Generalization of perfectly continuous,regular set-connected and clopen functions

Summary Noiri in 1984, Dontchev, Ganster and Reilly in recent years and Reilly and Vamanamurthy in 1983 introduced the notion of perfectly continuous, regular set-connected and clopen functions, respectively. The aim of this paper is to introduce the notion of a new class of functions which is called almost clopen functions including the classes of perfectly continuous, regular set-connected and clopen functions. Furthermore, properties of almost clopen functions are obtained and relationships among almost clopenness, perfect continuity, regular set-connectedness, clopenness and almost continuity are investigated.     

β−type fractional Sturm‐Liouville Coulomb operator and applied results

In this article, β‐type fractional Sturm‐Liouville Coulomb operator is considered by Hilfer fractional derivative. Fundamental spectral theory is investigated for the aforementioned problem. In this context, it is shown that the operator is self‐adjoint, eigenfunctions correspond to the distinct eigenfunctions are orthogonal, and eigenvalues are real. Furthermore, applications of this problem are given by the Adomian decomposition method and the results are shown with visual graphs.     

Electrochromic Properties of ‘Trimeric' Thiophene‐pyrrole‐thiophene Derivative Grown from Electrodeposited 6‐(2,5‐di(thiophen‐2‐yl)‐1H‐pyrrol‐1‐yl)hexan‐1‐amine and its Copolymer

A centrosymmetric polymer precursor, namely 6‐(2,5‐di(thiophen‐2‐yl)‐1H‐pyrrol‐1‐yl)hexan‐1‐amine (TPHA), was synthesized via a Knorr–Paal reaction using 1,4‐di(2‐thienyl)‐1,4‐butanedione and hexane‐1,6‐diamine. The resultant monomer was characterized by Nuclear Magnetic Resonance (¹H‐NMR). Electroactivity of TPHA was investigated via cyclic voltammetry. The electronic structure and the nature of electrochromism in P(TPHA) and its copolymer with EDOT, (P(TPHA‐co‐EDOT)), were examined via spectroelectrochemistry studies. P(TPHA) switches between claret red neutral state and blue oxidized state. Optical response times for coloring and bleaching processes of the P(TPHA) and P(TPHA‐co‐EDOT) were found as 2.1 s and 1.6 s, respectively.

The copolymer of TPHA was used to construct dual type polymer electrochromic devices (ECDs) against poly(3,4‐ethylenedioxythiophene) (PEDOT). Spectroelectrochemistry and electrochromic switching out of the devices were investigated.     

Mechanical, thermal, and fire retardant properties of poly(ethylene terephthalate) fiber containing zinc phosphinate and organo-modified clay

The effect of zinc bisdiethylphosphinate (ZnPi) and organoclay on mechanical, thermal, and flame retardant properties of poly(ethylene terephthalate) (PET) fiber was investigated. ZnPi was preferred due to its fusible character at spinning temperature and organoclay was used for synergistic interaction. The mechanical, thermal, and flame retardant properties of fibers were examined by tensile testing, thermogravimetric analysis (TG), and micro combustion calorimeter (MCC). The tensile strength of the PET fiber reduced with the addition of both ZnPi and organoclay. The TG results showed that the inclusion of ZnPi increased the char residue. The MCC results showed that the addition of organoclay increased the barrier effect of formed char which depends on char amount, thickness, and integrity and reduces the maximum heat evolved during the test. This result was also important in terms of showing that the organoclay was effective in thermally thin samples.     

Cationic dye adsorption by poly(N-isopropylacrylamide/maleic acid) copolymeric hydrogels prepared by gamma rays

N-isopropylacrylamide/maleic acid hydrogels containing different quantities of maleic acid have been synthesized with γ-radiation. The hydrogels were used in experiments on swelling, diffusion and adsorption of a cationic dye methylene blue. The diffusion of MB into the hydrogels was found to be the non-Fickian type. The factors influencing adsorption capacity of the hydrogel such as gel composition, and irradiation dose were systematically investigated. The equilibrium data for dye adsorption was better described by the Freundlich isotherm than Langmuir isotherm model. The kinetic studies showed that the pseudo-second-order kinetic model fits better than the data obtained from pseudo-first-order model.     

