Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of...Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.展开更多
New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s pa...New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.展开更多
With the help of a level mapping,this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems.First,we introduce a kind of level mapping which generali...With the help of a level mapping,this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems.First,we introduce a kind of level mapping which generalizes one given in Han and Gong(Optimization 65:1337–1347,2016).Then,we give a sufficient condition for the upper semicontinuity and the lower semicontinuity of the level mapping.Finally,in terms of the semicontinuity of the level mapping,we establish the upper semicontinuity and the lower semicontinuity of the minimal solution set mapping to parametric setvalued vector optimization problems under the C-Hausdorff continuity instead of the continuity in the sense of Berge.展开更多
A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of el...A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.展开更多
文摘Among the solutions of three kinds of nonlinear equations in one dimensional systems, cubic nonlinear Klein-Gordon (including Φ~4), Sine-Gordon and double Sine-Gordon, some mapping relations exist. When a solution of any one equation is known, so are the other two.
文摘New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.
基金This research was supported by the National Natural Science Foundation of China(No.11801051).
文摘With the help of a level mapping,this paper mainly investigates the semicontinuity of minimal solution set mappings for set-valued vector optimization problems.First,we introduce a kind of level mapping which generalizes one given in Han and Gong(Optimization 65:1337–1347,2016).Then,we give a sufficient condition for the upper semicontinuity and the lower semicontinuity of the level mapping.Finally,in terms of the semicontinuity of the level mapping,we establish the upper semicontinuity and the lower semicontinuity of the minimal solution set mapping to parametric setvalued vector optimization problems under the C-Hausdorff continuity instead of the continuity in the sense of Berge.
基金the National Natural Science Foundation of China(No.51005180)the Ao-Xiang Star Project of NPU(Northwestern Polytechnical University)+2 种基金the Research Fund of the State Key Laboratory of Solidification Processing(NPU,China)(No.69-QP- 2011)the Program for New Century Excellent Talents in University by the Ministry of Education of China (No.NECT-08-0463)the 111 Project(No.B08040)
文摘A 2D finite element model was established for inertia friction welding of GH4169 nickel-base superalloy based on the ABAQUS environment.The remeshing and map solution techniques were adopted to solve the problem of element distortion.The effect of rotation speed on the temperature field and axial shortening of joints was investigated.The results show that the interface temperature increases rapidly to higher than 900℃within 1s.And then,it increases slowly to a quasi-stable value.The axial shortening begins to augment quickly when a uniform interface temperature field has formed and the plasticized material is extruded from the interface to form an obvious flash.The rotation speed of the flywheel controls the welding process and has a significant influence on the temperature evolution and axial shortening of joints.
