In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displa...In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.展开更多
In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutio...In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.展开更多
In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρ...In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.展开更多
A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into...A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.展开更多
In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operato...In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.展开更多
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce...In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.展开更多
Discriminative region localization and efficient feature encoding are crucial for fine-grained object recognition.However,existing data augmentation methods struggle to accurately locate discriminative regions in comp...Discriminative region localization and efficient feature encoding are crucial for fine-grained object recognition.However,existing data augmentation methods struggle to accurately locate discriminative regions in complex backgrounds,small target objects,and limited training data,leading to poor recognition.Fine-grained images exhibit“small inter-class differences,”and while second-order feature encoding enhances discrimination,it often requires dual Convolutional Neural Networks(CNN),increasing training time and complexity.This study proposes a model integrating discriminative region localization and efficient second-order feature encoding.By ranking feature map channels via a fully connected layer,it selects high-importance channels to generate an enhanced map,accurately locating discriminative regions.Cropping and erasing augmentations further refine recognition.To improve efficiency,a novel second-order feature encoding module generates an attention map from the fourth convolutional group of Residual Network 50 layers(ResNet-50)and multiplies it with features from the fifth group,producing second-order features while reducing dimensionality and training time.Experiments on Caltech-University of California,San Diego Birds-200-2011(CUB-200-2011),Stanford Car,and Fine-Grained Visual Classification of Aircraft(FGVC Aircraft)datasets show state-of-the-art accuracy of 88.9%,94.7%,and 93.3%,respectively.展开更多
Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challeng...Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.展开更多
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The...This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.展开更多
The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futurist...The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futuristic,are quickly transitioning from strategic concepts to large-scale manufacturing industries.These sectors now drive China’s high-quality development and support a new framework for international engagement.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
New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the cond...New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.展开更多
By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations ...By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.展开更多
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ...The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.展开更多
The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit.The fractional calculus in the constitutive relationship of a non-Newtonian fluid is...The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit.The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced.We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform.The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.展开更多
In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the ...In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the form of -u = f(t, u, v) -v = g(t, u, v) u(0) = u(1) = 0 v(0) = v(1) = 0 in abstract space. Moreover, it is obtained unique solutions for system of equations and error estimations between approximation iteration sequence and exact solution under more simpler conditions. Therefore, some new results which extend and improve the related known works in the literatures are obtained.展开更多
In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and ...This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.展开更多
文摘In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.
基金supported by the Natural Science Foundation of Inner Mongolia,China (Grant No 200711020116)Open Fund of the Key Laboratory of Ocean Circulation and Waves,Chinese Academy of Sciences (Grant No KLOCAW0805)+1 种基金the Key Program of the Scientific Research Plan of Inner Mongolia University of Technology,China (Grant No ZD200608)the National Science Fund for Distinguished Young Scholars of China (Grant No 40425015)
文摘In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.
基金supported by the Technological Innovation Talents in Universities and Colleges in Henan Province(No.21HASTIT025)the Natural Science Foundation of Henan Province(No.222300420449)the Innovative Research Team of Henan Polytechnic University(No.T2022-7)。
文摘In this paper,we provide new sufficient conditions for the existence of positive periodic solutions for a class of indefinite singular differential equation x′′(t)+a(t)x(t)=h(t)/x^(ρ)(t)+g(t)x^(δ)(t)+e(t),whereρandδare two positive constants and 0<δ≤1,h,e∈L^(1)(R/TZ),g∈L^(1)(R/TZ)is positive.Our proofs are based on the fixed point theorems(Schauder’s fixed point theorem and Krasnoselskii-Guo fixed point theorem)and the positivity of the associated Green function.
基金supported by the National Science Foundation for Distinguished Young Scholars of China under contract No.40425015the Cooperative Project of Chinese Academy Sciences and the China National 0ffshore 0il Corporation("Behaviours of internal waves and their roles on the marine stuctures").
文摘A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.
文摘In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.
基金Supported by the Doctoral Research Start-up Project of Yuncheng University(YQ-2023067)Project of Shanxi Natural Science Foundation(202303021211189)+1 种基金Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Provinces(20220036)Shanxi ProvinceIntelligent Optoelectronic Sensing Application Technology Innovation Center and Shanxi Province Optoelectronic Information Science and TechnologyLaboratory,Yuncheng University.
文摘In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.
基金supported,in part,by the National Nature Science Foundation of China under Grant 62272236,62376128 and 62306139the Natural Science Foundation of Jiangsu Province under Grant BK20201136,BK20191401.
