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Revised iterative solution of Ground State of Double-Well Potential

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Communications in Theoretical Physics 2005年第6期43卷 1009-1018页

作者： ZHAOWei-Qin ChinaCenterofAdvancedScienceandTechnology（CCAST） P.O.Box8730Beijing100080China／／InstituteofHighEnergyPhysicstheChineseAcademyofSciencesP.O.Box918（4-1）Beijing100049China

The revised new iterative method for solving the ground state of Schroedingerequation is deduced. Based on Green functions defined by quadratures along a single trajectory thisiterative method is applied to solve the ground state of the double-well potential. The result iscompared to the one based on the original iterative method. The limitation of the asymptoticexpansion is also discussed.

关键词： iterative solution asymptotic expansion double-well potential

iterative solution for Systems of Nonlinear Two Binary Operator Equations

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Chinese Quarterly Journal of Mathematics 2004年第3期19卷 262-266页

作者： ZHANGZhi-hong LIWen-feng DepartmentofComputerScience ShangqiuTeacher＇sCollegeShangqiu476000China BasicSciencecollege YellowRiverConservancyTechnicalInstituteKaifeng475001China

Using the cone and partial ordering theory and mixed monotone operator theory, the existence and uniqueness of solutions for some classes of systems of nonlinear two binary operator equations in a Banach space with a partial ordering are discussed. And the error estimates that the iterative sequences converge to solutions are also given. Some relevant results of solvability of two binary operator equations and systems of operator equations are improved and generalized.

关键词： Banach spaces two binary operators systems of operator equations iterative solution

The iterative solution for a Class of Monotone Operator Equations

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Wuhan University Journal of Natural Sciences 1999年第2期4卷 24-26页

作者： Xiao Jin-sheng Lei Jin-gan Wuhan University College of Mathematical Sciences Wuhan China (GRID:grid.49470.3e) (ISNI:***)

The iterative solution for a class of multivalued monotone operator equations just like A(u)∈-B(u) is discussed, where A is a positive definite linear single valued operator, B is a bounded and monotone multivalued operator. The existence and convergence of approximate solutions are proved. The method of numerical realization is demonstrated in some examples.

关键词： multivalued operator monotone operator iterative solution

iterative solutions for low lying excited states of a class of SchrSdinger equation

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Chinese Physics B 2006年第9期15卷 1909-1913页

作者： R.Friendberg 李政道赵维勤 Physics Department Columbia University New York NY 10027 USA China Center of Advanced Science and Technology (CCAST/World Laboratory) Beijing 100080 China Institute of High Energy Physics Chinese Academy of Sciences Beijing 100039 China

The convergent iterative procedure for solving the groundstate Schrodinger equation is extended to derive the excitation energy and the wavefunction of the low-lying excited states. The method is applied to the one-dimensional quartic potential problem. The results show that the iterative solution converges rapidly when the coupling g is not too small.

关键词： iterative solution low-lying excited state convergence

Analytical model for ultimate loading capacities of continuous composite slabs with profiled steel sheets

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Science China(Technological Sciences) 2015年第11期58卷 1956-1962页

作者： WANG YuHang NIE JianGuo School of Civil Engineering Chongqing University Department of Civil Engineering Tsinghua University

Composite slabs with profiled steel sheet are widely applied in practical structures now. Plenty of literatures can be available about simply supported composite slabs with single span. However, continuous slabs always exist in high-rise building structures. In order to obtain the ultimate loading capacity of continuous composite slabs, the full scale test on slab specimens with high cost need to be carried out. This paper presented an analytical model for calculating the ultimate loading capacity of continuous composite slabs. Only the small-scale slide block test needed to be carried out for determining some mechanical parameters, resulting in less cost, compared with the conventional m-k test method. Various load conditions and parameters were considered in the analytical model. The comparison between test results and predicted results showed that the proposed method had enough precision. Furthermore, the simplified method was also proposed for practical design.

