A geometric characterization of a sharp Hardy inequality

In this paper, we prove that the distance function of an open connected set in $\mathbb R^{n+1}$ with a $C^{2}$ boundary is superharmonic in the distribution sense if and only if the boundary is {\em weakly mean convex}. We then prove that Hardy inequalities with a sharp constant hold on {weakly mean convex} $C^{2}$ domains. Moreover, we show that the {weakly mean convexity} condition cannot be weakened. We also prove various improved Hardy inequalities on mean convex domains along the line of Brezis-Marcus \cite{BM}.Comment: The results were improved to $C^2$ domain

Puzzling Tax Structures in Developing Countries: A Comparison of Two Alternative Explanations

Observed economic policies in developing countries differ sharply both from those observed among developed countries and from those forecast by existing models of optimal policies. For example, developing countries rely little on broad-based taxes, and make substantial use of tariffs and seignorage as nontax sources of revenue. The objective of this paper is to contrast the implications of two models designed to explain such anomalous policies. One approach, by Gordon-Li (2005), focuses on the greater difficulties faced in poor countries in monitoring taxable activity, and explores the best available policies given such difficulties. The other, building on Grossman-Helpman (1994), presumes that political-economy problems in developing countries are worse, leading to worse policy choices. The paper compares the contrasting theoretical implications of the two models with the data, and finds that the political-economy approach does poorly in reconciling many aspects of the data with the theory. In contrast, the forecasts from Gordon-Li model are largely consistent with the data currently available.

Tax Structure in Developing Countries: Many Puzzles and a Possible Explanation

Tax policies seen in developing countries are puzzling on many dimensions. To begin with, revenue/GDP is surprisingly small compared with that in developed economies. Taxes on labor income play a minor role. Taxes on consumption are important, but effective tax rates vary dramatically by firm, with many firms avoiding taxes entirely by operating through cash in the informal economy and others facing very high liabilities. Taxes on capital are an important source of revenue, as are tariffs and seignorage, all contrary to the theoretical literature. In this paper, we argue that all of these aspects of policy may be sensible responses if a government is able in practice to collect taxes only from those firms that make use of the financial sector. Through use of the financial sector, firms generate a paper trail, facilitating tax enforcement. The threat of disintermediation then limits how much can be collected in taxes. Taxes can most easily be collected from the firms most dependent on the financial sector, presumably capital-intensive firms. Given the resulting differential tax rates by sector, other policies would sensibly be used to offset these tax distortions. Tariff protection for capital-intensive firms is one. Inflation, imposing a tax on the cash economy is another.

Short-range ultrasonic communications in air using quadrature modulation

A study has been undertaken of ultrasonic communications methods in air, using a quadrature modulation method. Simulations were first performed to establish the likely performance of quadrature phase shift keying over the limited bandwidth available in an ultrasonic system. Quadrature phase shift keying modulation was then implemented within an experimental communication system, using capacitive ultrasonic sources and receivers. The results show that such a system is feasible in principle for communications over distances of several meters, using frequencies in the 200 to 400 kHz range

Progress and Challenges of Implementing Decentralized HIV Testing For Prevention of Mother-to-Child Transmission of HIV - Myanmar.

BackgroundMyanmar has adopted point-of-care (POC) HIV testing for its prevention of mother-to-child transmission of HIV program, and was initiated in 84 townships in 2013. This study assessed the progress of HIV testing uptake from 2012, one year prior to POC testing, to 2015, and the challenges faced by service providers during the rapid rollout of this testing strategy.MethodsThis serial cross-sectional study included 23 townships randomly selected from the 84 townships. An open-question survey was used to collect information on the challenges faced by service providers. A random effects logistic model was used for assessing the progress of HIV testing uptake among urban and rural health center groups.ResultsHIV testing uptake for antenatal care (ANC) attendees increased from 60% to 90% for rural and from 70% to 90% for urban attendees. The proportion of ANC attendees who were tested at their first visit increased from 70% to 80% for rural and from 70% to 90% for urban attendees. In addition, the proportion receiving same-day test results increased from less than 10% to 90% for both groups. Major challenges faced during the initial rollout included low health awareness among pregnant women, fear of stigma and discrimination, long travel times and costs, and increased workloads of providers in rural settings.Conclusions and global health implicationsThe program should consider recruiting local volunteers to help reduce the workloads of service providers. Professional education based on need and continued mentoring and quality control schemes for HIV testing need to be in place. This decentralized strategy would be applicable to other resource-limited countries