Algebras of Convolution Type Operators with Piecewise Slowly Oscillating Data. I: Local and Structural Study

Let ${\mathcal{B}_{p,w}}$ be the Banach algebra of all bounded linear operators acting on the weighted Lebesgue space ${L^{p}(\mathbb{R}, w)}$ , where ${p \in (1, \infty)}$ and w is a Muckenhoupt weight. We study the Banach subalgebra ${\mathfrak{A}_{p,w}}$ of ${\mathcal{B}_{p,w}}$ generated by all multiplication operators aI ( ${a \in PSO^{\diamond}}$ ) and all convolution operators W ⁰(b) ( ${b \in PSO_{p,w}^{\diamond}}$ ), where ${PSO^{\diamond} \subset L^{\infty}(\mathbb{R})}$ and ${PSO_{p,w}^{\diamond} \subset M_{p,w}}$ are algebras of piecewise slowly oscillating functions that admit piecewise slowly oscillating discontinuities at arbitrary points of ${\mathbb{R} \cup \{\infty\}}$ , and M _p,w is the Banach algebra of Fourier multipliers on ${L^{p}(\mathbb{R}, w)}$ . Under some conditions on the Muckenhoupt weight w, we construct a Fredholm symbol calculus for the Banach algebra ${\mathfrak{A}_{p,w}}$ and establish a Fredholm criterion for the operators ${A \in \mathfrak{A}_{p,w}}$ in terms of their Fredholm symbols. To study the Banach algebra ${\mathfrak{A}_{p,w}}$ we apply the theory of Mellin pseudodifferential operators, the Allan–Douglas local principle, the two idempotents theorem and the method of limit operators. The paper is divided in two parts. The first part deals with the local study of ${\mathfrak{A}_{p,w}}$ and necessary tools for studying local algebras.     

Synthesis and anion binding properties of 2,5-diamidothiophene polypyrrole Schiff base macrocycles

[reaction: see text] Two easy-to-synthesize polypyrrolic 2,5-diamidothiophene Schiff base macrocycles are reported, along with their anion binding properties as determined via UV-vis spectroscopic titrations carried out in dichloroethane. There is a striking difference between the interactions with anions of the two macrocycles, a finding ascribed to differences in their rigidity. For example, the more flexible dipyrromethane-derived macrocycle displays a 1.2:1 hydrogen sulfate versus nitrate selectivity, while its more rigid bipyrrole-derived congener shows a 7.4:1 selectivity in favor to hydrogen sulfate.     

Estrogenic Activity of Mycoestrogen (3β,5α,22E)-Ergost-22-en-3-ol via Estrogen Receptor α-Dependent Signaling Pathways in MCF-7 Cells

Armillariella tabescens (Scop.) Sing., a mushroom of the family Tricholomataceae, has been used in traditional oriental medicine to treat cholecystitis, improve bile secretion, and regulate bile-duct pressure. The present study evaluated the estrogen-like effects of A. tabescens using a cell-proliferation assay in an estrogen-receptor-positive breast cancer cell line (MCF-7). We found that the methanol extract of A. tabescens fruiting bodies promoted cell proliferation in MCF-7 cells. Using bioassay-guided fractionation of the methanol extract and chemical investigation, we isolated and identified four steroids and four fatty acids from the active fraction. All eight compounds were evaluated by E-screen assay for their estrogen-like effects in MCF-7 cells. Among the tested isolates, only (3β,5α,22E)-ergost-22-en-3-ol promoted cell proliferation in MCF-7 cells; this effect was mitigated by the ER antagonist, ICI 182,780. The mechanism underlying the estrogen-like effect of (3β,5α,22E)-ergost-22-en-3-ol was evaluated using Western blot analysis to detect the expression of extracellular signal-regulated kinase (ERK), phosphatidylinositol 3-kinase (PI3K), Akt, and estrogen receptor α (ERα). We found that (3β,5α,22E)-ergost-22-en-3-ol induced an increase in phosphorylation of ERK, PI3K, Akt, and ERα. Together, these experimental results suggest that (3β,5α,22E)-ergost-22-en-3-ol is responsible for the estrogen-like effects of A. tabescens and may potentially aid control of estrogenic activity in menopause.     

