A nonlinear control model of a firm describing the change of production and accumulated R&D investment is investigated. An optimal control problem with R&D investment rate as a control parameter is solved. Optimal dynamics of economic growth of a firm versus the current cost of innovation is studied. It is analytically determined that dependent on the model parameters, the optimal control must ...

A deterministic model of economic growth and pollution accumulation, in the form of a system of partial differential equations, is designed and analyzed. The model assumes pollution as a by-product of production. The stock of pollution has a negative impact on production. The accumulation of pollution is dampened by a share of the investments, in the form of an environmental tax. We consider a ...

Given an x0 ∈ Rn we study the infinite horizon problem of minimizing the expression ∫ T 0 f(t, x(t), x ′(t))dt as T grows to infinity where x : [0,∞) → Rn satisfies the initial condition x(0) = x0. We analyse the existence and the properties of approximate solutions for every prescribed initial value x0. We also establish that for every bounded set E ⊂ Rn the C([0, T ]) norms of approximate sol...

In this study, three extraction methods of polysaccharides in Purslane were compared and analyzed, and the best method was ascertained. Purslane polysaccharides were extracted using water, ultrasonic and microwave. By the results of single factor experiments and orthogonal experiments, the optimal extracting conditions were selected and then the best extraction method was determined. In order t...

inulin is widely distributed throughout the plant kingdom. it has been increasingly used in various foods due to its beneficial nutritional attributes as prebiotic ingredient. the helianthus tuberosus could be a source of inulin, but scarce studies about its extraction exist. ultrasound has attracted considerable interest in food science and technology due to its promising effects in food proce...

This paper applies real options theory into a resource extraction problem with capacity constraints and demand uncertainty. The producer decides on the optimal rate of extraction and the optimal time to build further capacity simultaneously. It is shown that previous results which suggest that extraction capacity should be built at the beginning, are not necessarily true under uncertainty. The ...

An extensive literature concerned with optimal depletion of an exhaustible resource, with only a few exceptions, ignores the economy-wide and sectoral distribution effects of resource depletion. This paper presents a dynamic computable general equilibrium model to link the underlying natural resource base to economic performance. The model consists of an intra-temporal price endogenous model of...