Volterra Convolution Operators with Values in Rearrangement Invariant Spaces

The Volterra convolution operator Vf(x) = ^x₀(x–y)f(y)dy,where (·) is a non-negative non-decreasing integrablekernel on [0, 1], is considered. Under certain conditions onthe kernel , the maximal Banach function space on [0, 1] onwhich the Volterra operator is a continuous linear operatorwith values in a given rearrangement invariant function spaceon [0, 1] is identified in terms of interpolation spaces. Thecompactness of the operator on this space is studied.     

Modeling of one-dimensional smoldering of polyurethane in microgravity conditions

Results are presented from a model of forward smoldering combustion of polyurethane foam in microgravity. The transient one-dimensional numerical-model is based on that developed at the University of Texas at Austin. The conservation equations of energy, species, and mass in the porous solid and in the gas phases are numerically solved. The solid and the gas phases are not assumed to be in thermal or in chemical equilibrium. The chemical reactions modeled consist of foam oxidation and pyrolysis reactions, as well as char oxidation. The model has been modified to account for new polyurethane kinetics parameters and radial heat losses to the surrounding environment. The kinetics parameters are extracted from thermogravimetric analyses published in the literature and using Genetic Algorithms as the optimization technique. The model results are compared with previous tests of forward smoldering combustion in microgravity conducted aboard the NASA Space Shuttle. The model calculates well the propagation velocities and the overall smoldering characteristics. Direct comparison of the solution with the experimental temperature profiles shows that the model predicts well these profiles at high temperature, but not as well at lower temperatures. The effect of inlet gas velocity is examined, and the minimum airflow for ignition is identified. It is remarkable that this one-dimensional model with simplified kinetics is capable of predicting cases of smolder ignition but with no self-propagation away from the igniter region. The model is used for better understanding of the controlling mechanisms of smolder combustion for the purpose of fire safety, both in microgravity and normal gravity, and to extend the unique microgravity data to wider conditions avoiding the high cost of space-based experiments.     

Tuning the Lewis acid phenol $$\varvec{}$$-prenylation as a molecular diversity tool

A diversity-oriented approach for the synthesis of various structurally different prenylated alcohols from readily accessible and common precursors was developed. With varying approaches, this article describes some successful examples of a Friedel–Crafts alkylation using methoxyphenols and different prenyl alcohols (geraniol and (E,E)-farnesol). We demonstrated that just by varying the stoichiometry of the Lewis acid used, the course of the reaction can be shifted to produce the alkylated or the cyclized product. Eighteen unique products were obtained with good isolated yields by direct alkylation with or without a consecutive \(\pi \)-cationic cyclization.     

An unexpected Pummerer rearrangement in the synthetic route to ethyl (2′-hydroxy-4′,5′-methylenedioxyphenyl)acetate: An alternative approach to 2,3-dimethylthio benzofurans

The synthesis of ethyl (2′-hydroxy-4′,5′-methylendioxophenyl)acetate, a fragment of the antihyperglycemic natural coumarin subcoriacin, is reported. We found an expeditious route to the title compound in five steps. Final metal catalyzed acid ethanolysis of the vinylic 1,1-methylthio methylsulfoxide derivative afforded the required aryl acetic ester, but in the absence of metal catalyst, an unexpected Pummerer rearrangement produced the 2,3-dimethylthiofuran derivative as the major product. This last result provides an alternative entry to 2,3-dimethlythiobenzofurans.     

Synthesis, photophysical, photochemical, and computational studies of coumarin-labeled nicotinamide derivatives

The syntheses and photophysical/photochemical properties of two amide-tethered coumarin-labeled nicotinamides are described. Photochemical studies of 6-bromo-7-hydroxycoumarin-4-ylmethylnicotinamide (BHC-nicotinamide) revealed an unexpected solvent effect. This result is rationalized by computational studies of the different protonation states using TD-DFT with the M06L/6-311+G** method with implicit and explicit solvation models. Molecular orbital energies responsible for the λ(max) excitation show that the functionalization of the coumarin ring results in a strong red-shift from 330 to 370 nm when the pH of solution is increased from 3.06 to 8.07. From this MO analysis, a model for solvent interactions has been proposed. The BHC-nicotinamide proved to be photochemically stable, which is also interpreted in terms of NBO calculations. The results provide a set of principles for the rational design of either photostable labeling reagents or photolabile cage compounds.     

Conformational flexibility of a synthetic glycosylaminoglycan bound to a fibroblast growth factor. FGF-1 recognizes both the (1)C(4) and (2)S(O) conformations of a bioactive heparin-like hexasaccharide

The first direct NMR determination of the conformation of a conformationally flexible heparin-like hexasaccharide bound to a key receptor, FGF-1, is described. The determination has been based on the use of a 13C-labeled protein and a regular 12C sugar. FGF-1 recognizes several conformations of the iduronic moieties of the hexasaccharide. Therefore, this case is different than that described for the controversial recognition of heparin-like saccharides by AT-III, which seems to recognize just one conformation of the iduronic acid residues.     

Studies on Immobilization and Partial Characterization of Lipases from Wheat Seeds (<Emphasis Type="Italic">Triticum aestivum</Emphasis>)

The objective of this study was to provide some features on immobilization and partial characterization of lipases from wheat seeds. The optimum pH and temperature were found to be 5.5 and 32–37 °C, respectively. The stability of the concentrated enzymatic extract to high temperatures (25, 35, 45, and 55 °C) showed that the incubation of the extract at 55 °C led to its complete inactivation. The concentrated enzymatic extract kept 90% of its hydrolytic and esterification activities until 70 and 40 days of storage at 4 °C, respectively. The extract presented higher hydrolytic specificity to substrates of medium and long chains and higher esterification affinity to fatty acids of short and medium chains and alcohols with two and three carbon atoms. After the immobilization process using activated coal and sodium alginate as supports, an enhancement of about threefold in lipase activity was observed. The development of the present work permitted us to point out some characteristics of lipases from wheat seeds necessary for the proposition of new future industrial applications for this important biocatalyst.     

Polymeric Gene Carriers Bearing Pendant β‐Cyclodextrin: The Relevance of Glycoside Permethylation on the “In Vitro” Cell Response

The incorporation of cyclodextrins (CDs) to nonviral cationic polymer vectors is very attractive due to recent studies that report a clear improvement of their cytocompatibility and transfection efficiency. However, a systematic study on the influence of the CD derivatization is still lacking. In this work, the relevance of β‐CD permethylation has been addressed by preparing and evaluating two series of copolymers of the cationic N‐ethyl pyrrolidine methacrylamide (EPA) and styrenic units bearing pendant hydroxylated and permethylated β‐CDs (HCDSt and MeCDSt, respectively). For both cell lines, CDs permethylation shows a strong influence on plasmid DNA complexation, “in vitro” cytocompatibility and transfection efficiency of the resulting copolymers over two murine cell lines. While the incorporation of the hydroxylated CD moiety increased the cytotoxicity of the copolymers in comparison with their homopolycationic counterpart, the permethylated copolymers have shown full cytocompatibility as well as superior transfection efficiency than the controls. This behavior has been related to the different chemical nature of both units and tentatively to a different distribution of units along the polymeric chains. Cellular internalization analysis with fluorescent copo­lymers supports this behavior.