In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases a...In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases and investigated their finite sample properties. An empirical study is given to compare the performance of the proposed estimators with the existing estimators that utilize auxiliary variable(s) for finite population mean. It has been found that the generalized Ra-tio-cum-product estimator in full information case using multiple auxiliary variables is more efficient than mean per unit, ratio and product estimator using one auxiliary variable, ratio and product estimator using multiple auxiliary variable and ratio-cum-product estimators in both partial and no information case in two phase sampling. A generalized Ratio-cum-product estimator in partial information case is more efficient than Generalized Ratio-cum-product estimator in No information case.展开更多
In the paper,we consider the coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the newly proposed quadratic auxiliary variable method.The...In the paper,we consider the coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the newly proposed quadratic auxiliary variable method.Therefore,we develop the multiple quadratic auxiliary variable approach to deal with coupled systems and construct high-accuracy structure-preserving schemes for the equation.To fix the idea,we first apply the multiple quadratic auxiliary variable approach to the equation and obtain an equivalent system that possesses the original energy and mass.Then,a family of high-accuracy structure-preserving schemes that can conserve the mass and energy is derived by applying the Gauss collocation method and sine pseudo-spectral method to approximate the system in time and space.The given schemes have high-accuracy in time and can both inherit the mass and Hamiltonian energy of the system.Ample numerical results are given to confirm the accuracy and conservation of the developed schemes at last.展开更多
文摘In this paper, we have proposed estimators of finite population mean using generalized Ratio- cum-product estimator for two-Phase sampling using multi-auxiliary variables under full, partial and no information cases and investigated their finite sample properties. An empirical study is given to compare the performance of the proposed estimators with the existing estimators that utilize auxiliary variable(s) for finite population mean. It has been found that the generalized Ra-tio-cum-product estimator in full information case using multiple auxiliary variables is more efficient than mean per unit, ratio and product estimator using one auxiliary variable, ratio and product estimator using multiple auxiliary variable and ratio-cum-product estimators in both partial and no information case in two phase sampling. A generalized Ratio-cum-product estimator in partial information case is more efficient than Generalized Ratio-cum-product estimator in No information case.
基金supported by the National Natural Science Foundation of China(Grant Nos.12171245,11971416,11971242,11901513,11971481)the National Natural Science Foundation of Henan Province(No.222300420280)+3 种基金the Natural Science Foundation of Hunan(Grant Nos.2021JJ40655,2021JJ20053,2023JJ40656)the Program for Innovative Research Team(in Science and Technology)in University of Henan Province(No.23IRTSTHN018)the National Key R&D Program of China(No.2020YFA0709800)the scientific research Fund of Xuchang University(2024ZD010).
文摘In the paper,we consider the coupled nonlinear Schrödinger equation with high degree polynomials in the energy functional that cannot be handled by using the newly proposed quadratic auxiliary variable method.Therefore,we develop the multiple quadratic auxiliary variable approach to deal with coupled systems and construct high-accuracy structure-preserving schemes for the equation.To fix the idea,we first apply the multiple quadratic auxiliary variable approach to the equation and obtain an equivalent system that possesses the original energy and mass.Then,a family of high-accuracy structure-preserving schemes that can conserve the mass and energy is derived by applying the Gauss collocation method and sine pseudo-spectral method to approximate the system in time and space.The given schemes have high-accuracy in time and can both inherit the mass and Hamiltonian energy of the system.Ample numerical results are given to confirm the accuracy and conservation of the developed schemes at last.
