Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions

We establish new existence results for multiple positive solutions of fourth-order nonlinear equations which model deflections of an elastic beam. We consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non-local boundary conditions, with a unified approach. Our method is to show that each boundary-value problem can be written as the same type of perturbed integral equation, in the space $C[0,1]$, involving a linear functional $\alpha[u]$ but, although we seek positive solutions, the functional is not assumed to be positive for all positive $u$. The results are new even for the classic boundary conditions of clamped or hinged ends when $\alpha[u]=0$, because we obtain sharp results for the existence of one positive solution; for multiple solutions we seek optimal values of some of the constants that occur in the theory, which allows us to impose weaker assumptions on the nonlinear term than in previous works. Our non-local boundary conditions contain multi-point problems as special cases and, for the first time in fourth-order problems, we allow coefficients of both signs

Gravitational perturbations of the Higgs field

We study the possible effects of classical gravitational backgrounds on the Higgs field through the modifications induced in the one-loop effective potential and the vacuum expectation value of the energy-momentum tensor. We concentrate our study on the Higgs self-interaction contribution in a perturbed FRW metric. For weak and slowly varying gravitational fields, a complete set of mode solutions for the Klein-Gordon equation is obtained to leading order in the adiabatic approximation. Dimensional regularization has been used in the integral evaluation and a detailed study of the integration of nonrational functions in this formalism has been presented. As expected, the regularized effective potential contains the same divergences as in flat spacetime, which can be renormalized without the need of additional counterterms. We find that, in contrast with other regularization methods, even though metric perturbations affect the mode solutions, they do not contribute to the leading adiabatic order of the potential. We also obtain explicit expressions of the complete energy-momentum tensor for general nonminimal coupling in terms of the perturbed modes. The corresponding leading adiabatic contributions are also obtained.Comment: 15 pages. Version accepted for publication in PRD. Error corrected in the angular integration in Appendix B. Conclusions changed. New section include

The Stability pact Pains: A Forward-Looking Assessment of the Reform Debate

The Stability and Growth Pact has been under fire ever since it was born.But is the Pact a flawed fiscal rule?Against established criteria for an ideal fiscal rule, its design and compliance mechanisms show strengths and weaknesses. The latter tend to reflect tradeoffs typical of supra-national arrangements.In the end, only a higher degree of fiscal integration would remove the inflexibility inherent in the recourse to predefined budgetary rules.No alternative solution put forward in the literature appears clearly superior.This does not mean that the original Pact of 1997 could not be improved.The debate on the SGP has shown that any reform should aim at overcoming the excessive uniformity of the rules, improving their transparency, correcting pro-cyclicality and strengthening enforcement.The reform of the Pact agreed in 2005 moves in this direction but leaves open a number of issues.EMS;fiscal policy;fiscal rules;Economic and Monetary Union;Stability and Growth Pact

Budgetary Policies during Recessions - Retrospective Application of the "Stability and Growth Pact" to the Post-War Period

