Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was...Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.展开更多
In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are establishe...In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.展开更多
In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficien...In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.展开更多
In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theore...In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.展开更多
The adjusted GPS height is the height above the surface of the WGS-84ellipsoid. It is necessary to convert a GPS height into a normal height in engineering. The conicoidfitting method (CFM) and the neural networks met...The adjusted GPS height is the height above the surface of the WGS-84ellipsoid. It is necessary to convert a GPS height into a normal height in engineering. The conicoidfitting method (CFM) and the neural networks method (NNM) are used for this purpose, but each ofthem has its advantages and disadvantages. After studying these two methods, a new method (abbr.CF&NNM) is conceived. The procedure of the CF&NNM is introduced. A practical engineering example isused to study these three different methods. The results by the three methods are listed. The CF&NNMmethod can produce better results than either the CFM or the NNM in deriving normal height from GPSheight. The theory of the CF&NNM method is analyzed.展开更多
In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvatu...In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.展开更多
A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square ...A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.展开更多
The cross-sectional distortion usually appears during rotary-draw bending process of thin-walled rectangular tube with small bending radius.To study the cross-sectional distortion of the tube,a three-dimensional finit...The cross-sectional distortion usually appears during rotary-draw bending process of thin-walled rectangular tube with small bending radius.To study the cross-sectional distortion of the tube,a three-dimensional finite-element model of the process was developed based on ABAQUS/Explicit code and its reliability was validated by experiment.Then,the cross-sectional distortion behaviors of the tube were investigated.The results show that a zone of larger circumferential stress appears on the tube when bending angle reaches 30°.And in the larger circumferential stress zone,the sagging phenomenon is produced obviously.The maximum cross-sectional distortion is located in the larger circumferential stress zone and the angle between the plane of maximum cross-sectional distortion and the bending reference plane is about 50°.The position of the maximum cross-sectional distortion keeps almost unchanged with the variation of the clearances between dies and tube.展开更多
The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-di...The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.展开更多
Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, it...Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.展开更多
Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of ...Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of the simulation indicate that the WBC is prone to penetrating into the gap under northerly winds, and its path is more difficult to alter due to the larger interval between the two critical transition curves (C1P and C1L). For southerly winds, the WBC is prone to leaping across the gap, and its path is easier to alter due to the smaller interval between the two critical transition curves. The simulation results also indicate that the meridional winds over the southern region of the gap are the dominant factor determining the formation of the WBC. The dynamic mechanism influencing the transport of WBC near the gap is both Ekman transport and the blocking of Ekman transport. Ekman transport induced by northerly winds may reduce the transport of the WBC, causing the β-effect to dominate the meridional advection (promoting the penetration). Southerly winds, however, may enhance the transport of the WBC, causing the meridional advection to dominate the β-effect (promoting the leaping state). These results explain some structural features of the Kuroshio at the Luzon Strait.展开更多
The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal...The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .展开更多
Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equati...Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.展开更多
Gradation equation is one way to describe the gradation of coarse-grained soil conveniently,exactly and quantitatively.With the gradation equation,the influence of gradation on the mechanical behaviors of coarse-grain...Gradation equation is one way to describe the gradation of coarse-grained soil conveniently,exactly and quantitatively.With the gradation equation,the influence of gradation on the mechanical behaviors of coarse-grained soil can be expressed quantitatively.A new gradation equation with a parameter is proposed.The basic properties and applicability of the new equation are studied.The results show that the proposed equation has the applicability to express coarse-grained soil gradation(CSG),and the range of the parameter β is found to be 0<β<1.The value ofbdetermines the gradation curve shape.If β>0.5,the gradation curve is sigmoidal,otherwise the gradation curve is hyperbolic.For well graded gradations,the parameter has the value of 0.13<β<1.Several CSGs used in domestic and foreign earth-rockfill dams are probed,and the value of the parameterbfalls in the range of 0.18 to 0.97.The investigation of the range of β is of value to guide the design for CSG of earth-rockfill dam.展开更多
In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience ...In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.展开更多
A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations...A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.展开更多
In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesse...In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate' and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.展开更多
To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of t...To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.展开更多
文摘Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.
