Weighted Composition Operators from the Minimal Möbius Invariant Space into the Bloch Space

Let ${{\varphi}}$ be an analytic self-map of the open unit disk ${{\mathbb{D}}}$ in the complex plane ${{\mathbb{C}, H(\mathbb{D})}}$ the space of complex-valued analytic functions on ${{\mathbb{D}}}$ , and let u be a fixed function in ${{H(\mathbb{D})}}$ . The weighted composition operator is defined by $$(uC_{\varphi}f)(z) = u(z)f({\varphi}(z)), \quad z \in \mathbb{D}, f \in H(\mathbb{D}).$$ In this paper, we study the boundedness and the compactness of the weighted composition operators from the minimal Möbius invariant space into the Bloch space and the little Bloch space.     

Carleson and Vanishing Carleson Measures on Radial Trees

We extend a discrete version of an extension of Carleson’s theorem proved in [5] to a large class of trees that have certain radial properties. We introduce the geometric notion of s-vanishing Carleson measure on such a tree T (with s ≥ 1) and give several characterizations of such measures. Given a measure σ on T and p ≥ 1, let L ^p (σ) denote the space of functions g defined on T such that |g| ^p is integrable with respect to σ and let L ^p (? T) be the space of functions f defined on the boundary of T such that |f| ^p is integrable with respect to the representing measure of the harmonic function 1.We prove the following extension of the discrete version of a classical theorem in the unit disk proved by Power. A finite measure σ on T is an s-vanishing Carleson measure if and only if for any real number p > 1, the Poisson operator P : L ^p (? T) → L ^sp (σ) is compact. Characterizations of weak type for the case p = 1 and in terms of the tree analogue of the extended Poisson kernel are also given. Finally, we show that our results hold for homogeneous trees whose forward probabilities are radial and whose backward probabilities are constant, as well as for semihomogeneous trees.     

Preparation and characterization of boron-based bioglass by sol−gel process

45S5 bioglass has been widely studied in the last few decades because of its bioactivity and promising applications in the biomedical field. Boron, even few studied, represents a potential element to improve the properties of the 45S5 bioglass derivatives. The bioglasses are conventionally prepared by heat treatment of oxides and silicon. Here, the sol?gel method is proposed for the preparation of the boron-based 45S5 bioglass (45S5B) and the classical 45S5 bioglass (45S5), using water-soluble salts as raw materials. The bioglasses were characterized by FTIR, XRD, and SEM, indicating the success of the sol?gel method for preparation of the samples. The bioglasses were also tested in vitro for bioactivity in biological conditions and cytotoxicity against eukaryotic cells. The bioactivity of 45S5B was similar to the bioactivity of 45S5 bioglass, indicated by the deposition of hydroxyapatite crystals at the surface of the pristine bioglasses. The results of cytotoxicity tests revealed that the IC₅₀ of 45S5B (IC₅₀?=?7.56?mg?mL^?1) was similar to the IC₅₀ of 45S5 (IC₅₀?=?8.15?mg?mL^?1), indicating its safety for application in the biomedical field.

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Site selectivity in the protonation of a phosphinito bridged Pt(I)-Pt(I) complex: a combined NMR and density-functional theory mechanistic study

The protonation of the dinuclear phosphinito bridged complex [(PHCy2)Pt(mu-PCy2){kappa(2)P,O-mu-P(O)Cy2}Pt(PHCy2)] (Pt-Pt) (1) by Br?nsted acids affords hydrido bridged Pt-Pt species the structure of which depends on the nature and on the amount of the acid used. The addition of 1 equiv of HX (X = Cl, Br, I) gives products of formal protonation of the Pt-Pt bond of formula syn-[(PHCy2)(X)Pt(mu-PCy2)(mu-H)Pt(PHCy2){kappaP-P(O)Cy2}] (Pt-Pt) (5, X = Cl; 6, X = Br; 8, X = I), containing a Pt-X bond and a dangling kappa P-P(O)Cy2 ligand. Uptake of a second equivalent of HX results in the protonation of the P(O)Cy2 ligand with formation of the complexes [(PHCy2)(X)Pt(mu-PCy2)(mu-H)Pt(PHCy2){kappaP-P(OH)Cy2}]X (Pt-Pt) (3, X = Cl; 4, X = Br; 9, X = I). Each step of protonation is reversible, thus reactions of 3, 4, with NaOH give, first, the corresponding neutral complexes 5, 6, and then the parent compound 1. While the complexes 3 and 4 are indefinitely stable, the iodine analogue 9 transforms into anti-[(PHCy2)(I)Pt(mu-PCy2)(mu-H)Pt(PHCy2)(I)] (Pt-Pt) (7) deriving from substitution of an iodo group for the P(OH)Cy2 ligand. Complexes 3 and 4 are isomorphous crystallizing in the triclinic space group P1 and show an intramolecular hydrogen bond and an interaction between the halide counteranion and the POH hydrogen. The occurrence of such an interaction also in solution was ascertained for 3 by (35)Cl NMR. Multinuclear NMR spectroscopy (including (31)P-(1)H HOESY) and density-functional theory calculations indicate that the mechanism of the reaction starts with a prior protonation of the oxygen with formation of an intermediate (12) endowed with a six membered Pt(1)-X...H-O-P-Pt(2) ring that evolves into thermodynamically stable products featuring the hydride ligand bridging the Pt atoms. Energy profiles calculated for the various steps of the reaction between 1 and HCl showed very low barriers for the proton transfer and the subsequent rearrangement to 12, while a barrier of 29 kcal mol(-1) was found for the transformation of 12 into 5.     

