Boundary optimal control of the Westervelt and the Kuznetsov equations

This paper is concerned with optimal Neumann boundary control for the Westervelt and the Kuznetsov equations, which are equations of nonlinear acoustics. Specifically, functionals of tracking type with applications in noninvasive ultrasonic medical treatments are considered. Existence of optimal controls is established and first order necessary optimality conditions are derived. Stability of the minimizer with respect to perturbations in the data as well as convergence of the controls when the regularization parameter tends to zero is shown.     

Replication and shortfall risk in a binomial model with transaction costs

The shortfall risk is defined as the optimal mean value of the terminal deficit produced by a self-financing portfolio whose initial value is smaller than what is required to replicate a contingent claim. In this paper we look for an explicit expression for it, as well as for the optimal strategy, when the market model is a binomial model with proportional transaction costs. We first study replication of European claims which satisfy suitable assumptions. We then investigate the shortfall minimization problem in a framework very similar to that without transaction costs. The author thanks the referee for useful comments on an earlier version of the present paper.     

Sodium dodecyl sulphate-polyacrylamide gel electrophoresis of proteins in dry-cured hams: data registration and multivariate analysis across multiple gels

This study investigates whether dry-cured hams from two European countries can be distinguished using SDS-PAGE. Thirty-seven commercial hams (19 Spanish, 18 French) were used in the study. Four protein fractions were extracted from each sample, with sufficient material prepared to allow each fraction to be analysed in triplicate lanes. The complete extraction process was carried out in duplicate. The 24 specimens originating from each ham sample were randomly allocated to different lane positions and gels, as were at least two reference lanes (for reference proteins). In total, 118 gels were prepared. Mathematical routines were developed using a matrix language to process the gel image files. Procedures were written to carry out 'within-gel' image correction, lane extraction and normalization, 'between-gel' data registration and linear discriminant analysis (LDA) of each fraction's data to establish whether the provenance could be systematically distinguished. The between-gel registration was carried out using a genetic algorithm (GA). Feature selection was also performed using a GA, to pass subsets of features to the LDA routine. Cross-validated classification success rates were 84, 91, 81 and 85%, respectively, for the four fractions. We conclude that SDS-PAGE can be conducted in a sufficiently quantitative manner and can potentially verify the provenance of regional speciality dry-cured hams.     

Modification of surface properties of a poly(dimethylsiloxane)-based elastomer, RTV11, upon exposure to seawater

Atomic force microscopy (AFM) was combined with surface analytical techniques to investigate the rarely addressed issue of the effect of seawater on the surface properties of a selected fouling-release coating, silicon elastomer RTV11 (trademark of General Electric). The exposure of the RTV11 surface to seawater resulted in a modification of its morphology and mechanical properties, as confirmed by AFM and scanning electron microscopy (SEM). Surface modification was dependent on sample preparation and curing process, namely, curing agent concentration and relative humidity during curing. The RTV11 surface remained largely unaltered for samples cured under 100% relative humidity. SEM and X-ray photoelectron spectroscopy studies confirmed that the modified surface of RTV11 had the same elemental composition as the unexposed surface of the elastomer and showed excess Ca. However, the modified surface deformed plastically under load and was stiffer than the original surface. No major change was found on surfaces exposed to nanopure water during similar times of exposure as in seawater, regardless of curing conditions. The rate of increase in the aggregate formation in seawater can be described by an exponential function, with a decay constant of approximately 4.99 x 10(-)(3) min(-)(1) and a pre-exponential factor of approximately 1.77 x 10(-)(2) microm/min.     

Pegylated tetraarylporphyrin entrapped in liposomal membranes. A possible novel drug-carrier system for photodynamic therapy

A system of poly(ethylene glycol) bound tetraarylporphyrin entrapped in liposomal membranes was investigated. The interactions between the 5-(4-hydroxymethylphenyl)-10,15,20-tritolylporphyrin (Po) covalently attached to the poly(ethylene glycol) chain (PEG-Po), and phosphatidylcholine liposomes in the aqueous solution were studied. The adsorption of the investigated polymer to lipid vesicles was confirmed by measurements of dynamic light scattering and zeta potential. Experimental results demonstrate that the diameter of liposomes increased and the absolute value of the zeta potential decreased after addition of PEG-Po. The binding constants (K(b)) of Po chromophores to liposome in pH range from 5.2 to 9.0 were determined using fluorescence spectroscopy. The degree of binding was found to be pH-independent and the average value was 24.6 +/- 0.9 mg ml(-1). The acid-base properties of the porphyrin chromophores and their aggregation in an aqueous solution were also studied. pK values associated with imine-N protonation of the porphyrin core were found to be 2.59 and 0.68 at the ionic strength of 0.1 M. The equilibrium constant for dimerization, K(D), was found to be 5 x 10(3) M(-1).     

