Extrapolation Using a Modified Projection Method

In [14 R.P. Kulkarni ( 2003 ). A superconvergence result for solutions of compact operator equations . Bull. Aust. Math. Soc. 68 : 517 – 528 . [Google Scholar]], a new method based on projections onto a space of piecewise polynomials of degree ≤r ? 1 has been shown to give a convergence of order 4r for second-kind integral equations. The size of the system of equations that must be solved, in implementing this method, remains the same as for the Galerkin/collocation method. In this article the solution obtained by the proposed method is shown to have an asymptotic series expansion which remains valid in the discrete version. The Richardson extrapolation can then be used to further improve the order of convergence to 4r + 2.     

Regularity of the free boundary of an American option on several assets

We establish the C^∞ regularity of the free boundary for an American option on several assets in the case where the payoff is convex and the assets follow correlated geometric Brownian motions. Our work builds on results concerning the qualitative properties and initial regularity of the free boundary by Broadie and Detemple; Jaillet, Lamberton, and Lapeyre; and Villeneuve. © 2008 Wiley Periodicals, Inc.     

Multi-item lot-sizing with joint set-up costs

We consider a multi-item lot-sizing problem with joint set-up costs and constant capacities. Apart from the usual per unit production and storage costs for each item, a set-up cost is incurred for each batch of production, where a batch consists of up to C units of any mix of the items. In addition, an upper bound on the number of batches may be imposed. Under widely applicable conditions on the storage costs, namely that the production and storage costs are nonspeculative, and for any two items the one that has a higher storage cost in one period has a higher storage cost in every period, we show that there is a tight linear program with O(mT ²) constraints and variables that solves the joint set-up multi-item lot-sizing problem, where m is the number of items and T is the number of time periods. This establishes that under the above storage cost conditions this problem is polynomially solvable. For the problem with backlogging, a similar linear programming result is described for the uncapacitated case under very restrictive conditions on the storage and backlogging costs. Computational results are presented to test the effectiveness of using these tight linear programs in strengthening the basic mixed integer programming formulations of the joint set-up problem both when the storage cost conditions are satisfied, and also when they are violated.     

MC1R Gene Polymorphism Affects Skin Color and Phenotypic Features Related to Sun Sensitivity in a Population of French Adult Women

The melanocortin-1 receptor ( MC1R ) gene is known to play a major role in skin and hair pigmentation and to be highly polymorphic in Caucasians. This study was performed to investigate the relationships between MC1R gene polymorphisms and skin color in a large sample of French middle-aged Caucasian women. The codons 60 to 265 and the codon 294 of the MC1R gene were sequenced in 488 women. The skin color was measured on the inner side of the forearm using a spectrophotometric instrument. Fifteen variants were identified: Arg151Cys, Arg160Trp, Arg142His, Asp294His, Ile155Thr, Asp84Glu, Val60Leu, Val92Met, Arg163Gln, Ser83Pro, Thr95Met, Pro256Ser, Val265Ile, Ala166Ala and Gln233Gln. Women carrying Arg151Cys, Asp294His, Arg160Trp and Asp84Glu variants had a significantly higher reflectance in the red region, which indicates a lower level of functional melanin. This association was the most pronounced for women carrying Asp84Glu. In contrast, no significant difference was observed for other variants. Moreover, associations between MC1R polymorphisms and the risks of experiencing sunburn and of having freckles were found independently of skin color. Our findings support the hypothesis that MC1R polymorphisms do not necessarily alter the skin color but should sensitize the skin to UV-induced DNA damage.     

Irradiation of Skin and Contrasting Effects on Absorption of Hydrophilic and Lipophilic Compounds

Increasing legal requirements for risk assessment and efficacy testing in the dermo-cosmetic field have led to the development of alternative test methods. In this study, the porcine skin model was chosen to test the effect of irradiation on the penetration habits of UV filters and caffeine. For decades, the pig has been recognized as an experimental animal in biomedical research thanks to its morphological and physiological similarities to humans. In this study, we wanted to investigate the effect of UV irradiation on the absorption of octocrylene (OC) and benzophenone-3 (B3) sunscreens used under those circumstances and a model hydrophilic molecule, caffeine (Caf). These particular compounds were chosen due to their different lipophilic profiles. The percutaneous penetration of the two UV filters and Caf was studied after two simulated solar radiation doses of 61.4 kJ m⁻². After irradiation simulation, the total absorbed dose was increased for OC while for B3 and Caf it was lower. Thus, modifications in percutaneous absorption have been observed, and it appears that UV could play a crucial role in this process. Moreover, it has been observed that the lipophilic profile of the studied compounds affects percutaneous penetration when irradiated.     

