第一卷(三部分)第一部分:听力(略)第二部分:英语知识运用(共两节)第一节:单项填空(共15小题) 从A、B、C、D四个选项中,选出可以填入空白处的最佳选项。21.-You mean you know the man? No,Iknow man exactly like him. A.other B.the C...第一卷(三部分)第一部分:听力(略)第二部分:英语知识运用(共两节)第一节:单项填空(共15小题) 从A、B、C、D四个选项中,选出可以填入空白处的最佳选项。21.-You mean you know the man? No,Iknow man exactly like him. A.other B.the C.不填 D.a22.He is late, is often the case.展开更多
We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Lapla...We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.展开更多
A method exactly determining an event horizon and its temperature in a nonstatic space-time is proposed.Using the generalised Tortoise coordinate,we give exact location of event horison and exact Hawking temperature f...A method exactly determining an event horizon and its temperature in a nonstatic space-time is proposed.Using the generalised Tortoise coordinate,we give exact location of event horison and exact Hawking temperature for a general spherically symmetric evaporating black hole.展开更多
A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a probl...A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a problem that has never been resolved before, for the Green＇s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.展开更多
In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzent...In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.展开更多
The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction...The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion equation.When these parameters are taken to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.展开更多
Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presen...Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.展开更多
Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference...Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.展开更多
By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived sol...By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.展开更多
By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solu...By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.展开更多
The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical ...The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.展开更多
The present study develops a conformal mapping technique and deals with the exact analytic solutions in closed form to the finite width strip with single edge crack.Some exact solutions including a universal suitable ...The present study develops a conformal mapping technique and deals with the exact analytic solutions in closed form to the finite width strip with single edge crack.Some exact solutions including a universal suitable constant are found,which are very useful in science and engineering.展开更多
Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a La...Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.展开更多
By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of ...By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.展开更多
The conventional Markov chain Monte Carlo （MCMC） method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target ...The conventional Markov chain Monte Carlo （MCMC） method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis （AM） algorithm and delayed rejection （DR） algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset （AVO） inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and longoffset ranges but also it is more stable, accurate and antinoise.展开更多
The highpower pulsed power supply system for the magnetic field of the HL-2A Tokamak is described in this paper. The total output power of its eight magnetic field power supply units of nearly 250 MW. Their highest DC...The highpower pulsed power supply system for the magnetic field of the HL-2A Tokamak is described in this paper. The total output power of its eight magnetic field power supply units of nearly 250 MW. Their highest DC output voltage and current are 3510 V and 45 kA, respectively. All the units are operated in a pulsed mode. The pulse duration is 5 s, and the cyclic period is 15 min. The power supply system consists mainly of pulsed flywheel motor generators, rectifying transformers, thyristor converters, diode rectifiers and switches. The system incorporates many key technologies-supply equalization with two generators and four diode bridges, constant-angle phase triggers with a wide frequency range, current equalization, a status detector for the high current 6-phase converter, and advanced monitoring based on a programmable logic computer and engineering parameter measurement. The experimental results show that the performance of the power supply system satisfies the requirements of HL-2A experiments very well.展开更多
The dressed Hamiltonian describing the multiphoton process is presented by means of a canonical transformation.The exact eigenvalues and eigenstates are given for any set of parameters ω_(0),ω and ε.The general evo...The dressed Hamiltonian describing the multiphoton process is presented by means of a canonical transformation.The exact eigenvalues and eigenstates are given for any set of parameters ω_(0),ω and ε.The general evolution of this system is obtained.展开更多
In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified...In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.展开更多
文摘第一卷(三部分)第一部分:听力(略)第二部分:英语知识运用(共两节)第一节:单项填空(共15小题) 从A、B、C、D四个选项中,选出可以填入空白处的最佳选项。21.-You mean you know the man? No,Iknow man exactly like him. A.other B.the C.不填 D.a22.He is late, is often the case.
文摘We consider a profound problem of two-point resistance in the resistor network with a null resistor edge and an arbitrary boundary,which has not been solved before because the Green＇s function technique and the Laplacian matrix approach are invalid in this case.Looking for the exact solutions of resistance is important but difficult in the case of the arbitrary boundary since the boundary is a wall or trap which affects the behavior of a finite network.In this paper,we give a general resistance formula that is composed of a single summation by using the recursion-transform method.Meanwhile,several interesting results are derived by the general formula.Further,the current distribution is given explicitly as a byproduct of the method.
基金Supported by the National Natural Science Foundation of China.
文摘A method exactly determining an event horizon and its temperature in a nonstatic space-time is proposed.Using the generalised Tortoise coordinate,we give exact location of event horison and exact Hawking temperature for a general spherically symmetric evaporating black hole.
基金Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University,China(Grant No.15ZY16)
文摘A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform（RT） method, a problem that has never been resolved before, for the Green＇s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h_1= 1-cosφ_i-sinφ_icotnφ_i. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia Autonomous Region, Natural Science Foundation of Inner Mongolia Autonomous Region （Grant No 2004080201103） and the Youth Research Program of Inner Mongolia Normal University （Grant No QN005023）.
文摘In this paper, based on hyperbolic tanh-function method and homogeneous balance method, and auxiliary equation method, some new exact solitary solutions to the generalized mKdV equation and generalized Zakharov-Kuzentsov equation are constructed by the method of auxiliary equation with function transformation with aid of symbolic computation system Mathematica. The method is of important significance in seeking new exact solutions to the evolution equation with arbitrary nonlinear term.
文摘The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion equation.When these parameters are taken to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
基金Project supported by the National Natural Science Foundation of China （Grant No 10372053） and the Natural Science Foundation of Henan Province, China （Grant No 0311010900）.
