We introduce a Wilson line distribution function W τ (v) to study gluon saturation at small Feynman x F , or large τ = ln(1/x F ). This new distribution can be obtained from the distribution Wτ (α) of the Color Glass Condensate model and the JIMWLK renormalization group equation. W τ (v) is physically more relevant, and mathematically simpler to deal with because of unitarity of the Wilson line...

A short description is given of the K-matrix formalism. The formalism, which is normally applied to two-body scattering processes, is generalized to production of two-body channels with nal-state interactions. A multi-channel treatment of production of J P C = 0 ++ and J P C = 2 ++ resonances has been worked out in the P-vector approach of Aitchison. An alternative approach, derived from the P-...

Let X = SpecA be a normal affine variety over an algebraically closed field k of characteristic 0 endowed with an effective action of a torus of dimension n. Let also ∂ be a homogeneous locally nilpotent derivation on the normal affine Zn-graded domain A, so that ∂ generates a k+-action on X. We provide a complete classification of pairs (X,∂) in two cases: for toric varieties (n = dimX) and in...

Curado and Rego-Monteiro introduced in [2] a new algebraic structure generalizing the Heisenberg algebra and containing also the q-deformed oscillator as a particular case. This algebra, called generalized Heisenberg algebra, depends on an analytical function f and the eigenvalues αn of the Hamiltonian are given by the one-step recurrence αn+1 = f(αn). This structure has been used in different ...

We consider the valued field K := R((Γ)) of generalised series (with real coefficients and monomials in a totally ordered multiplicative group Γ ). We investigate how to endow K with a series derivation, that is a derivation that satisfies some natural properties such as commuting with infinite sums (strong linearity) and (an infinite version of) Leibniz rule. We characterize when such a deriva...

PCFG Extraction and Pre-typed Sentences Analysis This article explains the way we extract a PCFG from the Paris VII treebank. Firslty, we need to transform the syntactic trees of the corpus into derivation trees. The transformation is done with a generalized tree transducer, a variation of the usual top-down tree transducers, and gives as result some derivation trees for an AB grammar. Secondel...