Limit solutions of the Chern-Simons equation

We investigate the scalar Chern-Simons equation $-\Delta u + e^u(e^u-1) = \mu$ in cases where there is no solution for a given nonnegative finite measure $\mu$. Approximating $\mu$ by a sequence of nonnegative $L^1$ functions or finite measures for which this equation has a solution, we show that the sequence of solutions of the Dirichlet problem converges to the solution with largest possible datum \mu^# \le \mu and we derive an explicit formula of \mu^# in terms of $\mu$. The counterpart for the Chern-Simons system with datum $(\mu, \nu)$ behaves differently and the conclusion depends on how much the measures $\mu$ and $\nu$ charge singletons

Wave-like Solutions for Bianchi type-I cosmologies in 5D

We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and "wave-like". In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type-I, which can be applied to our universe after the big-bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry

Barriers to Diversification and Regional Allocation of Capital

In order to evaluate the allocational effectiveness of regional policy when harmonizing regional economic conditions firms? preferences play a pivot role. If harmonization hinders risk diversification of the firm, then instead of regional diversification of capital agglomeration of capital occurs. Hence, regional policy will not achieve its objective to equal the spatial allocation of capital. --Regional policy,agglomeration,diversification,allocation,risk aversion,prudence

A framework for closed-loop supply chains of reusable articles

Reuse practices contribute to the environmental and economical sustainability of production and distribution systems. Surprisingly, reuse closed-loop supply chains (CLSC) have not been widely researched for the moment. In this paper, we explore the scientific literature on reuse and we propose a framework for reusable articles. This conceptual structure includes a typology integrating under the reusable articles term different categories of articles (transportation items, packaging materials, tools) and addresses the management issues that arise in reuse CLSC. We ground our results in a set of case studies developed in real industrial settings, which have also been contrasted with cases available in existing literature.reverse logistics;case studies;closed-loop supply chains;returns managment

The Hardy Uncertainty Principle Revisited

We give a real-variable proof of the Hardy uncertainty principle. The method is based on energy estimates for evolutions with positive viscosity, convexity properties of free waves with Gaussian decay at two different times, elliptic $L^2$-estimates and the invertibility of the Fourier transform on L^2(\Rn) and \mathcal S'(\Rn)