Size reduction and partial decoupling of systems of equations

A method is presented that reduces the number of terms of systems of linear equations (algebraic, ordinary and partial differential equations). As a byproduct these systems have a tendency to become partially decoupled and are more likely to be factorizable or integrable. A variation of this method is applicable to non-linear systems. Modifications to improve efficiency are given and examples are shown. This procedure can be used in connection with the computation of the radical of a differential ideal (differential Groebner basis)

A Policy Impact Evaluation Model For Scotland: Decoupling Single Farm Payments

The purpose of this paper is to assess the impacts of decoupling single farm payments in Scotland. It focuses on aggregate impacts on the agricultural products in domestic and external markets and the spill-over effect of this on the non-agricultural sector as well as an aggregate impact on the Scottish GDP. In order to capture system-wide impacts of the policy reform, a CGE model was formulated and implemented using a social accounting matrix constructed for Scotland. The simulation results suggest that the Scottish agricultural sector may encounter declines in output and factor us as a result of the policy reform. However, this critically depends on two factors: (a) the price effect of the policy reform on Scottish agricultural products relative to the EU average as well as the conditions of changes in world agricultural market prices; and (b) the extent to which customers would be sensitive to price effects of the policy reform. As far as the spill-over effect to the non-agricultural sector is concerned, decoupling of direct payments seems to have a positive spill-over effect. Similarly, the aggregate GDP effect is positive under all simulation scenarios. Critically, the simulation experiments indicate that policy shock may have a symmetrical outcome across the two sectors, with contractions in agriculture being accompanied by expansions in the non-agricultural sector, mainly because of factor market interactions between the two sectors.

Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities

Extending investigations of M\'etivier&Zumbrun in the hyperbolic case, we treat stability of viscous shock and boundary layers for viscous perturbations of multidimensional hyperbolic systems with characteristics of variable multiplicity, specifically the construction of symmetrizers in the low-frequency regime where variable multiplicity plays a role. At the same time, we extend the boundary-layer theory to ``real'' or partially parabolic viscosities, Neumann or mixed-type parabolic boundary conditions, and systems with nonconservative form, in addition proving a more fundamental version of the Zumbrun--Serre--Rousset theorem, valid for variable multiplicities, characterizing the limiting hyperbolic system and boundary conditions as a nonsingular limit of a reduced viscous system. The new effects of viscosity are seen to be surprisingly subtle; in particular, viscous coupling of crossing hyperbolic modes may induce a destabilizing effect. We illustrate the theory with applications to magnetohydrodynamics

From low-momentum interactions to nuclear structure

We present an overview of low-momentum two-nucleon and many-body interactions and their use in calculations of nuclei and infinite matter. The softening of phenomenological and effective field theory (EFT) potentials by renormalization group (RG) transformations that decouple low and high momenta leads to greatly enhanced convergence in few- and many-body systems while maintaining a decreasing hierarchy of many-body forces. This review surveys the RG-based technology and results, discusses the connections to chiral EFT, and clarifies various misconceptions.Comment: 76 pages, 57 figures, two figures updated, published versio

The Renormalization Group in Nuclear Physics

Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and its implementation in systems ranging from the deuteron to neutron stars, both formally and in practice. Flow equation approaches applied to Hamiltonians both in free space and in the medium will be emphasized. This is a conceptually simple technique to transform interactions to more perturbative and universal forms. An unavoidable complication for nuclear systems from both the EFT and flow equation perspective is the need to treat many-body forces and operators, so we will consider these aspects in some detail. We'll finish with a survey of current developments and open problems in nuclear RG.Comment: 37 pages; 49th Schladming Theoretical Physics Winter School lecture notes; to appear in Nucl. Phys. B Proc. Suppl. (2012

Welfare distribution between EU Member States through different national decoupling options. Implications for Spain

SUMMARY: This paper makes use of an agricultural sector model to analyse welfare effects derived from different national implementation options of the CAP Reform 2003. It shows that agricultural prices developed more favourable in a full premium decoupling scenario, since agricultural production declines more pronounced compared to a partial decoupling scenario. The use of the partial decoupling mechanism helps Member States to distribute income into less favoured areas but is not the optimal policy choice. However, if other Member States follow the same path of reform, a "prisoner's dilemma" will most likely be observed: partial decoupling appears as the preferred option for individual Member States, since high domestic production and high producer prices would be expected, but this would lead to welfare losses for consumers and taxpayers. Distribución de bienestar económico entre Estados Miembros ante distintas opciones de desacoplamiento en el marco de la nueva PAC – Consecuencias para España RESUMEN: Este trabajo modeliza los efectos en el bienestar económico derivados de distintas op-ciones de desacoplamiento de las primas contenidas en la reforma de la Política Agraria Común apro-bada tras los Acuerdos de Luxemburgo en 2003. Se observa como bajo un escenario de pleno desaco-plamiento, los precios agrarios evolucionan más favorablemente que bajo un desacoplamiento parcial debido a una caída de la producción más pronunciada. El uso del mecanismo de desacoplamiento par-cial permite a los estados miembros mantener determinados cultivos en zonas marginales, lo que resul-ta en una solución no óptima. Si los demás países siguieran el mismo camino de reforma, podría surgir un problema tipo "dilema del prisionero". La opción de desacoplamiento parcial aparecería como la opción preferida desde el punto de vista individual al asegurar una mayor producción doméstica y altos precios de producción. No obstante, a nivel agregado, el resultado sería una reducción de renta de consumidores y contribuyentes. PALABRAS CLAVE: Política Agraria Común, análisis de equilibrio parcial, modelización, desaco-plamiento, análisis de bienestar.Common Agricultural Policy, partial equilibrium analysis, modelling, decoupling, welfare analysis., Agricultural and Food Policy, C61, D60, Q18,