In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties...In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
This paper carefully analyses the possibility of that a generalized KdV equa- tion possesses a family of solutions of the finite series form,and thus a kind of its explicit complex exact solutions is cxhibited.These c...This paper carefully analyses the possibility of that a generalized KdV equa- tion possesses a family of solutions of the finite series form,and thus a kind of its explicit complex exact solutions is cxhibited.These complex solutions constitute real exact so- lutions to th e system of complex form of the above generalized KdV equation.展开更多
In this paper, a new generating method-opposite-direction accumulated generating operation is presented. The effectiveness of the method for different original sequences to choose different generating operation is dis...In this paper, a new generating method-opposite-direction accumulated generating operation is presented. The effectiveness of the method for different original sequences to choose different generating operation is discussed and the optimal parameters ɑ and b of grey model by a new structure of background and initial value are obtained. Some properties of a grey model are studied. The calculating precision of the example shows that the method is very effective.展开更多
文摘In 1992, Cooper [2] has presented some new stability concepts for Runge-Kutta methods whichis based on two slightly different test problems, and obtained the algebraic conditions that guarantee newstability properties. In this paper, we extend these results to general linear methods and to more generalproblem class Kστ. The concepts of (k, p, q)-secondary stability and (k, p. q)-secondary stability are introduced, and the criteria of secondary algebraic stability are also established. The criteria relax algebraicstability conditions while retaining the virtues of a nonlinear test problem.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
文摘This paper carefully analyses the possibility of that a generalized KdV equa- tion possesses a family of solutions of the finite series form,and thus a kind of its explicit complex exact solutions is cxhibited.These complex solutions constitute real exact so- lutions to th e system of complex form of the above generalized KdV equation.
文摘In this paper, a new generating method-opposite-direction accumulated generating operation is presented. The effectiveness of the method for different original sequences to choose different generating operation is discussed and the optimal parameters ɑ and b of grey model by a new structure of background and initial value are obtained. Some properties of a grey model are studied. The calculating precision of the example shows that the method is very effective.
基金This work was partly supported by the National Natural Science Foundation of China （11501581）, the Project by Central South Uni- versity （502042032）, and the China Postdoctoral Science Foundation （2015M570683）.
