THE EXISTENCE THEOREM OF OPTIMAL GROWTH MODEL

This paper proves a general existence theorem of optimal growth theory. This theorem is neither restricted to the case of a constant technology progress, nor stated in terms of mathematical conditions which have no direct economic interpretation and moreover, are difficult to apply.

Optimal transient growth in turbulent pipe flow

The optimal transient growth process of perturbations driven by the pressure gradient is studied in a turbulent pipe flow. A new computational method is proposed, based on the projection operators which project the governing equations onto the sub- space spanned by the radial vorticity and radial velocity. The method is validated by comparing with the previous studies. Two peaks of the maximum transient growth am- plification curve are found at different Reynolds numbers ranging from 20 000 to 250 000. The optimal flow structures are obtained and compared with the experiments and DNS results. The location of the outer peak is at the azimuthal wave number n = 1, while the location of the inner peak is varying with the Reynolds number. It is observed that the velocity streaks in the buffer layer with a spacing of 100δv are the most amplified flow structures. Finally, we consider the optimal transient growth time and its dependence on the azimuthal wave length. It shows a self-similar behavior for perturbations of different scales in the optimal transient growth process.

AN URBAN ECONOMIC GROWTH MODEL WITH ENDOGENOUS INFRASTRUCTURE ALLOCATION

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.

THE DYNAMICS OF FERTILITY IN C-K MODEL WITH ENDOGENOUS FERTILITY

Based on the Cass-Koopmans Model with endogenous fertility given in the paper [1-4], the fertility dynamics is discussed in this paper. It is proved that the first quadrant of the k,c plane is separated into two parts by a increasingly differentiable curve. The fertility increases with time on the upper half and decreases with time on the lower half. The fertility decreases along one arm of the economic growth path on which the per capita capital and per consumption increase and increases along the other arm of the economic growth path on which the per capita capital and per person consumption decrease under the condition 0 <θ≤α. This confirms the empirical finds that negative relationship between the economic growth and population growth.

China's Optimal Industrial Structure:Theoretical Model and Econometric Estimation

With analysis of producer's and factor supplier's dual optimization motives,this paper developed an optimal nominal output growth rate model that can conduct quantified estimation.Result of estimation of China's optimal industrial structure between1992 and 2009 indicates that optimal nominal output growth rate model has successfully quantified the impact of major events occurring in the process of China's economic operation on the level of deviation between actual industrial structure and optimal industrial structure.Quantitative indicators involved in this model can provide industrial policy instruments for the Chinese government in developing and adjusting industrial structure targets,optimizing resource allocation and advancing industrial structure optimization and upgrade.

Optimal Parameters for in Vitro Development of the Fungus Hydrocarbonoclastic Penicillium sp.

México has extensive areas that have been impacted by oil spills for several decades. Current bioremediation technologies mostly used microorganisms to decontaminate sites with hydrocarbons. This research evaluated the conditions for the optimal development of the strain of a hydrocarbonoclastic fungus, which was found in samples of soil contaminated with 4.0 × 105 mg·kg-1 of Total Petroleum Hydrocarbons (TPH). A completely randomized experimental design with a 3 × 3 × 4 factor arrangement was used: three levels of temperature (T1 = 29℃, T2 = 35℃ and T3 = 40℃), three of pH (pH1 = 3.5, pH2 = 5.0 and pH3 = 6.0) and four nutrients (N1 = Urea, N2 = Triple-17, N3 = Nitrophoska-Blue and N4 = Pure-Salts). Total fungi were isolated from the sampled soil and were sown in a combined carbon medium for hydrocarbonoclastic fungi and a strain was selected to be adapted to a liquid mineral medium. The selected strain was classified as Penicillium sp. Analyses of variance and mean tests were performed, using the SPSS-11.0 statistical software. The microorganisms showed the highest population growth in the treatment N2pH2T1, which reached a value of 2.1 × 106 CFU·mL-1 in a biorreactor. To reach it, by bioaugmentation, the same development of Penicillium sp. in a conditioned soil would allow to implement a bioremediation strategy with great potential to retrieve soil contaminated with hydrocarbons both in Tabasco and in general in Mexico.

Designing Electrochemical Nanoreactors to Accelerate Li_(2)S_(1/2) Three-Dimensional Growth Process and Generating More Li_(2)S for Advanced Li–S Batteries

With advantages of low costs and high energy density,Li–S batteries are considered as one of the most promising energy storage devices.However,Li_(2)S_(2) with a high dissociation energy and insulative properties is hard to convert into Li_(2)S,resulting in underutilization of sulfur capacity.Herein,Co-Mo_(2)C@C yolk–shell spheres as nanoreactors were designed to confront this challenge rationally.The Co-Mo_(2)C@C-induced Li_(2)S_(1/2) nucleation and growth in the three-dimensional process and the cathode produced more Li_(2)S after full discharge.Experimental studies and theoretical calculations reveal that the conversion barrier from Li_(2)S_(2) into Li_(2)S was lowered while the diffusion of lithium ions and electron transfer accelerated when using the Co-Mo_(2)C@C catalyst.Based on the above advantages,the Co-Mo_(2)C@C/S cathode exhibits a high reversible capacity and excellent cyclic stability,such as an initial specific capacity of 1200 mAh g^(−1) at 0.1 C with 709 mAh g^(−1) at 1.0 C after 1000 cycles with a low capacity fading rate of 0.04%per cycle.Even at high densities of 3.0 C and 5.0 C,the specific capacities are 647.6 and 557.7 mAh g^(−1) after 400 cycles,respectively.Impressively,it also shows ca.770 and 900 mAh g^(−1) at 0.2 C after 50 cycles with high sulfur loadings of 4.2 and 5.1 mg cm−2,respectively.The present work may provide new insights into the design of nanoreactors to promote Li_(2)S_(1/2) growth in a three-dimensional process and accelerate conversion from solid Li_(2)S_(2) to solid Li_(2)S in high performance Li–S batteries.

Transient growth in turbulent particle-laden channel flow

Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work.The problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid flow.The model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical simulation.It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel flow.This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region.The current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.

OPTIMAL CONTROL OF GROWTH RATE FOR A CLASS OF POPULATION SYSTEMS

In this paper,we discuss the optimal control of growth rate for a class of population systems governed by nonlinear degenerate parabolic equations.Given an ap-propriate cost functional,we prove the existence of the optimal growth rate and give some necessary conditions for optimal growth rate.

The Optimal Control for Regional Economic Growth

The model of consumption principle to realize the optimal growth of the regional economyis proposed on the base of analysing the relation of production and consumption with consumptionutility as optimization object. According to the model, the numerical value of the optimal control ofconsumption is given in order to realize the ninth five-year plan of the regional economic growth.

Parameter Estimation of S-Shaped Growth Model:A Modified Particle Swarm Algorithm

Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others.In this paper,a modified particle swarm optimization algorithm based on the diffusion phenomenon（DPPSO） was employed to estimate the parameters for this model.Under the sense of least squares,the parameter estimation problem of S-shaped growth model,taking the Gompertz and Logistic models for example,is transformed into a multi-dimensional function optimization problem.The results show that the DPPSO algorithm can effectively estimate the parameters of the S-shaped growth model.