Finite-Volume Excitations of the¶111 Interface in the Quantum XXZ Model

We show that the ground states of the three-dimensional XXZ Heisenberg ferromagnet with a 111 interface have excitations localized in a subvolume of linear size R with energies bounded by O(1/R²). As part of the proof we show the equivalence of ensembles for the 111 interface states in the following sense: In the thermodynamic limit the states with fixed magnetization yield the same expectation values for gauge invariant local observables as a suitable grand canonical state with fluctuating magnetization. Here, gauge invariant means commuting with the total third component of the spin, which is a conserved quantity of the Hamiltonian. As a corollary of equivalence of ensembles we also prove the convergence of the thermodynamic limit of sequences of canonical states (i.e., with fixed magnetization).     

SOLVERSTAT: a new utility for multipurpose analysis. An application to the investigation of dioxygenated Co(II) complex formation in dimethylsulfoxide solution

A new utility for multipurpose analysis, SOLVERSTAT, taking advantage of the versatility of spreadsheets is here described. By means of this tool advanced statistical tests have introduced in Microsoft Excel Solver thus allowing regression diagnostic and discrimination between different models. The utility is here applied to the determination, by UV-Vis spectroscopy, of the stability constant for the uptake of molecular dioxygen by the 1:2 complex of Co(II) with N,N′-dimethylethylenediamine (dmen) in the aprotic solvent dimethylsulfoxide (dmso) at 298 K and in a medium adjusted to 0.1 mol dm⁻³ with Et₄NClO₄. The reliability of the model and parameters obtained are discussed and the results compared with those obtained by Dynafit, a different software package, and by independent voltammetric measurements. The validity of SOLVERSTAT has been also examined applying it to the discrimination between different models already discussed in the literature.     

A mathematical study of the plasticity effects in muscle contraction

Hill's three-element model of contracting muscle is expanded by replacing the series and the parallel elastic elements with elastoplastic elements. The contractile element is structurally described making use of the sliding filament theory. The resulting mathematical model is formulated in terms of an evolution variational inequality for a nonlinear and nonlocal transport-type operator. The existence and uniqueness of the solution are described along with a numerical approach.This work was supported by M.P.I. (fondi per la ricerca scientifica) and by I.A.N. of C.N.R. Pavia.     

The quantum analog of a symmetric pair: a construction in type

Let be the ideal in the enveloping algebra of generated by the maximal compact subalgebra of . In this paper we construct an analog of in the quantized enveloping algebra corresponding to a type diagram at generic . We find generators for and explicit bases for .

     

A finite differences MATLAB code for the numerical solution of second order singular perturbation problems

We show the main features of the MATLAB code HOFiD_UP for solving second order singular perturbation problems. The code is based on high order finite differences, in particular on the generalized upwind method. Within its simplicity, it uses order variation and continuation for solving any difficult nonlinear scalar problem. Several numerical tests on linear and nonlinear problems are considered. The best performances are reported on problems with perturbation parameters near the machine precision, where most of the codes for two-point BVPs fail.