In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries(SKd V)equations.These solutions are characterized by trigonometric functions as backgrounds.For the discrete SKd V equ...In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries(SKd V)equations.These solutions are characterized by trigonometric functions as backgrounds.For the discrete SKd V equation,its solutions are derived by using trigonometric function seeds and B?cklund transformation.Solutions for the continuous SKd V equation are obtained by taking continuum limits.展开更多
In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with ...In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.展开更多
The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic...The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic solutions of hyper-order strictly less than 1 to the Fermat-type functional equation(a0f(z)+a1f(z+c))^(3)+(b0f(z)+b1f(z+c))3=e^(αz+β),where a0,a1,b0,b1,α,β,c are complex constants and c≠0.展开更多
The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long...The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long derivatives V_(x),V_(y),V_(t).Two different constraints on the kernel function K are introduced under the reality of the solution u of the 2DG equation.Then,two classes of exact solutions with constant asymptotic values at infinity u|x^(2)+y^(2)→∞→0 are constructed by means of the∂¯-dressing method for the casesσ=1 andσ=i.The rational and multiple pole solutions of the 2DG equation are obtained with the kernel functions of zero-order and higher-order Dirac delta functions,respectively.展开更多
In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved ...In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.展开更多
In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the e...In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.展开更多
In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as...In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.展开更多
[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a cont...[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.展开更多
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a...This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.展开更多
Molecular dynamics simulations were carried out to study the configuration energy and radial distribution functions of mmonium dihydrogen phosphate solution at different temperatures. The dihydrogen phosphate ion was ...Molecular dynamics simulations were carried out to study the configuration energy and radial distribution functions of mmonium dihydrogen phosphate solution at different temperatures. The dihydrogen phosphate ion was treated as a seven-site model and the ammonium ion was regarded as a five-site model, while a simple-point-charge model for water molecule. An unusually local particle number density fluctuation was observed in the system at saturation temperature. It can be found that the potential energy increases slowly with the temperature from 373 K to 404 K, which indicates that the ammonium dihydrogen phosphate has partly decomposed. The radial distribution function between the hydrogen atom of ammonium cation and the oxygen atom of dihydrogen phosphate ion at three different temperatures shows obvious difference, which indicates that the average H-bond number changes obviously with the temperature. The temperature has an influence on the combination between hydrogen atoms and phosphorus atoms of dihydrogen phosphate ion and there are much more growth units at saturated solutions.展开更多
The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are ...The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.展开更多
The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold s...The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold showed that gel Amberlite IRA-400 resin with Type Ⅰ quaternary ammonium functional group had better adsorption performance.The increases of resin dosage,ammonia concentration and solution pH were favorable to gold adsorption,whereas the rises of cupric and thiosulfate concentrations were disadvantageous to gold loading.Microscopic characterization results indicated that gold was adsorbed in the form of [Au(S_(2)O_(3))_(2)]^(3–) complex anion by exchanging with the counter ion Cl^(–) in the functional group of the resin.Density functional theory calculation result manifested that gold adsorption was mainly depended on the hydrogen bond and van der Waals force generated between O atom in [Au(S_(2)O_(3))_(2)]^(3–) and H atom in the quaternary ammonium functional group of the resin.展开更多
A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions o...A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.展开更多
We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex dif...We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.展开更多
Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollo...Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.展开更多
In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning ...In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.展开更多
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(...By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].展开更多
A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problem...A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.展开更多
This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
基金supported by the NSF of China(Grant No.12271334)。
文摘In the paper we derive new solutions for the discrete and continuous Schwarzian Korteweg–de Vries(SKd V)equations.These solutions are characterized by trigonometric functions as backgrounds.For the discrete SKd V equation,its solutions are derived by using trigonometric function seeds and B?cklund transformation.Solutions for the continuous SKd V equation are obtained by taking continuum limits.
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.
基金Supported by the National Natural Science Foundation of China(Grant No.11971344)。
文摘The functional equation f(z)^n+g(z)^n=1 can be interpreted as the Fermat-type equations over function field.In this paper,by using Nevanlinna theory of meromorphic functions,we investigate the existence of meromorphic solutions of hyper-order strictly less than 1 to the Fermat-type functional equation(a0f(z)+a1f(z+c))^(3)+(b0f(z)+b1f(z+c))3=e^(αz+β),where a0,a1,b0,b1,α,β,c are complex constants and c≠0.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1237125611971475)。
文摘The(2+1)-dimensional integrable generalization of the Gardner(2DG)equation is solved via the inverse scattering transform method in this paper.A kind of general solution of the equation is obtained by introducing long derivatives V_(x),V_(y),V_(t).Two different constraints on the kernel function K are introduced under the reality of the solution u of the 2DG equation.Then,two classes of exact solutions with constant asymptotic values at infinity u|x^(2)+y^(2)→∞→0 are constructed by means of the∂¯-dressing method for the casesσ=1 andσ=i.The rational and multiple pole solutions of the 2DG equation are obtained with the kernel functions of zero-order and higher-order Dirac delta functions,respectively.
