<Emphasis Type=Italic>ϕ</Emphasis>-pairs and common fixed points in cone metric spaces

In this paper we introduce a contractive condition, called ϕ-pair, for two mappings in the framework of cone metric spaces and we prove a theorem which assures existence and uniqueness of common fixed points for ϕ-pairs. Also we obtain a result on points of coincidence. These results extend and generalize well-known comparable results in the literature. The authors are supported by Università degli Studi di Palermo, R. S. ex 60%.     

A symbolic treatment of Riordan arrays

We approach Riordan arrays and their generalizations via umbral symbolic methods. This new approach allows us to derive fundamental aspects of the theory of Riordan arrays as immediate consequences of the umbral version of the classical Abel?s identity for polynomials. In particular, we obtain a novel non-recursive formula for Riordan arrays and derive, from this new formula, some known recurrences and a new recurrence relation for Riordan arrays.     

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.     

Monomer reactivity ratios for acrylonitrile–methyl acrylate free‐radical copolymerization

Nonlinear monomer reactivity ratios for the homogeneous free‐radical copolymerization of acrylonitrile and methyl acrylate were determined from ¹H NMR and real‐time Fourier transform infrared (FTIR) analyses. All ¹H NMR data were obtained on polymers isolated at low conversions (<10%), whereas the FTIR data were collected in situ. The copolymerizations were conducted in N,N‐dimethylformamide at 62 °C and were initiated with azobisisobutyronitrile. The real‐time FTIR technique allowed for many data points to be collected for each feed composition, which enabled the calculation of copolymer compositions (dM₁/dM₂) with better accuracy. Monomer reactivity ratios were estimated with the Mayo–Lewis method and then were refined via a nonlinear least‐squares analysis first suggested by Mortimer and Tidwell. Thus, monomer reactivity ratios at the 95% confidence level were determined to be 1.29 ± 0.2 and 0.96 ± 0.2 for acrylonitrile and methyl acrylate, respectively, which were valid under the specific system conditions (i.e., solvent and temperature) studied. The results are useful for the development of acrylonitrile (<90%) and methyl acrylate, melt‐processable copolymer fibers and films, including precursors for carbon fibers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2994–3001, 2004     

Semi‐Covalent Surface Molecular Imprinting of Polymers by One‐Stage Mini‐emulsion Polymerization: Glucopyranoside as a Model Analyte

This paper describes a new type of surface imprinting technique that combines the advantages of both the semi‐covalent approach and one‐stage miniemulsion polymerization. This process has been successfully applied for the preparation of glucose surface‐imprinted nanoparticles. The selective artificial receptors for glucopyranoside were fully characterized by IR, TEM and BET analyses, and their molecular recognition abilities by binding experiments carried out in batch processes. The molecular affinity and selectivity of the glucose molecularly imprinted polymers were accurately quantified. These characteristics are essential for verification of the efficiency of the developed surface imprinting process. The imprinting effect was clearly demonstrated using the batch rebinding method. We have found that the glucose imprinted polymers produced using the optimized one‐stage mini‐emulsion exhibited quite fast kinetics of binding and equilibration with glucopyranoside templates, compared to polymers prepared by bulk polymerization technique, as well as extremely low levels of unspecific bindings. We also demonstrated that glucose molecular imprinted polymer (MIP) exhibited very good selectivity for its original template compared to other glycopyranoside derivatives, such as galactose. Finally, the extraction of the binding properties from isotherms of binding by fitting to the bi‐Langmuir and Freundlich models allowed the determination of the affinity constant distribution of the binding sites. This imprinting protocol allowed the determination of an affinity constant (K_D), involving exclusively H‐bonding interactions, for the glucose MIP ( P2C ) with the best template 1 , in CH₃CN as the solvent system.

     

Morphology of platinum electrodeposits in the three-dimensional sublayer to full layer range produced under different potential modulations on highly oriented pyrolytic graphite

The topography of platinum electrodes produced by electrodeposition (19 to 200 mC cm-2) on highly oriented pyrolytic graphite (HOPG) under different potential modulations was investigated by atomic force microscopy, scanning tunneling microscopy, and H-atom electrosorption voltammetry. To modulate electrodeposition, (i) triangular potential cycling at 0.1 V s-1, (ii) a linear cathodic potential at 0.1 V s-1 and anodic potential step cycling, and (iii) square wave potential cycling at 5000 Hz were utilized. AFM and STM imaging showed that at lower platinum loading the HOPG surface was partially covered by a 3D sublayer of platinum. Electrodes produced by procedure (i) were made of faceted platinum aggregates of about 200 nm and nanoclusters in the range of 5-20 nm; those that resulted from procedure (ii) consisted of anisotropic aggregates of nanoclusters arranged as quasi-parallel domains. These electrodes from (i) and (ii) behaved as fractal objects. The electrodes resulting from procedure (iii) exhibited a flat surface that behaved as a Euclidean object. For all WEs, as the platinum loading was increased the HOPG surface was fully covered by a thin 3D layer of platinum aggregates produced by electrodeposition and coalescence phenomena. Large platinum loading led to electrodes with fractal geometry. Statistical parameters (root-mean-square height, skewedness, kurtosis, anisotropy, Abbot curve, number of protrusions and valleys, and fractal dimension) were obtained from the analysis of AFM and STM imaging data. Platinum electrodeposition coupled to either H-adatom formation for procedures (i) and (ii) or phonon dispersion for (iii) was involved in the surface atom rearrangements related to electrofaceting. The H-adatom electrosorption voltammetry data were used to evaluate the real electrode surface area via the voltammetric charge and to advance a tentative explanation of the contribution of the different crystallographic facets to the global electrochemical process dominated by weak H-Pt adsorption interactions.     

PEGDA‐based luminescent polymers prepared by frontal polymerization

Frontal polymerization (FP) of poly(ethylene glycol) diacrylate (PEGDA) was carried out using benzoyl peroxide (BPO) as radical initiator. In addition, a pyrene containing monomer, 1‐pyrenebutyl acrylate (PyBuAc), was incorporated as a fluorescent probe in order to obtain luminescent materials with different chromophore contents. The resulting polymers were characterized by FT‐IR spectroscopy in the solid state and their thermal properties were determined by thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC). Moreover, the optical properties of these materials were studied by absorption and fluorescence spectroscopy. The maximum amount of the incorporated pyrene‐containing monomer into the polymer matrix was limited to 1 wt % by the polymerization process. The obtained labeled polymers poly(PEGDA‐co‐PyBuAc) exhibited a broad absorption band at 345 nm. The fluorescence spectra of these polymers exhibited mainly “monomer emission” so that no excimer emission was observed. It is possible to tune the color of the emitted light by varying the pyrene content in the samples. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2890–2897