An obstruction for q-deformation of the convolution product

We consider two independent q-Gaussian random variables X and Y and a function f chosen in such a way that f(X) and X have the same distribution. For 0 < q < 1 we find that at least the fourth moments of X + Y and f(X) + Y are different. We conclude that no q-deformed convolution product can exist for functions of independent q-Gaussian random variables.Comment: The proof of proposition 2 is corrected on 11 january 199

On matrices for which norm bounds are attained

Let $\|A\|_{p,q}$ be the norm induced on the matrix $A$ with $n$ rows and $m$ columns by the H\"older $\ell_p$ and $\ell_q$ norms on $R^n$ and $R^m$ (or $C^n$ and $C^m$), respectively. It is easy to find an upper bound for the ratio $\|A\|_{r,s}/\|A\|_{p,q}$. In this paper we study the classes of matrices for which the upper bound is attained. We shall show that for fixed $A$, attainment of the bound depends only on the signs of $r-p$ and $s-q$. Various criteria depending on these signs are obtained. For the special case $p=q=2$, the set of all matrices for which the bound is attained is generated by means of singular value decompositions

Internet-based 'social sharing' as a new form of global production: The case of SETI@home

Benkler ('Sharing Nicely', Yale Law Journal, 2004, Vol. 114, pp. 273-358) has argued that 'social sharing' via Internet-based distributed computing is a new, so far under-appreciated modality of economic production. This paper presents results from an empirical study of SETI@home (the Search for Extraterrestrial Intelligence), which is the classic example of such a computing project. The aim is to explain SETI@home participation and its intensity in a cross-country setting. The data are for a sample of 172 developed and developing countries for the years 2002-2004. The results indicate that SETI@home participation and its intensity can be explained largely by the degree of ICT access (proxied by the International Telecommunication Union's 'Digital Access Index'), as well as GDP per capita and dummy variables for major country groups. Some other variables, such as the Human Development Index, perform less well. Although SETI@home is a global phenomenon, it is never-the-less mostly concentrated in rich countries. However, there are indications of a slowly narrowing global SETI@home digital divide

The EU as a security actor in Africa

Instability and conflict in Africa create a range of security problems for Europe. Rapidly increasing migration via the Mediterranean Sea, extremism and terrorism, as well as cross-border crime, all have implications for security in Europe, but are spill-over effects of instability outside Europe. The European Union has a considerable interest in a stable Africa, and also seems willing to assume a special responsibility for the continent. This Clingendael report focuses on the European Union’s role as a security actor in Africa. It considers the use of all the policy instruments at the EU’s disposal. The authors concentrate mainly on the question how the integrated approach is evolving, and what consequences this has for the Common Security and Defence Policy

Baptism, Confirmation and First Communion: Christian Initiation in the Contemporary Church

(Excerpt) Made, Not Born, is the title of a remarkable book produced by the remarkable program of liturgical studies conducted at the University of Notre Dame, and also the title of Frank Quinn\u27s keynote address yesterday. The correspondence of the two titles is surely no accident. The notion that Christians are made and not born may well come as a shock not only to Lutherans but to all those Christians that prize the Reformation emphasis on the priority of grace. We have for so long insisted on the gift character of baptism that such a title jars. A Christian is made? Never! is our first response, for faith is the gift of God, the necessary undergirding for the new life bestowed in baptism

Transfer functions for infinite-dimensional systems

In this paper, we study three definitions of the transfer function for an infinite-dimensional system. The first one defines the transfer function as the expression $C(sI-A)^{-1}B+D$. In the second definition, the transfer function is defined as the quotient of the Laplace transform of the output and input, with initial condition zero. In the third definition, we introduce the transfer function as the quotient of the input and output, when the input and output are exponentials. We show that these definitions always agree on the right-half plane bounded to the left by the growth bound of the underlying semigroup, but that they may differ elsewhere