On typically real functions which are generated by a fixed typically real function

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ.     

Comprehensive Characterisation of the Ketoprofen-β-Cyclodextrin Inclusion Complex Using X-ray Techniques and NMR Spectroscopy

Racemic ketoprofen (KP) and β-cyclodextrin (β-CD) powder samples from co-precipitation (1), evaporation (2), and heating-under-reflux (3) were analysed using X-ray techniques and nuclear magnetic resonance (NMR) spectroscopy. On the basis of NMR studies carried out in an aqueous solution, it was found that in the samples obtained by methods 1 and 2, there were large excesses of β-CD in relation to KP, 10 and 75 times, respectively, while the sample obtained by method 3 contained equimolar amounts of β-CD and KP. NMR results indicated that KP/β-CD inclusion complexes were formed and the estimated binding constants were approximately 2400 M⁻¹, showing that KP is quite strongly associated with β-CD. On the other hand, the X-ray single-crystal technique in the solid state revealed that the (S)-KP/β-CD inclusion complex with a stoichiometry of 2:2 was obtained as a result of heating-under-reflux, for which the crystal and molecular structure were examined. Among the methods used for the preparation of the KP/β-CD complex, only method 3 is suitable.     

Self-organisation of di(perfluorohexyl)hexane in Langmuir and LB films

Symmetrical triblock semifluorinated n-alkane, di(perfluorohexyl)hexane of the formula F(CF₂)₆(CH₂)₆(CF₂)₆F (abbreviated F₆H₆F₆), has been synthesised and investigated at the air/water interface. Our results show for the first time that this unusual film-forming material, completely hydrophobic in nature and possessing no polar group, is capable of stable film formation at the free water surface. The surface pressure–area isotherm of the studied compound exhibited two regions: corresponding to monotonous pressure rise, followed by a pseudo-plateau region. Visualisation of film structure with Brewster angle microscope (BAM) proved the formation of domains within the pseudo-plateau region. A closer insight into the structure of these domains with atomic force microscope (AFM) proved their ordered, circular shape. The average area of F₆H₆F₆ domain was found to depend on surface pressure value, as it is 4.98 ± 1.75 μm² at π = 1.2 mN/m to 16.54 ± 0.31 μm² at π = 1.7 mN/m. Following performed quantum-chemical calculations, it can be concluded that the observed surface aggregates from F₆H₆F₆ are formed by linear conformers with shifted CF and CH parts. The calculated domain thickness is between 20 and 21 Å, which perfectly agrees with the experimental value estimated from AFM measurements (20.3 ± 1.4 Å).     

Simultaneous determination of uranium(IV) and thorium(IV) ions with Arsenazo III by partial least squares method

A multivariate calibration method, Partial Least Squares Type 1 (PLS-1), is proposed for simultaneous spectrophotometric determination of uranium and thorium ions as their complexes with arsenazo III in hydrochloric acid medium. Several data characteristics are taking into account in order to minimize the optimum number of factors required for the construction of calibration model, while using various statistical criterions of selection. Finally, the evaluated calibration model is satisfactorily applied to determination of these ions in samples that resemble sulfuric acid leach solution obtained from a uranium ore.     

Pure phase correlation with improved discrimination capability

Pure phase correlation with improved discrimination capability is proposed. The improvement is achieved by designing a region of support based on the discrimination capability (DC). We propose four approaches for designing this region; some of them consider the input scene in the design, while others are input scene invariant. The performances of these approaches are compared by numerical simulation. The DC is improved significantly for the multi-object scenes even when using an input scene invariant region of support design.     

A novel femtosecond-laser formation of CdS nanocrystallites in zirconia matrices

A novel method for direct laser writing of two-dimensional cadmium sulfide (CdS) semiconductor nanoparticle microstructures is reported. A two photon or a higher-order multiphoton absorption process, originating from femtosecond laser pulses, was used to decompose CdS precursors dispersed in a zirconia thin film previously dip-coated on a glass substrate. The kinetics of nanoparticle formation as a function of laser power were monitored in situ by photoluminescence spectroscopy. Raman spectroscopy was also performed to characterize the structural changes of the zirconia matrix under irradiation and to verify the formation of CdS nanoparticles. Results show that CdS nanoparticles were formed by two-photon absorption (TPA) with or without the help of an additional carbazole photoinitiator.     

