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 this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with ...In this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.展开更多
In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the seri...In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.展开更多
In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarante...In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarantee that the solution exists globally in time. Finally, the infinite propagation speed of this equation is also investigated.展开更多
This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructe...This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.展开更多
The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to con...The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.展开更多
The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, ...The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.展开更多
On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node fi...On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.展开更多
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions o...By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.展开更多
For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy princi...For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.展开更多
A new dinuclear Y(3+) coordination polymer{[Y2(H2O)2(C(14)H8O4)3(C(12)H8N2)2]·3 H2O}n (1, C(14)H8 O4 = 2,2'-biphenyldicarboxylate, phen = 1,10-phenanthroline), has been obtained by means of a mi...A new dinuclear Y(3+) coordination polymer{[Y2(H2O)2(C(14)H8O4)3(C(12)H8N2)2]·3 H2O}n (1, C(14)H8 O4 = 2,2'-biphenyldicarboxylate, phen = 1,10-phenanthroline), has been obtained by means of a mixed-solvothermal method using ethylene glycol and water as solvent. The compound was characterized by elemental analysis, energy-dispersive X-ray spectroscopy(EDS), IR spectrum and single-crystal X-ray diffraction. The results reveal that 1 belongs to monoclinic system, space group C2/c with a = 24.249(3), b = 12.069(48), c = 22.7304(08) A, β = 113.480(7)°, Z = 4, V = 6102(2) A3, Dc = 1.462 g·cm^-3, F(000) = 2728, μ = 1.968 mm(-1), the final R = 0.0673, w R = 0.1508 and S = 1.085. Its structure can be regarded as a 1-D coordination polymer constructed by Y^3+ cations, 2,2A-biphenyldicarboxylate, 1,10-phenanthroline and water molecules. The compound not only contains two kinds of organic ligands, but also exhibits interesting wave-like infinite chains and 18-MR windows with the diameter of 4.070(7)A × 5.326(9)A. The structure is further stabilized by means of O–H…O hydrogen bonds and π-π stacking interactions. Furthermore, the luminescent properties(including emission spectrum, CIE chromaticity coordinate and decay curve) of 1 were also investigated in the solid-state at room temperature.展开更多
We study the following elliptic problem:{-div(a(x)Du)=Q(x)|u|2-2u+λu x∈Ω,u=0 onδΩ Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are pr...To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.展开更多
The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam.Initially,by solving the three-dimensional elastodynamic equations a general analytic solution was deri...The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam.Initially,by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam.And then for the beam with stress-free boundaries,the propagation characteristics of elastic waves were presented.This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.展开更多
Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolutio...Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.展开更多
The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,...The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,u). Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.展开更多
Recently we have suggested that the state of a single particle should be jointly defined by two wave functions.In this letter we use this suggestion to discuss the motion of a single particle in an infinitely deep squ...Recently we have suggested that the state of a single particle should be jointly defined by two wave functions.In this letter we use this suggestion to discuss the motion of a single particle in an infinitely deep square potential well;the results obiained in the classical limit correctly describe the motion of the single particle with clarity.展开更多
Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions hav...Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.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 this paper,by an approximating argument,we obtain two disjoint and infinite sets of solutions for the following elliptic equation with critical Hardy-Sobolev exponents■whereΩis a smooth bounded domain in RN with 0∈?Ωand all the principle curvatures of?Ωat 0 are negative,a∈C1(Ω,R*+),μ>0,0<s<2,1<q<2 and N>2(q+1)/(q-1).By2*:=2N/(N-2)and 2*(s):(2(N-s))/(N-2)we denote the critical Sobolev exponent and Hardy-Sobolev exponent,respectively.