文摘In this paper, oscillatory properties of solutions of certain nonlinear hyperbolic partial differential equations are investigated and a series of sufficient conditions for oscillations of the equations are established. The results fully indicate that the oscillations are caused by delay.
文摘In this paper, the existence and uniqueness of the local generalized solution of the initial boundary value problem for a nonlinear hyperbolic equation are proved by the contraction mapping principle and the sufficient conditions of blow_up of the solution in finite time are given.
文摘In this paper, we study a class singular perturbed elliptic equation boundary value problem with a super surface of turning point in n-dimensional space by using the method of multiple scales and the comparison theorem. The uniformly valid asymptotic approxmations of solutions for the boundary value problem is constructed.
文摘The adjusted GPS height is the height above the surface of the WGS-84ellipsoid. It is necessary to convert a GPS height into a normal height in engineering. The conicoidfitting method (CFM) and the neural networks method (NNM) are used for this purpose, but each ofthem has its advantages and disadvantages. After studying these two methods, a new method (abbr.CF&NNM) is conceived. The procedure of the CF&NNM is introduced. A practical engineering example isused to study these three different methods. The results by the three methods are listed. The CF&NNMmethod can produce better results than either the CFM or the NNM in deriving normal height from GPSheight. The theory of the CF&NNM method is analyzed.
文摘In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.
文摘A rational equation of state of the perturbation type with a repulsion and attraction term has been applied to reproduce critical curves of six different binary systems up to high temperatures and pressures. A square well potential for intermolecular interaction is used. With pairwise combination rules for these potentials three adjustable parameters are needed. The experimental critical point and phase equilibrium data are compared with the values predicted using the equation of state. Good agreement is obtained for the analysis of the critical pressure composition data and molar volumes.
基金Projects(50575184,50975235) supported by the National Natural Science Foundation of ChinaProject(YF07057) supported by Science and Technology Development Program of Xi'an City,Shaanxi Province,China+1 种基金Project(NPU-FFR-200809) supported by Foundation for Fundamental Research of Northwestern Polytechnical University,ChinaProject(08-3) supported by State Key Laboratory of Materials Processing and Die & Mould Technology,Huazhong University of Science and Technology,China
文摘The cross-sectional distortion usually appears during rotary-draw bending process of thin-walled rectangular tube with small bending radius.To study the cross-sectional distortion of the tube,a three-dimensional finite-element model of the process was developed based on ABAQUS/Explicit code and its reliability was validated by experiment.Then,the cross-sectional distortion behaviors of the tube were investigated.The results show that a zone of larger circumferential stress appears on the tube when bending angle reaches 30°.And in the larger circumferential stress zone,the sagging phenomenon is produced obviously.The maximum cross-sectional distortion is located in the larger circumferential stress zone and the angle between the plane of maximum cross-sectional distortion and the bending reference plane is about 50°.The position of the maximum cross-sectional distortion keeps almost unchanged with the variation of the clearances between dies and tube.
基金supported by National Natural Science Foundation of China under Grant No.10562002Natural Science Foundation of Inner Mongolia under Grant Nos.200508010103 and 200711020106
文摘The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.
基金*Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, the Natural Science Foundation of Shanghai urlder Grant No. 09ZR1410800, the Shanghai Leading Academic Discipline Project under Grant No. J50101, and the National Key Basic Research Project of China under Grant No. KLMM0806
文摘Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (Nos. KZCX1-YW-12, KZCX2-YW-201)the National Natural Science Foundation of China (No. 90411013)+2 种基金the National Basic Research Program of China (973 Program, No. 2006CB403600)NSFC's Outstanding Youth Grant (No. 40888001)the 100-Talent Program of the CAS, and the Outstanding Youth Grant of Shandong Province
文摘Using a 1.5-layer reduced-gravity nonlinear shallow-water equation model, we studied the effect of the meridional wind on the western boundary currents (WBC) at critical states with hysteresis courses. The results of the simulation indicate that the WBC is prone to penetrating into the gap under northerly winds, and its path is more difficult to alter due to the larger interval between the two critical transition curves (C1P and C1L). For southerly winds, the WBC is prone to leaping across the gap, and its path is easier to alter due to the smaller interval between the two critical transition curves. The simulation results also indicate that the meridional winds over the southern region of the gap are the dominant factor determining the formation of the WBC. The dynamic mechanism influencing the transport of WBC near the gap is both Ekman transport and the blocking of Ekman transport. Ekman transport induced by northerly winds may reduce the transport of the WBC, causing the β-effect to dominate the meridional advection (promoting the penetration). Southerly winds, however, may enhance the transport of the WBC, causing the meridional advection to dominate the β-effect (promoting the leaping state). These results explain some structural features of the Kuroshio at the Luzon Strait.
