A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyp...A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyperspherical harmonic method. This approach is numerically competitive with the variational methods, such as that using the Hylleraas-type basis functions. Numerical comparisons are made to demonstrate the efficiency of this approach, by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom. The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in this paper and the true wavefunction. This full matching was not reached by most other methods. For example, the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock. Two important approaches are proposed in this work to reach this full matching: the coordinate transformation method and the asymptotic series method. Besides these, this work makes use of the least square method to substitute complicated numerical integrations in solving the Schr?dinger equation without much loss of accuracy, which is routinely used by people to fit a theoretical curve with discrete experimental data, but here is used to simplify the computation.展开更多
Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a ty...Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.展开更多
In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac function and llcavisidc step fu...In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac function and llcavisidc step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.展开更多
The program system described in this paper is a microcomputer analytic system for X-ray crystal structure used in chemical laboratories.The abbreviated name is NOMCSDP.NOMCSDP has been developed on the basis of NRCVAX...The program system described in this paper is a microcomputer analytic system for X-ray crystal structure used in chemical laboratories.The abbreviated name is NOMCSDP.NOMCSDP has been developed on the basis of NRCVAX and SHELXS-86.It is a software for X- ray crystal structure analysis of organic molecules,especially natural organic molecules(1-7).展开更多
The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail. The nature of these two kinds of fuzzy controllers...The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail. The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.展开更多
We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties...We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve (or vice versa). For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the "galactic rotation number" that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity (such as the "flat" value in a typical ro- tation curve) and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.展开更多
Diffusion has been systematically described as the main mechanism of chloride transport in reinforced concrete(RC) structure, especially when the concrete is in a saturated state. However, the single mechanism of di...Diffusion has been systematically described as the main mechanism of chloride transport in reinforced concrete(RC) structure, especially when the concrete is in a saturated state. However, the single mechanism of diffusion is not able to describe the actual chloride ingress in the nonsaturated concrete. Instead, it is dominated by the interaction of diffusion and convection. With the synergetic effects of various factors taken into account, this study aimed to modify and develop an analytical convection- diffusion coupling model for chloride transport in nonsaturated concrete. The model was verified by simulation of laboratory tests and field measurement. The results of comparison study demonstrate that the analytical model developed in this study is efficient and accurate in predicting the chloride profiles in the nonsaturated concrete.展开更多
The analytic properties theoretical investigations of baryon of scattering amplitudes provide a meeting point for experimental and resonances. Pole positions and residues allow for a parameterization of resonances in ...The analytic properties theoretical investigations of baryon of scattering amplitudes provide a meeting point for experimental and resonances. Pole positions and residues allow for a parameterization of resonances in a well-defined way which relates different reactions. The recent progress made within the Jiilich model is summarized.展开更多
In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important information. Beside...In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.展开更多
文摘A powerful approach to solve the Coulombic quantum three-body problem is proposed. The approach is exponentially convergent and more efficient than the hyperspherical coordinate method and the correlation-function hyperspherical harmonic method. This approach is numerically competitive with the variational methods, such as that using the Hylleraas-type basis functions. Numerical comparisons are made to demonstrate the efficiency of this approach, by calculating the nonrelativistic and infinite-nuclear-mass limit of the ground state energy of the helium atom. The exponential convergency of this approach is due to the full matching between the analytical structure of the basis functions that are used in this paper and the true wavefunction. This full matching was not reached by most other methods. For example, the variational method using the Hylleraas-type basis does not reflects the logarithmic singularity of the true wavefunction at the origin as predicted by Bartlett and Fock. Two important approaches are proposed in this work to reach this full matching: the coordinate transformation method and the asymptotic series method. Besides these, this work makes use of the least square method to substitute complicated numerical integrations in solving the Schr?dinger equation without much loss of accuracy, which is routinely used by people to fit a theoretical curve with discrete experimental data, but here is used to simplify the computation.