IR spectroscopic features of gaseous C7H7O+ ions: benzylium versus tropylium ion structures

Gaseous [C7H7O]+ ions have been formed by protonation of benzaldehyde or tropone (2,4,6-cycloheptatrienone) in the cell of an FT-ICR mass spectrometer using C2H5(+) as a Br?nsted acid. The so-formed species have been assayed by infrared multiphoton dissociation (IRMPD) using the free electron laser (FEL) at the CLIO (Centre Laser Infrarouge Orsay) facility. The IRMPD features are quite distinct for ions from the two different precursors, pointing to two different isomers. A number of potential structures for [C7H7O]+ ions have been optimized at the B3LYP/6-31+G(d,p) level of theory, and their relative energies and IR spectra are reported. On this basis, the IRMPD spectra of [C7H7O]+ ions are found to display features characteristic of O-protonated species, with no evidence of any further skeletal rearrangements. The so-formed ions are thus hydroxy-substituted benzylium and tropylium ions, respectively, representative members of the benzylium/tropylium ion family. The IRMPD assay using the FEL laser light has allowed their unambiguous discrimination where other mass spectrometric techniques have yielded a less conclusive answer.     

Method development for the determination of residual fluorotelomer raw materials and perflurooctanoate in fluorotelomer-based products by gas chromatography and liquid chromatography mass spectrometry

The methodology for the determination of perfluorooctanoate (C(7)F(15)COO-, PFO), fluorotelomer alcohols (FTOHs: 6-2, 8-2, and 10-2), perfluorooctyl iodide (PFOI), and 8-2-8 fluorotelomer alcohol ester in complex fluorotelomer-based commercial products has been demonstrated and validated. Sample preparation procedures allowing determination of residual levels of these compounds were developed. The analytes were detected either by LC/MS/MS (PFO), LC/MS (FTOHs), or GC/MS (PFOI, 8-2-8 ester). The methods were validated by investigating the recoveries of analytes spiked at multiple levels to authentic sample matrices. The recoveries generally were between 70 and 130%. The limits of detection were in sub-microg/g range and the limits of quantitation were in the mug/g range. The methods were applied to fluorotelomer-based raw materials and fluorotelomer-based surfactants and polymeric products and represent methods useful for the determination of higher carbon chain length homologs as well.     

Effect of visible light on normal and P23H-3 transgenic rat retinas: characterization of a novel retinoic acid derivative present in the P23H-3 retina

Transgenic rats with the P23H mutation in rhodopsin exhibit increased susceptibility to light damage, compared with normal animals. It is known that light-induced retinal damage requires repetitive bleaching of rhodopsin and that photoreceptor cell loss is by apoptosis; however, the underlying molecular mechanism(s) leading to photoreceptor cell death are still unknown. Photoproducts, such as all-trans retinal or other retinoid metabolites, released by the extensive bleaching of rhodopsin could lead to activation of degenerative processes, especially in animals genetically predisposed to retinal degenerations. Using wild-type and transgenic rats carrying the P23H opsin mutation, we evaluated the effects of acute intense visible light on retinoid content, type and distribution in ocular tissues. Rats were exposed to green light (480-590 nm) for 0, 5, 10, 30 and 120 min. Following light treatment, rats were sacrificed and neural retinas were dissected free of the retinal pigment epithelium. Retinoids were extracted from retinal tissues and then subjected to HPLC and mass spectral analysis. We found that the light exposure affected relative levels of retinoids in the neural retina and retinal pigment epithelium of wild-type and P23H rat eyes similarly. In the P23H rat retina but not the wild-type rat retina, we found a retinoic acid-like compound with an absorbance maximum of 357 nm and a mass of 304 daltons. Production of this retinoic acid-like compound in transgenic rats is influenced by the age of the animals and the duration of light exposure. It is possible that this unique retinoid may be involved in the process of light-induced retinal degeneration.