文摘In this paper, we study the relationship between the convergence of the sinusoidal series and the infinity integrals (any real number α ∈[0,1], parameter p > 0). First of all, we study the convergence of the series (any real number α ∈[0,1], parameter p > 0), mainly using the estimation property of the order to obtain that the series diverges when 0 p ≤1-α, the series converges conditionally when 1-α p ≤1, and the series converges absolutely when p >1. In the next part, we study the convergence state of the infinite integral (any real number α ∈[0,1], parameter p > 0), and get that when 0 p ≤1-α, the infinite integral diverges;when 1-α p ≤1, the infinite integral conditionally converges;when p >1, the infinite integral absolutely converges. Comparison of the conclusions of the above theorem, it is not difficult to derive the theorem: the level of and the infinity integral with the convergence of the state (any real number α ∈[0,1], the parameter p >0), thus promoting the textbook of the two with the convergence of the state requires the function of the general term or the product of the function must be monotonically decreasing conditions.
文摘In this paper, we study the fifth-order Camassa-Holm equation with weakly dissipative term. We first give the local well-posedness result and the blow up criterion. Then, we establish sufficient conditions to guarantee that the solution exists globally in time. Finally, the infinite propagation speed of this equation is also investigated.
基金supported by the National Natural Science Foundation of China (Grant No.11505090)Liaocheng University Level Science and Technology Research Fund (Grant No.318012018)+2 种基金Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology (Grant No.319462208)Research Award Foundation for Outstanding Young Scientists of Shandong Province (Grant No.BS2015SF009)the Doctoral Foundation of Liaocheng University (Grant No.318051413)。
文摘This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.
基金Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2022KTSCX150)Zhaoqing Education Development Institute Project,China(No.ZQJYY2021144)Zhaoqing College Quality Project and Teaching Reform Project,China(Nos.zlgc202003 and zlgc202112)。
文摘The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.
基金Science Council Under Grant No.NSC 89-2211-E-002-020
文摘The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains. The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements, and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper, some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations. All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one.
文摘On the basis of the one-dimension infinite element theory, the coordinate translation and shape function of 3D point-radiate 8-node and 4-node infinite elements are derived. They are coupled with 20-node and 8-node finite elements to compute the compression distortion of the prestressed anchorage segment. The results indicate that when the prestressed force acts on the anchorage head and segment, the stresses and the displacements in the rock around the anchorage head and segment concentrate on the zone center with the anchor axis, and they decrease with exponential forms. Therefore,the stresses and the displacement spindles are formed. The calculating results of the infinite element are close to the theoretical results. This indicates the method is right. This article introduces a new way to study the mechanism of prestressed anchors. The obtained results have an important role in the research of the anchor mechanism and engineering application.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11462020,11262017,and 11262012)the Key Project of Inner Mongolia Normal University,China(Grant No.2014ZD03)
文摘By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal.
基金Supported by the National Natural Science Foundation of China under Grant No. 10962004the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20070126002+1 种基金the Natural Science Foundation of Inner Mongolia under Grant No. 20080404MS0104the Research Foundation for Talented Scholars of Inner Mongolia University under Grant No. 207066
文摘For the off-diagonal infinite dimensional Hamiltonian operators, which have at most countable eigenvalues, a necessary and sufficient condition of the eigenfunction systems to be complete in the sense of Cauchy principal value is presented by using the spectral symmetry and new orthogonal relationship of the operators. Moreover, the above result is extended to a more general case. At last, the completeness of eigenfunction systems for the operators arising from the isotropic plane magnetoelectroelastic solids is described to illustrate the effectiveness of the criterion. The whole results offer theoretical guarantee for separation of variables in Hamiltonian system for some mechanics equations.
