In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation of irreducible admissible representat...

We look at topological equisingularity of a holomorphic family of reduced mapping germs ft : (C , O) → C over a contractible base T having non-isolated singularities, by means of their normalisations. The relation between surfaces in C with non-isolated singularities and normal surface singularities via the normalisation is a very convenient way of exchanging information between both categories...

In this paper we provide an overall description of a model of social behaviour that allows a flexible parametrisation of cultural expectations. These expectations are associated to how people perceive and treat others from a socio-relational perspective.

This paper studies a class of real-rational matrix bilateral Diophantine equations (BDE) arising in numerous control problems. A necessary and sufficient solvability condition is derived in terms of state-space realizations of rational matrices involved in the equation. This condition is given in terms of a constrained matrix Sylvester equation and is numerically tractable. An explicit state-sp...

Abstract. In this note, dedicated to the memory of Professor Tiberiu Constantinescu, we discuss the applications of two parametrizations of positive matrices to issues in quantum information theory. The first, which we propose be dubbed the Schur-Constantinescu parametrization, is used in a twin fashion to construct examples of separable states in arbitrary dimensions. The second, called the Ja...

In this paper, we study fundamental properties of real curves, especially of rational real curves, and we derive several algorithms to decide the reality and rationality of curves in the complex plane. Furthermore, if the curve is real and rational, we determine a real parametrization. More precisely, we present a reality test algorithm for plane curves, and three different types of real parame...

Automatic verification of concurrent systems is an active area of research since at least a quater of a century. We focus here on analyses of systems designed to operate with an arbitrary number of processes. German and Sistla, already in 1992, initiated in depth investigation of this problem for finite state systems. For infinite state systems, like pushdown systems, extra care is needed to av...

A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions in terms of Abelian functions of Kleinian type (i.e. the higher-genus analogues of the Weierstrass elliptic functions) is discussed as well as the connections...

In this note, we summarize and compare various model predictions for pp total cross-section σ tot , giving an estimate of the range of predictions for the total crosssection, σ tot expected at the LHC. We concentrate on the results for σ tot obtained in a particular QCD based model of the energy dependence of the total cross-section, including the effect of soft gluon radiation. We obtain the r...