The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plo...The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.展开更多
An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be f...An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.展开更多
This paper presents a finite-difference(FD)method with spatially non-rectangular irregular grids to simulate the elastic wave propagation.Staggered irregular grid finite difference oper- ators with a second-order time...This paper presents a finite-difference(FD)method with spatially non-rectangular irregular grids to simulate the elastic wave propagation.Staggered irregular grid finite difference oper- ators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations.This method is very simple and the cost of computing time is not much.Complicated geometries like curved thin layers,cased borehole and nonplanar interfaces may be treated with non- rectangular irregular grids in a more flexible way.Unlike the multi-grid scheme,this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration.Compared with the rectangular irregular grid FD,the spurious diffractions from'staircase' interfaces can easily be eliminated without using finer grids.Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme.The Higdon's absorbing boundary condition is adopted to eliminate boundary reflections.Numerical simu- lations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces.The computation costs are less than those using a regular grid and rectangular grid FD method.展开更多
In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions ...In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions and trigonometric functions. The method used is a promising method to solve other nonlinear evaluation equations.展开更多
We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only ...We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.展开更多
Hyperbola is one of the important knowledge points in high school mathematics, and it is also a very common question type in the final question of college entrance examination mathematics. For the current hyperbola te...Hyperbola is one of the important knowledge points in high school mathematics, and it is also a very common question type in the final question of college entrance examination mathematics. For the current hyperbola teaching method, there is too single problem. It is not enough to only pay attention to the explanation of classroom knowledge. In the long run, students will lack practical application ability, and the cultivation of students' overall thinking will be ignored. This paper mainly analyzes some common learning mistakes in hyperbola teaching, and puts forward how to improve these mistakes, explores specific strategies to improve hyperbola teaching methods and teaching ideas, focusing on how to improve students' ability of mathematical analysis and application in senior high school.展开更多
基金funded by the National Natural Science Foundation of China(91025015,51178209)the Project of Arid Meteorological Science Research Foundation of China Meteorological Administration(IAM201608)
文摘The non-rectangular hyperbola(NRH)equation is the most popular method that plots the photosynthetic light-response(PLR)curve and helps to identify plant photosynthetic capability.However,the PLR curve can't be plotted well by the NRH equation at different plant growth phases due to the variations of plant development.Recently,plant physiological parameters have been considered into the NRH equation to establish the modified NRH equation,but plant height(H),an important parameter in plant growth phases,is not taken into account.In this study,H was incorporated into the NRH equation to establish the modified NRH equation,which could be used to estimate photosynthetic capability of herbage at different growth phases.To explore photosynthetic capability of herbage,we selected the dominant herbage species Potentilla anserina L.and Elymus nutans Griseb.in the Heihe River Basin,Northwest China as the research materials.Totally,twenty-four PLR curves and H at different growth phases were measured during the growing season in 2016.Results showed that the maximum net photosynthetic rate and the initial slope of PLR curve linearly increased with H.The modified NRH equation,which is established by introducing H and an H-based adjustment factor into the NRH equation,described better the PLR curves of P.anserina and E.nutans than the original ones.The results may provide an effective method to estimate the net primary productivity of grasslands in the study area.
文摘An extended hyperbola function method is proposed to construct exact solitary wave solutions to nonlinear wave equation based upon a coupled Riccati equation. It is shown that more new solitary wave solutions can be found by this new method, which include kink-shaped soliton solutions, bell-shaped soliton solutions and new solitary wave.The new method can be applied to other nonlinear equations in mathematical physics.
文摘This paper presents a finite-difference(FD)method with spatially non-rectangular irregular grids to simulate the elastic wave propagation.Staggered irregular grid finite difference oper- ators with a second-order time and spatial accuracy are used to approximate the velocity-stress elastic wave equations.This method is very simple and the cost of computing time is not much.Complicated geometries like curved thin layers,cased borehole and nonplanar interfaces may be treated with non- rectangular irregular grids in a more flexible way.Unlike the multi-grid scheme,this method requires no interpolation between the fine and coarse grids and all grids are computed at the same spatial iteration.Compared with the rectangular irregular grid FD,the spurious diffractions from'staircase' interfaces can easily be eliminated without using finer grids.Dispersion and stability conditions of the proposed method can be established in a similar form as for the rectangular irregular grid scheme.The Higdon's absorbing boundary condition is adopted to eliminate boundary reflections.Numerical simu- lations show that this method has satisfactory stability and accuracy in simulating wave propagation near rough solid-fluid interfaces.The computation costs are less than those using a regular grid and rectangular grid FD method.
文摘In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms of hyperbolic functions and trigonometric functions. The method used is a promising method to solve other nonlinear evaluation equations.
文摘We study a special class of lower trigonometric matrix value boundary value problems on hyperbolas. Firstly, the pseudo-orthogonal polynomial on hyperbola is given in bilinear form and it is shown that it is the only one. Secondly, a special boundary value problem of lower triangular matrix is presented and transformed into four related boundary value problems. Finally, Liouville theorem and Painlevé theorem and pseudo-orthogonal polynomials are used to give solutions.
文摘Hyperbola is one of the important knowledge points in high school mathematics, and it is also a very common question type in the final question of college entrance examination mathematics. For the current hyperbola teaching method, there is too single problem. It is not enough to only pay attention to the explanation of classroom knowledge. In the long run, students will lack practical application ability, and the cultivation of students' overall thinking will be ignored. This paper mainly analyzes some common learning mistakes in hyperbola teaching, and puts forward how to improve these mistakes, explores specific strategies to improve hyperbola teaching methods and teaching ideas, focusing on how to improve students' ability of mathematical analysis and application in senior high school.
