Approximation of functions of two variables by certain linear positive operators

We introduce certain linear positive operators and study some approximation properties of these operators in the space of functions, continuous on a compact set, of two variables. We also find the order of this approximation by using modulus of continuity. Moreover we define an rth order generalization of these operators and observe its approximation properties. Furthermore, we study the convergence of the linear positive operators in a weighted space of functions of two variables and find the rate of this convergence using weighted modulus of continuity.     

Thiophenol derivatives as a reducing agent for in situ generation of Cu(I) species via electron transfer reaction in copper‐catalyzed living/controlled radical polymerization of styrene

The copper‐catalyzed living radical polymerization (LRP) of styrene (St) was carried out in the presence of thiophenol derivative such as sodium thiophenolate (PhSNa) or p‐methoxythiophenol as a reducing agent for Cu(II) by using either 1‐chloro‐1‐phenyl ethane or ethyl‐2‐bromoisobutyrate as an initiator and N,N,N′,N″,N″‐pentamethyldiethylenetriamine as ligand at 110 °C. Kinetic experiments were carried out to reveal the effect of PhSNa concentration on copper‐catalyzed LRP of St. This technique was successfully applied for the preparation of both chain‐extended polymer and block copolymer polystyrene‐b‐poly(methyl methacrylate). The obtained polymers were characterized using GPC, ¹H‐NMR, and MALDI‐TOF measurements. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5923–5932, 2006     

Focusing with two-dimensional angular-symmetric circular acoustic lenses

Focusing properties of an acoustic lens based on a modified triangular sonic crystal slab whose columns are aligned on concentric arcs of equal radial distance are investigated. Capability of focusing normally-incident plane waves is demonstrated by means of Finite Element Method. Focusing mechanisms are discussed on the basis of band structures and equifrequency contours considering a model where triangular lattice is elongated along ΓK direction. Focusing behavior of the proposed lens is argued to arise from negative refractions at the air-lens interfaces accompanied by index guiding in its interiors. Wavelength-order confinement in the transverse direction is observed. Double focusing is attributed to geometrical effects and contribution of self guiding is discussed. Possibility of occurrence of birefraction at the input face of the lens together with positive refraction at the output face is also discussed.     

Radiation-induced molecular imprinting of d-glucose onto poly(2-hydroxyethyl methacrylate) matrices using various crosslinking agents

Radiation-induced molecular imprinting of d-glucose onto poly(2-hydroxyethyl methacrylate) matrix was achieved to create three-dimensional cavities to recognize and bind d-glucose. The optimization of imprinting capability of matrices was achieved by investigating the effects of various parameters such as the type and amount of crosslinking agent, type of solvent, template to monomer ratio and total absorbed dose. Crosslinking agents with increasing chain lengths and different flexibilities were used in an attempt to elucidate the impact of relevant imprint parameters on the effectiveness of imprinting technique. The absorbed dose varied from 1 to 15 kGy. Cavity sizes of MIPs were measured by positron annihilation lifetime (PAL) experiments. Control matrices were synthesized with exactly the same composition in the absence of d-glucose. Separation of d-glucose has been shown to be successfully achieved in HPLC columns filled with MIPs whereas no separation was observed for non-imprint matrices.     

ESR study of gamma irradiated 2-methyl nylon3

Gamma radiation-induced radicals of 2-methyl nylon3 (2mN3) have been investigated by electron spin resonance spectrometry. The type of radicals generated, conversion into other radicalic species and their room temperature stability were evaluated. Two types of radicals have been detected. Two different formation mechanisms have been proposed for each radical. As suggested in literature for commercial polyamides, in our system we also observed two different radicals (R1 and R2). Among these radicals, R1 is expected to convert to R2, which is a chemically favorable process.     

Some new oscillation results for a nonlinear dynamic system on time scales

We study the oscillation of a system of two first order nonlinear equations on time scales. This form includes the classical Emden-Fowler differential equation and many of its extensions. We generalize some well-known results of Atkinson, Bohner, Erbe, Peterson and others. We illustrate the results by several examples, including a superlinear Emden-Fowler dynamic system.     

A Highly Efficient Chelating Polymer for the Adsorption of Uranyl and Vanadyl Ions at Low Concentrations

A new polymer containing double amidoxime groups per repeating unit was synthesized to enhance the metal ion uptake capacity. The adsorption properties of this new polymeric adsorbent, amidoximated poly(N,N-dipropionitrile acrylamide), for U(VI), V(V), Cu(II), Co(II) and Ni(II) ions were investigated by batch and flow-through processes at very low concentration levels (ppb). The chelating polymer showed high adsorption capacity for uranyl as well as vanadyl ions. In selectivity studies from a mixture of metal ions in aqueous solutions, the adsorbent showed high selectivity for uranyl and vanadyl ions in the following order: U(VI) > V(V) Co(II) = Cu(II) Ni(II) as determined by calculating the distribution coefficients D, of corresponding ions. The adsorption of uranyl and vanadyl ions from natural seawater by the new adsorbent was also examined in flow through mode.     

Preparation of antimicrobial polycaprolactone‐silica composite films with nanosilver rods and triclosan using roll‐milling method

In this study, antimicrobial polycaprolactone composite films containing 12.5% silica and 0.15% silver nanorods were prepared using the roll‐milling method. The destruction of E. coli and S. aureus on the surface of the composite films was evaluated after 6 hr of incubation at 37°C. For the E. Coli, no bacterial contamination was detected after 6 hr and the film surface was completely disinfected with 100% reduction of the microbial contamination. For the S. aureus, 94% reduction of the bacterial contamination was observed after 6 hr. The results were compared with the composite films containing triclosan, a broad‐spectrum antimicrobial agent. The antimicrobial activity tests with 0.25% triclosan incorporated polycaprolactone‐silica composite films showed only 70% reduction of E. coli and 95% reduction of S. aureus after 6 hr. The results demonstrated that the use of silver nanoparticles in the biopolymer industry has huge potential for the self‐cleaning applications. Copyright © 2009 John Wiley & Sons, Ltd.     

A Novel and Selective Methylene Blue Imprinted Polymer Modified Carbon Paste Electrode

In this study, methylene blue (MB) imprinted microbeads were synthesized and characterized by Fourier transform infrared spectroscopy (FTIR) and scanning electron microscopy (SEM).Differential pulse voltammetric responses of carbon paste electrodes modified with MB imprinted polymer were used to evaluate the adsorption and selectivity features of the polymer. For selectivity studies two basic dyestuffs (thionine blue and toluidine blue) which have similar structure to MB were chosen. Comparison of the voltammetric responses obtained with pure carbon paste and carbon paste modified with either imprinted or nonimprinted polymer electrodes revealed that MB imprinted polymer presented a higher selectivity to the template molecule MB in contrast to structurally similar molecules, thionine blue and toluidine blue.