In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeew...In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.展开更多
The relationship between forms and forces is one of the main topics of structural morphology. This harmonious coexisting link is very strong for systems in tensegrity state, commonly called ＂tensegrity systems＂. It ...The relationship between forms and forces is one of the main topics of structural morphology. This harmonious coexisting link is very strong for systems in tensegrity state, commonly called ＂tensegrity systems＂. It is currently apparent that, among the tensegrity systems, there also exist cable-bar cells with a discontinuous network of cables. It is possible to design a separate set of cables inside the cable-bar elementary cell and to establish a self-stress state of equilibrium. In this connection, the author of this paper suggested to assume a new Class-Theta tensegrity systems. Each of the basic tensegrity systems termed Class-Theta possesses an external and internal set of tension components. The shape of Greek capital letter 69 （Theta） reflects two sets of such components （two sets of tendons, cables, etc.）. This notation corresponds to Skelton＇s Class-k tensegrity structure. As shown in this paper, the Class-Theta tensegrity cell can exemplify a geometrically and practically useful form for the lightweight and long-span modular structures, mainly but not only in view of civil engineering and architecture.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.10671124
文摘In this paper, we investigate a class of mixed initial-boundary value problems for a kind of n × n quasilinear hyperbolic systems of conservation laws on the quarter plan. We show that the structure of the pieeewise C^1 solution u = u（t, x） of the problem, which can be regarded as a perturbation of the corresponding Riemann problem, is globally similar to that of the solution u = U（x/t） of the corresponding Riemann problem. The piecewise C^1 solution u = u（t, x） to this kind of problems is globally structure-stable if and only if it contains only non-degenerate shocks and contact discontinuities, but no rarefaction waves and other weak discontinuities.
文摘The relationship between forms and forces is one of the main topics of structural morphology. This harmonious coexisting link is very strong for systems in tensegrity state, commonly called ＂tensegrity systems＂. It is currently apparent that, among the tensegrity systems, there also exist cable-bar cells with a discontinuous network of cables. It is possible to design a separate set of cables inside the cable-bar elementary cell and to establish a self-stress state of equilibrium. In this connection, the author of this paper suggested to assume a new Class-Theta tensegrity systems. Each of the basic tensegrity systems termed Class-Theta possesses an external and internal set of tension components. The shape of Greek capital letter 69 （Theta） reflects two sets of such components （two sets of tendons, cables, etc.）. This notation corresponds to Skelton＇s Class-k tensegrity structure. As shown in this paper, the Class-Theta tensegrity cell can exemplify a geometrically and practically useful form for the lightweight and long-span modular structures, mainly but not only in view of civil engineering and architecture.