Molecular weight dependent charge carrier mobility in poly(3,3' '-dioctyl-2,2':5',2' '-terthiophene)

Poly(3,3' '-dioctyl-2,2':5',2' '-terthiophene), a polymer recently used for the fabrication of organic field effect transistors, has been fractionated into five fractions distinctly differing in their molecular weights (Mn), with the goal of determining the influence of the degree of polymerization (DPn) on its principal physicochemical parameters. It has been demonstrated that within the Mn range studied (from 1.5 kDa to 10.5 kDa by SEC), corresponding to DPn from 10 to 38, the polymer band gap steadily decreases with growing molecular weight, which is clearly manifested by an increasing bathochromic shift of the band originating from the pi-pi* transition. The same trend is observed for the HOMO level, determined from the onset of the p-doping in cyclic voltammetry, which shifts from -5.10 eV to -4.90 eV for the lowest and the highest molecular weight fractions, respectively. The most pronounced influence of DPn has been found for the charge carriers' mobility-one of the most important parameters of field effect transistors (FETs) fabricated from this polymer. A fourfold increase in DPn results in an increase of the carriers' mobility by more than 3 orders of magnitude. Comparison of these results with those obtained for fractionated regioregular poly(3-hexylthiophene) shows a strikingly similar behavior of both polymers with respect to the molecular weight.     

Interaction between rhodanine and silver species on a nanocolloidal surface and in the solid state

This paper discusses and compares molecular interactions of rhodanine (Rd), the heterocyclic compound containing N, S, and O atoms, with two forms of silver species, i.e. Ag(I) ions and silver nanocolloidal particles. Vibrational spectroscopic and powder crystallography studies on coordination of Ag(I) ions in the solid state, supported by density functional theory, clearly indicate complexation through the nitrogen (the deprotonated imino group) and exocyclic sulfur atoms. Molecules of the complex are arranged in a one‐dimensional infinite polymeric chain structure that intertwines to give a helix motif. On the other hand, adsorption geometry of Rd on the silver surface was determined by using surface‐enhancement Raman scattering (SERS) spectroscopy. Observed differences between the SERS and the normal Raman spectra of Rd suggest that Rd adsorbs on the silver species after the rearrangement of the keto‐thione form into the enol‐thiol tautomer in acidic and neutral solutions. This leads to adsorption on this silver species through the thiolate ion. On the other hand, the alkaline pH forces first N‐deprotonation of Rd, and, in consequence, the obtained anion of the keto‐thione form interacts with the silver surface as a result of the presence of lone pairs of nitrogen and sulfur atoms, similar to the case discussed for the solid state. Copyright © 2009 John Wiley & Sons, Ltd.     

The wettability of poly(tetrafluoroethylene) by aqueous solutions of ternary surfactant mixtures

Contact angle measurements on poly(tetrafluoroethylene) (PTFE) surface were carried out for the systems containing ternary mixtures of cetyltrimethylammonium bromide (CTAB) and p-(1,1,3,3-tetramethylbutyl)phenoxypoly(ethylene glycols), Triton X-100 (TX100) and Triton X-165 (TX165). The aqueous solution of ternary surfactant mixtures were prepared by adding the third surfactant to the binary mixture of the surfactants where the synergetic effect in the reduction of the surface tension of water was determined, to compare the influence of the third surfactants on the values of surface tension of this binary mixture and the values of the contact angle on PTFE. The obtained results and calculations indicate that the ternary mixtures of CTAB + TX165 (αCTAB = 0.2, γ_LV = 60 and 50 mN/m) + TX100 (C = 10⁻⁸ to 10⁻² M) have the biggest efficiency of the reduction of contact angle of water on PTFE in comparison to aqueous solutions of the single surfactants and their binary and ternary mixtures. Also in the case of all studied ternary mixtures of surfactants at concentrations of the bulk phase corresponding to unsaturated monolayer at water-air interface the adsorption of surfactants at PTFE-water interface is different than that at water-air interface, but is the same at concentrations near the critical micelle concentration (CMC). Thus the linear dependences between γ_LV cos θ − γ_LV and cos θ − 1/γ_LV, in the range of concentration studied for all systems confirm the same adsorption at two interfaces only at C near the CMC.