Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the...Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.展开更多
Let P=(po, p1,..., pn-1 ) and Q=(qo,q1..., qm-1) be two arbitrary convex polygonsin plane. In this paper, the author studies the problems of how to quickly determine their possiblecollision range and movable range. In...Let P=(po, p1,..., pn-1 ) and Q=(qo,q1..., qm-1) be two arbitrary convex polygonsin plane. In this paper, the author studies the problems of how to quickly determine their possiblecollision range and movable range. In the paper, a new sufficient and necessary condition for decidingpossible collision is proposed,and the basic characters of the oblique supporting lines are investigated,and on these grounds the problem to determine the possible collision range is transformed into thatof searching the supporting points on the sets of convex polygon vertexs. Using the strategy ofsearching simultaneously the sets of vertexes of P and Q, the author constructs the fast algorithmfor finding the supporting points, the time-complexity of which is O(log2(m + n)). Based on theseresults, the algorithms to quickly determine the range are given, which possess the time-complexityof O(log2(m+n)).展开更多
A new kind of tunnel support was put forward on the basis of the anchor spraysupport principle. The mechanics of the new three-dimensional steel bar shotcrete liningsupport was studied and the structure's internal...A new kind of tunnel support was put forward on the basis of the anchor spraysupport principle. The mechanics of the new three-dimensional steel bar shotcrete liningsupport was studied and the structure's internal forces were analyzed. The model experiment was done relying on the industrial test. The conclusion of numerical calculationsproved that the ANSYS program is reasonable and creditable. It was compared to otherkinds of support that are commonly used in soft rock tunnels. The technique and economiccontrasts of the typical tunnel with support three-dimensional steel bar were completed.展开更多
This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces ...This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.展开更多
文摘Guidance is offered for understanding and using the Legendre transformation and its associated duality among functions and curves. The genesis of this paper was encounters with colleagues and students asking about the transformation. A main feature is simplicity of exposition, while keeping in mind the purpose or application for using the transformation.
文摘Let P=(po, p1,..., pn-1 ) and Q=(qo,q1..., qm-1) be two arbitrary convex polygonsin plane. In this paper, the author studies the problems of how to quickly determine their possiblecollision range and movable range. In the paper, a new sufficient and necessary condition for decidingpossible collision is proposed,and the basic characters of the oblique supporting lines are investigated,and on these grounds the problem to determine the possible collision range is transformed into thatof searching the supporting points on the sets of convex polygon vertexs. Using the strategy ofsearching simultaneously the sets of vertexes of P and Q, the author constructs the fast algorithmfor finding the supporting points, the time-complexity of which is O(log2(m + n)). Based on theseresults, the algorithms to quickly determine the range are given, which possess the time-complexityof O(log2(m+n)).
文摘A new kind of tunnel support was put forward on the basis of the anchor spraysupport principle. The mechanics of the new three-dimensional steel bar shotcrete liningsupport was studied and the structure's internal forces were analyzed. The model experiment was done relying on the industrial test. The conclusion of numerical calculationsproved that the ANSYS program is reasonable and creditable. It was compared to otherkinds of support that are commonly used in soft rock tunnels. The technique and economiccontrasts of the typical tunnel with support three-dimensional steel bar were completed.
文摘This paper presents presents a new analytical solution of transverse vibration ofrectangular plaies simply supported at two opposite edges with arbitrary number ofelastic line supports in one way. The reaction forces of the elastic line supports areregarded as foe unknown external forces acted on the plate. The analytical solution ofthe differential equation of motion of the rectangular plate, which includes theunknown reaction forces. is gained. The frequency' equation is derived by using thelinear relationships between the reaction forces of the elastic line supports and thetransverse displacements of the plale along the elastic line supports. Therepresentations of foe frequency equation and the mode shape functions are differentfrom those obtained by other methods.