基金supported by the National Natural Science Foundation of China(No.21601095)the Youth Project of Nanyang Normal University(No.QN2017065)the Opening Laboratory Project of Nanyang Normal University(No.SYKF2016075)
文摘A new dinuclear Y(3+) coordination polymer{[Y2(H2O)2(C(14)H8O4)3(C(12)H8N2)2]·3 H2O}n (1, C(14)H8 O4 = 2,2'-biphenyldicarboxylate, phen = 1,10-phenanthroline), has been obtained by means of a mixed-solvothermal method using ethylene glycol and water as solvent. The compound was characterized by elemental analysis, energy-dispersive X-ray spectroscopy(EDS), IR spectrum and single-crystal X-ray diffraction. The results reveal that 1 belongs to monoclinic system, space group C2/c with a = 24.249(3), b = 12.069(48), c = 22.7304(08) A, β = 113.480(7)°, Z = 4, V = 6102(2) A3, Dc = 1.462 g·cm^-3, F(000) = 2728, μ = 1.968 mm(-1), the final R = 0.0673, w R = 0.1508 and S = 1.085. Its structure can be regarded as a 1-D coordination polymer constructed by Y^3+ cations, 2,2A-biphenyldicarboxylate, 1,10-phenanthroline and water molecules. The compound not only contains two kinds of organic ligands, but also exhibits interesting wave-like infinite chains and 18-MR windows with the diameter of 4.070(7)A × 5.326(9)A. The structure is further stabilized by means of O–H…O hydrogen bonds and π-π stacking interactions. Furthermore, the luminescent properties(including emission spectrum, CIE chromaticity coordinate and decay curve) of 1 were also investigated in the solid-state at room temperature.
基金supported by Key Project (10631030) of NSFCKnowledge Innovation Funds of CAS in Chinasupported by ARC in Australia
文摘We study the following elliptic problem:{-div(a(x)Du)=Q(x)|u|2-2u+λu x∈Ω,u=0 onδΩ Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method.
基金supported by the National Natural Science Foundation of China(Grant No.10862003)the Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No.NJZZ07031)the Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No.2010MS0111)
文摘To construct the infinite sequence new exact solutions of nonlinear evolution equations and study the first kind of elliptic function, new solutions and the corresponding B^cklund transformation of the equation are presented. Based on this, the generalized pentavalent KdV equation and the breaking soliton equation are chosen as applicable examples and infinite sequence smooth soliton solutions, infinite sequence peak solitary wave solutions and infinite sequence compact soliton solutions are obtained with the help of symbolic computation system Mathematica. The method is of significance to search for infinite sequence new exact solutions to other nonlinear evolution equations.
文摘The Fourier series method was extended for the exact analysis of wave propagation in an infinite rectangular beam.Initially,by solving the three-dimensional elastodynamic equations a general analytic solution was derived for wave motion within the beam.And then for the beam with stress-free boundaries,the propagation characteristics of elastic waves were presented.This accurate wave propagation model lays a solid foundation of simultaneous control of coupled waves in the beam.
文摘Backlund transformation, exact solitary wave solutions, nonlinear supperposi tion formulae and infinite conserved laws are presented by using TU-pattern. The algorithm involves wide applications for nonlinear evolution equations.
文摘The existence of high energy periodic solutions for the second-order Hamiltonian system -ü(t)+A(t)u(t)=▽F(t,u(t)) with convex and concave nonlinearities is studied, where F(t, u) = F1(t,u)+F2(t,u). Under the condition that F is an even functional, infinitely many solutions for it are obtained by the variant fountain theorem. The result is a complement for some known ones in the critical point theory.
基金supported by Institute of Theoretical Physics,Academia Sinica.
文摘Recently we have suggested that the state of a single particle should be jointly defined by two wave functions.In this letter we use this suggestion to discuss the motion of a single particle in an infinitely deep square potential well;the results obiained in the classical limit correctly describe the motion of the single particle with clarity.
文摘Various kinds of Riemann boundary value problems (BVPs) for analytic functions on closed curves or on open arc, doubly periodic Riemann BVPs, doubly quasi-periodic Riemann BVPs, and BVPs for polyanalytic functions have been widely investigated in [1-8]. The main ap- proach is to use the decomposition of polyanalytic functions and their generalization to transform the boundary value problems to their corresponding boundary value problems for analytic functions. Recently, inverse Riemann BVPs for generalized analytic functions or bianalytic functions have been investigated in [9-12]. In this paper, we consider a kind of Riemann BVP of non-normal type on the infinite straight line and discuss the solvable conditions and the general solution for it.