On the solution of indefinite systems arising in nonlinear programming problems

This work is concerned with the convergence properties and the numerical analysis of the preconditioned conjugate gradient (PCG) method applied to the solution of indefinite linear systems arising in nonlinear optimization. Our approach is based on the choice of quasidefinite preconditioners and of a suitable factorization routine. Some theoretical and numerical results about these preconditioners are obtained. Furthermore, we show the behaviour of the PCG method for different formulations of the indefinite system and we compare the effectiveness of the proposed variants. Copyright © 2007 John Wiley & Sons, Ltd.     

Inner solvers for interior point methods for large scale nonlinear programming

This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution. In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported. This research was supported by the Italian Ministry for Education, University and Research (MIUR) projects: FIRB Project: “Parallel Nonlinear Numerical Optimization PN ² O” (grant n. RBAU01JYPN, ) and COFIN/PRIN04 Project “Numerical Methods and Mathematical Software for Applications” (grant n. 2004012559, ).     

“A priori” estimates, uniqueness and existence of positive solutions of Yamabe type equations on complete manifolds

We study the asymptotic behaviour of non-negative solutions of Yamabe type equations on a complete Riemannian manifold. Then we provide a comparison result, based on a form of the weak maximum principle at infinity, which together with the “a priori” estimates previously obtained, yields uniqueness under very general Ricci assumptions. The paper ends with an existence result and an application to the non-compact Yamabe problem.     

Risk-neutral valuation with infinitely many trading dates

The first Fundamental Theorem of Asset Pricing establishes the equivalence between the absence of arbitrage in financial markets and the existence of Equivalent Martingale Measures, if appropriate conditions hold. Since the theorem may fail when dealing with infinitely many trading dates, this paper draws on the A.A. Lyapunov Theorem in order to retrieve the equivalence for complete markets such that the Sharpe Ratio is adequately bounded.     

Chemical modification of chitosan under high-intensity ultrasound

Chitosan (CTS), a biocompatible, biodegradable, non-toxic polymer, dissolves in water only if pH is lowered under 6.5, when a substantial fraction of the amino groups is protonated. Its range of application has been much extended by partially depolymerising it or converting it to water-soluble derivatives. Working under high-intensity ultrasound at 17.8-18.5 kHz, using either a simple horn or a cup horn, we achieved a controlled depolymerization of CTS, also prepared in high yields several derivatives that can be useful intermediates for further chemical modification, as well as several water-soluble derivatives that lend themselves to a host of industrial applications. Compared to conventional methods, all these reactions went to completion in considerably shorter times at lower temperatures.     

Online re-optimization of optical filters on a production sputter tool

This contribution presents a magnetron sputter deposition tool with broadband optical monitor and online re-optimization capability for high volume production. The layer termination relies on a comparison of the actually measured reflection spectrum with a pre-calculated target spectrum. Spectra recorded after each deposited layer are analyzed by the re-optimization module and in case of significant deviations layer thicknesses and target spectra for the remaining layers are recalculated. This technique significantly improves the performance and reproducibility in case of highly denlanding coating designs and is able to correct abnormal production errors in individual layers, which will lead to coating failure without re- optimization.     

Optical resonances in one-dimensional dielectric nanorod arrays: field-induced fluorescence enhancement

Arrays of transparent dielectric nanorods are shown to produce very large local field enhancements at specific resonant conditions. These structures would lead to enhancement of molecular fluorescence signals without quenching. The resonant angular width and field enhancements are analytically derived as a function of wavelength, grating period, rod radius, and dielectric constant.     

Cosmological Relativity: A New Theory ofCosmology1

A new general-relativistic theory of cosmology, the dynamical variables of whichare those of Hubble's, namely distances and redshifts, is presented. The theorydescribes the universe as having a three-phase evolution with a deceleratingexpansion followed by a constant and an accelerating expansion, and it predictsthat the universe is now in the latter phase. The theory is actually a generalizationof Hubble's law taking gravity into account by means of Einstein's theory ofgeneral relativity. The equations obtained for the universe expansion are elegantand very simple. It is shown, assuming ₀ = 0.24, that the time at which theuniverse goes over from a decelerating to an accelerating expansion, i.e., theconstant expansion phase, occurs at 0.03 from the big bang, where is theHubble time in vacuum. Also, at that time the cosmic radiation temperature was11 K. Recent observations of distant supernovae imply, in defiance of expectations,that the universe's growth is accelerating, contrary to what has always beenassumed, that the expansion is slowing down due to gravity. Our theory confirmsthese recent experimental results by showing that the universe now is definitelyin a stage of accelerating expansion.     

Interpreting technical evidence from spectral imaging of paintings by Édouard Manet in the Courtauld Gallery

The paintings by Édouard Manet in The Courtauld Gallery Déjeuner sur l'herbe (1863–68), Marguerite de Conflans en Toilette de Bal (1870–1880), Banks of the Seine at Argenteuil (1874), and A Bar at the Folies–Bergère (1882) were investigated for the first time using a range of non-invasive in situ analyses. The aims of the study were to investigate the painting techniques and materials used for this group of works and to critically evaluate the technical evidence derived from the integrated use of imaging techniques and portable spectroscopic methods in this context. The paintings were investigated by means of macro X-ray fluorescence (MA-XRF), reflection spectral imaging, portable UV–Vis–NIR spectroscopy, portable Raman spectroscopy, and reflection FTIR. MA-XRF and reflection spectral imaging allowed visualising elements in the compositions that were not visible using traditional methods of technical study. For example, MA-XRF analysis of Déjeuner sur l'herbe revealed elements of the development of the composition that provided new evidence to consider its relationship to other versions of the composition. The study also highlighted questions about the interpretation of elemental distribution maps and spectral images that did not correspond to the reworking visible in X-radiographs. For example, in A Bar at the Folies–Bergère Manet made numerous changes during painting, which were not clearly visualised with any of the techniques used. The research has wider implications for the study of Impressionist paintings, as the results will support technical studies of works by other artists of the period who used similar materials and painting methods.     

Deconvolution of UV-VIS spectroelectrochemical thin-layer data for an EE electrochemical process

A deconvolution method, based on Fixed Size Window Evolving Factor Analysis (FSWEFA) has been developed to analyse the spectroelectrochemical sequence of spectra obtained in OTTLE electrodes for EE electrochemical processes. The analysis of the data permits to reconstruct the concentration profiles, the spectra of the intermediates and an optical analogue of the i vs E curve.