By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for general...By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.展开更多
A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Sats...A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative.Our solutions were obtained using MAPLE software.This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering.Since a standard equation has not been used as an auxiliary equation for this technique,different and novel solutions are obtained via this technique.展开更多
Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable wi...Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable, A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.展开更多
Some new systems of exponentially general equations are introduced and investigated, which can be used to study the odd-order, non-positive and nonsymmetric exponentially boundary value problems. Some important and in...Some new systems of exponentially general equations are introduced and investigated, which can be used to study the odd-order, non-positive and nonsymmetric exponentially boundary value problems. Some important and interesting results such as Riesz-Frechet representation theorem, Lax-Milgram lemma and system of absolute values equations can be obtained as special cases. It is shown that the system of exponentially general equations is equivalent to nonlinear optimization problem. The auxiliary principle technique is used to prove the existence of a solution to the system of exponentially general equations. This technique is also used to suggest some new iterative methods for solving the system of the exponentially general equations. The convergence analysis of the proposed methods is analyzed. Ideas and techniques of this paper may stimulate further research.展开更多
This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differenti...This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.展开更多
In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we...In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.展开更多
The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The ...The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.展开更多
Published auxiliary information can be helpful in conducting statistical inference in a new study.In this paper,we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data...Published auxiliary information can be helpful in conducting statistical inference in a new study.In this paper,we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is available.We express the auxiliary information as constraints on the regression coefficients and the covariate distribution,then use empirical likelihood method for general estimating equations to improve the efficiency of the interested parameters in the specified model.The consistency and asymptotic normality of the resulting regression parameter estimators established.Also numerical simulation and application with different supposed conditions show that the proposed method yields a substantial gain in efficiency of the interested parameters.展开更多
In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are establis...In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions.The key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting approach.Numerical examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.展开更多
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are...In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.展开更多
In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method...In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.展开更多
基金The project supported by the Natural Science Foundation of Anhui Province of China under Grant No. 01041188 and the Foundation of Classical Courses of Anhui Province
文摘By making use of extended mapping method and auxiliary equation for finding new periodic wave solu tions of nonlinear evolution equations in mathematical physics, we obtain some new periodic wave solutions for generalized Klein-Cordon equation and Benjamin equation, which cannot be found in previous work. This method also can be used to find new periodic wave solutions of other nonlinear evolution equations.
文摘A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional derivative.Our solutions were obtained using MAPLE software.This technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean engineering.Since a standard equation has not been used as an auxiliary equation for this technique,different and novel solutions are obtained via this technique.
基金Supported by the National Natural Science Funds for Distinguished Young Scholar (No.70825004)National Natural Science Foundation of China (NSFC) (No.10731010)+3 种基金the National Basic Research Program (No.2007CB814902)Creative Research Groups of China (No.10721101)Shanghai University of Finance and Economics through Project 211 Phase ⅢShanghai Leading Academic Discipline Project,Project Number:B803
文摘Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution. In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information, for example, a symmetric distribution of this variable, A smoothing technique is employed to handle the non-differentiable function. Hence, a distribution can be estimated based on smoothed auxiliary information. Asymptotic properties of the distribution estimator are derived and analyzed. The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information. Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.
文摘Some new systems of exponentially general equations are introduced and investigated, which can be used to study the odd-order, non-positive and nonsymmetric exponentially boundary value problems. Some important and interesting results such as Riesz-Frechet representation theorem, Lax-Milgram lemma and system of absolute values equations can be obtained as special cases. It is shown that the system of exponentially general equations is equivalent to nonlinear optimization problem. The auxiliary principle technique is used to prove the existence of a solution to the system of exponentially general equations. This technique is also used to suggest some new iterative methods for solving the system of the exponentially general equations. The convergence analysis of the proposed methods is analyzed. Ideas and techniques of this paper may stimulate further research.
