Non compact euclidean cone 3-manifolds with cone angles less than 2∏

We study of noncompact Euclidean cone manifolds with cone angles less than c&2π and singular locus a submanifold. More precisely, we describe its structure outside a compact set. As a corol lary we classify those with cone angles & 2π/3 and those with cone angles = 2π/3.

Tropical varieties for non-archimedean analytic spaces

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Cooperative vs. non-cooperative mechanisms in the EU decision making process

According to the account of the European Union (EU) decision making proposed in this paper, this is a bargaining process during which actors shift their policy positions with a view to reaching agreements on controversial issues.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

The EU as a security provider in its neighbourhood: the case of non-proliferation of WMD in the Mediterranean area

As a consequence of the terrorist attacks of 9/11 and the US-led war against Iraq, WMD and their proliferation have become a central element of the EU security agenda. In December 2003, the European Council adopted even a EU Strategy against Proliferation of WMD. The approach adopted in this Strategy can be largely described as a ‘cooperative security provider’ approach and is based on effective multilateralism, the promotion of a stable international and regional environment and the cooperation with key partners. The principal objective of this paper is to examine in how far the EU has actually implemented the ‘cooperative security provider’ approach in the area which the Non-proliferation Strategy identifies as one of its priorities – the Mediterranean. Focusing on the concept of security interdependence, the paper analyses first the various WMD dangers with which the EU is confronted in the Mediterranean area. Afterwards, it examines how the EU has responded to these hazards in the framework of the Barcelona process and, in particular, the new European Neighbourhood Policy. It is argued that despite its relatively powerful rhetoric, the EU has largely failed, for a wide range of reasons, to apply effectively its non-proliferation approach in the Mediterranean area and, thus, to become a successful security provider.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

Study of the influence of grain size and precipitates on the electromagnetic losses in different grades of non-oriented fully processed electrical steel

The study was performed in the installations of OCAS, a Steel Research Centre of ArcelorMittal. Taking M32 steel (3.25%Si+0.9%Al) as the basis chemical composition and three different thicknesses (0.35, 0.5 and 0.65mm), different annealing conditions (temperature and time) have been applied in the laboratory simulator at St. Chély, France. The aim was to link annealing parameters, grain size and energy loss. It was determined the optimum annealing parameters to reach the lowest power losses for three different grades of non-oriented fully processed electrical steel. In addition, M250-50 samples having different magnetic behaviour (high and low losses) but the same grain size and texture, have been analyzed in terms of TEM observations of their precipitates, in the University of Marseille. The results reveal that a high amount of medium and big precipitates (&10 nm) worsen the magnetic properties of the material. The small precipitates (&10nm) do not have a strong influence on the magnetic properties. The presence of precipitates can have a great influence on the power losses and further work is clearly necessary.

Link between microstructure and properties in new metallurgical concepts for very low loss non-oriented electrical steel

The influence of chemistry and soaking temperature (maximal temperature of the continuous annealing) on the final properties of non-oriented electrical steels has been studied. With this objective two different studies have been performed. First the Mn, Ni and Cr content of a low loss electrical steel composition has been modified. An intermediate content and a high content of each element has been added in order to study the influence of this components on the magnetic looses, grain size and texture. Secondly the influence of the soaking temperature on magnetic properties, grain size and oxidation in four grades of non-oriented electrical steels (Steel A, B, C and D) was studied.

Quasiconformal maps, analytic capacity, and non linear potentials

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The non-linear Dirichlet problem in Hadamard manifolds

We prove existence theorems for the Dirichlet problem for hypersurfaces of constant special Lagrangian curvature in Hadamard manifolds. The first results are obtained using the continuity method and approximation and then refined using two iterations of the Perron method. The a-priori estimates used in the continuity method are valid in any ambient manifold.

An Introduction to parametric and non-parametric models for bivariate positive insurance claim severity distributions

We present a real data set of claims amounts where costs related to damage are recorded separately from those related to medical expenses. Only claims with positive costs are considered here. Two approaches to density estimation are presented: a classical parametric and a semi-parametric method, based on transformation kernel density estimation. We explore the data set with standard univariate methods. We also propose ways to select the bandwidth and transformation parameters in the univariate case based on Bayesian methods. We indicate how to compare the results of alternative methods both looking at the shape of the overall density domain and exploring the density estimates in the right tail.

Stable stationary states of non-local interaction equations

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Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.