In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified...In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the c...In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.展开更多
Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume...Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine （Pinus massoniana Lamb.） in southern China, we constructed one-, two- and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations by using error-in-variable simultaneous equations. The prediction precision of aboveground biomass estimates from one variable equa- tion exceeded 95%. The regressions of aboveground biomass equations were improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically insignificant. For the biomass conversion function on one variable, the conversion factor decreased with increasing diameter, but for the conversion function on two variables, the conversion factor increased with increasing diameter but decreased with in- creasing tree height.展开更多
Experimental studies on the rheological properties of a Ca O–Si O2–Al2O3–Mg O–Ti O2–(Ti C) blast furnace(BF) slag system were conducted using a high-temperature rheometer to reveal the non-Newtonian behavior of h...Experimental studies on the rheological properties of a Ca O–Si O2–Al2O3–Mg O–Ti O2–(Ti C) blast furnace(BF) slag system were conducted using a high-temperature rheometer to reveal the non-Newtonian behavior of heterogeneous titanium-bearing molten slag. By measuring the relationships among the viscosity, the shear stress and the shear rate of molten slags with different Ti C contents at different temperatures, the rheological constitutive equations were established along with the rheological parameters; in addition, the non-Newtonian fluid types of the molten slags were determined. The results indicated that, with increasing Ti C content, the viscosity of the molten slag tended to increase. If the Ti C content was less than 2wt%, the molten slag exhibited the Newtonian fluid behavior when the temperature was higher than the critical viscosity temperature of the molten slag. In contrast, the molten slag exhibited the non-Newtonian pseudoplastic fluid characteristic and the shear thinning behavior when the temperature was less than the critical viscosity temperature. However, if the Ti C content exceeded 4wt%, the molten slag produced the yield stress and exhibited the Bingham and plastic pseudoplastic fluid behaviors when the temperature was higher and lower than the critical viscosity temperature, respectively. When the Ti C content increased further, the yield stress of the molten slag increased and the shear thinning phenomenon became more obvious.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some prop...Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.展开更多
A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the c...A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.展开更多
We investigate the equation of state of the strong interaction matter in a background magnetic field via the two flavor Nambu–Jona-Lasinio model. Starting from the mean-field thermodynamical potential density ?, we c...We investigate the equation of state of the strong interaction matter in a background magnetic field via the two flavor Nambu–Jona-Lasinio model. Starting from the mean-field thermodynamical potential density ?, we calculate the pressure density p, the entropy density s, the energy density ε, and the interaction measure(ε- 3p)/T4 of the strong interaction matter at finite temperature and finite magnetic field. The results manifest that the chiral phase transition is just a crossover but not a low order phase transition. Moreover there may exist magnetic catalysis effect, and its mechanism is just the effective dimension reduction induced by the magnetic field.展开更多
In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we ...In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.展开更多
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p...This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.展开更多
In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for osc...In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.展开更多
In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation ...In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.展开更多
Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equat...Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.展开更多
The isobaric vapor-liquid equilibrium data of butanone1-N, N-dimethylformamide DMF2 at 100.92kPa, 93.32kPa, and 79.99kPa and of toluene1-DMF2 at 100.92kPa were measured using a modified Rose–Williams still. The above...The isobaric vapor-liquid equilibrium data of butanone1-N, N-dimethylformamide DMF2 at 100.92kPa, 93.32kPa, and 79.99kPa and of toluene1-DMF2 at 100.92kPa were measured using a modified Rose–Williams still. The above data met the thermodynamic consistency test and were correlated with the Wilson, NRTL, and UNIQUAC equations. These data can be used in the analysis and design of the process that involves separating DMF from butanone and toluene in the leather synthesis industry.展开更多
文摘In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
文摘In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.
基金the National Biomass Modeling Program for Continuous Forest Inventory(NBMP-CFI) funded by the State Forestry Administration of China
文摘Because of global climate change, it is necessary to add forest biomass estimation to national forest resource monitoring. The biomass equations developed for forest biomass estimation should be compatible with volume equations. Based on the tree volume and aboveground biomass data of Masson pine （Pinus massoniana Lamb.） in southern China, we constructed one-, two- and three-variable aboveground biomass equations and biomass conversion functions compatible with tree volume equations by using error-in-variable simultaneous equations. The prediction precision of aboveground biomass estimates from one variable equa- tion exceeded 95%. The regressions of aboveground biomass equations were improved slightly when tree height and crown width were used together with diameter on breast height, although the contributions to regressions were statistically insignificant. For the biomass conversion function on one variable, the conversion factor decreased with increasing diameter, but for the conversion function on two variables, the conversion factor increased with increasing diameter but decreased with in- creasing tree height.