文摘This paper reflects the execution of a reliable technique which we proposed as a new method called the double auxiliary equations method for constructing new traveling wave solutions of nonlinear fractional differential equation.The proposed scheme has been successfully applied on two very important evolution equations,the space-time fractional differential equation governing wave propagation in low-pass electrical transmission lines equation and the time fractional Burger’s equation.The obtained results show that the proposed method is more powerful,promising and convenient for solving nonlinear fractional differential equations(NFPDEs).To our knowledge,the solutions obtained by the proposed method have not been reported in former literature.
基金Supported by the National Natural Science Foundation of China(10571093)
文摘In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator（or GREG）.
基金supported by the National Key Research and Development Program of China(No.2017YFA0700300)the Fundamental Research Funds for the Central Universities(No.N2025032)the Liaoning Provincial Natural Science Foundation(No.2020-MS-362)。
文摘The equilibrium compositions and thermodynamic properties(density,enthalpy,etc at constant pressure)of plasma of pure gases and mixtures under local thermodynamic nonequilibrium have been calculated in this paper.The homotopy Levenberg-Marquardt algorithm was proposed to accurately solve nonlinear equations with singular Jacobian matrices,and is constructed by the Saha equation and Guldberg-Waage equation combined with mass conservation,the electric neutrality principle and Dalton’s partial pressure law,to solve the problem of dependence on the initial value in the process of iteration calculation.In this research,the equations at a higher temperature were solved and used as the auxiliary equations,and the homotopy control parameters’sequence of the homotopy equations was selected by equal ratios.For auxiliary equations,the iterative initial value was obtained by assuming that there were only the highestvalence atomic cations and electrons at this temperature,and the plasma equilibrium composition distribution with the required accuracy was ultimately solved under the current conditions employing the Levenberg-Marquardt algorithm.The control parameter sequence was arranged according to the geometric sequence and the homotopy step was gradually shortened to ensure continuity of the homotopy process.Finally,the equilibrium composition and thermodynamic properties of pure N_(2),Mg(30%)-CO_(2)(70%)and Mg(40%)-CO(50%)-N_(2)(10%)mixture plasma at atmospheric pressure were calculated and the calculation process of some specified temperatures was shown and analyzed.The calculation accuracy of equilibrium composition is higher than other findings in the literature.The results for the thermodynamic properties are in good agreement with data reported by the literature.
基金supported by the State Key Program of National Natural Science Foundation of China(No.71331006)by the Graduate Innovation Foundation of Shanghai University of Finance and Economics of China(No.CXJJ-2018-408)。
文摘Published auxiliary information can be helpful in conducting statistical inference in a new study.In this paper,we synthesize the auxiliary information with semiparametric likelihood-based inference for censoring data with the total sample size is available.We express the auxiliary information as constraints on the regression coefficients and the covariate distribution,then use empirical likelihood method for general estimating equations to improve the efficiency of the interested parameters in the specified model.The consistency and asymptotic normality of the resulting regression parameter estimators established.Also numerical simulation and application with different supposed conditions show that the proposed method yields a substantial gain in efficiency of the interested parameters.
基金supported by National Natural Science Foundation of China (Grant Nos. 11771162,11771128,11871106,11871092 and 11926356)National Safety Administration Fund (Grant No. U1930402)。
文摘In this paper,we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations.Optimal error estimates in time and superconvergent error estimates in space are established without certain time-step restrictions.The key is to estimate directly the solution bounds in the H-norm for both the nonlinear wave equation and the corresponding fully discrete scheme,while the previous investigations rely on the temporal-spatial error splitting approach.Numerical examples are presented to confirm energy-conserving properties,unconditional convergence and optimal error estimates,respectively,of the proposed fully discrete schemes.
基金Project supported by the Anhui Key Laboratory of Information Materials and Devices (Anhui University),China
文摘In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for （2＋1）-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions （m → 1）. This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations.
文摘In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the variant Boussinesq equations and the coupled KdV equations by using the extended mapping method and auxiliary equation method. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.