文摘Based on the invariance of differential equations under infinitesimal transformations, Lie symmetry, laws of conservations, perturbation to the symmetries and adiabatic invariants of Poincaré equations are presented. The concepts of Lie symmetry and higher order adiabatic invariants of Poincaré equations are proposed. The conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are also given. In addition, an example is presented to illustrate these results.
基金Project supported by the National Natural Science Foundation of China （Grant No 10461006）, the Natural Science Foundation （Grant No 200408020103）, the High Education Science Research Program （Grant No NJ02035） of Inner Mongolia, China and the Youth Foundation （Grant No QN004024） of Inner Mongolia Normal University, China.
文摘Some new exact solitary wave solutions of the Hybrid lattice and discrete mKdV lattice are obtained by using a hyperbolic function approach. This approach can also be applied to other nonlinear differential-difference equations.
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y6100257, Y6110140, and Y6090681)the Natural Science Foundation of Zhejiang Lishui University, China (Grant Nos. KZ09005 and KY08003)
文摘By improved projective equation approach and a linear variable separation approach, a new family of exact solutions of the （2＋1）-dimensional Boiti-Leon-Pempinelli （BLP） system is derived. Based on the derived solitary wave solution, some dromion and solitoff excitations and chaotic behaviours are investigated.
文摘By using an improved projective Riccati equation method, this paper obtains several types of exact travelling wave solutions to the Benjamin Ono equation which include multiple soliton solutions, periodic soliton solutions and Weierstrass function solutions. Some of them are found for the first time. The method can be applied to other nonlinear evolution equations in mathematical physics.
基金Project supported by the National Natural Science Foundation of China (Grant No 10472067)
文摘The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.
基金Supported by the Doctorate Station Foundation of State Education Commission of China。
文摘The present study develops a conformal mapping technique and deals with the exact analytic solutions in closed form to the finite width strip with single edge crack.Some exact solutions including a universal suitable constant are found,which are very useful in science and engineering.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10472040 and 10372053）, the Natural Science Foundation of Hunan Province, China （Grant No 03JJY3005）, the Natural Science Foundation of Henan Province, China （Grant No 0311010900）, the 0utstanding Young Talents Training Fund of Liaoning Province, China （Grant No 3040005） and the Foundation of Young Key Member of the teachers in Institutions of Higher Learning of Henan Province of China.
文摘Based on the invariance of differential equations under infinitesimal transformations of group, Lie symmetries, exact invariants, perturbation to the symmetries and adiabatic invariants in form of non-Noether for a Lagrange system are presented. Firstly, the exact invariants of generalized Hojman type led directly by Lie symmetries for a Lagrange system without perturbations are given. Then, on the basis of the concepts of Lie symmetries and higher order adiabatic invariants of a mechanical system, the perturbation of Lie symmetries for the system with the action of small disturbance is investigated, the adiabatic invariants of generalized Hojman type for the system are directly obtained, the conditions for existence of the adiabatic invariants and their forms are proved. Finally an example is presented to illustrate these results.
基金Project supported by the National Natural Science Foundation of China（Grant No 10461006）, the High Education Science Research Program（Grant No NJ02035） of Inner Mongolia Autonomous Region, Natural Science Foundation of Inner Mongolia Autonomous Region（Grant No 2004080201103） and the Youth Research Program of Inner Mongolia Normal University（Grant No QN005023）.
文摘By use of an auxiliary equation and through a function transformation, the Jacobi elliptic function wave-like solutions, the degenerated soliton-like solutions and the triangle function wave solutions to two kinds of Korteweg de Vries （KdV） equations with variable coefficients and a KdV equation with a forcible term are constructed with the help of symbolic computation system Mathematica, where the new solutions are also constructed.
基金sponsorship of the National Natural Science Foundation of China (41674130, 41404088)the National Basic Research Program of China (973 Program, 2013CB228604, 2014CB239201)+1 种基金the National Oil and Gas Major Projects of China (2016ZX05027004-001, 2016ZX05002005-09HZ)the Fundamental Research Funds for the Central Universities (14CX02113A, 15CX08002A) for their funding in this research
文摘The conventional Markov chain Monte Carlo （MCMC） method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis （AM） algorithm and delayed rejection （DR） algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset （AVO） inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and longoffset ranges but also it is more stable, accurate and antinoise.
文摘The highpower pulsed power supply system for the magnetic field of the HL-2A Tokamak is described in this paper. The total output power of its eight magnetic field power supply units of nearly 250 MW. Their highest DC output voltage and current are 3510 V and 45 kA, respectively. All the units are operated in a pulsed mode. The pulse duration is 5 s, and the cyclic period is 15 min. The power supply system consists mainly of pulsed flywheel motor generators, rectifying transformers, thyristor converters, diode rectifiers and switches. The system incorporates many key technologies-supply equalization with two generators and four diode bridges, constant-angle phase triggers with a wide frequency range, current equalization, a status detector for the high current 6-phase converter, and advanced monitoring based on a programmable logic computer and engineering parameter measurement. The experimental results show that the performance of the power supply system satisfies the requirements of HL-2A experiments very well.
基金Supported by the National Natural Science Foundation of China.
文摘The dressed Hamiltonian describing the multiphoton process is presented by means of a canonical transformation.The exact eigenvalues and eigenstates are given for any set of parameters ω_(0),ω and ε.The general evolution of this system is obtained.
文摘In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space-time fractional modified Benjamin-Bona- Mahoney （mBBM） equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions： amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional deriva- tives are described in the modified Riemann-Liouville sense.