文摘In this article,several kinds of novel exact waves solutions of three well-known different space-time fractional nonlinear coupled waves dynamical models are constructed with the aid of simpler and effective improved auxiliary equation method.Firstly we will investigate space-time fractional coupled Boussinesq-Burger dynamical model,which is used to model the propagation of water waves in shallow sea and harbor,and has many applications in ocean engineering.Secondly,we will investigate the space-time fractional coupled Drinfeld-SokolovWilson equation which is used to characterize the nonlinear surface gravity waves propagation over horizontal seabed.Thirdly,we will investigate the space-time-space fractional coupled Whitham-Broer-Kaup equation which is used to model the shallow water waves in a porous medium near a dam.We obtained different solutions in terms of trigonometric,hyperbolic,exponential and Jacobi elliptic functions.Furthermore,graphics are plotted to explain the different novel structures of obtained solutions such as multi solitons interaction,periodic soliton,bright and dark solitons,Kink and anti-Kink solitons,breather-type waves and so on,which have applications in ocean engineering,fluid mechanics and other related fields.We hope that our results obtained in this article will be useful to understand many novel physical phenomena in applied sciences and other related fields.
基金Supported by the National Natural Science Foundation of China(11226337)the Science and Technology Research Projects of Henan Education Committee(22B110017).
文摘In this paper,we study the existence of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations in Banach spaces.By using the principle of Banach contractive mapping,the existence and uniqueness of pseudo S-asymptotically ω-periodic mild solutions of abstract partial neutral differential equations are obtained.To illustrate the ab-stract result,a concrete example is given.
基金Supported by the Innovation Platform Open Fund in Hunan Province Colleges and Universities of China(201485).
文摘In this paper,a class of quaternion-valued cellular neural networks(QVCNNS)with time-varying delays are considered.Combining graph theory with the continuation theorem of Mawhin’s coincidence degree theory as well as Lyapunov functional method,we establish new criteria on the existence and exponential stability of periodic solutions for QVCNNS by removing the assumptions for the boundedness on the activation functions and the assumptions that the values of the activation functions are zero at origin.Hence,our results are less conservative and new.
文摘[Objectives]To observe the effect of Shuanghuanglian oral solution on liver function in BABL/cJ mice in non-alcoholic steatohepatitis(NASH)model.[Methods]The BABL/cJ mice were randomly divided into three groups:a control group,a model group,and an experimental group.The experimental group was administered with 10%Shuanghuanglian oral solution at a dose of 0.1 mL/(10 g·d),while the control group and experimental group received an equivalent dosage of normal saline.All three groups were treated for a period of 28 d.The liver function of the mice in each group was examined after the treatment.[Results]The body mass,liver index,triacylglycerol(TG),total cholesterol(TC),aspartate aminotransferase(AST),and alanine aminotransferase(ALT)levels were all significantly reduced compared to the model group(P<0.05).[Conclusions]Shuanghuanglian oral solution has a beneficial effect on liver function in BABL/cJ mice.
文摘This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.
文摘Molecular dynamics simulations were carried out to study the configuration energy and radial distribution functions of mmonium dihydrogen phosphate solution at different temperatures. The dihydrogen phosphate ion was treated as a seven-site model and the ammonium ion was regarded as a five-site model, while a simple-point-charge model for water molecule. An unusually local particle number density fluctuation was observed in the system at saturation temperature. It can be found that the potential energy increases slowly with the temperature from 373 K to 404 K, which indicates that the ammonium dihydrogen phosphate has partly decomposed. The radial distribution function between the hydrogen atom of ammonium cation and the oxygen atom of dihydrogen phosphate ion at three different temperatures shows obvious difference, which indicates that the average H-bond number changes obviously with the temperature. The temperature has an influence on the combination between hydrogen atoms and phosphorus atoms of dihydrogen phosphate ion and there are much more growth units at saturated solutions.
文摘The existence of periodic solutions for a kind of generalized Liénard typed functional differential equation is studied. By means of the continuation theorem of coincidence degree theory, existence criteria are established for the existence of periodic solutions and some previous results are extended.
