Complete sets and completion of sets in Banach spaces

In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and centers. The results are illustrated by several examples.     

Efficient Differentiation of the Hydroxyl Groups of 3,4-O-Isopropylidene-D-Galactopyranosides by Lipase Catalyzed Esterification and De - Esterification

Abstract

The Pseudomonas sp. (LPS) promoted acyl transfer from vinyl acetate to selected 3,4-O-isopropylidene-D-galactopyranosides takes place in a completely selective manner giving in high yield the corresponding 6-O-acetates. The acetylation rate is strongly dependent on the type and the orientation of the aglycon, varying from a maximum of reactivity for the 1-deoxy derivative, 1,5-anhydro-3,4-O-isopropylidene-D-galactitol (1d), to a minimum for β configurated alkyl glycosides and showing a complete loss of reactivity for 3′,4′:2,3:5,6-tri-O-isopropylidenelactose dimethyl acetal (1e). The latter compound is, however, selectively 6′-O-esterified in good yield by lipase from Candida Antarctica and vinyl acetate. Also the course of the enzymatic hydrolysis of 2,6-di-O-acetyl-3,4-O-isopropylidene-D-galactopyranosides 2 is dependent on the type of the aglycon, both for the reaction rate and the selectivity. The 2-O-acetates 4 are selectively obtained in good yields with porcine pancreatic lipase (PPL) promoted hydrolysis in the case of β and α-methyl, and 1-deoxy derivatives (2a, 2b and 2d), while for β-benzyl (2c) and lactose (2e) analogues satisfactory results are obtained with lipase from Mucor miehei (IM20).

     

Hybrid sol–gel based coatings for the protection of historical window glass

Medieval glass is commonly attacked by atmospheric pollutants conveyed by water, triggering the corrosion process. Current conservation strategies aim to maintain window glass in its original context, and so it is necessary to protect it from further degradation. Sol–gel technology is very effective for the preparation of protective films, using Si-alkoxide precursors chemically similar to the substrate. The present work discusses water-repellent hybrid sol–gel coatings made from tetra-ethyl-ortho-silicate with different quantities of Si-alkoxides, functionalized with various alkyl groups. The coatings were deposited using the dip-coating technique and characterized by UV–VIS and FT-IR spectroscopy. Static and dynamic contact angle measurements showed an overall homogeneity of the coatings and indicated improved water-repellency when functionalized by long alkyl chains. The coatings with best performance in terms of transparency and contact angle, and with the lowest organic content, were selected and applied to medieval-like glass samples. Colorimetric characterization was carried out using a spectrophotometric scanner before and after application of the coatings and no significant color changes were found. The electron microscopy images revealed relatively even, crack-free coatings, especially with higher organic contents. Contact angle and colorimetric measurements were repeated after accelerated ageing by exposure to UV light and an SO₂-saturated atmosphere. A significant decrease in the contact angle was observed only for the samples treated at the highest SO₂ concentration. The silica-based materials did not give reaction by-products, were water-repellent, compatible with the substrate, colorless, transparent, and stable under exposure to chemicals and light, thereby satisfying the main requirements for the conservation of Cultural Heritage.     

Evaluation of Selected White-Rot Fungal Isolates for Improving the Sugar Yield from Wheat Straw

Biological pretreatment of lignocellulosic biomass by fungi can represent a low-cost and eco-friendly alternative to physicochemical methods to facilitate enzymatic hydrolysis. However, fungal metabolism can cause cellulose loss and it is therefore necessary to use the appropriate fungal strain-biomass type combination. In this work, the effects of biological pretreatments carried out by five different fungi on enzymatic hydrolysis of wheat straw were investigated. The best results were obtained with a Ceriporiopsis subvermispora strain, which minimized weight and cellulose losses and gave the highest net sugar yield (calculated with respect to the holocellulose content of the untreated straw), up to 44 % after a 10-week pretreatment, more than doubling the yields obtained with the other isolates. Moreover, prolonging the pretreatment from 4 up to 10 weeks produced a 2-fold increase, up to 60 %, in digestibility (sugar yield, calculated considering the holocellulose content of the pretreated material). The hemicellulose content of the pretreated material resulted inversely correlated with digestibility, and it could thus be utilized as an index of the pretreatment efficacy. Finally, a correlation was also found between digestibility and the difference between the absorbance values at 290 and 320 nm of pretreated wheat straw extracts.     

