A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic functio...A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.展开更多
In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the B...In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.展开更多
This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of ...This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of （G＇/G）-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.展开更多
The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is present...The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.展开更多
In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is prop...In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.展开更多
Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Pain...Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.展开更多
The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper...The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.展开更多
In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented t...In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential Equations into nonlinear ordinary differential Equations. Afterwards, the (G'/G)-expansion method has been implemented, to celebrate the exact solutions of these Equations, in the sense of modified Riemann-Liouville derivative. As application, the exact solutions of time-space fractional Burgers’ Equation have been discussed.展开更多
In this paper,some travelling wave solutions involving parameters of the Modified Zakharov-Kuznetsovequation [Phys.Lett.A 372 (2008) 3400] are investigated.We will show that these solutions are not new travellingwave ...In this paper,some travelling wave solutions involving parameters of the Modified Zakharov-Kuznetsovequation [Phys.Lett.A 372 (2008) 3400] are investigated.We will show that these solutions are not new travellingwave solutions.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special param...In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special parameter where satisfies a second order linear differential equation , , where and are functions of .展开更多
In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The trav...In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.展开更多
In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burger...In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.展开更多
The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave sol...The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave solutions for the (1 + 1)-dimensional combined KdV-mKdV equation by using the novel (G'/G)-expansion method. Consequently, various traveling wave solutions patterns including solitary wave solutions, periodic solutions, and kinks are detected and exhibited.展开更多
In order to smooth the trajectory of a robot and reduce dwell time,a transition curve is introduced between two adjacent curves in three-dimensional space.G2 continuity is guaranteed to transit smoothly.To minimize th...In order to smooth the trajectory of a robot and reduce dwell time,a transition curve is introduced between two adjacent curves in three-dimensional space.G2 continuity is guaranteed to transit smoothly.To minimize the amount of calculation,cubic and quartic Bezier curves are both analyzed.Furthermore,the contour curve is characterized by a transition parameter which defines the distance to the corner of the deviation.How to define the transition points for different curves is presented.A general move command interface is defined for receiving the curve limitations and transition parameters.Then,how to calculate the control points of the cubic and quartic Bezier curves is analyzed and given.Different situations are discussed separately,including transition between two lines,transition between a line and a circle,and transition between two circles.Finally,the experiments are carried out on a six degree of freedom(DOF) industrial robot to validate the proposed method.Results of single transition and multiple transitions are presented.The trajectories in the joint space are also analyzed.The results indicate that the method achieves G2 continuity within the transition constraint and has good efficiency and adaptability.展开更多
SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 co...SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 code named STELLA is developed and verified at SNERDI （Shanghai Nuclear Engineering Research and Design Institute）. For SP3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation. In this work, SANM （semi-analytic nodal method） is used to solve diffusion-like equation, due to its easy to handle multi-group problem. Whole core nodal boundary net current coupling is used to improve convergence stability in SANM, instead of solving two-node problem. CMFD （coarse-mesh finite difference） acceleration method is employed for 0-th SP3 equation, which represents the neutron balance relationship. Three benchmarks are used to verify the SP3 code, STELLA. The first one is a self-defined one dimensional problem, which demonstrates SP3 method is extremely accurate, due to no academic approximation in one dimensional for SP3. The second one is a two dimensional one-group problem cited from Larsen＇s paper, which is usually used to verify and prove the SP3 code correct and accurate. And the third one is modified from 2D C5G7-MOX benchmark, whose numerical results indicate that STELLA is accurate and efficient in pin size level, compared to diffusion model.展开更多
In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental preci...In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10205007the National Natural Science Foundation Gansu Province of China under Grant No. 3zS041-A25-011
文摘A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.
文摘In this article, a novel （G＇/G）-expansion method is proposed to search for the traveling wave solutions of nonlinear evolution equations. We construct abundant traveling wave solutions involving parameters to the Boussinesq equation by means of the suggested method. The performance of the method is reliable and useful, and gives more general exact solutions than the existing methods. The new （G＇/G）-expansion method provides not only more general forms of solutions but also cuspon, peakon, soliton, and periodic waves.
文摘This paper presents a new function expansion method for finding travelling wave solutions of a nonlinear evolution equation and calls it the （w/g）-expansion method, which can be thought of as the generalization of （G＇/G）-expansion given by Wang et al recently. As an application of this new method, we study the well-known Vakhnenko equation which describes the propagation of high-frequency waves in a relaxing medium. With two new expansions, general types of soliton solutions and periodic solutions for Vakhnenko equation are obtained.
基金Supported by the International Cooperation and Exchanges Foundation of Henan Province (084300510060)the Youth Science Foundation of Henan University of Science and Technology of China (2008QN026)
文摘The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.
文摘In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.
