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.     

Stable manifolds under very weak hyperbolicity conditions

We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.     

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy

We study the asymptotic time behavior of global smooth solutions to general entropy, dissipative, hyperbolic systems of balance laws in m space dimensions, under the Shizuta‐Kawashima condition. We show that these solutions approach a constant equilibrium state in the L^p‐norm at a rate O(t^{? (m/2)(1 ? 1/p)}) as t → ∞ for p ∈ [min{m, 2}, ∞]. Moreover, we can show that we can approximate, with a faster order of convergence, the conservative part of the solution in terms of the linearized hyperbolic operator for m ≥ 2, and by a parabolic equation, in the spirit of Chapman‐Enskog expansion in every space dimension. The main tool is given by a detailed analysis of the Green function for the linearized problem. © 2007 Wiley Periodicals, Inc.     

An Improved Branch & Bound Method for the Uncapacitated Competitive Location Problem

In this paper, the problem of locating new facilities in a competitive environment is considered. The problem is formulated as the firm expected profit maximization and a set of nodes is selected in a graph representing the geographical zone. Profit depends on fixed and deterministic location costs and, since customers are independent decision-makers, on the expected market share. The problem is an instance of nonlinear integer programming, because the objective function is concave and submodular. Due to this complexity a branch & bound method is developed for solving small size problems (that is, when the number of nodes is less than 50), while a heuristic is necessary for larger problems. The branch & bound is called data-correcting method, while the approximate solutions are obtained using the heuristic-concentration method.     

Tools for the eigenvalue distribution in a non-Hermitian setting

Under mild trace norm assumptions on the perturbing sequence, we extend a recent perturbation result based on a theorem by Mirsky. The analysis concerns the eigenvalue distribution and localization of a generic (non-Hermitian) complex perturbation of a bounded Hermitian sequence of matrices. Some examples of application are considered, ranging from the product of Toeplitz sequences to the approximation of PDEs with given boundary conditions. A final discussion on open questions and further lines of research ends the note.