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This paper discuss the resource efficiency evaluation in complex network system. By using network DEA theory, we proposes a network DEA model that embodies the internal network structure for complex production efficiency evaluation. A sufficient condition for a complex production to be input efficient is discussed. Furthermore, by using the network DEA model, we investigate the internal resource waste in complex production from two different situations. One is the intermediate resource waste that called visible internal resource waste, and another is invisible internal resource waste. Examples shows that to improve the technical efficient of the production may increase its internal resource waste in complex network production1

The travelling wave solutions for Kdv-Burgers-Kuramoto equation are considered. the nonexistence of first integrals of traveling wave solutions equation of Kdv-Burgers-Kuramoto equation is shown. therefore, a sufficient condition of nonexistence of travelling wave solutions of Kdv-Burgers-Kuramoto equation is given. two independent one-parameter lie groups admitted by travelling wave solutions equation of Kdv-Burgers-Kuramoto equation are obtained.

The aim of this paper is to evaluate the agro-planting subsystem and mushroom cultivation subsystem and both the two's circulation system of a case study in Beijing Miyun water protective area using the emergy accounting methodology. The main findings of this work were that the agro-planting stage uses the highest amount of resources and has lower emergy yield rate (EYR) and emergy loading rate(ELR), the mushroom stage has higher EYR, is a more effective method to increase economic output using more non-renewable resources and purchased resources, but its environmental loading ratio is very high which means its sustainability is low. Actually, mushroom production is economically profitable and sustainable only when the system is syncretic with the planting system by affording the original materials of which is a circulation system. The circulation system's emergy yield rate(EYR) and emergy sustainability index(ESI) is comparative high than the two subsystems. Result demonstrate that extending the planting system chain to produce mushroom using planting wastes is one important method that can ensure higher economic profit and lower environment stress, the government should encourage this mode and provide so quantitative subsidies to the farmers and managers who takes this mode.

The classical gyroscope system (Euler-Poisson equations) is an important mechanics system, which describes the motion of a heavy rigid body moving around a fixed point. In this paper, the stability of an equilibrium state of gyroscope system is studied by using the energy-Casimir function method. The stability of a class of dynamics of gyroscope system is obtained.