Classical Dynamical Systems from q-algebras:"cluster" variables and explicit solutions

A general procedure to get the explicit solution of the equations of motion for N-body classical Hamiltonian systems equipped with coalgebra symmetry is introduced by defining a set of appropriate collective variables which are based on the iterations of the coproduct map on the generators of the algebra. In this way several examples of N-body dynamical systems obtained from q-Poisson algebras are explicitly solved: the q-deformed version of the sl(2) Calogero-Gaudin system (q-CG), a q-Poincare' Gaudin system and a system of Ruijsenaars type arising from the same (non co-boundary) q-deformation of the (1+1) Poincare' algebra. Also, a unified interpretation of all these systems as different Poisson-Lie dynamics on the same three dimensional solvable Lie group is given.Comment: 19 Latex pages, No figure

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

Misure ambientali in mare aperto: sviluppo di tecnologie per l'acquisizione e l'analisi di dati meteo-mareografici misurati da una boa oceanografica in Mar Ligure

Obiettivo del presente lavoro è lo sviluppo di un metodo di analisi in grado di stimare i parametri fondamentali del moto ondoso, a partire dai dati acquisiti da tre altimetri acustici installati a bordo di una boa meteo-oceanografica operante in mare aperto. Il metodo di analisi sviluppato compie opportune operazioni di filtraggio sulle sequenze temporali delle misure effettuate dai tre altimetri, quindi, elaborando tali sequenze, fornisce le stime di alcuni parametri caratteristici del moto ondoso (tra cui l’altezza e la direzione di propagazione). I diversi tipi di filtraggio ed il metodo di stima sviluppati si basano sul calcolo di alcuni parametri statistici (tra cui media, mediana e deviazione standard) delle serie temporali di dati acquisiti, sulla conoscenza delle loro densità spettrali di potenza (calcolate mediante FFT), e sul calcolo delle funzioni di crosscorrelazione delle sequenze di dati prese a due a due. Il procedimento di stima realizzato è stato sperimentato su una notevole quantità di dati reali acquisiti in Mar Ligure tramite l’utilizzo della stazione di misura fissa su cui sono montati gli altimetri acustici, ed ha fornito risultati soddisfacenti per quanto riguarda affidabilità e precisione. Nell’ambito della valutazione delle prestazioni del sistema di acquisizione dati e del metodo di stima, i risultati ottenuti sono stati confrontati con misure provenienti da altri sensori a bordo della stazione e con stime analoghe effettuate a partire dai dati acquisiti da un’altra stazione di misura, operante anch’essa in Mar Ligure, ma dotata di strumentazione di altro tipo

Blow-up solutions for linear perturbations of the Yamabe equation

For a smooth, compact Riemannian manifold (M,g) of dimension N \geg 3, we are interested in the critical equation $$\Delta_g u+(N-2/4(N-1) S_g+\epsilon h)u=u^{N+2/N-2} in M, u>0 in M,$$ where \Delta_g is the Laplace--Beltrami operator, S_g is the Scalar curvature of (M,g), $h\in C^{0,\alpha}(M)$, and $\epsilon$ is a small parameter

Bubble concentration on spheres for supercritical elliptic problems

We consider the supercritical Lane-Emden problem (P_\eps)\qquad -\Delta v= |v|^{p_\eps-1} v \ \hbox{in}\ \mathcal{A} ,\quad u=0\ \hbox{on}\ \partial\mathcal{A} where $\mathcal A$ is an annulus in \rr^{2m}, $m\ge2$ and p_\eps={(m+1)+2\over(m+1)-2}-\eps, \eps>0. We prove the existence of positive and sign changing solutions of (P_\eps) concentrating and blowing-up, as \eps\to0, on $(m-1)-$dimensional spheres. Using a reduction method (see Ruf-Srikanth (2010) J. Eur. Math. Soc. and Pacella-Srikanth (2012) arXiv:1210.0782)we transform problem (P_\eps) into a nonhomogeneous problem in an annulus \mathcal D\subset \rr^{m+1} which can be solved by a Ljapunov-Schmidt finite dimensional reduction

Growth inhibition of human ovarian carcinoma by a novel AvidinOX-anchored biotinylated camptothecin derivative

Oxidized form of avidin, named AvidinOX, provides stable fixation of biotinylated molecules in tissues thus representing a breakthrough in topical treatment of cancer. AvidinOX proved to be a stable receptor for radiolabeled biotin, biotinylated antibodies and cells. In order to expand applicability of the AvidinOX-based delivery platform, in the present study we investigated the possibility to hold biotinylated chemotherapeutics in AvidinOX-treated sites. A novel biotinylated gimatecan-derived camptothecin, coded ST8161AA1, was injected at suboptimal doses into human tumors xenografted in mice alone or pre-complexed to AvidinOX. Significantly higher growth inhibition was observed when the drug was anchored to AvidinOX suggesting the potential utility of this delivery modality for the local treatment of inoperable tumors

New Formula for the Eigenvectors of the Gaudin Model in the sl(3) Case

We propose new formulas for eigenvectors of the Gaudin model in the \sl(3) case. The central point of the construction is the explicit form of some operator P, which is used for derivation of eigenvalues given by the formula $| w_1, w_2) = \sum_{n=0}^\infty P^n/n! | w_1, w_2,0>$, where $w_1$, $w_2$ fulfil the standard well-know Bethe Ansatz equations