Coincidence and common fixed point theorems for Suzuki type hybrid contractions and applications

Coincidence and common fixed point theorems for a class of Suzuki hybrid contractions involving two pairs of single-valued and multivalued maps in a metric space are obtained. In addition, the existence of a common solution for a certain class of functional equations arising in a dynamic programming is also discussed.

Optical and surface properties of hybrid TiO2/ormosil planar waveguide prepared by the sol-gel process

Two kinds of silanes, 3-glycidoxypropyltrimethoxysilane (GLYMO) and 3-trimethoxysililpropylmethacrylate (TMSPM), were used to prepare ormosil waveguide films by the sol-gel method. Thirty percent Ti(OBu)(4) and 70% silane were contained in the precursor sets. The properties of films were measured by scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), UV/VIS/NIR spectrophotometer (UV-vis), atomic force microscopy (AFM), m-line and scattering-detection method. The films from GLYMO and TMSPM precursors exhibit similar thickness (2.58 mu m for GLYMO, 2.51 mu m for TMSPM) and refractive index (1.5438 for GLYMO, 1.5392 for TMSPM, lambda=632.8 nm), but the film from TMSPM precursor has higher propagation loss (1.024 dB/cm, lambda=632.8 nm) than the film prepared from GLYMO (0.569 dB/cm, lambda=632.8 nm). Furthermore, the film prepared from TMSPM is easy to be opaque and cracks during coating whereas the same phenomenon was not found for the film prepared with GLYMO. It is confirmed that GLYMO is a better precursor than TMSPM for waveguide film preparation. (C) 2005 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

Effect of water content in sol on optical properties of hybrid sol-gel derived TiO2/SiO2/ormosil film

Sol-gel derived TiO2/SiO2/ormosil hybrid planar waveguides have been deposited on soda-lime glass slides and silicon substrates, films were heat treated at 150 degreesC for 2 h or dried at room temperature. Different amounts of water were added to sols to study their impacts on microstructures and optical properties of films. The samples were characterized by m-line spectroscopy, Fourier transform infrared spectroscopy (FT-IR), UV/VIS/NIR spectrophotometer (UV-vis), atomic force microscopy (AFM), thermal analysis instrument and scattering-detection method. The refractive index was found to have the largest value at the molar ratio H2O/OR = 1 in sol (OR means -OCH3, -OC2H5 and -OC4H9 in the sol), whereas the thickest film appears at H2O/OR = 1/2. The rms surface roughness of all the films is lower than 1.1 nm, and increases with the increase of water content in sol. Higher water content leads to higher attenuation of film. (C) 2004 Elsevier B.V. All rights reserved.

Study of hybrid TiO2/ormosil films doped with laser dyes

TiO2/ormosil films doped with laser dyes have been prepared by the sol-gel method. Spectroscopic properties of the entrapped dyes are studied by the absorption and emission techniques. The results indicate that the absorption and fluorescence spectra of kiton red depend strongly on the properties of the ormosil matrices. The heat-treatment of the kiton red-doped film obviously leads to the increasing fluorescence intensity and the largest fluorescence intensity is obtained after heat-treatment of 150 degrees C for 2 h. However, the fluorescence intensity of the rhodamine 6G-doped film decreases with the increase of the heat-treatment temperature. (c) 2005 Elsevier B.V. All rights reserved.

Preparation and characterization of hybrid ZnO/ormosils films

Hybrid ZnO/ormosils Elms are prepared by the sol-gel method. A FT-IR spectrometer, 900 UV/VIS/NIR spectrophotometer, atomic force microscope, and ellipsometer are employed to investigate microstructure and optical properties of the films fired at different temperatures. The results show that the films with high transmittance and low surface roughness could be obtained at the heat-treatment temperature of 150 degrees C, the refractive index and thickness of the film are 1.413, 2.11 mu m, respectively. Higher temperatures (350 degrees C, 550 degrees C) change the Elm microstructure severely, and then decrease the transmittance of the films.