Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions

We develop the concept and the calculus of anti-self dual (ASD) Lagrangians which seems inherent to many questions in mathematical physics, geometry, and differential equations. They are natural extensions of gradients of convex functions --hence of self-adjoint positive operators-- which usually drive dissipative systems, but also rich enough to provide representations for the superposition of such gradients with skew-symmetric operators which normally generate unitary flows. They yield variational formulations and resolutions for large classes of non-potential boundary value problems and initial-value parabolic equations. Solutions are minima of functionals of the form $I(u)=L(u, \Lambda u)$ (resp. $I(u)=\int_{0}^{T}L(t, u(t), \dot u (t)+\Lambda_{t}u(t))dt$) where $L$ is an anti-self dual Lagrangian and where $\Lambda_{t}$ are essentially skew-adjoint operators. However, and just like the self (and antiself) dual equations of quantum field theory (e.g. Yang-Mills) the equations associated to such minima are not derived from the fact they are critical points of the functional $I$, but because they are also zeroes of the Lagrangian $L$ itself.Comment: 50 pages. For the most updated version of this paper, please visit http://www.pims.math.ca/~nassif/pims_papers.htm

NATIONAL INNOVATION SYSTEM AND MACROECONOMIC POLICIES: BRAZIL AND INDIA IN COMPARATIVE PERSPECTIVE

Efforts towards economic development in Brazil and India share some common aspects. From the beginning of the 1950s to the end of the 1980s, both countries adopted import substitution policies including high tariffs and non-tariff barriers. Since the beginning of the 1990s, liberalizing economic reforms have been implemented by the respective Governments. If we compare the reach of the Brazilian reform to that of India, one could easily conclude that the former was more extensive and profound than the latter; and in conventional indicators of innovative effort such as research and development expenditures, education coverage, average years of education and literacy rate, Brazil’s results are a little bit better than those of India. However, since the beginning of the 1980s, India has been showing better general economic performance than Brazil. This paper argues and gives some empirical evidence to show that India’s performance is explained by its institutional capacity for coordinating conventional macroeconomic policies with other policies related to its National Innovation System.