On the smooth locus of aligned Hilbert schemes: the k-secant lemma and the general projection theorem

Let X be a smooth, connected, dimension n, quasi-projective variety imbedded in \PP_N. Consider integers {k_1,...,k_r}, with k_i>0, and the Hilbert Scheme H_{k_1,...,k_r}(X) of aligned, finite, degree \sum k_i, subschemes of X, with multiplicities k_i at points x_i (possibly coinciding). The expected dimension of H_{k_1,...,k_r}(X) is 2N-2+r-(\sum k_i)(N-n). We study the locus of points where H_{k_1,...,k_r}(X) is not smooth of expected dimension and we prove that the lines carrying this locus do not fill up \PP_NComment: 17 pages, revised versio

Price Stability and the ECB'S monetary policy strategy

This paper focuses on the price stability objective within the framework of the single monetary policy strategy. It starts by reviewing what this objective, which is common to all central banks, means. Second, this paper focuses exclusively on the anchoring of short- to medium-term inflation expectations (Part 2). Several measures show that this anchoring is effective. A 'two-pillar' small structural macro-economic model framework is used to analyze the impact that this anchoring of expectations has on the determination of the short- to medium-term inflation rate. From this point of view, observed inflation in the euro area seems to be in line with the theory and the ECB's action seems to be very effective. Third, we focus on the other aspect of monetary stability: the degree of price-level uncertainty and the anchoring of inflation expectations in the medium to long term. Even though this assessment is more difficult than it is in the short to medium term, since we only have a track record covering 6 years, various indicators from the theoretical analysis paint a fairly reassuring picture of the effectiveness of the device used by the ECB.European Central Bank • Inflation • Monetary policy

Parallel computing for the finite element method

A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This paper describes how the modeling of large devices has been made possible using parallel computation, New algorithms are then proposed to implement this formulation on a cluster of workstations (10 DEC ALPHA 300X) and on a CRAY C98. Analysis of the computation efficiency is performed using simple problems. The electromagnetic scattering of a plane wave by a perfect electric conducting airplane is finally given as example

Stock Markets, Banks and Long Run Economic Growth: A Panel Cointegration-Based Analysis

The aim of this paper is to investigate the long run relationship between the development of banks and stock markets and economic growth. We make use of the Groen and Kleibergen (2003) panel cointegration methodology to test the number of cointegrating vectors among these three variables for 5 developing countries. In addition, we test the direction of potential causality between financial and economic development. Our results conclude to the existence of a single cointegrating vector between financial development and growth and of causality going from financial development to economic growth. We find little evidence of reverse causation as well as bi-directional causality.

Effective dielectric constant of random composite materials

The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for two-and three-dimensional structures, respectively. Owing to possible anisotropy the orientation of spatially fixed inhomogeneities of permittivity e1, embedded in a matrix of permittivity e2, affects the effective permittivity of the composite material sample. The primary goal of this paper is to analyze this orientation dependence. Second, the effect of the components geometry on the dielectric properties of the medium is studied. Third the effect of inhomogeneities randomly distributed within a matrix is investigated. Changing these three parameters provides a diverse array of behaviors useful to understand the dielectric properties of random composite materials. Finally, the data obtained from this numerical simulation are compared to the results of previous analytical wor

Complex effective permittivity of a lossy composite material

In recent work, boundary integral equations and finite elements were used to study the (real) effective permittivity for two-component dense composite materials in the quasistatic limit. In the present work, this approach is extended to investigate in detail the role of losses. We consider the special but important case of the axisymmetric configuration consisting of infinite circular cylinders (assumed to be parallel to the z axis and of permittivity e1) organized into a crystalline arrangement (simple square lattice) within a homogeneous background medium of permittivity e2=1. The intersections of the cylinders with the x – y plane form a periodic two-dimensional structure. We carried out simulations taking e15320.03i or e1=3-0.03i and e2=1. The concentration dependence of the loss tangent of the composite material can be fitted very well, at low and intermediate concentrations of inhomogeneities, with a power law. In the case at hand, it is found that the exponent parameter depends significantly on the ratio of the real part of the permittivity of the components. We argue, moreover, that the numerical results discussed here are consistent with the Bergman and Milton theory

Effective dielectric constant of periodic composite materials

We present computer simulation data for the effective permittivity (in the quasistatic limit) of a system composed of discrete inhomogeneities of permittivity e1, embedded in a three-dimensional homogeneous matrix of permittivity e2. The primary purpose of this paper is to study the related issue of the effect of the geometric shape of the components on the dielectric properties of the medium. The secondary purpose is to analyse how the spatial arrangement in these two-phase materials affects the effective permittivity. The structures considered are periodic lattices of inhomogeneities. The numerical method proceeds by an algorithm based upon the resolution of boundary integral equations. Finally, we compare the prediction of our numerical simulation with the effective medium approach and with results of previous analytical works and numerical experiments