Indium determination using slotted quartz tube-atom trap-flame atomic absorption spectrometry and interference studies

Sensitivity enhancement of indium determination by flame atomic absorption spectrometry (FAAS) was achieved; using a slotted quartz tube (SQT-FAAS) and slotted quartz tube atom trap (SQT-AT-FAAS). SQT was used as an atom trap (AT) where the analyte is accumulated in its inner wall prior to re-atomization. The signal is formed after re-atomization of analyte on the trap surface by introduction of 10 μL of isobutyl methyl ketone (IBMK). Sensitivity was improved 400 times using SQT-AT-FAAS system with respect to conventional FAAS and 279 times with respect to SQT-FAAS without any collection. Characteristic concentration (C₀) and limit of detection values were found to be 3.63 ng mL⁻¹ and 2.60 ng mL⁻¹, respectively, using a sample flow rate of 7.0 mL min⁻¹ and a collection period of 5.0 min. In addition, interference effects of some elements on indium signal were studied. In order to characterize indium species trapped, X-ray Photoelectron Spectrometry (XPS) was utilized and it was found that indium was collected on the inner surface of SQT as In₂O₃. The accuracy of the procedure was checked to determine indium in the standard reference material (Montana Soil, SRM 2710).     

Fixed point theorems for operators on partial metric spaces

Fixed point theorems for operators of a certain type on partial metric spaces are given. Orbitally continuous operators on partial metric spaces and orbitally complete partial metric spaces are defined, and fixed point theorems for these operators are given.     

Synergistic effect of boron containing substances on flame retardancy and thermal stability of clay containing intumescent polypropylene nanoclay composites

The functions of nanoclay and three different boron containing substances, zinc borate (ZnB), borophosphate (BPO₄), and boron silicon containing preceramic oligomer (BSi), were studied to improve the flame retardancy of polypropylene (PP)‐nanoclay‐intumescent system composed of ammonium polyphosphate (APP) and pentaerythritol (PER). The flame retardancy of PP composites was investigated using limiting oxygen index (LOI), UL‐94 standard, thermogravimetric analysis (TGA), and cone calorimeter. According to the results obtained, the addition of 20 wt% intumescent flame retardant (IFR) improved the flame retardancy by increasing the char formation. Addition of clay slightly increases the LOI value and reduces the maximum heat release rate (HRR). Addition of clay also increases the barrier effect due to intumescent char, especially in thin samples. Boron compounds show their highest synergistic effect at about 3 wt% loading. According to UL‐94 test and LOI test, 3 wt% ZnB containing composite shows the highest rating (V0) and BPO₄ containing sample shows the highest LOI value (26.5). Copyright © 2010 John Wiley & Sons, Ltd.     

Optical CO<Subscript>2</Subscript> Sensing with Ionic Liquid Doped Electrospun Nanofibers

The first use of electrospun nanofibrous materials as highly responsive fluorescence quenching-based optical CO₂ sensors is reported. Poly(methyl methacrylate) and ethyl cellulose were used as polymeric materials. Sensing slides were fabricated by electrospinning technique. A fiber-optic bundle was used for the gas detection. CO₂ sensors based on the change in the fluorescence signal intensity of ion pair form of 8-hydroxypyrene-1,3,6-trisulfonic acid (HPTS). The sensor slides showed high sensitivities due to the high surface area-to-volume ratio of the nanofibrous membrane structures. The preliminary results of Stern-Volmer analysis show that the sensitivities of electrospun nanofibrous membranes to detect CO₂ are 24 to 120 fold higher than those of the thin film based sensors. The response times of the sensing reagents were short and the signal changes were fully reversible. The stability of ion pair form of HPTS in the employed matrix materials was excellent and when stored in the ambient air of the laboratory there was no significant drift in signal intensity after 7 months. Our stability tests are still in progress.     

Coupled coincidence point results on generalized distance in ordered cone metric spaces

In this paper, we establish some coupled coincidence point results in the setting of partially ordered cone metric spaces via $c$ -distance. We also proved some related coupled common fixed point theorems for such mappings. Our results generalize, extend, and unify several well-known comparable results in the literature regarding this topic. We present some examples to illustrate the concepts and results.