基金Project supported by the National Key Basic Research Project of China (Grant No. 2004CB318000)the National Natural Science Foundation of China (Grant No. 10771072)
文摘Recently the （G′/G）-expansion method was proposed to find the traveling wave solutions of nonlinear evolution equations. This paper shows that the （G′/G）-expansion method is a special form of the truncated Painlev＇e expansion method by introducing an intermediate expansion method. Then the generalized （G′/G）-（G/G′） expansion method is naturally derived from the standpoint of the nonstandard truncated Painlev＇e expansion. The application of the generalized method to the mKdV equation shows that it extends the range of exact solutions obtained by using the （ G′/ G）-expansion method.
基金Projects(51504286,51374242)supported by the National Natural Science Foundation of ChinaProject(2015M572270)supported by China Postdoctoral Science FoundationProject(2015RS4004)supported by the Science and Technology Plan of Hunan Province,China
文摘The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.
文摘In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex transformation has been implemented to convert nonlinear partial fractional differential Equations into nonlinear ordinary differential Equations. Afterwards, the (G'/G)-expansion method has been implemented, to celebrate the exact solutions of these Equations, in the sense of modified Riemann-Liouville derivative. As application, the exact solutions of time-space fractional Burgers’ Equation have been discussed.
基金Supported by National Natural Science Foundation of China under Grant No.10671171
文摘In this paper,some travelling wave solutions involving parameters of the Modified Zakharov-Kuznetsovequation [Phys.Lett.A 372 (2008) 3400] are investigated.We will show that these solutions are not new travellingwave solutions.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
文摘In this paper, the generalized (G'/G)-expansion method is used for construct an innovative explicit traveling wave solutions involving parameter of the generalized FitzHugh-Nagumo equation , for some special parameter where satisfies a second order linear differential equation , , where and are functions of .
基金Supported by National Natural Science Foundation of China under Grant No. 10671172
文摘In a recent article [Physics Letters A 372 （2008） 417], Wang et al. proposed a method, which is called the （G′/G）-expansion method, to look for travelling wave solutions of nonlinear evolution equations. The travelling wave solutions involving parameters of the KdV equation, the mKdV equation, the variant Boussinesq equations, and the Hirota-Satsuma equations are obtained by using this method. They think the （G′/G）-expansion method is a new method and more travelling wave solutions of many nonlinear evolution equations can be obtained. In this paper, we will show that the （G′/G）-expansion method is equivalent to the extended tanh function method.
文摘In this work, the (G'/G)-expansion method is proposed for constructing more general exact solutions of two general form of Burgers type equation arising in fluid mechanics namely, Burgers-Korteweg-de Vries (Burgers-KdV) and Burger-Fisher equations. Our work is motivated by the fact that the (G'/G)-expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.
文摘The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave solutions for the (1 + 1)-dimensional combined KdV-mKdV equation by using the novel (G'/G)-expansion method. Consequently, various traveling wave solutions patterns including solitary wave solutions, periodic solutions, and kinks are detected and exhibited.
基金Supported by the National Natural Science Foundation of China(No.61573358)Research and Development of Large Multi-function Demolition Equipment in Disaster Site(No.2015BAK06B00)
文摘In order to smooth the trajectory of a robot and reduce dwell time,a transition curve is introduced between two adjacent curves in three-dimensional space.G2 continuity is guaranteed to transit smoothly.To minimize the amount of calculation,cubic and quartic Bezier curves are both analyzed.Furthermore,the contour curve is characterized by a transition parameter which defines the distance to the corner of the deviation.How to define the transition points for different curves is presented.A general move command interface is defined for receiving the curve limitations and transition parameters.Then,how to calculate the control points of the cubic and quartic Bezier curves is analyzed and given.Different situations are discussed separately,including transition between two lines,transition between a line and a circle,and transition between two circles.Finally,the experiments are carried out on a six degree of freedom(DOF) industrial robot to validate the proposed method.Results of single transition and multiple transitions are presented.The trajectories in the joint space are also analyzed.The results indicate that the method achieves G2 continuity within the transition constraint and has good efficiency and adaptability.
文摘SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 code named STELLA is developed and verified at SNERDI （Shanghai Nuclear Engineering Research and Design Institute）. For SP3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation. In this work, SANM （semi-analytic nodal method） is used to solve diffusion-like equation, due to its easy to handle multi-group problem. Whole core nodal boundary net current coupling is used to improve convergence stability in SANM, instead of solving two-node problem. CMFD （coarse-mesh finite difference） acceleration method is employed for 0-th SP3 equation, which represents the neutron balance relationship. Three benchmarks are used to verify the SP3 code, STELLA. The first one is a self-defined one dimensional problem, which demonstrates SP3 method is extremely accurate, due to no academic approximation in one dimensional for SP3. The second one is a two dimensional one-group problem cited from Larsen＇s paper, which is usually used to verify and prove the SP3 code correct and accurate. And the third one is modified from 2D C5G7-MOX benchmark, whose numerical results indicate that STELLA is accurate and efficient in pin size level, compared to diffusion model.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575160 and 11805074)the Postdoctoral Science Foundation of China(Grant Nos.2017M620308 and 2018T110750).
文摘In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.
