The simple-shear condition is closer to reality than the direct-shear condition for simulating the mechanical behavior of vegetated soil slope under shallow failure.However,study on simple-shear characteristics for ve...The simple-shear condition is closer to reality than the direct-shear condition for simulating the mechanical behavior of vegetated soil slope under shallow failure.However,study on simple-shear characteristics for vegetated slope is still insufficient,and there lacks intuitive comparison of characteristics between these two shear conditions.In this study,large-scale simple-shear and direct-shear experiments were conducted on soil permeated by roots of Amorpha fruticosa to investigate the shear strength and stiffness.The stress-displacement relationship of each sample was obtained and further normalized to unify the influence of root content.The results reveal that the direct-shear condition overestimates the shear strength of root-permeated soils(by 41%)and thus the estimation of slope stability based on the parameters of direct-shear condition is not conservative.Furthermore,the initial stiffness of root-permeated soil under simple-shear condition is 34%lower than that under direct-shear condition.The higher strength and stiffness under direct-shear condition are caused by the following reasons:the shear plane does not have the lowest strength,the shear area is decreasing,and the shear zone is thinner.The significant deformation(lower stiffness)revealed by the simple-shear condition facilitates the application of early warning for vegetated shallow landslides.展开更多
The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Househo...The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.展开更多
In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this metho...In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence.展开更多
In this paper, we present a new family of iterative methods for solving nonlinear equations. It is proved that the order of convergence of this family is five. Two functions and two derivative evaluations should be co...In this paper, we present a new family of iterative methods for solving nonlinear equations. It is proved that the order of convergence of this family is five. Two functions and two derivative evaluations should be computed per iteration. To demonstrate convergence properties of the proposed family of methods, some numerical examples are given. Further numerical comparisons are made with several other existing fifth-order methods.展开更多
In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_...In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.展开更多
基金the financial supports from the National Natural Science Foundation of China(Grant No.41925030 and 4179043)the Second Tibetan Plateau Scientific Expedition and Research Program(STEP,Grant No.2019QZKK0904)the Natural Science Foundation of Shaanxi Province(2020JQ-041)。
文摘The simple-shear condition is closer to reality than the direct-shear condition for simulating the mechanical behavior of vegetated soil slope under shallow failure.However,study on simple-shear characteristics for vegetated slope is still insufficient,and there lacks intuitive comparison of characteristics between these two shear conditions.In this study,large-scale simple-shear and direct-shear experiments were conducted on soil permeated by roots of Amorpha fruticosa to investigate the shear strength and stiffness.The stress-displacement relationship of each sample was obtained and further normalized to unify the influence of root content.The results reveal that the direct-shear condition overestimates the shear strength of root-permeated soils(by 41%)and thus the estimation of slope stability based on the parameters of direct-shear condition is not conservative.Furthermore,the initial stiffness of root-permeated soil under simple-shear condition is 34%lower than that under direct-shear condition.The higher strength and stiffness under direct-shear condition are caused by the following reasons:the shear plane does not have the lowest strength,the shear area is decreasing,and the shear zone is thinner.The significant deformation(lower stiffness)revealed by the simple-shear condition facilitates the application of early warning for vegetated shallow landslides.
基金This research was supported by Universiti Kebangsaan Malaysia under research grant GUP-2019-033.
文摘The classical iterative methods for finding roots of nonlinear equations,like the Newton method,Halley method,and Chebyshev method,have been modified previously to achieve optimal convergence order.However,the Householder method has so far not been modified to become optimal.In this study,we shall develop two new optimal Newton-Householder methods without memory.The key idea in the development of the new methods is the avoidance of the need to evaluate the second derivative.The methods fulfill the Kung-Traub conjecture by achieving optimal convergence order four with three functional evaluations and order eight with four functional evaluations.The efficiency indices of the methods show that methods perform better than the classical Householder’s method.With the aid of convergence analysis and numerical analysis,the efficiency of the schemes formulated in this paper has been demonstrated.The dynamical analysis exhibits the stability of the schemes in solving nonlinear equations.Some comparisons with other optimal methods have been conducted to verify the effectiveness,convergence speed,and capability of the suggested methods.
文摘In this paper, we are going to present a class of nonlinear equation solving methods. Steffensen’s method is a simple method for solving a nonlinear equation. By using Steffensen’s method and by combining this method with it, we obtain a new method. It can be said that this method, due to not using the function derivative, would be a good method for solving the nonlinear equation compared to Newton’s method. Finally, we will see that Newton’s method and Steffensen’s hybrid method both have a two-order convergence.
文摘In this paper, we present a new family of iterative methods for solving nonlinear equations. It is proved that the order of convergence of this family is five. Two functions and two derivative evaluations should be computed per iteration. To demonstrate convergence properties of the proposed family of methods, some numerical examples are given. Further numerical comparisons are made with several other existing fifth-order methods.
文摘In this paper,we obtain the factorization of direct production and order of group GL（n,Z_m） in a simple method.Then we generalize some properties of GL（2,Z_p） proposed by Huppert,and prove that the group GL（2,Z_z^y） is solvable.We also prove that group GL（n,Z_p）is solvable if and only if GL（n,Z_p） is solvable,and list the generators of groups GL（n,Z_p） and SL（n,Z_p）.At last,we prove that PSL（2,Z_p）（ p〉3） and PSL（n,Z_p） （ n〉3） are simple.
