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, ).     

Wavelets for multichannel signals

In this paper, we introduce and investigate multichannel wavelets, which are wavelets for vector fields, based on the concept of full rank subdivision operators. We prove that, like in the scalar and multiwavelet case, the existence of a scaling function with orthogonal integer translates guarantees the existence of a wavelet function, also with orthonormal integer translates. In this context, however, scaling functions as well as wavelets turn out to be matrix-valued functions.     

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.     

QUANTUM YIELD OF PRODUCTION OF SINGLET MOLECULAR OXYGEN (xδg) IN AQUEOUS DISPERSIONS OF SMALL UNILAMELLAR LIPID VESICLES. A TIME-RESOLVED NEAR-IR PHOSPHORESCENCE STUDY*,†

The quantum yield of formation and kinetic behaviour of O2(1 delta g) in D2O dispersions of small unilamellar vesicles (SUVs) of dipalmitoyl phosphatidylcholine were studied by time-resolved detection of near-IR phosphorescence. At a SUV concentration of 26 nM, O2(1 delta g) is not quenched by the vesicles. It diffuses quickly through the lipid bilayer and a partition equilibrium of O2(1 delta g) between the lipid bilayer and the buffer is attained before decay occurs. In this equilibrium situation O2(1 delta g) is mostly located in the buffer phase, which permits the determination of absolute quantum yields for O2(1 delta g) production, phi delta, by comparison of the luminescence in the dispersions with that in neat D2O. The maximal phi delta values for the sensitizers incorporated in the SUV bilayer were 0.47 +/- 0.09 for the dipyridyl complex of zinc(II) phthalocyanine (ZnPc), 0.35 +/- 0.08 for porphycene, and 0.36 +/- 0.08 for 2,7,12,17-tetra-n-propylporphycene. These values are equal to those in neat organic solvents but lower than those previously obtained in SUVs by using chemical trapping agents. The high degree of organization of the environment around the sensitizers does not influence their efficiency of producing O2(1 delta g). While no concentration dependence is observed for ZnPc (at least up to a local concentration of 20 mM in the bilayer), phi delta for both porphycenes significantly decreases above a local concentration of 4 mM in the bilayer. This result is expected in view of previous observations on the concentration dependence of other photophysical parameters of the porphycenes in such microheterogeneous media.     

A particle transport problem with a quadratic nonlinearity and general boundary conditions: The stationary solution

Summary We study a stationary, nonlinear, particle transport problem in slab geometry with general boundary conditions. The existence and uniqueness of the solution is proved by means of fixed point techniques, provided that the source term is sufficiently small.

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Sommario Si studia un problema stazionario nonlineare di particelle in geometria piana con condizioni al contorno generali. L'esistenza e unicitá della soluzione è dimostrata con tecniche di punto fisso purchè il termine di sorgente sia sufficientemente piccolo.

     

Dipolar Rotors Orderly Aligned in Mesoporous Fluorinated Organosilica Architectures

New mesoporous covalent frameworks, based on hybrid fluorinated organosilicas, were prepared to realize a periodic architecture of fast molecular rotors containing dynamic dipoles in their structure. The mobile elements, designed on the basis of fluorinated p‐divinylbenzene moieties, were integrated into the robust covalent structure through siloxane bonds, and showed not only the rapid dynamics of the aromatic rings (ca. 10⁸ Hz at 325 K), as detected by solid‐state NMR spectroscopy, but also a dielectric response typical of a fast dipole reorientation under the stimuli of an applied electric field. Furthermore, the mesochannels are open and accessible to diffusing in gas molecules, and rotor mobility could be individually regulated by I₂ vapors. The iodine enters the channels of the periodic structure and reacts with the pivotal double bonds of the divinyl‐fluoro‐phenylene rotors, affecting their motion and the dielectric properties.     

Microporous Molecular Materials from Dipeptides Containing Non‐proteinogenic Residues

Dipeptides with two hydrophobic side chains have proved to be an exceptional source of microporous organic materials, but since previous structures were limited to the incorporation of only proteinogenic residues, their full potential as adsorbents has remained unexplored. Single‐crystal XRD data for ten new compounds with non‐proteinogenic L ‐2‐aminobutanoic acid and/or L ‐2‐amino‐pentanoic acid are presented. The gas‐phase accessibility of their crystal pores, with cross‐sections of 2.3 to 5.1 Å, was monitored by CO₂ and CH₄ adsorption isotherms. Included CO₂ was also detected spectroscopically by 2D MAS NMR. An extensive conformational analysis reveals that the use of linear rather than branched side chains (such as L ‐valine and L ‐isoleucine) affords peptides with a greater degree of conformational freedom and yields more‐flexible channel surfaces that may easily adapt to a series of potential guest molecules.     

Chemical composition and antioxidant activity of essential oil from aerial parts of Teucrium flavum L. subsp. flavum growing spontaneously in Tunisia

The objectives of this study were to chemically characterise and evaluate the antioxidant potential of the essential oil from Teucrium flavum L. subsp. flavum growing spontaneously in Tunisia. The volatile oil was extracted by hydrodistillation of the aerial parts in a Clevenger type apparatus. Forty constituents were identified via GC and GC-MS analysis. β-caryophyllene (32.5%) and α-humulene (17.8%) were the most abundant components. The evaluation of free radical scavenging activity using stable DPPH free radical showed that the volatile oil exhibits a moderate antioxidant activity and reduces DPPH to 50% at EC₅₀ value of 1230 μg mL^? 1.     

Supercritical fluid chromatography with photodiode array detection for pesticide analysis in papaya and avocado samples

To improve the analysis of pesticides in complex food matrices with economic importance, alternative chromatographic techniques, such as supercritical fluid chromatography, can be used. Supercritical fluid chromatography has barely been applied for pesticide analysis in food matrices. In this paper, an analytical method using supercritical fluid chromatography coupled to a photodiode array detection has been established for the first time for the quantification of pesticides in papaya and avocado. The extraction of methyl parathion, atrazine, ametryn, carbofuran, and carbaryl was performed through the quick, easy, cheap, effective, rugged, and safe methodology. The method was validated using papaya and avocado samples. For papaya, the correlation coefficient values were higher than 0.99; limits of detection and quantification ranged from 130–380 and 220–640 μg/kg, respectively; recovery values ranged from 72.8–94.6%; precision was lower than 3%. For avocado, limit of detection values were ?450 μg/kg; precision was lower than 11%; recoveries ranged from 50.0–94.2%. Method feasibility was tested for lime, banana, mango, and melon samples. Our results demonstrate that the proposed method is applicable to methyl parathion, atrazine, ametryn, and carbaryl, toxics pesticides used worldwide. The methodology presented in this work could be applicable to other fruits.