Age-dependent variations of cell response to oxidative stress: proteomic approach to protein expression and phosphorylation

We investigated the protein profiles of variously aged rat astrocytes in response to oxidative stress. After H2O2-exposure of cells at 100 microM for 30 min, the relative intensity of ten protein spots changed on two-dimensional (2-D) gels compared with control gels after silver staining. Matrix-assisted laser desorption/ionization-time of flight-mass spectrometry (MALDI-TOF-MS) analysis after in-gel digestion revealed that six of these spots corresponded to three kinds of proteins, each of which was composed of a protein and its modified form with a different isoelectric point (pI). These three proteins were identified as peroxiredoxins (PRDXs) II and III, and calpactin I light chain (p11). H2O2-exposure increased the intensity of the spot with lower pI and simultaneously decreased that of the spot with higher pI for both PRDXs II and III. In addition, the expression of annexin VII, S-adenosyl-L-homocysteine hydrolase, elongation factor II fragment (EF-II), and adenosine deaminase was increased by H2O2-exposure in astrocytes from variously aged rats. Using the Pro-Q Diamond staining, heat shock protein 60 kDa (Hsp 60) and alpha-tubulin were observed to be phosphorylated upon H2O2-exposure. While phosphorylation of alpha-tubulin was correlated positively with age, the changes in abundance of ten protein spots as described above were independent of age. These results suggest that aging does not suppress the responses aimed at limiting injury and promoting repair brought about by severe oxidative stress, and might affect cell dynamics including the formation of microtubules.     

Olefin Cyclopropanation by Radical Carbene Transfer Reactions Promoted by Cobalt(II)/Porphyrinates: Active‐Metal‐Template Synthesis of [2]Rotaxanes

A Co^II/porphyrinate‐based macrocycle in the presence of a 3,5‐diphenylpyridine axial ligand functions as an endotopic ligand to direct the assembly of [2]rotaxanes from diazo and styrene half‐threads, by radical‐carbene‐transfer reactions, in excellent 95 % yield. The method reported herein applies the active‐metal‐template strategy to include radical‐type activation of ligands by the metal‐template ion during the organometallic process which ultimately yields the mechanical bond. A careful quantitative analysis of the product distribution afforded from the rotaxane self‐assembly reaction shows that the Co^II/porphyrinate subunit is still active after formation of the mechanical bond and, upon coordination of an additional diazo half‐thread derivative, promotes a novel intercomponent C?H insertion reaction to yield a new rotaxane‐like species. This unexpected intercomponent C?H insertion illustrates the distinct reactivity brought to the Co^II/porphyrinate catalyst by the mechanical bond.     

Impact of phase composition on water adsorption on inorganic hybrids "salt/silica"

The effect of a "guest-host" interaction on the phase composition and sorption properties of the composite sorbents "salt in a porous host matrix" has been studied. The matrix was a mesoporous silica of KSK type, while the confined salts were CaCl(2), CuSO(4), MgSO(4), and Na(2)SO(4). Both structure and properties of the composites were studied by X-ray diffraction, titration in the pH range of 2-9, differential dissolution, and TG techniques. Chemical interaction between the silica surface and the salt during preparation results in the formation of the salt surface complexes and stabilization of the dispersed salt in two phases, namely, a crystalline phase and an X-ray amorphous phase. The water sorption properties of the composites depend on the phase composition and can be intently modified by using variation of the preparation conditions.     

Comparison of a Rapid Light-Induced and Forced Test to Study the Oxidative Stability of White Wines

The oxidation processes of white wines can occur during storage and commercialization due to several factors, and these can negatively affect the color, aroma, and quality of the wine. Wineries should have faster and simpler methods that provide valuable information on oxidation stability of wines and allow fast decision-making procedures, able to trigger suitable technological interventions. Using a portable prototype instrument for light irradiations at different wavelengths and times was considered and evaluated on sensorial, spectrophotometric, and colorimetric parameters of white wines. The sensorial analysis revealed that white and light blue were the most significant, after only 1 h of irradiation. The experimental results showed that hydrogen peroxide could enhance the effect of light treatment, allowing a contemporary evaluation of the oxidation stability of wine against light and chemical stresses. As expected, a good correlation (R² > 0.89) between optical density at 420 nm and b* parameter was highlighted. The synergic effect of light and H₂O₂ was also studied on the hydrolyzable and condensed tannins’ additions to white wine. The proposed methodology could be used to evaluate the oxidative stability of white wines, but also to evaluate the effect of some oenological adjuvants on wine stability.     

Asymmetric synthesis of polymer-supported cyanohydrin acetates

A bimetallic titanium(salen) complex has been used to catalyze the asymmetric addition of potassium cyanide to aldehydes attached to Wang resin giving polymer supported cyanohydrin propionates with up to 91% enantiomeric excesses.     

Catalytic, asymmetric synthesis of α,α-disubstituted amino acids

Copper(salen) complex 1 has been found to catalyse the asymmetric alkylation of enolates derived from a variety of amino acids. There is a clear relationship between the size of the side chain in the substrate and the enantioselectivity of the process, so that the enantioselectivity decreases in the order alanine>aminobutyric acid>allylglycine>leucine>phenylalanine>valine. A transition state model which accounts for the influence of the size of the side chain on the enantioselectivity of the reactions is presented.