Cover pagesText AnnexesThe purpose of this paper is to analyse budgetary policies carried out during and after severe recessions. Since the agreement on the "Stability and Growth Pact" by the European Council in Dublin in December 1996, interest in this issue has increased significantly. The Stability and Growth Pact, which sets the rules for budgetary behaviour in stage three of EMU, singles out severe recessions as specifically problematical periods during which a certain budgetary flexibility could be allowed. The rules laid out in the Stability and Growth Pact are used in this paper as a benchmark to evaluate past budgetary behaviour during recessions in the fifteen European Union Member States. More specifically, the paper provides elements to examine the following issues: what type of budgetary policies have been adopted during severe recessions in the past? Were the automatic stabilisers allowed to operate fully and did governments adopt an expansionary budgetary policy stance? Which factors influenced the policies undertaken and what was the composition of the measures adopted? Can the accumulation of debt, which took place in the past two decades in Europe, be explained by "tax smoothing" during periods of economic hardship?II/195/97-ENConcluding remarks The application of the provisions of the Excessive Deficit Procedure and the Stability and Growth Pact to the past is obviously a highly speculative exercise. Its results do not address the following questions: to what extent is past budgetary behaviour a reliable guide to assess the likely behaviour of national budgetary policies in EMU during recessions? More specifically, would Member States need larger or smaller changes in their budgetary positions to provide the degree of stabilisation which occurred in the past?A number of factors will play an important role:New policy regime under EMUDuring the third phase of EMU, the conduct of monetary policy will be centralised at the European level and will therefore no longer be available as a policy tool at the national level. Budgetary policy will thus be the main macroeconomic policy instrument still available for individual Member States to combat recessions, especially when shocks are asymmetric. The impossibility of lowering interest rates and resorting to currency devaluations might require larger deficit changes.On the other hand, according to the Mundell-Fleming framework, budgetary policy will in principle become more effective in dampening the amplitude of cyclical fluctuations in the new policy environment of EMU with centralised monetary policy and irrevocably fixed exchange rates between Member States.If, however, EMU enhances the process of economic integration, trade leakages of budgetary policies will gradually increase, thereby reducing the "domestic" effectiveness of budgetary policies. Unless national policies are co-ordinated, this factor raises the changes in the budget deficit required in order to attain the same degree of stabilisation achieved in the past."Pre-recession" deficit levelActual deficit changes observed during past recessions were applied in our retrospective exercise to "pre-recession" deficit levels chosen specifically for the exercise (0% and 2% of GDP). However, the actual deficit changes which took place during past severe recessions usually started from markedly higher pre-recession deficit levels. The impact on the economy of budgetary policy changes during recessions also varies depending on the deficit and debt levels. For instance, the markets' perception of an increase in the deficit from 0% to 2% of GDP during a severe recession will be different from that of a rise in the deficit from, say, 8% to 10% of GDP, the latter more likely being interpreted as shifting the deficit to an unsustainable path. This may lead to an increase in the risk premium on interest rates which reduces the effectiveness of the fiscal expansion.High budgetary imbalances may inhibit policy makers from using the budgetary instrument for stabilisation purposes. Indeed, the higher risk premiums which would raise the interest burden may represent a powerful disincentive to expanding fiscal policy in spite of the recession. As was pointed out in Section 4, budgetary reactions to economic downturns differ depending on the initial public finance conditions before the recession: countries with high deficit and debt levels tend to conduct tighter fiscal policies during recessions than those with lower deficit and debt levels. In the future, when medium-term targets have been achieved, Member States would have more room for manoeuvre to undertake accommodating policies.These factors point in different directions. As a consequence, the net effect on the requirement for budgetary stabilisation is ambiguous. If it proved necessary to reinforce the working of the automatic stabilisers during recessions in EMU, larger swings in budget deficits compared to the past would have to be allowed for. Under the provisions of the Stability and Growth Pact, this would imply, however, that during the third phase of EMU, Member States, and especially those with large automatic stabilisers, would have to run budgetary surpluses when in medium-term equilibrium.The present paper far from exhausts the issue of what can be learnt from the past budgetary behaviour for the implementation of the Stability and Growth Pact and, more generally, how budgetary authorities actually behaved in different economic circumstances.The following areas were not or were only partially covered, and therefore, provide scope for further research:Budgetary policies over the full cycle: this paper has focused essentially on recession episodes. The exercise could therefore be extended to other cyclical phases besides the recession. Indeed, as already indicated in this paper, the problem in the past has not been so much that Member States let budget deficits get out of hand too much during recessions but that they did not seize the opportunity presented by post-recession economic recovery to immediately correct their budgetary position.Composition of budgetary policies: the paper addressed the issue of the composition of budgetary policy reactions to recessions via a preliminary analysis of the overall revenue and expenditure components. Two extensions can be envisaged: first, an analysis of the composition of retrenchment policies over the years following the recession to assess, for instance, whether the length of the adjustment depends on the composition of budgetary consolidation; second, a further disaggregation of the overall components into more detailed government revenue and expenditure categories is necessary. This detailed analysis would allow conclusions to be drawn on the mechanisms causing budgetary policies to become unsustainable, as well as on the possible effectiveness and durability of budgetary consolidation efforts.recessions, modelling, fiscal policy, public finances

Magnetic properties of the double perovskites LaPbMSbO6 (M = Mn, Co and Ni)

New double perovskites LaPbMSbO6, where M2+ = Mn2+, Co2+, and Ni2+, were synthesized as polycrystals by an aqueous synthetic route at temperatures below 1000 oC. All samples are monoclinic, space group P21/n, as obtained from Rietveld analysis of X-ray powder diffraction patterns. The distribution of M2+ and Sb5+ among the two octahedral sites have 3% of disorder for M2+ = Ni2+, whereas for M2+ = Mn2+ and Co2+ less disorder is found. The three samples have an antiferromagnetic transition, due to the antiferromagnetic coupling between M2+ through super-superexchange paths M2+ - O2- - Sb5+ - O2- - M2+. Transition temperatures are low: 8, 10 and 17 K for Mn2+, Co2+, and Ni2+ respectively, as a consequence of the relatively long distances between the magnetic ions M2+. Besides, for LaPbMnSbO6 a small transition at 45 K was found, with ferrimagnetic characteristics, possibly as a consequence of a small disorder between Mn2+ and Sb5+. This disorder would give additional and shorter interaction paths: superexchange Mn2+ - O2- - Mn2+.Comment: 4 pages, 4 figures included. Manuscript submitted to IEEE Transactions on Magnetics, proceedings of the LAW3M 2013 conferenc