The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1...The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature展开更多
This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. ...This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.展开更多
This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in ...This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.展开更多
The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic f...The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.展开更多
We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obt...We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.展开更多
The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of ...The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.展开更多
基金Project supported by the Science Foundation of China West Normal University （Grant No 05B016） and the Science Foundation of Sichuan province Educational Bureau of China （Grant No 2006A080）.
文摘The algebraic energy method （AEM） is applied to the study of molecular dissociation energy De for 11 heteronuclear diatomic electronic states： a^3∑＋ state of NaK, X^2∑＋ state of XeBr, X^2∑＋ state of HgI, X^1∑＋ state of LiH, A3∏（1） state of IC1, X^1∑＋ state of CsH, A（3∏1） and B0＋（3∏） states of CIF, 21∏ state of KRb, X^1∑＋ state of CO, and c^3∑＋ state of NaK molecule. The results show that the values of De computed by using the AEM are satisfactorily accurate compared with experimental ones. The AEM can serve as an economic and useful tool to generate a reliable De within an allowed experimental error for the electronic states whose molecular dissociation energies are unavailable from the existing literature
文摘This article deals with a class of numerical methods for retarded differential algebraic systems with time-variable delay. The methods can be viewed as a combination of Runge-Kutta methods and Lagrange interpolation. A new convergence concept, called DA-convergence, is introduced. The DA-convergence result for the methods is derived. At the end, a numerical example is given to verify the computational effectiveness and the theoretical result.
基金Project supported by the National Natural Science Foundation of China （Grant No 1057009）.
文摘This paper uses the Lie algebraic method to analyse the charged particle trajectories in the spherical electrostatic analyser, and obtains the nonlinear solutions. The results show that the focusing abilities both in the x and y directions of the analyser are almost the same. Moreover, there exist dispersion effects in the x direction, and no dispersion effects in the y direction.
基金Project supported by the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10471145 and 10372053） and the Natural Science Foundation of Henan Provincial Government of China （Grant Nos 0311011400 and 0511022200）.
文摘The algebraic structure and Poisson＇s integral theory of mechanico-electrical systems are studied. The Hamilton canonical equations and generalized Hamilton canonical equations and their the contravariant algebraic forms for mechanico-electrical systems are obtained. The Lie algebraic structure and the Poisson＇s integral theory of Lagrange mechanico-electrical systems are derived. The Lie algebraic structure admitted and Poisson＇s integral theory of the Lagrange-Maxwell mechanico-electrical systems are presented. Two examples are presented to illustrate these results.
文摘We study the conjugate gradient method for solving a system of linear equations with coefficients which are measurable functions and establish the rate of convergence of this method.
文摘We use the Bethe ansatz method to investigate the Schrdinger equation for a class of PT-symmetric non-Hermitian Hamiltonians. Elementary exact solutions for the eigenvalues and the corresponding wave functions are obtained in terms of the roots of a set of algebraic equations. Also, it is shown that the problems possess sl（2） hidden symmetry and then the exact solutions of the problems are obtained by employing the representation theory of sl（2） Lie algebra. It is found that the results of the two methods are the same.
文摘The goal of the present paper is to investigate some new HUR-stability results by applying the alternative fixed point of generalized quartic functional equationin β-Banach modules on Banach algebras. The concept of Ulam-Hyers-Rassias stability （briefly, HUR-stability） originated from Th. M. Rassias stability theorem that appeared in his paper： On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 （1978）, 297-300.