关键词： continuous composite slab profiled steel sheet loading capacity iterative solution

A survey on online learning and optimization for spark advance control of SI engines

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Science China(Information Sciences) 2018年第7期61卷 6-26页

作者： Yahui ZHANG Xun SHEN Tielong SHEN Department of Engineering and Applied Sciences Sophia University

One of the most important factors affecting fuel efficiency and emissions of automotive engines is combustion quality that is usually controlled by managing spark advance(SA) in spark ignition(SI) *** increasing sensing capabilities and enhancements in on-board computation capability, online learning and optimization techniques have been the subject of significant research interest. This article surveys the literature of learning and optimization algorithms with applications to combustion quality optimization and control of SI engines. In particular, this paper reviews extremum seeking control algorithms for iterative solution of online optimization problems, stochastic threshold control algorithms for iterative solution of probability control of stochastic knock event, as well as feedforward learning algorithms for iterative solution of operating-point-dependent feedforward adaptation problems. Finally, two experimental case studies including knock probabilistic constrained optimal combustion control and on-board map learning-based combustion control are carried out on an SI gasoline engine.

关键词： online learning stochastic optimization iterative solution combustion control spark ignition engine

Groundstate with Zero Eigenvalue for Generalized Sombrero-Shaped Potential in N-Dimensional Space

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Communications in Theoretical Physics 2008年第7期50卷 139-141页

作者： ZHAO Wei-Qin China Center of Advanced Science and Technology （CCAST）（World Lab.） P.O. Box 8730 Beijing 100080 China Institute of High Energy Physics the Chinese Academy of Sciences P.O. Box 918 （4-1） Beijing 100049 China

Based on an iterative method for solving the groundstate of Schrodinger equation, it is found that a kind of generalized Sombrero-shaped potentials in N-dimensional space has groundstates with zero eigenvalue. The res... 详细信息

关键词： iterative solution zero eigenvalue generalized Sombrero-shaped potential

On dynamic analysis method for large-scale train-track-substructure interaction

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Railway Engineering Science 2022年第2期30卷 162-182页

作者： Lei Xu School of Civil Engineering Central South UniversityChangsha 410075China National Engineering Laboratory for High-Speed Railway Construction Changsha 410075China

Train–track–substructure dynamic interaction is an extension of the vehicle–track coupled *** contributes to evaluate dynamic interaction and performance between train–track system and its *** the first time,this work devotes to presenting engineering practical methods for modeling and solving such large-scale train–track–substructure interaction systems from a unified *** this study,a train consists of several multi-rigid-body vehicles,and the track is modeled by various finite *** track length needs only satisfy the length of a train plus boundary length at two sides,despite how long the train moves on the *** substructures and their interaction matrices to the upper track are established as independent modules,with no need for additionally building the track structures above substructures,and accordingly saving computational ***–substructure local coordinates are defined to assist the confirming of the overlapped portions between the train–track system and the substructural system to effectively combine the cyclic calculation and iterative solution *** advancement of this model lies in its convenience,efficiency and accuracy in continuously considering the vibration participation of multi-types of substructures against the moving of a train on the *** examples have shown the effectiveness of this method;besides,influence of substructures on train–track dynamic behaviors is illustrated accompanied by clarifying excitation difference of different track irregularity spectrums.

关键词： Train Track dynamic interaction Railway substructures Finite elements Dynamics system iterative solution Tunnel Bridge

Integral Equation Method for Inverse Scattering Problem from the Far-Field Data

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Advances in Applied Mathematics and Mechanics 2021年第6期13卷 1558-1574页

作者： Yuqing Hu School of Science Jinling Institute of TechnologyNanjingJiangsu 211169China

Consider the inverse scattering problem in terms of Helmholtz *** study a simply connected domain with oblique derivative boundary *** the case of constant l,given a finite number of incident wave,the shape of the scatterer is reconstructed from the measured far-field *** propose a Newton method which is based on the nonlinear boundary integral *** computing the Fr´echet derivatives with respect to the unknown boundary,the nonlinear equation is transformed to its linear form,then we show the iteration scheme for the inverse *** conclude our paper by presenting several numerical examples for shape reconstruction to show the validity of the method we presented.

关键词： Helmholtz equation oblique derivative problem nonlinear integral equation iterative solution numerics.