文摘Discriminative region localization and efficient feature encoding are crucial for fine-grained object recognition.However,existing data augmentation methods struggle to accurately locate discriminative regions in complex backgrounds,small target objects,and limited training data,leading to poor recognition.Fine-grained images exhibit“small inter-class differences,”and while second-order feature encoding enhances discrimination,it often requires dual Convolutional Neural Networks(CNN),increasing training time and complexity.This study proposes a model integrating discriminative region localization and efficient second-order feature encoding.By ranking feature map channels via a fully connected layer,it selects high-importance channels to generate an enhanced map,accurately locating discriminative regions.Cropping and erasing augmentations further refine recognition.To improve efficiency,a novel second-order feature encoding module generates an attention map from the fourth convolutional group of Residual Network 50 layers(ResNet-50)and multiplies it with features from the fifth group,producing second-order features while reducing dimensionality and training time.Experiments on Caltech-University of California,San Diego Birds-200-2011(CUB-200-2011),Stanford Car,and Fine-Grained Visual Classification of Aircraft(FGVC Aircraft)datasets show state-of-the-art accuracy of 88.9%,94.7%,and 93.3%,respectively.
基金Supported by National Natural Science Foundation of China(Grant No.62173161).
文摘Let A be a 3×3 singular or diagonalizable matrix,all solutions to the Yang-Baxter-like matrix equation have been determined.However,finding all solutions for full rank,non-diagonalizable matrices remains challenging.By utilizing classification techniques,we establish all solutions of the Yang-Baxter-like matrix equation in this paper when the coefficient matrix A is similar to non-diagonalizable matrix diag(λ,J_(2)(λ))withλ̸=0.More specifically,we divide the non-diagonal elements of the solution into 10 different cases.By discussing each situation,we establish all solutions of the Yang-Baxter-like matrix equation.The results of this work enrich the existing ones.
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
基金Project supported by the National Science Fund for Distinguished Young Scholars （Grant No 40425015）, the Cooperative Project of Chinese Academy Sciences and the China National 0ffshore oil Corporation （＂Behaviours of internal waves and their roles on the marine structures＂） and the National Natural Science Foundation of China （Grant No10461005）.
文摘This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.
文摘The 15th Five-Year Plan will begin in 2026,amid heightened global technological competition and rapid supply chain changes.At this pivotal moment,the low-altitude economy and commercial aerospace,once seen as futuristic,are quickly transitioning from strategic concepts to large-scale manufacturing industries.These sectors now drive China’s high-quality development and support a new framework for international engagement.
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.
文摘New existence results are presented for the singular second-order nonlinear boundary value problems u ' + g(t)f(u) = 0, 0 < t < 1, au(0) - betau ' (0) = 0, gammau(1) + deltau ' (1) = 0 under the conditions 0 less than or equal to f(0)(+) < M-1, m(1) < f(infinity)(-)less than or equal to infinity or 0 less than or equal to f(infinity)(+)< M-1, m(1) < f (-)(0)less than or equal to infinity where f(0)(+) = lim(u -->0)f(u)/u, f(infinity)(-)= lim(u --> infinity)f(u)/u, f(0)(-)= lim(u -->0)f(u)/u, f(infinity)(+) = lim(u --> infinity)f(u)/u, g may be singular at t = 0 and/or t = 1. The proof uses a fixed point theorem in cone theory.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the MSnch fixed theorem combined with a monotone iterative technique, we investigate the existence of positive solutions for systems of second- order nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions. The results in this paper improve some known results.
基金Supported by the National Natural Science Foundation of China(11101096 )Guangdong Natural Science Foundation (S2012010010376, S201204006711)
文摘The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.
文摘The exact solutions are obtained for unsteady unidirectional flows of a generalized second-order fluid through a rectangular conduit.The fractional calculus in the constitutive relationship of a non-Newtonian fluid is introduced.We construct the solutions by means of Fourier transform and the discrete Laplace transform of the sequential derivatives and the double finite Fourier transform.The solutions for Newtonian fluid between two infinite parallel plates appear as limiting cases of our solutions.
文摘In this paper, it is discussed by using cone and upper and lower solutions mono- tone iterative theory of mixed monotone operator that the bounary value problem is more generalized style to system of equations in the form of -u = f(t, u, v) -v = g(t, u, v) u(0) = u(1) = 0 v(0) = v(1) = 0 in abstract space. Moreover, it is obtained unique solutions for system of equations and error estimations between approximation iteration sequence and exact solution under more simpler conditions. Therefore, some new results which extend and improve the related known works in the literatures are obtained.
基金Supported by the NNSF of China(10871116)Supported by the NSFSP of China(ZR2010AM005)
文摘In this paper,we are concerned with the existence of multiple positive solutions to a second-order three-point boundary value problem on the half-line.The results are obtained by the Leggett-Williams fixed point theorem.
基金supported by the NNSF of China(10671064)the second author was supported by the Australian Research Council's Discovery Projects(DP0450752)
文摘This article considers the Dirichlet problem of homogeneous and inhomogeneous second-order ordinary differential systems. A nondegeneracy result is proven for positive solutions of homogeneous systems. Sufficient and necessary conditions for the existence of multiple positive solutions for inhomogeneous systems are obtained by making use of the nondegeneracy and uniqueness results of homogeneous systems.
