Investigation of Zero-Modes for a Dynamical Dpp-Brane

In this article, we investigate zero-modes for a dynamical (rotating-moving) D$p$-brane, coupled to the electromagnetic and tachyonic background fields. This work is done by the boundary state methods, in three cases of bosonic and fermionic boundary states and superstring partition function. By analyzing the obtained zero-modes in either of the cases, interesting results will be obtained. Our findings demonstrate the importance of the zero-mode and its effects on the background fields and the defined internal properties of the described system.Comment: 15 pages, 1 tabl

Sustainability and Optimality in Economic Development: Theoretical Insights and Policy Prospects

This paper takes sustainability to be a matter of intergenerational welfare equality and examines whether an optimal development path can also be sustainable. It argues that the general “zero-net-aggregate-investment” condition for an optimal development path to be sustainable in the sense of the maximin criterion of intergenerational justice is too demanding to be practical, especially in the context of developing countries. The maximin criterion of sustainability may be more appealing to the rich advanced industrial countries, but is too costly and ethically unreasonable for developing nations as it would act as an intergenerational “poverty equalizer”. The paper suggests that a compromise development policy that follows the optimal growth approach but adopts certain measures to mitigate the intergenerational and intragenerational welfare inequalities may better serve these countries. Some of the principal elements of such a policy are highlighted.Sustainability, Intergenerational Equity, Optimality, Discounting, Development Policy

On the Hybrid Minimum Principle On Lie Groups and the Exponential Gradient HMP Algorithm

This paper provides a geometrical derivation of the Hybrid Minimum Principle (HMP) for autonomous hybrid systems whose state manifolds constitute Lie groups $(G,\star)$ which are left invariant under the controlled dynamics of the system, and whose switching manifolds are defined as smooth embedded time invariant submanifolds of $G$. The analysis is expressed in terms of extremal (i.e. optimal) trajectories on the cotangent bundle of the state manifold $G$. The Hybrid Maximum Principle (HMP) algorithm introduced in \cite{Shaikh} is extended to the so-called Exponential Gradient algorithm. The convergence analysis for the algorithm is based upon the LaSalle Invariance Principle and simulation results illustrate their efficacy