基金Project(2006BAJ01B02)supported by the National Science and Technology Pillar Program during the Eleventh Five-Year Plan Period of China
文摘The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .
文摘Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
基金Project(2018YFC1508505)supported by the National Key Research and Development Program of ChinaProject(U1865104)supported by Yalong River Joint Fund of Natural Science Foundation of China-Yalong River Basin Hydropower Development Co.,Ltd.,China+1 种基金Project(51479052)supported by National Natural Science of ChinaProject(2019T120443)supported by China Postdoctoral Science Foundation。
文摘Gradation equation is one way to describe the gradation of coarse-grained soil conveniently,exactly and quantitatively.With the gradation equation,the influence of gradation on the mechanical behaviors of coarse-grained soil can be expressed quantitatively.A new gradation equation with a parameter is proposed.The basic properties and applicability of the new equation are studied.The results show that the proposed equation has the applicability to express coarse-grained soil gradation(CSG),and the range of the parameter β is found to be 0<β<1.The value ofbdetermines the gradation curve shape.If β>0.5,the gradation curve is sigmoidal,otherwise the gradation curve is hyperbolic.For well graded gradations,the parameter has the value of 0.13<β<1.Several CSGs used in domestic and foreign earth-rockfill dams are probed,and the value of the parameterbfalls in the range of 0.18 to 0.97.The investigation of the range of β is of value to guide the design for CSG of earth-rockfill dam.
文摘In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatie surface through their experience to analyze the stability, which is unsafe in the project. To find a solution of the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratios and achieves an analytic solution equation through fitting curves. The correctness of the equation is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.
基金supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.
基金Projects(2012CB619505,2010CB731703)supported by the National Basic Research Program of ChinaProject(CX2013B065)supported by Hunan Provincial Innovation Foundation for Postgraduate,China+1 种基金Project(51405520)supported by the National Natural Science Foundation of ChinaProject(zzyjkt2013-06B)supported by the State Key Laboratory of High Performance Complex Manufacturing(Central South University),China
文摘In order to study the bending behavior of aluminum alloy 7050 thick plate during snake hot rolling, several coupled thermo-mechanical finite element(FE) models were established. Effects of different initial thicknesses, pass reductions, speed ratios and offset distances on the bending value of the plate were analyzed. ‘Quasi smooth plate' and optimum offset distance were defined and quasi smooth plate could be acquired by adjusting offset distance, and then bending control equation was fitted. The results show that bending value of the plate as well as the extent of the increase grows with the increase of pass reduction and decrease of initial thickness; the bending value firstly increases and then keeps steady with the ascending speed ratio; the bending value can be reduced by enlarging the offset distance. The optimum offset distance varies for different rolling parameters and it is augmented with the increase of pass reduction and speed ratio and the decrease of initial thickness. A proper offset distance for different rolling parameters can be calculated by the bending control equation and this equation can be a guidance to acquire a quasi smooth plate. The FEM results agree well with experimental results.
基金Supported by the National Natural Science Foundation of China under Grant No.10971031
文摘To extend the study scopes of integrable couplings, the notion of double integrable couplings is proposed in the paper. The zero curvature equation appearing in the constructing method built in the paper consists of the elements of a new loop algebra which is obtained by using perturbation method. Therefore, the approach given in the paper has extensive applicable values, that is, it applies to investigate a lot of double integrable couplings of the known integrable hierarchies of evolution equations. As for explicit applications of the method proposed in the paper, the double integrable couplings of the AKNS hierarchy and the KN hierarchy are worked out, respectively.