On the Treves theorem for the AKNS equation

According to a theorem of Treves, the conserved functionals of the AKNS equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of B\"acklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV, with some non trivial technical differences.Comment: LaTeX, 16 page

Poly(HPMA)-based copolymers with biodegradable side chains able to self assemble into nanoparticles

N-(2-Hydroxypropyl)methacrylamide (HPMA) is a water soluble monomer used in the synthesis of biocompatible and non-immunogenic polymers. In particular, poly(HPMA) can be exploited to sterically stabilize nanoparticles (NPs) suitable for the delivery of lipophilic therapeutics without the concerns related to the use of the polyethylene glycol (PEG), such as allergic reactions and the accelerated blood clearance effect. In addition, the use of the ring opening polymerization (ROP) of a lactone in the presence of an initiator that bears a double bond and a hydroxyl group is a promising way (the so called “macromonomer method”) to produce oligoester-based monomers and, in turn, to obtain biodegradable NPs via free radical polymerization. However, HPMA cannot be used as initiator being a secondary alcohol and thus hampering the control over the polymer molecular weight (MW). For this reason, in this work, a novel class of amphiphilic block copolymers that consists of a poly(HPMA) backbone and several short oligo(3-caprolactone) side chains were produced via the adoption of the reversible addition– fragmentation chain transfer (RAFT) polymerization and the “inversion” of the macromonomer method. The oligoester was first synthesized via the ROP of 3-caprolactone in the presence of a primary alcohol and then attached to HPMA using a succinic acid unit as spacer. The NPs obtained via the self-assembly of these novel block copolymers are designed to degrade into completely water soluble poly(HPMA) chains with a MW lower than the threshold value for the renal excretion. The cytotoxicity of these novel carriers and their ability to load trabectedin, a hydrophobic anticancer therapeutic, were assessed

Robust wave function optimization procedures in quantum Monte Carlo methods

The energy variance optimization algorithm over a fixed ensemble of configurations in variational Monte Carlo is formally identical to a problem of fitting data: we reexamine it from a statistical maximum-likelihood point of view. We detect the origin of the problem of convergence that is often encountered in practice and propose an alternative procedure for optimization of trial wave functions in quantum Monte Carlo. We successfully test this proposal by optimizing a trial wave function for the Helium trimer.Comment: Submitted for publicatio

The quasi-bi-Hamiltonian formulation of the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the possible reductions of the Poisson tensors, the vector field and its Hamiltonian functions on a four-dimensional space. We show that the vector field of the Lagrange top possesses, on the reduced phase space, a quasi-bi-Hamiltonian formulation, which provides a set of separation variables for the corresponding Hamilton-Jacobi equation.Comment: 12 pages, no figures, LaTeX, to appear in J. Phys. A: Math. Gen. (March 2002

Quasi-BiHamiltonian Systems and Separability

Two quasi--biHamiltonian systems with three and four degrees of freedom are presented. These systems are shown to be separable in terms of Nijenhuis coordinates. Moreover the most general Pfaffian quasi-biHamiltonian system with an arbitrary number of degrees of freedom is constructed (in terms of Nijenhuis coordinates) and its separability is proved.Comment: 10 pages, AMS-LaTeX 1.1, to appear in J. Phys. A: Math. Gen. (May 1997

A class of Poisson-Nijenhuis structures on a tangent bundle

Equipping the tangent bundle TQ of a manifold with a symplectic form coming from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis structure from a given type (1,1) tensor field J on Q. It is argued that the complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ, but plays a crucial role in the construction of a different tensor R, which appears to be the pullback under the Legendre transform of the lift of J to co-tangent manifold of Q. We show how this tangent bundle view brings new insights and is capable also of producing all important results which are known from previous studies on the cotangent bundle, in the case that Q is equipped with a Riemannian metric. The present approach further paves the way for future generalizations.Comment: 22 page