An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential e...An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.展开更多
To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an und...To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.展开更多
In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study...In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.展开更多
In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed ext...In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.展开更多
This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equati...This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.展开更多
In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebra...In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.展开更多
Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the ext...Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.展开更多
The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrationalinteractions being considered, the eige...The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrationalinteractions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.展开更多
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain condition...Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.展开更多
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
In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions ...In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.展开更多
This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic st...This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that: (1) although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.展开更多
This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the al- gebraic method (AM) for some electronic states of halogen diatomic molecules. Motivated by the recent s...This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the al- gebraic method (AM) for some electronic states of halogen diatomic molecules. Motivated by the recent success of obtaining the dissociation energies of Li2 molecule by using a new analytical formula, it further extends the formula to study the dissociation energies of halogen diatomic molecules. The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.展开更多
We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of trans...We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.展开更多
Reliability engineering implemented early in the development process has a significant impact on improving software quality.It can assist in the design of architecture and guide later testing,which is beyond the scope...Reliability engineering implemented early in the development process has a significant impact on improving software quality.It can assist in the design of architecture and guide later testing,which is beyond the scope of traditional reliability analysis methods.Structural reliability models work for this,but most of them remain tested in only simulation case studies due to lack of actual data.Here we use software metrics for reliability modeling which are collected from source codes of post versions.Through the proposed strategy,redundant metric elements are filtered out and the rest are aggregated to represent the module reliability.We further propose a framework to automatically apply the module value and calculate overall reliability by introducing formal methods.The experimental results from an actual project show that reliability analysis at the design and development stage can be close to the validity of analysis at the test stage through reasonable application of metric data.The study also demonstrates that the proposed methods have good applicability.展开更多
This paper calculates the equilibrium structure and the potential energy functions of the ground state (X^2∑^+) and the low lying excited electronic state (A^2Л) of CN radical are calculated by using CASSCF met...This paper calculates the equilibrium structure and the potential energy functions of the ground state (X^2∑^+) and the low lying excited electronic state (A^2Л) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ωe) and other spectroscopic constants (ωeχe, βe and αe) are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.展开更多
An improved U(2) algebraic model is introduced to study the stretching and bending vibrational spectra of methane and its isotopomers.The algebraic model with fewer parameters reproduces the experimental spectra wit...An improved U(2) algebraic model is introduced to study the stretching and bending vibrational spectra of methane and its isotopomers.The algebraic model with fewer parameters reproduces the experimental spectra with good precision.Moreover,the obtained parameters describe well the correct behavior of isotopic substitution.It is shown that the Fermi resonance leads to a very fast intramolecular vibrational redistribution among stretches and bends.展开更多
We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the g...We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the generalizations of the two Casimir operators.展开更多
Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. C...Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. Considering Rb atoms as an example, it finds that the numerical results are relevant to the recent experimental laser cooling investigations.展开更多
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen t...We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.展开更多
基金National Natural Science Foundation of China under Grant No.10672053
文摘An extended Fan's algebraic method is used for constructing exact traveling wave solution of nonlinearpartial differential equations.The key idea of this method is to introduce an auxiliary ordinary differential equationwhich is regarded as an extended elliptic equation and whose degree Υ is expanded to the case of r>4.The efficiency ofthe method is demonstrated by the KdV equation and the variant Boussinesq equations.The results indicate that themethod not only offers all solutions obtained by using Fu's and Fan's methods,but also some new solutions.
基金National Natural Science Foundation of China(Grant Nos.51925502,51575150).
文摘To avoid impacts and vibrations during the processes of acceleration and deceleration while possessing flexible working ways for cable-suspended parallel robots(CSPRs),point-to-point trajectory planning demands an under-constrained cable-suspended parallel robot(UCPR)with variable angle and height cable mast as described in this paper.The end-effector of the UCPR with three cables can achieve three translational degrees of freedom(DOFs).The inverse kinematic and dynamic modeling of the UCPR considering the angle and height of cable mast are completed.The motion trajectory of the end-effector comprising six segments is given.The connection points of the trajectory segments(except for point P3 in the X direction)are devised to have zero instantaneous velocities,which ensure that the acceleration has continuity and the planned acceleration curve achieves smooth transition.The trajectory is respectively planned using three algebraic methods,including fifth degree polynomial,cycloid trajectory,and double-S velocity curve.The results indicate that the trajectory planned by fifth degree polynomial method is much closer to the given trajectory of the end-effector.Numerical simulation and experiments are accomplished for the given trajectory based on fifth degree polynomial planning.At the points where the velocity suddenly changes,the length and tension variation curves of the planned and unplanned three cables are compared and analyzed.The OptiTrack motion capture system is adopted to track the end-effector of the UCPR during the experiment.The effectiveness and feasibility of fifth degree polynomial planning are validated.
文摘In this study,the potential Kadomtsev-Petviashvili(pKP)equation,which describes the oblique interaction of surface waves in shallow waters,is solved by the new extended direct algebraic method.The results of the study show that by applying the new direct algebraic method to the pKP equation,the behavior of the obliquely interacting surface waves in two dimensions can be analyzed.This article fairly clarifies the behaviors of surface waves in shallow waters.In the literature,several mathematical models have been developed in attempt to study these behaviors,with nonlinear mathematics being one of the most important steps;however,the investigations are still at a level that can be called‘baby steps’.Therefore,every study to be carried out in this context is of great importance.Thus,this study will serve as a reference to guide scientists working in this field.
