Pyrene‐Excimers‐Based Antenna Systems

A series of dendrimeric compounds bearing pyrene units were synthesized to afford light‐harvesting antennae based on the formation of intramolecular excimers. The synthetic plan profited from the efficiency of the Huisgen reaction, the 1,3‐dipolar cycloaddition of azides and terminal alkynes, which allowed ready assembly of the different building blocks. The three molecular antennae obtained, of increasing generation, revealed efficient energy transfer both in solution and in the solid state.     

Optimal control of stochastic differential equations with dynamical boundary conditions

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problems with nonstandard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with nonstandard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.     

Cost allocation protocols for supply contract design in network situations

The class of Construct and Charge (CC-) rules for minimum cost spanning tree (mcst) situations is considered. CC-rules are defined starting from the notion of charge systems, which specify particular allocation protocols rooted on the Kruskal algorithm for computing an mcst. These protocols can be easily implemented in practical network situations (for instance, in supply transportation networks), are flexible to changes in the network situation and meet the requirement of continuous monitoring by the agents involved. Special charge systems, that we call conservative, lead to a subclass of CC-rules that coincides with the class of obligation rules for mcst situations. The authors thank two anonymous referees both for detailed remarks and for interesting general comments on a previous version of the paper. Stef Tijs and Rodica Branzei are indebted to Daniel Granot for useful discussions on the topics treated in this paper and his hospitality during our research visit at British Columbia University at Vancouver in July–August 2003.     

Self-consistent check of the validity of Gibbs calculus using dynamical variables

The high- and low-energy limits of a chain of coupled rotators are integrable and correspond respectively to a set of free rotators and to a chain of harmonic oscillators. For intermediate values of the energy, numerical calculations show the agreement of finite time averages of physical observables with their Gibbsian estimate. The boundaries between the two integrable limits and the statistical domain are analytically computed using the Gibbsian estimates of dynamical observables. For large energies the geometry of nonlinear resonances enables the definition of relevant 1.5-degree-of-freedom approximations of the dynamics. They provide resonance overlap parameters whose Gibbsian probability distribution may be computed. Requiring the support of this distribution to be right above the large-scale stochasticity threshold of the 1.5-degree-of-freedom dynamics yields the boundary at the large-energy limit. At the low-energy limit, the boundary is shown to correspond to the energy where the specific heat departs from that of the corresponding harmonic chain.     

A theory of sets with the negation of the axiom of infinity

In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a non-standard development. MSC: 03E30, 03E35.     

Convergence of the orbital expansion in a correlated system: A test study on positronium

Positronium, the bound state of an electron and a positron, is an exactly soluble quantum system, similar to a light isotope of hydrogen. It can be studied using the finite basis quantum chemistry codes developed for atoms and molecules. In fact, positronium can be mimicked by two electrons with opposite spins, in the absence of any nucleus and having the sign of the Coulomb interaction reversed. The exact wave function has a cusp in the points of coalescence of the two particles (a “Coulomb peak”), and this fact makes the convergence of the total energy, as a function of the basis set size, extremely slow. For this reason, positronium can be used to test the convergence properties of the quantum chemistry methods used to describe the dynamic correlation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Polynomial auction algorithms for shortest paths

In this paper we consider strongly polynomial variations of the auction algorithm for the single origin/many destinations shortest path problem. These variations are based on the idea of graph reduction, that is, deleting unnecessary arcs of the graph by using certain bounds naturally obtained in the course of the algorithm. We study the structure of the reduced graph and we exploit this structure to obtain algorithms withO (n min{m, n logn}) andO(n ²) running time. Our computational experiments show that these algorithms outperform their closest competitors on randomly generated dense all destinations problems, and on a broad variety of few destination problems.Research supported by NSF under Grant No. DDM-8903385, by the ARO under Grant DAAL03-86-K-0171, by a CNR-GNIM grant, and by a Fullbright grant     

Particle–hole symmetric Luttinger liquids in a quantum Hall circuit

We report finite-bias differential conductance measurements through a split-gate constriction in the integer quantum Hall regime at ν=1. Both enhanced and suppressed zero-bias inter-edge backscattering can be obtained in a controllable way by changing the split-gate voltage. This behavior is interpreted in terms of local charge depletion and particle–hole symmetry. We discuss the relevance of particle–hole symmetry in connection with the chiral Luttinger model of edge states.