A generalization of the Pontryagin-Hill theorems to projective modules over Pr\"ufer domains

Motivated by the Pontryagin-Hill criteria of freeness for abelian groups, we investigate conditions under which unions of ascending chains of projective modules are again projective. Several extensions of these criteria are proved for modules over arbitrary rings and domains, including a genuine generalization of Hill's theorem for projective modules over Pr\"{u}fer domains with a countable number of maximal ideals. More precisely, we prove that, over such domains, modules which are unions of countable ascending chains of projective, pure submodules are likewise projective

A numerical method with properties of consistency in the energy domain for a class of dissipative nonlinear wave equations with applications to a Dirichlet boundary-value problem

In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model governing discrete arrays consisting of coupled harmonic oscillators. Associated with this method, there exists a discrete scheme of energy that consistently approximates its continuous counterpart. The method has the properties that the associated rate of change of the discrete energy consistently approximates its continuous counterpart, and it approximates both a fully continuous medium and a spatially discretized system. Conditional stability of the numerical technique is established, and applications are provided to the existence of the process of nonlinear supratransmission in generalized Klein-Gordon systems and the propagation of binary signals in semi-unbounded, three-dimensional arrays of harmonic oscillators coupled through springs and perturbed harmonically at the boundaries, where the basic model is a modified sine-Gordon equation; our results show that a perfect transmission is achieved via the modulation of the driving amplitude at the boundary. Additionally, we present an example of a nonlinear system with a forbidden band-gap which does not present supratransmission, thus establishing that the existence of a forbidden band-gap in the linear dispersion relation of a nonlinear system is not a sufficient condition for the system to present supratransmission

Una nova eina per a l’estudi del paper i les filigranes. Anàlisi i desenvolupament d’una base de dades per a l’estudi del paper i de les filigranes: font per a l’elaboració de la història del paper a Espanya

Podeu consultar el document complet a: http://hdl.handle.net/2445/47384L’aspiració de trobar una eina que pugui ajudar a identifi car els papers atenent les seves característiques sorgeix a fi nal segle XVIII amb les primeres descripcions de les filigranes papereres i va prenent cos al segle XIX com a ciència auxiliar de la codicologia. Des de les últimes dècades del segle XX, les filigranes han anat adquirint un interès creixent entre els restauradors de document gràfi c —com una eina més per a la presa de decisions i per a la valoració del procés de restauració— i entre els documentalistes, historiadors, museòlegs i bibliòfils —per a la datació i autenticació de les obres— i, fins i tot, en investigacions policials i jurídiques per aclarir algun fet delictiu. No obstant això, durant aquests 150 anys, l’estudi del paper a través de les filigranes papereres a Espanya no ha experimentat cap avenç significatiu pel que fa als mètodes i procediments seguits per a l’obtenció i gestió de les dades. En l’àmbit europeu, encara que a partir dels anys 90 sorgeixen noves propostes d’estudi, aquestes limiten la investigació a l’anàlisi de la filigrana sense assolir una visió global del plec sortit de la forma

Tool for fast mismatch analysis of analog circuits

A tool is presented that evaluates statistical deviations in performance characteristics of analog circuits, starting from statistical deviations in the technological parameters of MOS transistors. Performance is demonstrated via the analysis of a Miller OTA in two different configurations and a linearized CMOS transconductor. The CPU time is reduced by a factor of 25 to 90 with respect to conventional Monte Carlo simulation, while maintaining similar accuracy in the computations