Stability of submanifolds with parallel mean curvature in calibrated manifolds

On a Riemannian manifold $\bar{M}^{m+n}$ with an $(m+1)$-calibration $\Omega$, we prove that an $m$-submanifold $M$ with constant mean curvature $H$ and calibrated extended tangent space $\mathbb{R}H\oplus TM$ is a critical point of the area functional for variations that preserve the enclosed $\Omega$-volume. This recovers the case described by Barbosa, do Carmo and Eschenburg, when $n=1$ and $\Omega$ is the volume element of $\bar{M}$. To the second variation we associate an $\Omega$-Jacobi operator and define $\Omega$-stablility. Under natural conditions, we prove that the Euclidean $m$-spheres are the unique $\Omega$-stable submanifolds of $\mathbb{R}^{m+n}$. We study the $\Omega$-stability of geodesic $m$-spheres of a fibred space form $M^{m+n}$ with totally geodesic $(m+1)$-dimensional fibres.Comment: Final version (Bull. Braz. Math. Soc. NS 41(4)(2010), 495-530. v.4 We add a criteria on the calibration for spheres in Euclidean spaces to be $\Omega$-stable. We give some natural conditions that enable us to conclude that the m-spheres are the unique $\Omega$-stable submanifolds in Euclidean spaces. We correct a misprint (missing a term in $C_{\Omega}$

Foreign direct investment: a tool or a target for industrial policy in Eastern Countries?

Is there any linkage between industrial policy and the inflow of Foreign Direct Investment in Eastern European countries? This is the core question which is analysed and discussed in this paper. The transition process of Central and Eastern Europe to a market economy has raised a lot of challenging questions both to Applied Economics and to Management Science. Enterprise adjustment remains one of the most interesting and complex as it is closely related to a wide range of economic, policy and management issues. Foreign Direct Investment, privatisation and industrial policy and their sort of linkage, remain some of the most interesting factors in the transition process. It seems that no sharp distinction can be presented between FDI as a target and FDI as a tool for industrial policy, but national differences remain significant as well as enterprises adjustment capacity

Conditional tests for elliptical symmetry using robust estimators

This paper presents a procedure for testing the hypothesis that the underlying distribution of the data is elliptical when using robust location and scatter estimators instead of the sample mean and covariance matrix. Under mild assumptions that include elliptical distributions without first moments, we derive the test statistic asymptotic behaviour under the null hypothesis and under special alternatives. Numerical experiments allow to compare the behaviour of the tests based on the sample mean and covariance matrix with that based on robust estimators, under various elliptical distributions and different alternatives. This comparison was done looking not only at the observed level and power but we rather use the size-corrected relative exact power which provides a tool to assess the test statistic skill to detect alternatives. We also provide a numerical comparison with other competing tests.Comment: In press in Communications in Statistics: Theory and Methods, 201