基金supported by the Xinjiang Astronomical Observatory,China(No.2014KL012)the Major State Basic Research Development Program of China(No.2015CB857100)+1 种基金the National Natural Science Foundation of China(Nos.51490660 and 51405362)the Fundamental Research Funds for the Central Universities,China(No.SPSY021401)
文摘Type-2 fuzzy controllers have been mostly viewed as black-box function generators. Revealing the analytical structure of any type-2 fuzzy controller is important as it will deepen our understanding of how and why a type-2 fuzzy controller functions and lay a foundation for more rigorous system analysis and design. In this study, we derive and analyze the analytical structure of an interval type-2 fuzzy controller that uses the following identical elements: two nonlinear interval type-2 input fuzzy sets for each variable, four interval type-2 singleton output fuzzy sets, a Zadeh AND operator, and the Karnik-Mendel type reducer. Through dividing the input space of the interval type-2 fuzzy controller into 15 partitions, the input-output relationship for each local region is derived. Our derivation shows explicitly that the controller is approximately equivalent to a nonlinear proportional integral or proportional differential controller with variable gains. Furthermore, by comparing with the analytical structure of its type-1 counterpart, potential advantages of the interval type-2 fuzzy controller are analyzed. Finally, the reliability of the analysis results and the effectiveness of the interval type-2 fuzzy controller are verified by a simulation and an experiment.
文摘In this paper, based on the idea of finite element method, the initial parametric method in bending, problem of a beam is extended to analyse the bar-system structure by employing Dirac function and llcavisidc step function.Then a new method for analysing the internal forces and deformations of bar-system structure in space is suggested by improving the mixed method in statically indeterminate structure.The inferred process and obtained answer will be more succinct and accurate when the problem of internal forces and deformations of bar-system structure is analysed by using the new method provided in this paper.
文摘The program system described in this paper is a microcomputer analytic system for X-ray crystal structure used in chemical laboratories.The abbreviated name is NOMCSDP.NOMCSDP has been developed on the basis of NRCVAX and SHELXS-86.It is a software for X- ray crystal structure analysis of organic molecules,especially natural organic molecules(1-7).
基金This project was supported by the fundation of the Academy of Finland (201353)
文摘The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail. The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.
文摘We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve (or vice versa). For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the "galactic rotation number" that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity (such as the "flat" value in a typical ro- tation curve) and Rg the radius of the galactic disk. The predicted total galactic mass of the Milky Way is in good agreement with the star-count data.
基金Funded by the National Natural Science Foundation of China(Nos.51278304,U1134209,U1434204&51422814)the National Basic Research Program(973 Program)of China(No.011-CB013604)the Technology Research and Development Program(Basic Research Project)of Shenzhen(Nos.JCYJ20120613174456685&JCYJ20130329143859418)
文摘Diffusion has been systematically described as the main mechanism of chloride transport in reinforced concrete(RC) structure, especially when the concrete is in a saturated state. However, the single mechanism of diffusion is not able to describe the actual chloride ingress in the nonsaturated concrete. Instead, it is dominated by the interaction of diffusion and convection. With the synergetic effects of various factors taken into account, this study aimed to modify and develop an analytical convection- diffusion coupling model for chloride transport in nonsaturated concrete. The model was verified by simulation of laboratory tests and field measurement. The results of comparison study demonstrate that the analytical model developed in this study is efficient and accurate in predicting the chloride profiles in the nonsaturated concrete.
基金Supported by DFG (Deutsche Forschungsgemeinschaft, Gz: DO 1302/1-1)Helmholtz Association through funds provided to the virtual institute 'Spin and Strong QCD' (VH-VI-231)+1 种基金EU-Research Infrastructure Integrating Activity 'Study of Strongly Interacting Matter' (HadronPhysics2, grant n. 227431)under the Seventh Framework Program of EU and DFG (TR 16)COSY FFE grant No. 41445282 (COSY-58)
文摘The analytic properties theoretical investigations of baryon of scattering amplitudes provide a meeting point for experimental and resonances. Pole positions and residues allow for a parameterization of resonances in a well-defined way which relates different reactions. The recent progress made within the Jiilich model is summarized.
基金Supported by DFG (Deutsche Forschungsgemeinschaft, Gz: DO 1302/1-1)Helmholtz Association through funds provided to the virtual institute 'Spin and Strong QCD' (VH-VI-231)EU-Research Infrastructure Integrating Activity 'Study of Strongly Interacting Matter' (Hadron Physics2 (227431)) under the Seventh Framework Program of EU and by the DFG (TR 16), COSY FFE (41445282)(COSY-58)
文摘In this talk, I present the results on the pole structure of pion-nucleon scattering in an analytic model based on meson exchange. The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions.