A study of positive energy condition in Bianchi V spacetimes via Noether symmetries

In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motions in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Secondly we give physical interpretation of new cosmological solutions which satisfy positive energy condition and yield critical bounds on the expansion coefficient $\alpha$, in which the underlying non-flat spacetimes carry interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit $t\rightarrow \infty$. In particular a non-flat spacetime is obtained that mimics the expansion in a flat FRW universe dominated by vacuum energy such that the expansion factor has the same form in both. However, the energy density is dynamical in the former.Comment: Some typos are corrected. Some considerations into f(R) gravity is also carried out in the light of obtained results. Accepted for publication in EPJ

Linearizability of Systems of Ordinary Differential Equations Obtained by Complex Symmetry Analysis

Five equivalence classes had been found for systems of two second-order ordinary differential equations, transformable to linear equations (linearizable systems) by a change of variables. An "optimal (or simplest) canonical form" of linear systems had been established to obtain the symmetry structure, namely with 5, 6, 7, 8 and 15 dimensional Lie algebras. For those systems that arise from a scalar complex second-order ordinary differential equation, treated as a pair of real ordinary differential equations, a "reduced optimal canonical form" is obtained. This form yields three of the five equivalence classes of linearizable systems of two dimensions. We show that there exist 6, 7 and 15-dimensional algebras for these systems and illustrate our results with examples

Exogenous Shocks and Exchange Rate Management in Developing Countries

Even though globalization benefits less developed countries (LDCs), it also makes them more vulnerable to the exogenous shocks to the economies. Many LDCs rely on imported technologies and intermediate inputs to compete in the international export markets with better quality and cost efficient products. In this regard, exchange rate policies in respective countries have a direct bearing on the cost of production. This paper examines alternative exchange rate regimes to suggest an appropriate exchange rate policy in the context of developing countries. The paper utilizes a small open economy model involving direct supply-side effects of exchange rate and expectations of key economic variables and considers four possible exchange rate policies, e.g., fixed exchange rate, perfectly flexible exchange rate, leaning against the wind, and leaning with the wind. Contrary to the conventional wisdom, the paper finds that in the event of a shock, leaning against the wind is likely to be the most appropriate exchange rate policy. Moreover, in the event of rigid wages, a fixed exchange rate policy is advisable.globalization, exchange rate regimes, exchange rate policy

The influence of globalisation on the national education policies of developing countries

Globalisation as the most powerful phenomenon of the present time is widely contested for its positive and negative outcomes. This article distinguishes between political, economic and cultural globalisation and argues that globalisation as a process is mostly led and appreciated by the developed countries to meet their desired objectives, whereby underdeveloped countries are hurled into this process. Less equipped and less informed, these underdeveloped countries often stand in q disadvantaged position. The article maintains that several supra national economic, cultural and political organisations are the manifestation of the process of globalisation, which has made the policy making, process a complex phenomenon. The nation states have to deal with the pressures exerted by both other influential states and these international organisations, which seriously curtails the capacity of states to formulate its policies independent of any foreign influence and in favour of its citizens. Given this complex context, educational policies, like every other policy formed in underdeveloped countries,\u27 respond more to the globalisation process rather than national needs. This article tries to understand the globalisation phenomenon with respect to educational policy in underdeveloped countries and then explores the ways through which globalisation influences national educational policies

Leadership and management - are they alike?

This paper tries to distinguish between the leadership and management constructs to clarify the confusion caused by the loose usage of the terms in popular language. The two concepts should be understood as distinct for theoretical clarifications but not to argue for any hierarchical relationship. The paper tries to define both management and leadership, and then describes several ways the leadership construct is presented in the literature followed by a resolution of leadership definitions. Finally, the paper shares four criteria to distinguish between the leadership and the management functions. The paper concludes by arguing that leadership should be seen as a process and both leadership and management be differentiated from leader and manager, the former being the functions and later being actors. In addition, it is also fundamentally important that distinguishing between the two does not imply that one is superior to the other