基金the financial support from the Natural Science Foundation of Hunan Province, China (No. 2023JJ40723)China Postdoctoral Science Foundation (No. 2022M723549)the National Natural Science Foundation of China (Nos. 52174271, 51504293)。
文摘The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold showed that gel Amberlite IRA-400 resin with Type Ⅰ quaternary ammonium functional group had better adsorption performance.The increases of resin dosage,ammonia concentration and solution pH were favorable to gold adsorption,whereas the rises of cupric and thiosulfate concentrations were disadvantageous to gold loading.Microscopic characterization results indicated that gold was adsorbed in the form of [Au(S_(2)O_(3))_(2)]^(3–) complex anion by exchanging with the counter ion Cl^(–) in the functional group of the resin.Density functional theory calculation result manifested that gold adsorption was mainly depended on the hydrogen bond and van der Waals force generated between O atom in [Au(S_(2)O_(3))_(2)]^(3–) and H atom in the quaternary ammonium functional group of the resin.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12261064 and 11861048)the Natural Science Foundation of Inner Mongolia,China (Grant Nos.2021MS01004 and 2022QN01008)the High-level Talents Scientific Research Start-up Foundation of Inner Mongolia University (Grant No.10000-21311201/165)。
文摘A Hamiltonian system is derived for the plane elasticity problem of two-dimensional dodecagonal quasicrystals by introducing the simple state function. By using symplectic elasticity approach, the analytic solutions of the phonon and phason displacements are obtained further for the quasicrystal plates. In addition, the effectiveness of the approach is verified by comparison with the data of the finite integral transformation method.
基金Project Supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.
基金supported by National Natural Science Foundation of China (Grant No. 50875230)
文摘Hollow cylinders are widely used in spacecraft, rockets, weapons, metallurgy, materials, and mechanical manufacturing industries, and so on, hydraulic bulging roll cylinder and hydraulic press work all belong to hollow cylinders. However, up till now, the solution of the cylinder subjected to the pressures in the three-dimensional space is still at the stage of the analytical solution to the normal pressure or the approximate solution to the variable pressure by numerical method. The analytical solution to the variable pressure of the cylinder has not yet made any breakthrough in theory and can not meet accurate theoretical analysis and calculation requirements of the cylindrical in Engineering. In view of their importance, the precision calculation and theoretical analysis are required to investigate on engineering. A stress function which meets both the biharmonic equations and boundary conditions is constructed in the three-dimensional space. Furthermore, the analytic solution of a hollow cylinder subjected to exponential function distributed variable pressure on its inner and outer surfaces is deduced. By controlling the pressure subject to exponential function distributed variable pressure in the hydraulic bulging roller without any rolling load, using a static tester to record the strain supported hydraulic bulging roll, and comparing with the theoretical calculation, the experimental test result has a higher degree of agreement with the theoretical calculation. Simultaneously, the famous Lam6 solution can be deduced when given the unlimited length of cylinder along the axis. The analytic solution paves the way for the mathematic building and solution of hollow cylinder with randomly uneven pressure.
基金Project supported by NSF of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.
基金National Natural Science Foundation of China( 198710 0 5 )
文摘By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))].
文摘A new type of hybrid finite element formulation with fundamental solutions as internal interpolation functions, named as HFS-FEM, is presented in this paper and used for solving two dimensional heat conduction problems in single and multi-layer materials. In the proposed approach, a new variational functional is firstly constructed for the proposed HFS-FE model and the related existence of extremum is presented. Then, the assumed internal potential field constructed by the linear combination of fundamental solutions at points outside the elemental domain under consideration is used as the internal interpolation function, which analytically satisfies the governing equation within each element. As a result, the domain integrals in the variational functional formulation can be converted into the boundary integrals which can significantly simplify the calculation of the element stiffness matrix. The independent frame field is also introduced to guarantee the inter-element continuity and the stationary condition of the new variational functional is used to obtain the final stiffness equations. The proposed method inherits the advantages of the hybrid Trefftz finite element method （HT-FEM） over the conventional finite element method （FEM） and boundary element method （BEM）, and avoids the difficulty in selecting appropriate terms of T-complete functions used in HT-FEM, as the fundamental solutions contain usually one term only, rather than a series containing infinitely many terms. Further, the fundamental solutions of a problem are, in general, easier to derive than the T-complete functions of that problem. Finally, several examples are presented to assess the performance of the proposed method, and the obtained numerical results show good numerical accuracy and remarkable insensitivity to mesh distortion.
基金the National Natural Science Foundation of China(1 0 1 71 0 88) and the National Natural Science Foundation of Jiangsu Educational Committee(99KJ1 1 0 0 0 5 )
文摘This article deals with the reflective function of the mth-order nonlinear differential systems.The results are applied to discussing the stability property of periodic solutions of these systems.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
