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

Externalizing tacit knowledge for improving leadership practices: Experiences from leadership programmes under ESRA

This paper draws upon the experiences gained from a leadership development course held at AKU-IED that included participants from 9 districts from Sind and Balochistan provinces. It describes the attempt, by the course planners, to conceptualize and deliver the course with a focus on externalizing participants’ tacit knowledge. The paper shares strategies used during the course, and describes successes and challenges in this respect, and the subsequent impact on participants’ learning and practices. Based on the outcome of the course, the paper suggests that the design of leadership and management development courses should focus clearly on strategies that capture and build upon the tacit knowledge of participants. The paper asserts that this approach helps to add more energy and interaction to the sessions and consequently increases the chances of impacting leadership practices of participants

Optimization of depth-based routing for underwater wireless sensor networks through intelligent assignment of initial energy

Underwater Wireless Sensor Networks (UWSNs) are extensively used to explore the diverse marine environment. Energy efficiency is one of the main concerns regarding performance of UWSNs. In a cooperative wireless sensor network, nodes with no energy are known as coverage holes. These coverage holes are created due to non-uniform energy utilization by the sensor nodes in the network. These coverage holes degrade the performance and reduce the lifetime of UWSNs. In this paper, we present an Intelligent Depth Based Routing (IDBR) scheme which addresses this issue and contributes towards maximization of network lifetime. In our proposed scheme, we allocate initial energy to the sensor nodes according to their usage requirements. This idea is helpful to balance energy consumption amongst the nodes and keep the network functional for a longer time as evidenced by the results provided

Topological Sensitivity Based Far-Field Detection of Elastic Inclusions

The aim of this article is to present and rigorously analyze topological sensitivity based algorithms for detection of diametrically small inclusions in an isotropic homogeneous elastic formation using single and multiple measurements of the far-field scattering amplitudes. A $L^2-$cost functional is considered and a location indicator is constructed from its topological derivative. The performance of the indicator is analyzed in terms of the topological sensitivity for location detection and stability with respect to measurement and medium noises. It is established that the location indicator does not guarantee inclusion detection and achieves only a low resolution when there is mode-conversion in an elastic formation. Accordingly, a weighted location indicator is designed to tackle the mode-conversion phenomenon. It is substantiated that the weighted function renders the location of an inclusion stably with resolution as per Rayleigh criterion.Comment: 31 pages, 1 figur