Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact as...Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.展开更多
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wav...The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.展开更多
The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailab...The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.展开更多
We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modifie...We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations.展开更多
Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamilto...Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differentiM equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable ease of the two-dimensional Hamiltonian system.展开更多
Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following th...Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.展开更多
In this paper, the so-cMled Husimi operator △h（q,p; κ）, which is introduced by smoothing out the Wigner operator △ω（q,p） br averaging over the ＂coarse graining＂ function exp[-κ（q＇ - q）^2- （p＇- p）^2/κ...In this paper, the so-cMled Husimi operator △h（q,p; κ）, which is introduced by smoothing out the Wigner operator △ω（q,p） br averaging over the ＂coarse graining＂ function exp[-κ（q＇ - q）^2- （p＇- p）^2/κ], is now regarded as a Weft correspondence connecting the Husimi operator △h（q, p; κ） with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify ｜p, q; κ ） such that △ h （ q, p; κ ） = ｜p, q;κ ） （P, q; κ｜, where ｜P, q;κ） is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to tnd the Husimi operator is presented.展开更多
It is interesting to investigate the OZI-forbidden decays of orthoquarkoknium, J/ψ→γπ^0（γη,γη′）, J/ψ→π^＋π^-（π^0π^0）. At first glance, there is infrared divergence in the above processes. In this wo...It is interesting to investigate the OZI-forbidden decays of orthoquarkoknium, J/ψ→γπ^0（γη,γη′）, J/ψ→π^＋π^-（π^0π^0）. At first glance, there is infrared divergence in the above processes. In this work, to clear the mist we use the factorization method with the light cone wavefunction of the final state light meson. We prove straightforwardly that the infrared divergence can be eliminated completely.展开更多
基金Supported by Foundation of Key Item of Science and Technology of Education Ministry of China,Foundation of Higher School of Ningxia(No.JY2002107)Foundation of Science of Ningxia University (No.022101)
文摘Aim To construct an analytic solution for the asymptotic field near a tensile cracktip of power-law hardening material under Plane stress condition. Methods Constructing funtion method was used. Results The exact asymptotic field was found. Conclusion The exact analytic solution for the problem is available.
文摘The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
基金Project(2012CB725400)supported by the National Basic Research Program of ChinaProjects(71271023,71322102,7121001)supported by the National Natural Science Foundation of China
文摘The assumption widely used in the user equilibrium model for stochastic network was that the probability distributions of the travel time were known explicitly by travelers. However, this distribution may be unavailable in reality. By relaxing the restrictive assumption, a robust user equilibrium model based on cumulative prospect theory under distribution-free travel time was presented. In the absence of the cumulative distribution function of the travel time, the exact cumulative prospect value(CPV) for each route cannot be obtained. However, the upper and lower bounds on the CPV can be calculated by probability inequalities.Travelers were assumed to choose the routes with the best worst-case CPVs. The proposed model was formulated as a variational inequality problem and solved via a heuristic solution algorithm. A numerical example was also provided to illustrate the application of the proposed model and the efficiency of the solution algorithm.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272071 and the Natural Science Foundation of Zhejiang Province of China under Grant No. Y606049
文摘We present a method of special conditional similarity reduction solutions for nonlinear partial differential equations, As concrete examples of its application, we apply this method to the （2＋1）-dimensional modified Broer- Kaup equations and the variable coefficient KdV-mKdV equation, which have extensive physics backgrounds, and obtain abundant exact solutions derived from some reduction equations.
基金the Funds for Basic Research Project under Grant Nos.06XJC033 and 2008Bl10003
文摘Based on the second integrable ease of known two-dimensional Hamiltonian system with a quartie potentiM, we propose a 4 × 4 matrix speetrM problem and derive a hierarchy of coupled KdV equations and their Hamiltonian structures. It is shown that solutions of the coupled KdV equations in the hierarchy are reduced to solving two compatible systems of ordinary differentiM equations. As an application, quite a few explicit solutions of the coupled KdV equations are obtained via using separability for the second integrable ease of the two-dimensional Hamiltonian system.
文摘Complex dynamics are studied in the T system, a three-dimensional autonomous nonlinear system. In particular, we perform an extended Hopf bifurcation analysis of the system. The periodic orbit immediately following the Hopf bifurcation is constructed analytically for the T system using the method of multiple scales, and the stability of such orbits is analyzed. Such analytical results complement the numerical results present in the literature. The analytical results in the post-bifurcation regime are verified and extended via numerical simulations, as well as by the use of standard power spectra, autocorrelation functions, and fractal dimensions diagnostics. We find that the T system exhibits interesting behaviors in many parameter regimes.
基金The project supported by National Natural Science Foundation of China under Grant No.10775097the President Foundation of the Chinese Academy of Sciences
文摘In this paper, the so-cMled Husimi operator △h（q,p; κ）, which is introduced by smoothing out the Wigner operator △ω（q,p） br averaging over the ＂coarse graining＂ function exp[-κ（q＇ - q）^2- （p＇- p）^2/κ], is now regarded as a Weft correspondence connecting the Husimi operator △h（q, p; κ） with its classical correspondence, since the integration kernel is just the Wigner operator. In this way we can easily identify ｜p, q; κ ） such that △ h （ q, p; κ ） = ｜p, q;κ ） （P, q; κ｜, where ｜P, q;κ） is a new kind of squeezed coherent states. The entangled Husimi operator is also treated in this way. Thus a simple way to tnd the Husimi operator is presented.
基金Supported by National Natural Science Foundation of China under Grant No. 10847117the Nature Science Fund of Hebei Province under Grant No. A2005000090Fund of Education Department of Hebei Province under Grant No. 2007409
文摘It is interesting to investigate the OZI-forbidden decays of orthoquarkoknium, J/ψ→γπ^0（γη,γη′）, J/ψ→π^＋π^-（π^0π^0）. At first glance, there is infrared divergence in the above processes. In this work, to clear the mist we use the factorization method with the light cone wavefunction of the final state light meson. We prove straightforwardly that the infrared divergence can be eliminated completely.
