Lyapunov-type Inequalities for Partial Differential Equations

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones in the literature

Generalized effective hamiltonian for graphene under non-uniform strain

We use a symmetry approach to construct a systematic derivative expansion of the low energy effective Hamiltonian modifying the continuum Dirac description of graphene in the presence of non-uniform elastic deformations. We extract all experimentally relevant terms and describe their physical significance. Among them there is a new gap-opening term that describes the Zeeman coupling of the elastic pseudomagnetic field and the pseudospin. We determine the value of the couplings using a generalized tight binding model.Comment: 13 pages, 1 figure. Matches published version + 1 footnote added, typos correcte

Instrumental polarisation at the Nasmyth focus of the E-ELT

The ~39-m European Extremely Large Telescope (E-ELT) will be the largest telescope ever built. This makes it particularly suitable for sensitive polarimetric observations, as polarimetry is a photon-starved technique. However, the telescope mirrors may severely limit the polarimetric accuracy of instruments on the Nasmyth platforms by creating instrumental polarisation and/or modifying the polarisation signal of the object. In this paper we characterise the polarisation effects of the two currently considered designs for the E-ELT Nasmyth ports as well as the effect of ageing of the mirrors. By means of the Mueller matrix formalism, we compute the response matrices of each mirror arrangement for a range of zenith angles and wavelengths. We then present two techniques to correct for these effects that require the addition of a modulating device at the polarisation-free intermediate focus that acts either as a switch or as a part of a two-stage modulator. We find that the values of instrumental polarisation, Stokes transmission reduction and cross- talk vary significantly with wavelength, and with pointing, for the lateral Nasmyth case, often exceeding the accuracy requirements for proposed polarimetric instruments. Realistic ageing effects of the mirrors after perfect calibration of these effects may cause polarimetric errors beyond the requirements. We show that the modulation approach with a polarimetric element located in the intermediate focus reduces the instrumental polarisation effects down to tolerable values, or even removes them altogether. The E-ELT will be suitable for sensitive and accurate polarimetry, provided frequent calibrations are carried out, or a dedicated polarimetric element is installed at the intermediate focus.Comment: Accepted for publication in A&

Risk premium: insights over the threshold

The aim of this paper is twofold: First to test the adequacy of Pareto distributions to describe the tail of financial returns in emerging and developed markets, and second to study the possible correlation between stock market indices observed returns and return's extreme distributional characteristics measured by Value at Risk and Expected Shortfall. We test the empirical model using daily data from 41 countries, in the period from 1995 to 2005. The findings support the adequacy of Pareto distributions and the use of a log linear regression estimation of their parameters, as an alternative for the usually employed Hill's estimator. We also report a significant relationship between extreme distributional characteristics and observed returns, especially for developed countries

Capital market development : whither Latin America ?

Over the past decades, many countries have implemented significant reforms to foster capital market development. Latin American countries were at the forefront of this process. The authors analyze where Latin American capital markets stand after these reforms. They find that despite the intense reform effort, capital markets in Latin America remain underdeveloped relative to markets in other regions. Furthermore, stock markets are below what can be expected, given Latin America's economic and institutional fundamentals. The authors discuss alternative ways of interpreting this evidence. They argue that it is difficult to pinpoint which policies Latin American countries should pursue to overcome their poor capital market development. Moreover, they argue that expectations about the outcome of the reform process may need to be revisited to take into account intrinsic characteristics of emerging economies. The latter may limit the scope for developing deep domestic capital markets in a context of international financial integration.Markets and Market Access,Economic Theory&Research,Access to Markets,Financial Economics,Financial Intermediation

Innovative experiences in access to finance : market friendly roles for the visible hand ?

Interest in access to finance has increased significantly in recent years, as growing evidence suggests that lack of access to credit prevents lower-income households and small firms from financing high return investment projects, having an adverse effect on growth and poverty alleviation. This study describes some recent innovative experiences to broaden access to credit. These experiences are consistent with an emerging new view that recognizes a limited role for the public sector in financial markets, but contends that there might be room for well-designed, restricted interventions in collaboration with the private sector to foster financial development and broaden access. The authors illustrate this view with several recent experiences inLatin America and then discuss some open policy questions about the role of the public and private sectors in driving these financial innovations.Debt Markets,Banks&Banking Reform,,Emerging Markets,Bankruptcy and Resolution of Financial Distress