Study of MOCVD growth of InGaAsSb/AlGaAsSb/GaSb heterostructures using two different aluminium precursors TMAl and DMEAAl

The antimonide laser heterostructures growth technology using MBE epitaxy is currently well-developed, while MOVPE method is still being improved. It is known that the principal problem for MOVPE is the oxygen and carbon contamination of aluminium containing waveguides and claddings. The solution would be to apply a proper aluminium precursor. In this study we present the results of metal-organic epitaxy of In- and Al-containing layers and quantum well structures composing antimonide lasers devices. Special emphasis was put on the aluminium precursor and its relation to AlGaSb and AlGaAsSb materials properties. The crystalline quality of the layers grown with two different Al precursors was compared, very good structural quality films were obtained. The results suggested a substantial influence of precursors pre-reactions on the epitaxial process. The oxygen contamination was measured by SIMS, which confirmed its dependence on the precursor choice. We also optimised the GaSb substrate thermal treatment to deposit high quality GaSb homoepitaxial layers. Quaternary InGaAsSb layers were obtained even within the predicted miscibility gap, when arsenic content reached high above 10% values. InGa(As)Sb/AlGa(As)Sb quantum wells were grown and their optical properties were characterised by photoluminescence and photoreflectance spectroscopy. Type-I quantum wells showed a fundamental optical transition in the 1.9–2.1 μm range at room temperature. The epitaxial technology of the structures was subjected to an optimisation procedure. The investigated layers and heterostructures can be considered for application in laser devices.     

Friedel–Crafts Reaction of Benzyl Fluorides: Selective Activation of CF Bonds as Enabled by Hydrogen Bonding

A Friedel–Crafts benzylation of arenes with benzyl fluorides has been developed. The reaction produces 1,1‐diaryl alkanes in good yield under mild conditions without the need for a transition metal or a strong Lewis acid. A mechanism involving activation of the C? F bond through hydrogen bonding is proposed. This mode of activation enables the selective reaction of benzylic C? F bonds in the presence of other benzylic leaving groups.     

Extended Reaction Scope of Thiamine Diphosphate Dependent Cyclohexane‐1,2‐dione Hydrolase: From CC Bond Cleavage to CC Bond Ligation

ThDP‐dependent cyclohexane‐1,2‐dione hydrolase (CDH) catalyzes the C? C bond cleavage of cyclohexane‐1,2‐dione to 6‐oxohexanoate, and the asymmetric benzoin condensation between benzaldehyde and pyruvate. One of the two reactivities of CDH was selectively knocked down by mutation experiments. CDH‐H28A is much less able to catalyze the C? C bond formation, while the ability for C? C bond cleavage is still intact. The double variant CDH‐H28A/N484A shows the opposite behavior and catalyzes the addition of pyruvate to cyclohexane‐1,2‐dione, resulting in the formation of a tertiary alcohol. Several acyloins of tertiary alcohols are formed with 54–94 % enantiomeric excess. In addition to pyruvate, methyl pyruvate and butane‐2,3‐dione are alternative donor substrates for C? C bond formation. Thus, the very rare aldehyde–ketone cross‐benzoin reaction has been solved by design of an enzyme variant.     

A global Lipschitz continuity result for a domain-dependent Neumann eigenvalue problem for the Laplace operator

Let Ω be an open connected subset of Rⁿ of finite measure for which the Poincaré-Wirtinger inequality holds. We consider the Neumann eigenvalue problem for the Laplace operator in the open subset φ(Ω) of Rⁿ, where φ is a locally Lipschitz continuous homeomorphism of Ω onto φ(Ω). Then, we show Lipschitz-type inequalities for the reciprocals of the eigenvalues delivered by the Rayleigh quotient. Then, we further assume that the imbedding of the Sobolev space W^1,2(Ω) into the space L²(Ω) is compact, and we prove the same type of inequalities for the projections onto the eigenspaces upon variation of φ.