Infinitesimals without logic

We introduce a ring of the so-called Fermat reals, which is an extension of the real field containing nilpotent infinitesimals. The construction is inspired by Smooth Infinitesimal Analysis (SIA) and provides a powerful theory of actual infinitesimals without any background in mathematical logic. In particular, in contrast to SIA, which admits models in intuitionistic logic only, the theory of Fermat reals is consistent with the classical logic. We face the problem of deciding whether or not a product of powers of nilpotent infinitesimals vanishes, study the identity principle for polynomials, and discuss the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order-preserving geometrical representation. Using nilpotent infinitesimals, every smooth function becomes a polynomial because the remainder in Taylor's formulas is now zero. Finally, we present several applications to informal classical calculations used in physics, and all these calculations now become rigorous, and at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, which clarifies how to formalize the approximations tied with Hooke's law using the language of nilpotent infinitesimal

Industry reallocations in a globalizing economy

We distill the main insights from recent trade models on firms responses to globalisation. Our primary aim is to assess the economic impact and the welfare implications of the resulting reallocation of resources across firms and countries. In sodoing, we bring theory into life through the numerical implementation of a theoretical framework calibrated on European data, which encompasses aspects of economic geography, firm heterogeneity, and firms organizational choices. Our final purpose isto provide a comprehensive background for empirical investigations and to stimulate further theoretical research.international integration, resource reallocation, economic geography, firm heterogeneity, multinationals

Upward Point-Set Embeddability

We study the problem of Upward Point-Set Embeddability, that is the problem of deciding whether a given upward planar digraph $D$ has an upward planar embedding into a point set $S$. We show that any switch tree admits an upward planar straight-line embedding into any convex point set. For the class of $k$-switch trees, that is a generalization of switch trees (according to this definition a switch tree is a $1$-switch tree), we show that not every $k$-switch tree admits an upward planar straight-line embedding into any convex point set, for any $k \geq 2$. Finally we show that the problem of Upward Point-Set Embeddability is NP-complete

Successfull Blossom Thinning and Crop Load Regulation for Organic Apple Growing with Potassium-bi-carbonate (Armicarb(R)): Results of Field Experiments over 3 Years and with 11 Cultivars

With field trials over 3 years in a commercial organic orchard in Switzerland we have tested the efficacy of Armicarb® (potassium-bi-carbonate) for flower thinning in organic apple production. Over time, Armicarb was tested on 11 cultivars, at different application periods, in different concentrations, and always in comparison to other agents that are already allowed for thinning in organic fruit production in the European Union as e.g. lime sulphur, molasses, mechanical rope-thinner or combinations of methods. Armicarb proved to be an efficient and reliable thinning agent with an efficacy similar to the now recommended methods with rope device, molasses or lime sulphur but has the advantage to be an environmentally very friendly product. On the other hand, the risk for fruit russeting is comparably elevated especially with cultivars ‘Elstar’, ‘Golden Del.’ ’and ‘Gala’. Finally, we have elaborated cultivar-specific recommendations for the use of Armicarb for thinning purposes, which were the basis for the Swiss Federal approval to use Armicarb for thinning in conventional and organic apple production in 2011/2012

Critical behaviour of the O(3) nonlinear sigma model with topological term at theta=pi from numerical simulations

We investigate the critical behaviour at theta=pi of the two-dimensional O(3) nonlinear sigma model with topological term on the lattice. Our method is based on numerical simulations at imaginary values of theta, and on scaling transformations that allow a controlled analytic continuation to real values of theta. Our results are compatible with a second order phase transition, with the critical exponent of the SU(2)_1 Wess-Zumino-Novikov-Witten model, for sufficiently small values of the coupling.Comment: Revised version. 24 pages, 7 figure

Offshore Windfall: What Approval of the United States\u27 First Offshore Wind Project Means for the Offshore Wind Energy Industry

This comment explores the Cape Wind project with an emphasis on its role as the first United States offshore wind energy project. Part II of this comment explains the potential energy resource that offshore wind provides and examines some of the economic, technological, and regulatory challenges facing the development of offshore wind projects in United States waters. Part III of this comment introduces the Cape Wind project as a case study by briefly describing the particular political struggles and permitting challenges faced by its developers. Part IV of this comment analyzes how DOI approval and the eventual construction of Cape Wind will influence the offshore wind industry in the United States. This comment concludes that the offshore wind energy industry is poised for enormous growth immediately after Cape Wind\u27s turbines are spinning and providing electricity to the power grid