Functions with presribed singular values of the gradient

We prove the existence of infinitely many vector-valued Lipschitz-continuous functions u on an open set satisfying suitable Dirichlet boundary conditions such that the singular values of the gradient matrix u, i.e. the square roots of the eigenvalues of the symmetrized matrix , agree a.e. on with N given positive, bounded and lower semicontinuous functions. Received May 28, 1997     

Effect on structural relaxation of the poly(methyl‐methacrylate) copolymers chain flexibility

The structural relaxation of poly(methyl‐methacrylate) (PMMA)‐based copolymers with different chain flexibility has been studied by DSC with the classical procedure of the isothermal and dynamical approach. Modified PMMA with different chain flexibility have been prepared by free radical polymerization in solution using a mixture of monomers containing 10 mol % of alkyl methacrylate (i.e., ethyl, buthyl, and hexyl methacrylate). The molecular characteristics of all the prepared copolymers have been performed by a multiangle laser light scattering (MALS) photometer on‐line to a size exclusion chromatography (SEC) system (SEC‐MALS) after and before the thermal treatments, NMR (¹H and ¹³C) and MALDI‐TOF mass spectrometry. A comparison of the apparent relaxation rate (R_H) was appraised from the enthalpy loss by annealing the different samples at the same level of undercooling (T_a = T_g ? 18 °C). It was found an increase of R_H increasing the chain flexibility in the copolymers. Dynamical tests, performed at different cooling rates, have been used to estimate the apparent activation energy of the relaxation process. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 596–607, 2009     

Error Estimates for a Stochastic Impulse Control Problem

We obtain error bounds for monotone approximation schemes of a stochastic impulse control problem. This is an extension of the theory for error estimates for the Hamilton-Jacobi-Bellman equation. We obtain almost the same estimate on the rate of convergence as in the equation without impulsions [2], [3].     

Optimization and validation of a high-performance liquid chromatography method for the analysis of cardiac glycosides in Digitalis lanata

In this study, a simple and reliable HPLC method for the qualitative and quantitative analysis of cardiac glycosides in Digitalis lanata Ehrh. raw material was developed and applied to healthy and phytoplasma-infected plants. The target analytes cover a broad range of secondary metabolites, including primary, secondary and tertiary glycosides and the corresponding aglycones. The sample preparation was carried out by sonication of the plant material with 70% (v/v) aqueous methanol at room temperature, followed by reversed-phase solid-phase extraction purification from interfering pigments. The HPLC analyses were performed on a Symmetry C₁₈ column (75 mm × 4.6 mm I.D., 3.5 μm), with a gradient elution composed of water and acetonitrile, at a flow rate of 1.0 mL/min. The column temperature was set at 20 °C and the photodiode array detector monitored the eluent at 220 nm. The method was validated with respect to ICH guidelines and the validation parameters were found to be highly satisfactory. The application of the method to the analysis of D. lanata leaves indicated that air-drying was the optimum method for raw material processing when compared with freeze-drying. The analysis of healthy and phytoplasma-infected plants demonstrated that the secondary metabolite mainly affected by the pathogen presence was lanatoside C (153.2 μg/100 mg versus 76.1 μg/100 mg). Considering the importance of D. lanata plant material as source of cardiac glycosides, the developed method can be considered suitable for the phytochemical analysis and for the quality assurance of D. lanata used for pharmaceutical purpose.     

Efficient access to 5-substituted thiazoles by a novel metallotropic rearrangement

A novel rearrangement process involving the migration of trimethylstannanyl or trimethylsilanyl groups around the thiazole ring provides access to either 2- or 5-metallated thiazoles by tuning the reaction conditions. The proposed mechanism, based on experimental evidence, is characterized by the catalytic role of thiazole bisadducts as metal-transfer agents.     

Synthesis of biomimetic light-driven molecular switches via a cyclopropyl ring-opening/nitrilium ion ring-closing tandem reaction

A cyclopropyl ring-opening/nitrilium ion ring-closing tandem reaction has been conveniently used in an expeditious synthetic approach to light-driven Z/E molecular switches featuring an imine function conjugated to olefin groups that mimics natural protonated Schiff bases.     

On the minimum problem for nonconvex, multiple integrals of product type

We consider the problem of minimizing multiple integrals of product type, i.e. where is a bounded, open set in , is a possibly nonconvex, lower semicontinuous function with p-growth at infinity for some and the boundary datum is in (or simply in if ). Assuming that the convex envelope off is affine on each connected component of the set , we prove attainment for () for every continuous, positively bounded below function g such that (i) every point is squeezed between two intervals where g is monotone and (ii) g has no strict local minima. This shows in particular that the class of coefficents g that yield existence to () is dense in the space of continuous, positive functions on . We present examples which show that these conditions for attainment are essentially sharp. Received April 12, 2000 / Accepted May 9, 2000 / Published online November 9, 2000     

Ultratrace determination of highly hydrophilic compounds by 2,2,3,3,4,4,5,5-octafluoropentyl chloroformate-mediated derivatization directly in water

Highly hydrophilic compounds, with multiple carboxylic, hydroxylic, or aminic groups, have been determined at ultratrace level (3–30 fmol injected) in aqueous solution by direct derivatization with 2,2,3,3,4,4,5,5-octafluoropentyl chloroformate, followed by n-hexane extraction and analysis by gas chromatography-electron capture negative ion mass spectrometry (GC-ECNI-MS). The products have high molecular weights, but also high volatility, making their elution from the GC column efficient. The derivatizing agent was synthesized from the corresponding alcohol and phosgene. The derivatization reaction is catalyzed by a pyridine solution of N,N-dicyclohexylcarbodiimide. At 200 °C ion-source temperature, most negative ion mass spectra showed only a weak or no molecular ion, but a controlled and interpretable fragmentation, allowing the derivatives to be easily monitored by high-mass ion chromatograms. Typical distinctive fragments are located in the m/z 500–800 mass range. Optimization of the operating conditions for the derivatization was performed. This was done in order to minimize number and intensity of peaks due to the hydrolysis of chloroformate in the total ion chromatogram. Calibration curves proved linear over two orders of magnitude concentration.     

Multifaceted Effects of Lycopene: A Boulevard to the Multitarget-Based Treatment for Cancer

Lycopene is a pigment belonging to the group of carotenoids and it is among the most carefully studied antioxidants found especially in fruit and vegetables. As a carotenoid, lycopene exerts beneficial effects on human health by protecting lipids, proteins, and DNA from damage by oxidation. Lycopene is a powerful oxygen inactivator in the singlet state. This is suggestive of the fact that lycopene harbors comparatively stronger antioxidant properties over other carotenoids normally present in plasma. Lycopene is also reported to hinder cancer cell proliferation. The uncontrolled, rapid division of cells is a characteristic of the metabolism of cancer cells. Evidently, lycopene causes a delay in the progression of the cell cycle, which explains its antitumor activity. Furthermore, lycopene can block cell transformation by reducing the loss of contact inhibition of cancer cells. This paper collects recent studies of scientific evidence that show the multiple beneficial properties of lycopene, which acts with different molecular and cellular mechanisms.