http://repository.tml.nul.ls:80/handle/123456789/195 2006-01-03T20:12:53Z http://repository.tml.nul.ls:80/handle/123456789/1460 Group classification, symmetry reductions and exact solutions of a generalized Korteweg-de Vries-Burgers equation Molati, M.; Khaliqu, C. M.; Adem, A.R. Lie group classification is performed on the generalized Korteweg-de Vries-Burgers equationut+δuxxx+g(u)ux−νuxx+γu=f(x), which occurs in many applications of physical phenomena. We show that the equation admits a four-dimensional equivalenceLie algebra. It is also shown that the principal Lie algebra consists of a single translation symmetry. Several possibleextensions of theprincipal Lie algebra are computed and their associated symmetry reductions and exact solutions are obtained. Also, one-dimensionaloptimal system of subalgebras is obtained for the case when the principal Lie algebra is extended by two symmetries. 2015-01-01T00:00:00Z http://repository.tml.nul.ls:80/handle/123456789/1459 Direct approach to a group classification problem: Fisher equation with time-dependent coefficients Molati, M.; Khalique, C. M. We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations. 2016-01-01T00:00:00Z http://repository.tml.nul.ls:80/handle/123456789/1325 The Advent of Coalition Politics and the Crisis of Constitutionalism in Lesotho 'Nyane, Hoolo The advent of coalition politics in the aftermath of the inconclusive 2012 election brought with it fresh challenges to constitutionalism in Lesotho. The challenges started with the process of the formation of government, sustenance of a coalition, and much more importantly, the executive powers of the office of Prime Minister. The country transitioned into the era of coalition politics with the same constitutional and legal framework which undergirded government in a single-party majoritarian setup. It did not take long until the country was plunged into a constitutional crisis which manifested itself through a stand-off between the Prime Minister and the Deputy Prime Minister. The crisis led to the collapse of the coalition government, barely two years into its normal electoral cycle. The purpose of this chapter is to analyse the nature of this constitutional crisis by studying the various constitutional episodes which characterised this crisis in 2014. The chapter contends that while some of these episodes may qualify to be called ‘constitutional crises’, not all incidences of political disagreement amounted to that. 2017-01-08T00:00:00Z http://repository.tml.nul.ls:80/handle/123456789/1166 Assignment of functions to local authorities in Lesotho Nyane, H. In Lesotho the adoption of the new constitution in 1993 made provision for local development. These constitutional provisions were only operationalised in 1997 through an Act of parliament (Local Government Act 1997). The question of how functions are assigned between the central and local governments has always been an area of dispute. The Act attempted to demarcate the assignments through the Schedules to the Act which embody the functions of local authorities at various levels – community councils, urban councils and district councils. However, local development and service delivery continue by and large to be undertaken by central government despite the demarcation. The purpose of this paper, therefore, is to critically analyse the challenges of assignment of functions to local authorities in Lesotho. The paper contends that as the assignment of functions is integral to decentralisation in Lesotho, intergovernmental relations and assignment of functions should be incorporated into the country’s constitution. 2016-12-01T00:00:00Z