Overlapping generations economy, environmental externalities, and taxation

I set up in this paper an overlapping generations economy with envi-ronment degrading itself and pollution resulting from both consumption and production to show that there always exists an inter-temporal equi-librium and to determine the competitive steady state. This steady state is compared with the equilibrium steady state in the social benevolent planner's point of view. The paper shows the optimal golden rule allo-cation which maximizes the total utility of all generations, and whenever the capital ratio in the competitive framework is higher than the golden rule capital ratio, the economy stands on the dynamically inecient point. The width of the inecient range of capital ratio depends positively on the environment maintaining technology and depends negatively on the cleanness of production technology. For such any competitive economy, I introduce some combinations of taxes and transfer with purpose of de-centralizing the best steady state attainable through the good and factors markets.overlapping generations, environmental externality, taxes and transfer scheme.

Implementing steady state efficiency in overlapping generations economies with environmental externalities

We consider in this paper overlapping generations economies with polution resulting from both consumption and production. The competitive equilibrium steady state is compared to the optimal steady state from the social planner's viewpoint. We show that any competitive equilibrium steady state whose capital-labor ratio exceeds the golden rule ratio is dynamically inefficient. Moreover, the range of dynamically efficient steady states capital ratios increases with the effectiveness of the environment maintainance technology, and decreases for more polluting production technologies. We characterize some tax and transfer policies that decentralize as a competitive equilibrium outcome the social planner's steady state.Overlapping generations, environmental externality, tax and transfer policy.

Optimal Control of Sweeping Processes in Robotics and Traffic Flow Models

The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and completely calculate optimal solutions in particular situations

Initial trace of solutions of Hamilton-Jacobi parabolic equation with absorption

Here we study the initial trace problem for the nonnegative solutions of the equation $$u\_{t}-\Delta u+|\nabla u|^{q}=0$$ in $Q\_{\Omega,T}=\Omega\times\left( 0,T\right) ,$ $T\leqq\infty,$ where $q>0,$ and $\Omega=\mathbb{R}^{N},$ or $\Omega$ is a smooth bounded domain of $\mathbb{R}^{N}$ and $u=0$ on $\partial\Omega\times\left( 0,T\right) .$ We can define the trace at $t=0$ as a nonnegative Borel measure $(\mathcal{S} ,u\_{0}),$ where $S$ is the closed set where it is infinite, and $u\_{0}$ is a Radon measure on $\Omega\backslash\mathcal{S}.$ We show that the trace is a Radon measure when $q\leqq1.$ For $q\in(1,(N+2)/(N+1)$ and any given Borel measure, we show the existence of a minimal solution, and a maximal one on conditions on $u\_{0}.$ When $\mathcal{S}$ $=\overline{\omega}\cap\Omega$ and $\omega$ is an open subset of $\Omega,$ the existence extends to any $q\leqq2$ when $u\_{0}\in L\_{loc}^{1}(\Omega)$ and any $q>1$ when $u\_{0}=0$. In particular there exists a self-similar nonradial solution with trace $(\mathbb{R}^{N+},0),$ with a growth rate of order $\left\vert x\right\vert ^{q^{\prime}}$ as $\left\vert x\right\vert \rightarrow\infty$ for fixed $t.$ Moreover we show that the solutions with trace $(\overline{\omega},0)$ in $Q\_{\mathbb{R}^{N},T}$ may present near $t=0$ a growth rate of order $t^{-1/(q-1)}$ in $\omega$ and of order $t^{-(2-q)/(q-1)}$ on $\partial \omega.

Synthesis Of A Novel Family Of Amide Derivatives Of Podocarpic Acid

As a class, amides are of great interest in biological studies and pharmaceutical application. In this work, podocarpic acid, a natural tricyclic diterpene, derived from Podocarpus species, has been employed to form a novel family of amide derivatives which will later be studied for their potential as new drug leads. Novel amide derivatives of podocarpic acid were synthesized from podocarpic acid in three steps. The first step involved methylation with dimethylsulfate to form methyl-O-methylpodocarpate. This step was followed by iodination with iodine to give iodomethyl-O-methylpodocarpate. Finally amidation with various aliphatic amides using a copper catalyst yielded four amide derivatives of podocarpic acid. However, iodomethyl-O-methylpodocarpate did not react with aromatic amides. This is perhaps because of the reduction in electrophilicity of an aromatic amide versus an aliphatic amide. Thus this research had led to the discovery of a method that is selective for the synthesis of aliphatic amide derivatives of podocarpic acid. Furthermore, five novel derivatives of podocarpic acid have been synthesized. Therefore a small library of novel compounds has been synthesized by utilizing selective methodology, that are now available for future examination of their anticancer and anti-tuberculosis properties