Analysis of perfluorinated chemicals in sludge: Method development and initial results

A fast, rigorous method was developed to maximize the extraction efficacy for ten perfluorocarboxylic acids and perfluorooctanesulfonate from waste-water-treatment sludge and to quantitate using liquid chromatography, tandem-mass spectrometry (LC/MS/MS). First, organic solvents were tested for extraction efficiency, including acetonitrile (ACN), methanol (MeOH), isopropanol (IPA), tetrahydrofuran (THF), and 50/50 ACN/MeOH (v/v). Among the extractants tested, 50/50 ACN/MeOH yielded the best results for our combined criteria of extraction efficacy and solvent-handling convenience. Second, chemical pretreatment prior to solvent extraction was tested with sodium hydroxide (NaOH), potassium hydroxide (KOH), hydrochloric acid (HCl), and potassium persulfate (K₂S₂O₈). Pretreatment with NaOH and HCl effectively recovered additional PFCs from the sludge, but KOH and K₂S₂O₈ digestion were less effective than no pretreatment. Third, cleanup methods were investigated with solid-phase extraction using HLB (hydrophilic–lipophilic balanced) and WAX (weak-anion exchange) stationary phases, and with ion-pairing. The HLB stationary phase yielded a slight edge over the other two cleanup strategies in terms of recoverable PFCs and chromatographic separation. Finally, the appropriateness of isotopically labeled PFCs for quantitating unlabeled PFCs using isotopic dilution in complex sludge extracts was evaluated by comparison to results obtained with the standard-addition method. A National Institute of Standards and Technology (NIST) domestic sludge (CRM 2781) was analyzed using our finalized method and compared with previously reported results.     

A general procedure for the synthesis of isoxazolidin-5-ones

Conjugate addition of N-substituted hydroxylamines to α,β-unsaturated esters followed by cyclisation of the adducts with lithium bis (trimethylsily)amide provides the first general means of synthesising isoxazolidin-5-ones, the N-benzyl derivatives of which may be hydrogenolised to β-aminoacids.     

Diastereoselective synthesis of protected syn 1,3-diols: preparation of the C16-C24 portion of Dolabelides

We have designed a new method to make synthons encompassing a protected syn 1,3-diol motif and an aldehyde alpha to the 1,3-dioxane ring. An additional stereocenter was also created, potentially leading to stereochemically defined 1,2,4-triols. This method was successfully applied to the synthesis of the C16-C24 portion of Dolabelides.     

On the photobiological properties of chimeras combining quaternary ammonium derivatives of retinoic amides and psoralen. A study with cultured human keratinocytes

The effectiveness of the combination of retinoids with 8-methoxypsoralen (8-MOP) and ultraviolet-A (UV-A) light in the treatment of some cutaneous proliferative diseases has motivated the synthesis of new "chimera-type" molecules built from psoralen derivatives and retinoic amides and related molecules. The chimeras result from the combination of 8-(3-bromopropyloxy)-psoralen with amides prepared by reacting 4-amino-pyridine with 13E- and 13Z-retinoic acids or a "retinoid-like" derivative with an alkene chain of only three double bonds. The synthesis of chimeras built with the 8-(3-bromopropyloxy)-psoralen and the amide of cinnamic acid or its 4-methoxy derivative has also been carried out. In contrast to 8-MOP, all the chimeras exhibit strong molar absorptivities in the range 20 000-40 000 M(-1) cm(-1) in the 340-390 nm UV-A region. The "retinoid-like"- and retinoid-psoralen chimeras are characterized by a marked dark toxicity toward proliferating NCTC 2544 keratinocytes (with a lethal dose corresponding to 50% cell survival [LD50] of 1-5 microM) as compared with that of the cinnamic acid derivative-psoralen chimeras (LD50 > or = 50 microM). This toxicity leads to alteration of the mitochondrial membrane potential. At nontoxic concentrations, the chimeras demonstrate effective psoralens + UV-A-induced photocytotoxicity. They are moderate photosensitizers of membrane lipid peroxidation. Cell apoptosis is a major photocytotoxic process as suggested by the fluorescence-activated cell-sorting technique using annexin-fluorescein isothiocyanate and propidium iodide as apoptotic markers.