C^{(2)}_{N+1} Ruijsenaars-Schneider models

We define the notion of C^{(2)}_{N+1} Ruijsenaars-Schneider models and construct their Lax formulation. They are obtained by a particular folding of the A_{2N+1} systems. Their commuting Hamiltonians are linear combinations of Koornwinder-van Diejen ``external fields'' Ruijsenaars-Schneider models, for specific values of the exponential one-body couplings but with the most general 2 double-poles structure as opposed to the formerly studied BC_N case. Extensions to the elliptic potentials are briefly discussed.Comment: 15 pages, LaTeX, no figure

Classification of the solutions of constant rational semi-dynamical reflection equations

We propose a classification of the solutions K to the semi-dynamical reflection equation with constant rational structure matrices associated to rational scalar Ruijsenaars-Schneider model. Four sets of solutions are identified and simple analytic transformations generate all solutions from these sets.Comment: 12 pages, no figure. Dedicated to Daniel Arnaudo

Construction of dynamical quadratic algebras

We propose a dynamical extension of the quantum quadratic exchange algebras introduced by Freidel and Maillet. It admits two distinct fusion structures. A simple example is provided by the scalar Ruijsenaars-Schneider model.Comment: LaTeX, 13 pages, no figures Important changes. Changed the title. Added an example and a theorem on fusion on the quantum space. To appear in LM

Classification of Non-Affine Non-Hecke Dynamical R-Matrices

A complete classification of non-affine dynamical quantum $R$-matrices obeying the ${\mathcal G}l_n({\mathbb C})$-Gervais-Neveu-Felder equation is obtained without assuming either Hecke or weak Hecke conditions. More general dynamical dependences are observed. It is shown that any solution is built upon elementary blocks, which individually satisfy the weak Hecke condition. Each solution is in particular characterized by an arbitrary partition ${{\mathbb I}(i), i\in{1,...,n}}$ of the set of indices ${1,...,n}$ into classes, ${\mathbb I}(i)$ being the class of the index $i$, and an arbitrary family of signs $(\epsilon_{\mathbb I})_{{\mathbb I}\in{{\mathbb I}(i), i\in{1,...,n}}}$ on this partition. The weak Hecke-type $R$-matrices exhibit the analytical behaviour $R_{ij,ji}=f(\epsilon_{{\mathbb I}(i)}\Lambda_{{\mathbb I}(i)}-\epsilon_{{\mathbb I}(j)}\Lambda_{{\mathbb I}(j)})$, where $f$ is a particular trigonometric or rational function, $\Lambda_{{\mathbb I}(i)}=\sum\limits_{j\in{\mathbb I}(i)}\lambda_j$, and $(\lambda_i)_{i\in{1,...,n}}$ denotes the family of dynamical coordinates

History of the health notebook in France : a stake for mothers, doctors and state

The Health Notebook is a booklet distributed in France to mothers to take notes about the growth and the health accidents of their child. Those physicians who first took this initiative thought that mothers would be the best link between themselves and the health babies. The most ancient example discussed here came from a Montpellier medical doctor (1869). Many other initiatives followed until the Second World War. At the beginning of the 20th century, public health authorities became interested in this booklet, as an instrument of control of the population health. The idea to make this health notebook compulsory was implemented in 1945. Since 1970 it includes three health certificates signed by a physician. Therefore, the health notebook has become a stake for families, doctors and State