Optimal Consumption in a Growth Model with the CES Production Function

Abstract

This article studies the optimization problem of maximizing the expected discounted present value of lifetime utility of consumption in the framework of one-sector neoclassical growth model with the Constant Elasticity of Substitution (CES) production function. We establish the existence of a classical solution of the Hamilton–Jacobi–Bellman (HJB) equation associated with this problem by the technique of viscosity solutions under the strict concavity of the utility function, and hence derive an optimal consumption from the optimality conditions in the HJB equation.     

Free Convection of Non-Newtonian Nanofluids in Porous media with Gyrotactic Microorganisms

The free convection of non-Newtonian nanofluids along a vertical plate in porous medium is investigated numerically. It is assumed that the medium contains gyrotactic microorganisms along with nanoparticles and the plate is subjected to prescribed temperature, concentration of nanoparticles and density of motile microorganisms. It is further assumed that the plate is impermeable. The governing partial differential equations are reduced to nonlinear ordinary differential equations using similarity transformations. The nonlinear ordinary differential equations are then solved by a finite difference numerical method. The effects of controlling parameters on several dimensionless quantities and numbers of our interest are investigated. The numerical results are compared with the published data and an excellent agreement has been found. It is found that nanofluid and bioconvection parameters have strong effects on local Nusselt, Sherwood and density numbers.     

Effect of self-generated magnetic field on the two-plasmon decay instability in a laser-produced plasma

Summary In this paper we have made a theoretical investigation on the two-plasmon decay instability of laser radiation in the presence of the selfgenerated magnetic field at the quarter-critical density region in a laserproduced plasma. The Vlasov equation in terms of guiding centre coordinates has been employed to obtain the nonlinear response of electrons in the plasma. The threshold power density of the incident laser radiation for the two-plasmon decay instability is always exceeded in currently employed power densities in laser-target experiments and above the threshold the growth rate of the instability is quite large. It is also noticed that the selfgenerated magnetic field enhances the threshold to a large extent, thus drastically reducing the growth rate of the instability. To speed up publication, the author of this paper has agreed to not receive the proofs for correction     

Nature and decay of long-lived species in activated atmospheric nitrogen

Pure nitrogen activated in the column of a steady arc discharge at 1 atm flows through a glass tube with an axially movable isothermal calorimeter to measure the energy flux, and a metal oxide powder detector to time the onset of the colour change. By separating potential and thermal energy fluxes the absolute concentration of excited species is found. The predominant component is thought to be metastable A-state molecules whose decay is controlled essentially by de-activating collisions with ordinary molecules;     

Epr studies on copper(II) [2,5-diphenyloxazole]2 (Clo4)2·4H2O

EPR studies have been carried out on the title complex in polycrystalline and solution forms at room and low temperatures. These studies in polycrystalline sample are indicative of oxygen coordination. In N,N'-dimethylformamide and pyridine solutions of this complex, the solvent molecules are found to occupy the coordination positions of copper(II).     

Electronegativity and linear electric field effect on γ-anti 13C chemical shifts

The contribution from the existence of a 1,3-diaxial H-α ?H-γ arrangement to the γ-anti effects of substituents X, which was previously believed to be generally shielding, is shown to be extremely dependent on the electronegativity of substituent X. In the presence of axial γ-substituents Y, linear electric field effects appear to play a significant role if the C-γ—Y bond is highly polarizable.     

A new naphthoquinone from Polygonum aviculare

A new naphthoquinone, 6-methoxyplumbagin was isolated from the acetone extracts of Polygonum aviculare. Its structure was elucidated by various spectroscopic methods. The known compounds sitosterol, oleanolic acid and 5,6,7,4'-tetramethoxyflavanone were also obtained from this natural source.