A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Performance of the Public Electric Power Industry: Evidence from Pakistan

The study investigates the performance of electric power sector of Pakistan at the firm level, as well as the sector as a whole. It identifies and attempts to quantify the extent of inefficiencies. Since either physical or financial or productivity indicators alone are not able to explain the duality of public infrastructure purposes and the complexity of their multi-dimensional goals, a set of relevant physical, financial, and productivity indicators have been used in evaluating the performance of this sector. Further, a Cobb- Douglas production function has also been used to calculate the trend in the growth of total factor productivity. Economies of scale have also been studied in the case of electric power generation.

Low-complexity LSMR equalisation of FrFT-based multicarrier systems in doubly dispersive channels

The discrete fractional Fourier transform (FrFT) has been suggested to enhance performance over DFT-based multicarrier systems when transmitting over doubly-dispersive channels. In this paper, we propose a novel low-complexity equaliser for inter-symbol and inter-carrier interference arising in such multicarrier transmission system. Due to a lower spreading in the FrFT-domain compared to the DFTchannel matrix as compared to the DFT domain, the equaliser cam approximate the fractional-domain channel matrix by a band matrix. Further, we utilise the least squares minres (LSMR) algorithm in the calculation of the equalisation, which exhibits attractive numerical properties and low complexity. Simulation results demonstrate the superior performance of the proposed LSMR equaliser over benchmark schemes

Chirp-based multicarrier modulation

In this paper we demonstrate that in doubly-dispersive environments, a multicarrier (MC) system based on a fractional Fourier transform (FrFT) can achieve a better concentration of power near the main diagonal of the equivalent channel matrix compared to standard orthogonal frequency division multiplexing (OFDM). The resulting inter-symbol and inter-carrier interference in such a chirp- based MC system can therefore be suppressed with a reduced complexity equaliser. Simulations show that compared to an equalised OFDM system, the equalised FrFT-MC approach can either significantly reduce complexity or enhance performance in a time-varying environment

Great expectations: microfinance and poverty reduction in Asia and Latin America

Microfinance institutions (MFIs) are often seen by aid practitioners as a manifestly effective means of improving the position of the poor. Despite this widely held view, detailed research studies have been much more guarded about the impact of MFIs. In particular, several studies have raised doubts about the effectiveness of MFIs in reaching the “core poor”. This paper surveys the evidence from Asia and Latin America and contrasts experiences in the two regions. Studies on the former have been carried out more “rigorously”, but in both regions the evidence that microfinance is reaching the core poor is very limited.microfinance; poverty; Asia; Latin America

Industrial Policy in the Twenty-First Century

Industrial policy has attracted considerable controversy in the development context. This paper makes a case for a pragmatic and limited approach to interventions as a means of stimulating industrialization in the context of current and future challenges facing newly industrializing economies. It begins with a simple definition of industrial policy, a brief survey of the theoretical case, and a taxonomy of different possible interventions. Recent empirical evidence on the role of industrialization in development is examined, whilst considering how far government policy per se has contributed to manufacturing success. Finally, a series of key issues for today.s industrializing economies that industrial policy needs to address are highlighted.industrialization, government, trade, protection, productivity, exports

The Singular Set of Higher Dimensional Unstable Obstacle Type Problems

In this paper we will investigate the singular points of the following unstable free boundary problem: {equation}\label{Eq} \Delta u= -\chi_{\{u>0\}} \quad\quad\textrm{in} B_1(0) {equation} where $\chi_{\{u>0\}}$ is the characteristic function of the set $\{u>0\}$

China's Competitive Threat to Latin America: An Analysis for 1990-2002

This paper explores China's competitive threat to Latin America in trade in manufactures. The direct threat in exports to third country markets appears small: LAC's trade structure is largely complementary to that of China. In bilateral trade, several LAC countries are increasing primary and resource-based exports to China. However, the pattern of trade, with LAC specializing increasingly in resource-based products and China in manufactures, seems worrying. Given cumulative capability building, China's success in increasingly technology-based products with strong learning externalities can place it on a higher growth path than specialisation in 'simpler' goods, as in LAC. China may thus affect LAC's technological upgrading in exports and industrial production. The issue is not so much current competition as the 'spaces' open for LAC in the emerging technology-based world.