In order to solve the problems of excess ovality and cross-section distortion of longitudinally submerged arc welding pipes after forming,a new three-roller continuous setting round process was proposed.This process c...In order to solve the problems of excess ovality and cross-section distortion of longitudinally submerged arc welding pipes after forming,a new three-roller continuous setting round process was proposed.This process can be divided into three stages:loading stage,roll bending stage and unloading stage.Based on the discretization idea,the mechanical model of the primary statically indeterminate problem of the longitudinally submerged arc welding pipes at the roll bending stage was established,and the deformation response was obtained.The simulation and theoretical results show that there are three positive bending regions and three reverse bending regions along the circumference of the pipe.The loading force of each roller shows growth,stability and downward trend with time.The error between the theoretical fitting curve and the simulated data point is very small,and the simulation results verify the reliability of the theoretical calculation.The experimental results show that the residual ovality decreases with the increase of the reduction,and the reduction of the turning point is the optimum reduction.In addition,the residual ovality of the pipe is less than 0.7%without cross-section distortion,which verifies the feasibility of this process.展开更多
Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number...Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）展开更多
We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of posit...We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].展开更多
In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the fir...In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.展开更多
This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, suf...This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established展开更多
基金supported by the National Natural Science Foundation of China (Nos. 52005431, 51705449 and 51975509)the Natural Science Foundation of Hebei Province of China (No. E2020203086)the National Major Science and Technology Projects of China (No. 2018ZX04007002)
文摘In order to solve the problems of excess ovality and cross-section distortion of longitudinally submerged arc welding pipes after forming,a new three-roller continuous setting round process was proposed.This process can be divided into three stages:loading stage,roll bending stage and unloading stage.Based on the discretization idea,the mechanical model of the primary statically indeterminate problem of the longitudinally submerged arc welding pipes at the roll bending stage was established,and the deformation response was obtained.The simulation and theoretical results show that there are three positive bending regions and three reverse bending regions along the circumference of the pipe.The loading force of each roller shows growth,stability and downward trend with time.The error between the theoretical fitting curve and the simulated data point is very small,and the simulation results verify the reliability of the theoretical calculation.The experimental results show that the residual ovality decreases with the increase of the reduction,and the reduction of the turning point is the optimum reduction.In addition,the residual ovality of the pipe is less than 0.7%without cross-section distortion,which verifies the feasibility of this process.
基金the Natural Science Foundation of Gansu Province of China
文摘Very recently, we have found that the method used in our recent paper （appeared in 2005） could be extended to obtain two general series-transformation formulas for formal power series defined over the complex number field. As usual, △, △k, D, and Dk denote, respectively, the difference and differential operators with △f（t） = f（t ＋ 1） - f（t）, Dr（t） = （d/dr）f （t） and △^0 = D0 = 1 （the identity operator）. What we have obtained are the following two general transformation formulas （formal expansion formulas） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=0△^kf（0）φ^（k）（0）t^k/k! （1） ∞∑k=0 f（k）φ^（k）（0）t^k/k!=∞∑k=01/k!f（0）φ^（k）（0）t^k/k! （2）
基金the Natural Science Foundation of Gansu Province(3ZS051-A25-016)NWNU-KJCXGCthe Spring-sun program(Z2004-1-62033).
文摘We study the existence of positive solutions of the three-point boundary value problem u＂＋g（t）f（u）=0,t∈（0,1）,u′（0）=0,u（1）=αu（η）, where η∈（0, 1）, and α∈R with 0 〈α〈 1. The existence of positive solutions is studied by means of fixed point index theory under some conditions concerning the first eigenvalue with respect to the relevant linear operator. The results, here essentially extend and improve the main result in [1].
基金supported by the National Basic Research Program of China ("973" Program) (Grant No. 2012CB720000)the National Natural Science Foundation of China (Grant Nos. 10832004 and 11102020)
文摘In this paper,a two-level search method for searching transfer opportunities between interplanetary halo orbits,exploiting the invariant manifolds of the restricted three-body problem,is proposed.In the method,the first-level search procedure is performed under the conditions of the initial time of escape manifold trajectory of the Sun-Earth halo orbit and the terminal time of capture manifold of the target planet fixed,by solving the optimal two-impulsive heliocentric trajectory to connect the two manifold trajectories.The contour map,helpful to the understanding of the global characteristics of the transfer opportunities,taking the initial time of escape manifold and the terminal time of capture manifold as variables,the optimal velocity increment of the first-level search as objective function,is used for the second-level search.Finally,taking the Earth-Mars and Earth-Venus halo to halo transfers for example,the transfer opportunities in 2015-2017 are searched.The results show the effectiveness of the proposed method and reveal the property of quasi-period of transfer opportunities between interplanetary halo orbits.
基金the Tutorial Scientific Research Program Foundation of Education Department of Gansu Province (Nos. 0710-040810-03)
文摘This paper deals with the existence of three positive solutions for a class of nonlinear singular three-point boundary value problem with p-Laplacian. By means of a fixed point theorem duo to Leggett and Williams, sufficient condition for the existence of at least three positive solutions to the nonlinear singular three-point boundary value problem is established
