （t） in Banach space X. The nonlocal control/ability for the following nonlocal semilinear problems： u＇ （t） = Au （t） ＋ Bx（ t） ＋ f（ t, u（t） ）, 0≤t ≤ T with nonlocal initial condition u（0） = u0 ＋ g（u） is discussed in Banach space X. The results show that if semigroup S（t） is strongly continuous, the functionsf and g are compact and the control B is bounded, then it is nonlocally controllable. The nonlocal controllability for the above nonlocal problem is also studied when B and W are unbounded and the semigroup S（t） is compact or strongly continuous. For illustration, a partial differential equation is worked out.
文摘A class of nonlinear and continuous type Leontief model and its corresponding conditional input-output equation are introduced, and two basic problems under the so called positive or negative boundary assumption are presented. By approaches of nonlinear analysis some solvability results of this equation and continuous perturbation properties of the relative solution sets are obtained, and some economic significance are illustrated by the remark.
文摘The two-dimensional gravity model with a coupling constant and a vanishing cosmological constant coupled to a nonlinear matter field is investigated. We found that the classical equations of motion are exactly solvable and the static solutions of the induced metric and scalar curvature can be obtained analytically. These solutions may be used to describe the naked singularity at the origin.
基金Supported in part by National Natural Science Foundation of China under Grant Nos.10605013 and 10975075 the Fundamental Research Funds for the Central Universities
文摘The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.
文摘This paper deals with a nonlinear boundary value problem for a complex equation W_z = H(Z,W,W_z),Z ∈G : |Z|<1 with boundary eondition of the form I.l-i Re[Z-W(Z)] = ψ(Z,W(Z)) + Re[λ_0+sum from k=1 to |n|-1(λ_k + iλ_k)Z^k],Z∈Γ:|z|=1 k--1 in which the index is negative. By establishing a priori estimate and using the imbdding method combined with the the Newton interation procedure, it is proved that the above problem is solvable and the solution is unique in C^l+a(g) ,O<a<].
基金Acknowledgement This article is funded by the National Natural Science Foundation of China （11161052）, Guangxi Natural Science Foundation of China （201 ljjA10044） and Guangxi Education Hall Project （201012MS183）
文摘In this paper, a class of non-autonomous functional integro-differential stochastic equations in a real separable Hilbert space is studied. When the operators A（t） satisfy Acquistapace-Terreni conditions, and with some suitable assumptions, the existence and uniqueness of a square-mean almost periodic mild solution to the equations are obtained.
基金Supported by the National Natural Science Foundation of China(61374140,61403072)
文摘Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.
基金Supported by the National Natural Science Foundation of China under Grant No.11005092the Program for Innovative Research Team of Young Teachers under Grant No.2009RC01Scientific Research,and Developed Fund under Grant No.2009FK42 of Zhejiang A&F University
文摘This paper applies the exp-function method, which was originally proposed to find new exact travelling wave solutions of nonlinear evolution equations, to the Riccati equation, and some exact solutions of this equation are obtained. Based on the Riccati equation and its exact solutions, we find new and more general variable separation solutions with two arbitrary functions of （1＋1）-dimensional coupled integrable dispersionless system. As some special examples, some new solutions can degenerate into variable separation solutions reported in open literatures. By choosing suitably two independent variables p（x） and q（t） in our solutions, the annihilation phenomena of the fiat-basin soliton, arch-basin soliton, and fiat-top soliton are discussed.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 90511009 and 40305006 Cprrespondence author,
文摘In this paper, by applying the Jacobi elliptic function expansion method, the periodic solutions for two coupled nonlinear partial differential equations are obtained.
基金Supported by the National Natural Science Foundation of China under Grant No.10926036the Education Department of Zhejiang Province under Grant No.Y200906909the Zhejiang Provincial Natural Science Foundation of China under Grant No.Y6090172
文摘In this paper, a new 7×7 matrix spectral problem, which is associated with the super AKNS equation isconstructed.With the use of the binary nonlinearization method, a new integrable decomposition of the super AKNSequation is presented.
文摘In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and finite nonsolvabie CIT-groups.
基金supported by the National Natural Science Foundation of China (No.10771173)the Zheng Ge Ru Foundation,the Hong Kong RGC Earmarked Research (Nos.CUHK4028/04P,CUHK4040/06P,CUHK4042/08P)the RGC Central Allocation (No.CA05/06.SC01)
文摘In this paper,solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary.A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11305106 and 11505154
文摘A consistent tanh expansion(CTE) method is used to study the modified Boussinesq equation. It i proved that the modified Boussinesq equation is CTE solvable. The soliton-cnoidal periodic wave is explicitly given by a nonanto-BT theorem. Furthermore, the nonlocal symmetry for the modified Boussinesq equation is obtained by th Painlev′e analysis. The nonlocal symmetry is localized to the Lie point symmetry by introducing one auxiliary dependen variable. The finite symmetry transformation related with the nonlocal symemtry is obtained by solving the initia value problem of the prolonged systems. Thanks to the localization process, many interaction solutions among soliton and other complicated waves are computed through similarity reductions. Some special concrete soliton-cnoidal wav interaction behaviors are studied both in analytical and graphical ways.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030 and 11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No. Y201017148K.C. Wong Magna Fund in Ningbo University
文摘The integrable coupling is one of the most important topics in the nonlinear physics. This paper creates a novel integrable KP coupling and solves it via a recently-developed dark parameterization procedure.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11171041 and 11505090Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No.BS2015SF009the doctorial foundation of Liaocheng University under Grant No.31805
文摘This paper is concerned with the (2+1)-dimensional Benney types of equations. By the complete Lie group classification method, all of the point symmetries of the Benney types of equations are obtained, and the integrable condition of the equation is given. Then, the symmetry reductions and exact solutions to the (2+1)-dimensional nonlinear wave equations are presented. Especially, the shock wave solutions of the Benney equations are investigated by the symmetry reduction and trial function method.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171339 and 11171261)National Center for Mathematics and Interdisciplinary Sciences
文摘We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.