基金financially supported by the National Science Foundation of China (Nos. 51090383 and 51174051)
文摘Experimental studies on the rheological properties of a Ca O–Si O2–Al2O3–Mg O–Ti O2–(Ti C) blast furnace(BF) slag system were conducted using a high-temperature rheometer to reveal the non-Newtonian behavior of heterogeneous titanium-bearing molten slag. By measuring the relationships among the viscosity, the shear stress and the shear rate of molten slags with different Ti C contents at different temperatures, the rheological constitutive equations were established along with the rheological parameters; in addition, the non-Newtonian fluid types of the molten slags were determined. The results indicated that, with increasing Ti C content, the viscosity of the molten slag tended to increase. If the Ti C content was less than 2wt%, the molten slag exhibited the Newtonian fluid behavior when the temperature was higher than the critical viscosity temperature of the molten slag. In contrast, the molten slag exhibited the non-Newtonian pseudoplastic fluid characteristic and the shear thinning behavior when the temperature was less than the critical viscosity temperature. However, if the Ti C content exceeded 4wt%, the molten slag produced the yield stress and exhibited the Bingham and plastic pseudoplastic fluid behaviors when the temperature was higher and lower than the critical viscosity temperature, respectively. When the Ti C content increased further, the yield stress of the molten slag increased and the shear thinning phenomenon became more obvious.
基金supported by the National Natural Science Foundation of China(11171013)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(16XNH117)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.
基金supported by the National Natural Science Foundation of China(Nos.11472119 and11421062)
文摘A new boundary extension technique based on the Lagrange interpolat- ing polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coifiet-based solution procedure is established for general two-dimensional p^Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10935001,11175004 and 11435001the National Key Basic Research Program of China under Grant Nos.G2013CB834400 and 2015CB856900
文摘We investigate the equation of state of the strong interaction matter in a background magnetic field via the two flavor Nambu–Jona-Lasinio model. Starting from the mean-field thermodynamical potential density ?, we calculate the pressure density p, the entropy density s, the energy density ε, and the interaction measure(ε- 3p)/T4 of the strong interaction matter at finite temperature and finite magnetic field. The results manifest that the chiral phase transition is just a crossover but not a low order phase transition. Moreover there may exist magnetic catalysis effect, and its mechanism is just the effective dimension reduction induced by the magnetic field.
文摘In this paper,we will discuss smoothness of weak solutions for the system of second order differential equations eith non-negative characteristies.First of all,we establish boundary,and interior estimates and then we prove that solutions of regularization problem satisfy Lipschitz condition.
基金This work is supported by National Natural Science Foundation of China （Nos. 11401594, 11171125, 91130003） and the New Teachers＇ Specialized Research Fund for the Doctoral Program from Ministry of Education of China （No. 20120162120096）.
文摘This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.
文摘In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.
基金The work was supported by Jiangsu Province's Natural Science Foundation (BK97004)National Natural Science Foundation (19801007) of CHINA.
文摘In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.
基金the National Natural Science Foundation of China(No.10471065)the Natural Science Foundation of Guangdong Province(No.04010474)
文摘Using value distribution theory and techniques in several complex variables,we investigate the problem of existence of m components-admissible solutions of a class of systems of higher-order partial differential equations in several complex variables and estimate the number of admissible components of solutions.Some related results will also be obtained.
基金the National Natural Science Foundation of China (No.20376073)
文摘The isobaric vapor-liquid equilibrium data of butanone1-N, N-dimethylformamide DMF2 at 100.92kPa, 93.32kPa, and 79.99kPa and of toluene1-DMF2 at 100.92kPa were measured using a modified Rose–Williams still. The above data met the thermodynamic consistency test and were correlated with the Wilson, NRTL, and UNIQUAC equations. These data can be used in the analysis and design of the process that involves separating DMF from butanone and toluene in the leather synthesis industry.