In Vitro Antioxidant,Antitumor and Photocatalytic Activities of Silver Nanoparticles Synthesized Using Equisetum Species: A Green Approach

The ethanolic extracts of three Equisetum species (E. pratense Ehrh., E. sylvaticum L. and E. telmateia Ehrh.) were used to reduce silver ions to silver nanoparticles (AgNPs). The synthesized AgNPs were characterized using UV-Vis spectrophotometry, Fourier Transform Infrared Spectroscopy (FTIR), Energy Dispersive X-ray (EDX), Transmission Electron Microscopy (TEM) and Dynamic Light Scattering (DLS) measurements. FTIR data revealed the functional groups of biomolecules involved in AgNPs synthesis, such as O-H, C-H, C=O, C-O, and C-C. EDX spectroscopy was used to highlight the presence of silver, while DLS spectroscopy provided information on the mean diameter of AgNPs, that ranged from 74.4 to 314 nm. The negative Zeta potential values (−23.76 for Ep–AgNPs, −29.54 for Es–AgNPs and −20.72 for Et–AgNPs) indicate the stability of the obtained colloidal solution. The study also focused on establishing the photocatalytic activity of AgNPs, which is an important aspect in terms of removing organic dyes from the environment. The best photocatalytic activity was observed for AgNPs obtained from E. telmateia, which degraded malachite green in a proportion of 97.9%. The antioxidant action of the three AgNPs samples was highlighted comparatively through four tests, with the best overall antioxidant capacity being observed for AgNPs obtained using E. sylvaticum. Moreover, the biosynthesized AgNPs showed promising cytotoxic efficacy against cancerous cell line MG63, the AgNPs obtained from E. sylvaticum L. providing the best result, with a LD₅₀ value around 1.5 mg/mL.     

Chiral Nano-Liquid Chromatography and Dispersive Liquid-Liquid Microextraction Applied to the Analysis of Antifungal Drugs in Milk

A novel chromatographic application in chiral separation by using the nano-LC technique is here reported. The chiral recognition of 12 antifungal drugs was obtained through a 75 µm I.D. fused-silica capillary, which was packed with a CSP-cellulose 3,5-dichlorophenylcarbamate (CDCPC), by means of a lab-made slurry packing procedure. The mobile phase composition and the experimental conditions were optimized in order to find the optimum chiral separation for some selected racemic mixtures of imidazole and triazole derivatives. Some important parameters, such as retention faction, enantioresolution, peak efficiency, and peak shape, were investigated as a function of the mobile phase (pH, water content, type and concentration of both the buffer and the organic modifier, and solvent dilution composition). Within one run lasting 25 min, at a flow rate of approximately 400 nL min⁻¹, eight couples of enantiomers were baseline-resolved and four of them were separated in less than 25 min. The method was then applied to milk samples, which were pretreated using a classical dispersive liquid–liquid microextraction technique preceded by protein precipitation. Finally, the DLLME-nano-LC–UV method was validated in a matrix following the main FDA guidelines for bioanalytical methods.     

On the b-Coloring of Cographs and <Emphasis Type="Italic">P</Emphasis><Subscript>4</Subscript>-Sparse Graphs

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χ _b (G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every . We define a graph G to be b-monotonic if χ _b (H ₁) ≥ χ _b (H ₂) for every induced subgraph H ₁ of G, and every induced subgraph H ₂ of H ₁. In this work, we prove that P ₄-sparse graphs (and, in particular, cographs) are b-continuous and b-monotonic. Besides, we describe a dynamic programming algorithm to compute the b-chromatic number in polynomial time within these graph classes. Flavia Bonomo: Partially supported by ANPCyT PICT-2007-00533 and PICT-2007-00518, and UBACyT Grants X069 and X606 (Argentina). Guillermo Durán: Partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems” (Chile), and ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina). Javier Marenco: Partially supported by ANPCyT PICT-2007-00518 and UBACyT Grant X069 (Argentina).     

Biharmonic Green Functions on Homogeneous Trees

The study of biharmonic functions under the ordinary (Euclidean) Laplace operator on the open unit disk \mathbbD{\mathbb{D}} in \mathbbC{\mathbb{C}} arises in connection with plate theory, and in particular, with the biharmonic Green functions which measure, subject to various boundary conditions, the deflection at one point due to a load placed at another point. A homogeneous tree T is widely considered as a discrete analogue of the unit disk endowed with the Poincaré metric. The usual Laplace operator on T corresponds to the hyperbolic Laplacian. In this work, we consider a bounded metric on T for which T is relatively compact and use it to define a flat Laplacian which plays the same role as the ordinary Laplace operator on \mathbbD{\mathbb{D}}. We then study the simply-supported and the clamped biharmonic Green functions with respect to both Laplacians.     

Synthesis and applications of copillar[5]arene dithiols

Abstract

A novel copillar[4+1]arene incorporating alkylthiol substituents was synthesised in three steps and structurally characterised as the first example of a pillar[n]arene to incorporate two terminal thiols on the same aromatic ring. The macrocycle was attached to gold electrodes through a standard dipping technique. Cyclic voltammetry demonstrated selectivity for Li⁺ over other alkali metal cations. The copillar[4+1]arene was also used as a capping agent in the preparation of 3 nm gold nanoparticles.