文摘In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.
文摘This paper considers the pole placement in multivariable systems involving known delays by using dynamic controllers subject to multirate sampling. The controller parameterizations are calculated from algebraic equations which are solved by using the Kronecker product of matrices. It is pointed out that the sampling periods can be selected in a convenient way for the solvability of such equations under rather weak conditions provided that the continuous plant is spectrally controllable. Some overview about the use of nonuniform sampling is also given in order to improve the system's performance.
文摘In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.
基金Supported by National Natural Science Foundation of China (10075005)Specialized Research Fund for the Doctoral Program of Higher Education (20070001001)
文摘Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.
基金the Natural Science Foundation of Shandong Province of China(Grant No.Y98B08027)the National Natural Science Foundation of China(Grant No.20173031).
文摘The Hamiltonian describing rotational spectra of linear triatomic molecules has been derived by using the dynamical Lie algebra of symmetry group U1(4) U2(4). After rovibrationalinteractions being considered, the eigenvalue expression of the Hamiltonian has the form of term value equation commonly used in spectrum analysis. The molecular rotational constants can be obtained by using the expression and fitting it to the observed lines. As an example, the rotational levels of v2 band for transition (02°0-0110) of molecules N2O and HCN have been fitted and the fitting root-mean-square errors (RMS) are 0.00001 and 0.0014 cm-1, respectively.
文摘Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
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In this paper, we investigate some new traveling wave solutions to Vakhnenko-Parkes equation via three modified mathematical methods. The derived solutions have been obtained including periodic and solitons solutions in the form of trigonometric, hyperbolic, and rational function solutions. The graphical representations of some solutions by assigning particular values to the parameters under prescribed conditions in each solutions and comparing of solutions with those gained by other authors indicate that these employed techniques are more effective, efficient and applicable mathematical tools for solving nonlinear problems in applied science.
基金Project supported by the National Natural Science Foundation of China (Grant No 10774105)the Science Foundation of the Chinese Educational Ministry
文摘This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that: (1) although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.
基金supported by the National Natural Science Foundation of China (Grant No. 51071131)the Science Foundation of Educational Bureau of Sichuan Province of China (Grant No. 09ZA124)
文摘This paper obtains accurate vibrational spectroscopic constants and full vibrational energy spectrum by the al- gebraic method (AM) for some electronic states of halogen diatomic molecules. Motivated by the recent success of obtaining the dissociation energies of Li2 molecule by using a new analytical formula, it further extends the formula to study the dissociation energies of halogen diatomic molecules. The results show that the AM spectrum and the theoretical dissociation energies agree well with RKR data and experimental data respectively.
文摘We investigate the general condition for an operator to be unitary.This condition is introduced according to the definition of the position operator in curved space.In a particular case,we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator.Also we introduce a universal formula for adjoint of an arbitrary linear operator.Our procedure in this paper is totally different from others,as we explore a general approach based only on the algebra of the operators.Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.
基金This work was supported by the National Natural Science Foundation of China(61572167)the National Key Research and Development Program of China(2016YFC0801804)the Natural Science Foundation for Anhui Higher Education Institutions of China(KJ2019A0482).
文摘Reliability engineering implemented early in the development process has a significant impact on improving software quality.It can assist in the design of architecture and guide later testing,which is beyond the scope of traditional reliability analysis methods.Structural reliability models work for this,but most of them remain tested in only simulation case studies due to lack of actual data.Here we use software metrics for reliability modeling which are collected from source codes of post versions.Through the proposed strategy,redundant metric elements are filtered out and the rest are aggregated to represent the module reliability.We further propose a framework to automatically apply the module value and calculate overall reliability by introducing formal methods.The experimental results from an actual project show that reliability analysis at the design and development stage can be close to the validity of analysis at the test stage through reasonable application of metric data.The study also demonstrates that the proposed methods have good applicability.
基金Project supported by the National Natural Science Foundation of China (Grant No 60771038).
文摘This paper calculates the equilibrium structure and the potential energy functions of the ground state (X^2∑^+) and the low lying excited electronic state (A^2Л) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell-Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency (ωe) and other spectroscopic constants (ωeχe, βe and αe) are calculated by employing the Rydberg-Klei-Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional SchrSdinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11174099)
文摘An improved U(2) algebraic model is introduced to study the stretching and bending vibrational spectra of methane and its isotopomers.The algebraic model with fewer parameters reproduces the experimental spectra with good precision.Moreover,the obtained parameters describe well the correct behavior of isotopic substitution.It is shown that the Fermi resonance leads to a very fast intramolecular vibrational redistribution among stretches and bends.
文摘We extend the Poincaré group to the complex Minkowski space-time. Special attention is paid to the corresponding algebra that we achieve through matrices as well as differential operators. We also point out the generalizations of the two Casimir operators.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10704031)the National Science Foundation for Fostering Talents in Basic Research of the National Natural Science Foundation of China (Grant No. J0630313)+1 种基金the fundamental Research Fund for Physical and Mathematical of Lanzhou University (Grant No. Lzu05001)the Natural Science Foundation of Gansu,China (Grant No. 3ZS061-A25-035)
文摘Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. Considering Rb atoms as an example, it finds that the numerical results are relevant to the recent experimental laser cooling investigations.
文摘We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.