On new forms of motive differential equations of a mechanical system relative to non-inertial frame

Based on D'Alembert's principle of a mechanical system relative to non-inertial frame and by introducing the concept of the generalized inertial potential, new forms of differential equations of motion of a mechanical system with holonomic and the non-holonomic constraints relative to the non-inertial frame are obtained. The merits and demerits between our method and the Newtonian dynamic method as well as the analytic dynamic method are discussed comparatively. Finally, two examples are given to illustrate the application of the motive differential equations in the new forms.     

On existence of solutions for some hyperbolic-parabolic-type chemotaxis systems

In this paper, we discuss the local and global existence ofweak solutions for some hyperbolic–parabolic systems modellingchemotaxis.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

Numerical analysis for the periodic response of nonsmooth dynamic systems of high-dimension

This paper deals with the numerical solution of high dimensional dynamic systems with nonsmooth characteristics, such as structural elastoplasticity, mechanical clearance and dry friction. As a stable periodic response of the system attracts its transient response, it may be extracted from the transient response somehow. The paper suggests a novel iteration scheme to extrapolate the periodic response from a short time history of its transient response by curve fitting. Compared with the current schemes such as shooting and incremental harmonic balancing, the present scheme makes full use of the information within the transient response and the system characters, then its computation efficiency has increased by an order and the numerical convergence depending on the initial iteration has greatly improved.The subject supported by the Chinese Foundation of Aeronautical Science     

THE MODELING AND ESTIMATION OF THE SHORT-RUN SUPPLY OF ROUNDWOOD UNDER NONLINEAR INCOME TAXES

This paper deals with the theory and estimation of the short-run supply of roundwood under nonlinear (progressive) income taxation. The theoretical part of the paper uses the two-period consumption harvesting model to introduce nonlinear income taxes into the forest management problem and presents a simple method to determine the optimal supply of roundwood in this case. In the empirical part of the paper, the model is specified in a way suitable for econometric analysis. The estimation method is the maximum likelihood method, and the estimation results seem to support the theoretical model. Finally, some results from model simulation imply that income taxation may have a nonnegligible impact on the supply of roundwood.     

The modified characteristic finite difference fractional steps method for the coupled system of fluid dynamics in porous media and its analysis

For the coupled system of multilayer fluid dynamics in porous media, the modified characteristic finite difference fractional steps method applicable to parallel arithmetic is put forward and two‐dimensional and three‐dimensional schemes are used to form a complete set. Some techniques, such as calculus of variations, energy method, piecewise biquadratic interpolation, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L² norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of multilayer fluid dynamics in porous media. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 665–681, 2003.     

A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

USING A SYSTEM DYNAMICS APPROACH TO MODEL SUSTAINABILITY INDICATORS FOR IRRIGATION SYSTEMS IN AUSTRALIA

ABSTRACT. An indicator defined as a function of the total water diversion through the Coleambally canal and the potential irrigation demand is selected to represent the sustainability of the irrigation water system in the Coleambally irrigation area, Australia. A simulation procedure using a system dynamics approach was developed to evaluate the indicator. The procedure includes water diversion assessment, potential crop water demand and total gross margin. Three cases of water supply options (surface water, ground water pumping and water trading), two cases of changes in the total agricultural area and three cropping pattern scenarios were simulated to better understand their impact on sustainability. The simulated results indicate that increasing the agricultural area reduces the sustainability of the irrigation system because the demand of water increased despite increase in the gross margin. The scenarios show that imposed water trading and ground water pumping would considerably increase the supply system having a positive impact on the sustainability. The paper concludes that a multi‐objective sustainability indicator taking account of economic and environmental issues could be more useful.     

Boundary control of a hyperbolic system with time lags

This paper considers an optimal boundary control problem fora hyperbolic system in which constant time lags appear in thestate equation and in the boundary condition simultaneously.Making use of Lion's scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.