In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directr...In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.展开更多
Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In ...Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.展开更多
In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obt...In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.展开更多
It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides tota...It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.展开更多
文摘In this paper, evolutions of ruled surfaces generated by the quasi normal and quasi binormal vector fields of space curve are presented. These evolutions of the ruled surfaces depend on the evolutions of their directrix using quasi frame along a space curve.
基金Supported by the National Natural Science Foundation of China(No.51575143)
文摘Tool path generated by space-filling curve always turns frequently causing trembling to machine,reducing toollife and affecting workpiece quality. Length and generation time of tool paths are both relatively long. In order to solve these problems,a toolpath generation method of NC milling based on space-filling curve is proposed. First,T-spline surface is regarded as the modeling surface,the grid,which is based on the limited scallop-height,can be got in the parameter space,and the influence value of grid node is determined. Second,a box is defined and planned,and the tool paths are got preliminarily,which is based on minimal spanning tree; Finally,based on an improved chamfering algorithm,the whole tool paths are got. A simulation system is developed for computer simulation,and an experiment is carried out to verify the method. The results of simulation and experiment show that the method is effective and feasible,and length and time of the tool paths are reduced.
基金jointly supported by the National Nature Science Foundation of China(Grants No.11774157,No.11934008,No.12075117,No.51721001,No.11890702,No.11625418,No.11535005,No.11690030)funded by the Natural Science Foundation of Shandong Province of China(Grant No.ZR2020MA091)。
文摘In Minkowski space M,we derive the effective Schrodinger equation describing a spin-less particle confined to a rotating curved surface S.Using the thin-layer quantization formalism to constrain the particle on we obtain the relativity-corrected geometric potential V_(g)’,and a novel effective potential V(g) related to both the Gaussian curvature and the geodesic curvature of the rotating surface.The Coriolis effect and the centrifugal potential also appear in the equation.Subsequently,we apply the surface Schrodinger equation to a rotating cylinder,sphere and toms surfaces,in which we find that the interplays between the rotation and surface geometry can contribute to the energy spectrum based on the potentials they offer.
文摘It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space form M12（4ε） of constant holomorphic sectional curvature 4s is of constant curvature 6. A natural question is ＂Besides totally geodesic ones how many Lagrangian surfaces of constant curvature εin M12（46） are there？＂ In an earlier paper an answer to this question was obtained for the case e = 0 by Chen and Fastenakels. In this paper we provide the answer to this question for the case ε≠0. Our main result states that there exist thirty-five families of Lagrangian surfaces of curvature ε in M12（4ε） with ε ≠ 0. Conversely, every Lagrangian surface of curvature ε≠0 in M12（4ε） is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.
